How to reconstruct with Agda the proof of a theorem produced by one ATP -


i trying prove theorem of differential geometry: cartan structural equation.

i using following code

 cnf(axio1,axiom,    (w(h(x))= zero)).  cnf(axio2,axiom,    (w(v(x))= v(x))). cnf(axio2a,axiom,    (x= sum(h(x),v(x))  )).  cnf(axio3a,axiom,    (dw(sum(x,y),z)= sum(dw(x,z),dw(y,z))  )). cnf(axio3,axiom,    (dw(x,sum(y,z))= sum(dw(x,y),dw(x,z))  )).  cnf(axio4,axiom,    (w(sum(x,y))= sum(w(x),w(y))  )).  cnf(axio5,axiom,    (sum(zero,x)= x  )).  cnf(axio5a,axiom,    (sum(x,sum(y,z))= sum(sum(x,y),z)  )).  cnf(axio6,axiom,    (dw(x,y)= divi(subst(subst(act(x,w(y)),act(y,w(x))),w(commu(x,y))),two)  )).   cnf(axio6a,axiom,    (subst(zero,zero) = 0      )).  cnf(axio6b,axiom,    (subst(zero,x) = minus(x)      )).   cnf(axio7,axiom,    (act(x,w(v(y)))=zero                )).   cnf(axio7a,axiom,    (act(x,zero)=zero                )).  cnf(axio8,axiom,    (commu(h(x),v(y))=h(z)                    )).  cnf(axio9,axiom,     (minus(zero)=zero)).  cnf(axio10,axiom,     (divi(zero,two) = 0      )).  cnf(axio11,axiom,     (commu(x,y)=minus(commu(y,x))      )).  cnf(axio12,axiom,     (w(minus(x))=minus(w(x))  )).  cnf(axio13,axiom,    (sum(zero,x) = x        )).  cnf(axio14,axiom,    (divi(minus(x),two) =minus(divi(x,two))  )).  cnf(axio14a,axiom,    (sum(minus(x),x) = 0       )).  cnf(axio15,axiom,     (w(commu(v(x),v(y))) = commu(v(x),v(y))      )).  cnf(axio15a,axiom,    ( omega(x,y)=dw(h(x),h(y))              )).    cnf(goal,negated_conjecture,    (sum(dw(x,y),divi(commu(w(x),w(y)),two))!=   omega(x,y)   )).

the following atps able produce proof: bliksem, cime, cvc4, e, eqp, fiesta, geo, isabelle, isabelle-hot, leo-ii, matita, metis, otter, prover9, snark, spass, vampire, vampire-sat.

my question is: how reconstruct agda proof generated mentioned atps?


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