TSTP Solution File: GRP514-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:42:04 EDT 2022
% Result : Unsatisfiable 0.18s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 40
% Syntax : Number of clauses : 125 ( 67 unt; 0 nHn; 66 RR)
% Number of literals : 212 ( 211 equ; 89 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 330 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))))]]) ).
cnf(refute_0_1,plain,
multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) = X_1,
inference(subst,[],[single_axiom:[bind(A,$fot(B)),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != X_1
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) ),[0,1,0],$fot(X_1)]]) ).
cnf(refute_0_3,plain,
( multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),X_1) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),inverse(multiply(A,multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) = X_4,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_4)),bind(B,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))) = X_5,
inference(subst,[],[single_axiom:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
( multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) != X_4
| multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))) != X_5
| multiply(X_4,multiply(X_5,inverse(X_5))) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))),X_4) ),[0,1,1,0],$fot(X_5)]]) ).
cnf(refute_0_8,plain,
( multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))) != X_4
| multiply(X_4,multiply(X_5,inverse(X_5))) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6)))),X_5) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(X_4,multiply(X_5,inverse(X_5))) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_4,multiply(X_5,inverse(multiply(X_4,multiply(multiply(X_5,X_6),inverse(multiply(X_4,X_6))))))),X_4) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(a2,multiply(b2,inverse(b2))) = a2,
inference(subst,[],[refute_0_9:[bind(X_4,$fot(a2)),bind(X_5,$fot(b2))]]) ).
cnf(refute_0_11,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(subst,[],[refute_0_4:[bind(X_2,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_12,plain,
multiply(X_1,multiply(X_8,inverse(X_8))) = X_1,
inference(subst,[],[refute_0_9:[bind(X_4,$fot(X_1)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_13,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(X_1,multiply(X_8,inverse(X_8))) != X_1
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) ),[0,1,1,0,1,0],$fot(X_1)]]) ).
cnf(refute_0_14,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B ),
inference(resolve,[$cnf( $equal(multiply(X_1,multiply(X_8,inverse(X_8))),X_1) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(multiply(X_1,multiply(X_8,inverse(X_8))),inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(B,multiply(X_8,inverse(X_8))) = B,
inference(subst,[],[refute_0_9:[bind(X_4,$fot(B)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_17,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(multiply(B,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(B,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_18,plain,
( multiply(B,multiply(X_8,inverse(X_8))) != B
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(multiply(B,multiply(X_8,inverse(X_8))))
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(multiply(B,multiply(X_8,inverse(X_8))))) ),[1,0],$fot(B)]]) ).
cnf(refute_0_19,plain,
( multiply(B,multiply(X_8,inverse(X_8))) != B
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B) ),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(multiply(B,multiply(X_8,inverse(X_8))))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
inverse(multiply(B,multiply(X_8,inverse(X_8)))) = inverse(B),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_22,plain,
( multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))
| inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(B)
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_23,plain,
( inverse(multiply(B,multiply(X_8,inverse(X_8)))) != inverse(B)
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) = multiply(X_1,inverse(B)),
inference(resolve,[$cnf( $equal(inverse(multiply(B,multiply(X_8,inverse(X_8)))),inverse(B)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_26,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))
| multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(B))
| multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) ),[1,1],$fot(multiply(X_1,inverse(B)))]]) ).
cnf(refute_0_27,plain,
( multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))) != multiply(X_1,inverse(B))
| multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(X_1,inverse(B))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))),multiply(X_1,inverse(B))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))]]) ).
cnf(refute_0_30,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(B)))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) ),[1,0],$fot(multiply(A,multiply(X_1,inverse(B))))]]) ).
cnf(refute_0_31,plain,
( multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(X_1,inverse(B)))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) = inverse(multiply(A,multiply(X_1,inverse(B)))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(X_1,inverse(B)))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),
introduced(tautology,[refl,[$fot(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))]]) ).
cnf(refute_0_34,plain,
( multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))
| inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(B))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) ),[1,1],$fot(inverse(multiply(A,multiply(X_1,inverse(B)))))]]) ).
cnf(refute_0_35,plain,
( inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))) != inverse(multiply(A,multiply(X_1,inverse(B))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) = multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))),inverse(multiply(A,multiply(X_1,inverse(B))))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))))]]) ).
cnf(refute_0_38,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))
| multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))) ),[1,1],$fot(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))]]) ).
cnf(refute_0_39,plain,
( multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))) != multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) = multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8)))))))),multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) ),[0],$fot(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))))]]) ).
cnf(refute_0_42,plain,
( multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))) != B
| multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B))))))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(B)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_1,inverse(multiply(A,multiply(X_1,inverse(multiply(B,multiply(X_8,inverse(X_8))))))))),B) )],[refute_0_15,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C))))))) = multiply(X_11,C),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_11)),bind(B,$fot(multiply(X_11,C))),bind(X_1,$fot(multiply(B,C)))]]) ).
cnf(refute_0_45,plain,
multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C)))) = B,
inference(subst,[],[single_axiom:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_46,plain,
( multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C)))) != B
| multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C))))))) != multiply(X_11,C)
| multiply(X_11,multiply(multiply(B,C),inverse(B))) = multiply(X_11,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C))))))),multiply(X_11,C)) ),[0,1,1,0],$fot(B)]]) ).
cnf(refute_0_47,plain,
( multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C))))))) != multiply(X_11,C)
| multiply(X_11,multiply(multiply(B,C),inverse(B))) = multiply(X_11,C) ),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C)))),B) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(X_11,multiply(multiply(B,C),inverse(B))) = multiply(X_11,C),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,multiply(multiply(B,C),inverse(multiply(X_11,C))))))),multiply(X_11,C)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_11,multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B))) = multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))),
inference(subst,[],[refute_0_48:[bind(C,$fot(multiply(X_27,inverse(multiply(X_27,inverse(B))))))]]) ).
cnf(refute_0_50,plain,
multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) = B,
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(B,X_2)))]]) ).
cnf(refute_0_51,plain,
multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B,
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(X_8,inverse(X_8))))]]) ).
cnf(refute_0_52,plain,
( multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(B,multiply(X_8,inverse(X_8))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) ),[0,1,0],$fot(B)]]) ).
cnf(refute_0_53,plain,
( multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B ),
inference(resolve,[$cnf( $equal(multiply(B,multiply(X_8,inverse(X_8))),B) )],[refute_0_16,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(B,multiply(X_8,inverse(X_8))),inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(A,multiply(X_8,inverse(X_8))) = A,
inference(subst,[],[refute_0_9:[bind(X_4,$fot(A)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_56,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(multiply(A,multiply(X_8,inverse(X_8)))),
introduced(tautology,[refl,[$fot(inverse(multiply(A,multiply(X_8,inverse(X_8)))))]]) ).
cnf(refute_0_57,plain,
( multiply(A,multiply(X_8,inverse(X_8))) != A
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(multiply(A,multiply(X_8,inverse(X_8))))
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(multiply(A,multiply(X_8,inverse(X_8))))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_58,plain,
( multiply(A,multiply(X_8,inverse(X_8))) != A
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(multiply(A,multiply(X_8,inverse(X_8))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
inverse(multiply(A,multiply(X_8,inverse(X_8)))) = inverse(A),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_8,inverse(X_8))),A) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),
introduced(tautology,[refl,[$fot(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))]]) ).
cnf(refute_0_61,plain,
( multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))
| inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(A)
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) ),[1,1],$fot(inverse(A))]]) ).
cnf(refute_0_62,plain,
( inverse(multiply(A,multiply(X_8,inverse(X_8)))) != inverse(A)
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)) ),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) = multiply(B,inverse(A)),
inference(resolve,[$cnf( $equal(inverse(multiply(A,multiply(X_8,inverse(X_8)))),inverse(A)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),
introduced(tautology,[refl,[$fot(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))))]]) ).
cnf(refute_0_65,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))
| multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(A))
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))) ),[1,1],$fot(multiply(B,inverse(A)))]]) ).
cnf(refute_0_66,plain,
( multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))) != multiply(B,inverse(A))
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) = multiply(A,multiply(B,inverse(A))),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8))))),multiply(B,inverse(A))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != multiply(A,multiply(B,inverse(A)))
| multiply(A,multiply(B,inverse(A))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) ),[0],$fot(multiply(A,multiply(B,inverse(A))))]]) ).
cnf(refute_0_69,plain,
( multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))) != B
| multiply(A,multiply(B,inverse(A))) = B ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),multiply(A,multiply(B,inverse(A)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(resolve,[$cnf( $equal(multiply(A,multiply(B,inverse(multiply(A,multiply(X_8,inverse(X_8)))))),B) )],[refute_0_54,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) = multiply(X_1,X_2),
inference(subst,[],[refute_0_70:[bind(A,$fot(multiply(B,X_2))),bind(B,$fot(multiply(X_1,X_2)))]]) ).
cnf(refute_0_72,plain,
( multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))) != multiply(X_1,X_2)
| multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) ),[0,1,1,0],$fot(multiply(X_1,X_2))]]) ).
cnf(refute_0_73,plain,
( multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))) != B
| multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2)))),multiply(X_1,X_2)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(X_1,X_2)))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,X_2),multiply(X_1,inverse(multiply(multiply(B,X_2),multiply(multiply(X_1,X_2),inverse(multiply(B,X_2))))))),B) )],[refute_0_50,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16))))))) = B,
inference(subst,[],[refute_0_74:[bind(X_1,$fot(multiply(X_14,X_16))),bind(X_2,$fot(multiply(X_15,inverse(multiply(X_15,X_16)))))]]) ).
cnf(refute_0_76,plain,
multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16)))) = X_14,
inference(subst,[],[refute_0_74:[bind(B,$fot(X_14)),bind(X_1,$fot(X_15)),bind(X_2,$fot(X_16))]]) ).
cnf(refute_0_77,plain,
( multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16))))))) != B
| multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16)))) != X_14
| multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16))))))),B) ),[0,1,1,0],$fot(X_14)]]) ).
cnf(refute_0_78,plain,
( multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16))))))) != B
| multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16)))),X_14) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(multiply(multiply(X_14,X_16),multiply(X_15,inverse(multiply(X_15,X_16))))))),B) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) = multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16),
inference(subst,[],[refute_0_48:[bind(B,$fot(X_14)),bind(C,$fot(X_16)),bind(X_11,$fot(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16))))))]]) ).
cnf(refute_0_81,plain,
( multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) != B
| multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) != multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16)
| multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))),B) ),[0],$fot(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16))]]) ).
cnf(refute_0_82,plain,
( multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))) != B
| multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))),multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),X_16) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_15,inverse(multiply(X_15,X_16)))),multiply(multiply(X_14,X_16),inverse(X_14))),B) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B)) = B,
inference(subst,[],[refute_0_83:[bind(X_15,$fot(X_27)),bind(X_16,$fot(inverse(B)))]]) ).
cnf(refute_0_85,plain,
( multiply(X_11,multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B))) != multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))
| multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B)) != B
| multiply(X_11,B) = multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B))),multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))) ),[0,1],$fot(B)]]) ).
cnf(refute_0_86,plain,
( multiply(X_11,multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B))) != multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))
| multiply(X_11,B) = multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B)),B) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(X_11,B) = multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(multiply(B,multiply(X_27,inverse(multiply(X_27,inverse(B))))),inverse(B))),multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))) )],[refute_0_49,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(A,multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A))) = multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),
inference(subst,[],[refute_0_70:[bind(B,$fot(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))))]]) ).
cnf(refute_0_89,plain,
multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A)) = X_26,
inference(subst,[],[refute_0_83:[bind(B,$fot(X_26)),bind(X_15,$fot(X_27)),bind(X_16,$fot(inverse(A)))]]) ).
cnf(refute_0_90,plain,
( multiply(A,multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A))) != multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))
| multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A)) != X_26
| multiply(A,X_26) = multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A))),multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_91,plain,
( multiply(A,multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A))) != multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))
| multiply(A,X_26) = multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A)),X_26) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(A,X_26) = multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))),inverse(A))),multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_94,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_95,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( multiply(A,X_26) != multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))
| multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))) = multiply(A,X_26) ),
inference(subst,[],[refute_0_95:[bind(X,$fot(multiply(A,X_26))),bind(Y,$fot(multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))))]]) ).
cnf(refute_0_97,plain,
multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A))))) = multiply(A,X_26),
inference(resolve,[$cnf( $equal(multiply(A,X_26),multiply(X_26,multiply(X_27,inverse(multiply(X_27,inverse(A)))))) )],[refute_0_92,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))) = multiply(B,X_11),
inference(subst,[],[refute_0_97:[bind(A,$fot(B)),bind(X_26,$fot(X_11))]]) ).
cnf(refute_0_99,plain,
( multiply(X_11,B) != multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))
| multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))) != multiply(B,X_11)
| multiply(X_11,B) = multiply(B,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_11,B),multiply(B,X_11)) ),[0],$fot(multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))))]]) ).
cnf(refute_0_100,plain,
( multiply(X_11,B) != multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))
| multiply(X_11,B) = multiply(B,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B))))),multiply(B,X_11)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(X_11,B) = multiply(B,X_11),
inference(resolve,[$cnf( $equal(multiply(X_11,B),multiply(X_11,multiply(X_27,inverse(multiply(X_27,inverse(B)))))) )],[refute_0_87,refute_0_100]) ).
cnf(refute_0_102,plain,
( multiply(X_11,B) != multiply(B,X_11)
| multiply(B,X_11) = multiply(X_11,B) ),
inference(subst,[],[refute_0_95:[bind(X,$fot(multiply(X_11,B))),bind(Y,$fot(multiply(B,X_11)))]]) ).
cnf(refute_0_103,plain,
multiply(B,X_11) = multiply(X_11,B),
inference(resolve,[$cnf( $equal(multiply(X_11,B),multiply(B,X_11)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(inverse(b2),b2) = multiply(b2,inverse(b2)),
inference(subst,[],[refute_0_103:[bind(B,$fot(inverse(b2))),bind(X_11,$fot(b2))]]) ).
cnf(refute_0_105,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(inverse(b2),b2)),
introduced(tautology,[refl,[$fot(multiply(a2,multiply(inverse(b2),b2)))]]) ).
cnf(refute_0_106,plain,
( multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(inverse(b2),b2))
| multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) ),[1,1],$fot(multiply(b2,inverse(b2)))]]) ).
cnf(refute_0_107,plain,
( multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),multiply(b2,inverse(b2))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_110,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_95,refute_0_109]) ).
cnf(refute_0_111,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(a2,multiply(inverse(b2),b2)) = a2 ),
inference(subst,[],[refute_0_110:[bind(X,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Y,$fot(multiply(a2,multiply(b2,inverse(b2))))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_112,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(a2,multiply(inverse(b2),b2)) = a2 ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
multiply(a2,multiply(inverse(b2),b2)) = a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_10,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(inverse(b2),b2)),
inference(subst,[],[refute_0_103:[bind(B,$fot(multiply(inverse(b2),b2))),bind(X_11,$fot(a2))]]) ).
cnf(refute_0_115,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(inverse(b2),b2))
| multiply(a2,multiply(inverse(b2),b2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(subst,[],[refute_0_110:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_116,plain,
( multiply(a2,multiply(inverse(b2),b2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),a2) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_119,plain,
( a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_119,prove_these_axioms_2]) ).
cnf(refute_0_121,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_122,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_121,refute_0_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:41:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.37
% 0.18/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41
%------------------------------------------------------------------------------