我试图证明微分几何的定理：Cartan结构方程。
我正在使用以下代码
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) = zero )).
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) = zero )).
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) = zero )).
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) )).
以下ATP能够生成证据：Bliksem, CiME, CVC4, E, EQP, Fiesta, Geo, Isabelle, Isabelle-HOT, LEO-II, Matita, Metis, Otter, Prover9, SNARK, SPASS, Vampire, Vampire-SAT.
我的问题是：如何用Agda重建上述ATP产生的证据？