TSTP Solution File: GRP520-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:42:06 EDT 2022
% Result : Unsatisfiable 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 23
% Syntax : Number of clauses : 91 ( 50 unt; 0 nHn; 45 RR)
% Number of literals : 152 ( 151 equ; 63 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 265 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(refute_0_0,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(multiply(A,B)))),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) != X_2
| multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) ),[0,1,0],$fot(X_2)]]) ).
cnf(refute_0_3,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),X_2) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C,
inference(subst,[],[single_axiom:[bind(B,$fot(multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)))]]) ).
cnf(refute_0_6,plain,
multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_7,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) != X_2
| multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) != C
| multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) ),[0,1,0,0,0],$fot(X_2)]]) ).
cnf(refute_0_8,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) != C
| multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)),X_2) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) = X_4,
inference(subst,[],[refute_0_9:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(C,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) != X_4
| multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)) != X_6
| multiply(multiply(inverse(X_6),X_4),X_6) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))),X_4) ),[0,1],$fot(X_6)]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) != X_4
| multiply(multiply(inverse(X_6),X_4),X_6) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)),X_6) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(multiply(inverse(X_6),X_4),X_6) = X_4,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))),X_4) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B))),bind(X_6,$fot(X_8))]]) ).
cnf(refute_0_16,plain,
multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_8)))]]) ).
cnf(refute_0_17,plain,
( multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) != C
| multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) ),[0,0],$fot(C)]]) ).
cnf(refute_0_18,plain,
( multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),C) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(C,X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(C,X_8))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)))]]) ).
cnf(refute_0_24,plain,
multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8),
inference(resolve,[$cnf( $equal(multiply(C,X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) = multiply(X_2,multiply(A,B)),
inference(subst,[],[refute_0_24:[bind(B,$fot(X_1)),bind(C,$fot(X_2)),bind(X_8,$fot(multiply(A,B)))]]) ).
cnf(refute_0_26,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) != multiply(X_2,multiply(A,B))
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_2,B)),multiply(X_2,multiply(A,B))) ),[0],$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1))]]) ).
cnf(refute_0_27,plain,
( multiply(A,multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)
| multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),multiply(X_2,multiply(A,B))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_4,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_9)),bind(B,$fot(X_10)),bind(X_2,$fot(multiply(inverse(X_10),X_4)))]]) ).
cnf(refute_0_30,plain,
multiply(multiply(inverse(X_10),X_4),X_10) = X_4,
inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_31,plain,
( multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(multiply(inverse(X_10),X_4),X_10) != X_4
| multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_32,plain,
( multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),X_10),X_4) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_9,X_4) = multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),
inference(resolve,[$cnf( $equal(multiply(X_9,multiply(multiply(inverse(X_10),X_4),X_10)),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) = multiply(X_11,X_10),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(multiply(X_11,X_10)))]]) ).
cnf(refute_0_35,plain,
multiply(inverse(X_6),multiply(X_11,X_10)) = multiply(X_11,multiply(inverse(X_6),X_10)),
inference(subst,[],[refute_0_28:[bind(A,$fot(inverse(X_6))),bind(B,$fot(X_10)),bind(X_2,$fot(X_11))]]) ).
cnf(refute_0_36,plain,
( multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) != multiply(X_11,X_10)
| multiply(inverse(X_6),multiply(X_11,X_10)) != multiply(X_11,multiply(inverse(X_6),X_10))
| multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6),multiply(X_11,X_10)) ),[0,0],$fot(multiply(X_11,multiply(inverse(X_6),X_10)))]]) ).
cnf(refute_0_37,plain,
( multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) != multiply(X_11,X_10)
| multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_6),multiply(X_11,X_10)),multiply(X_11,multiply(inverse(X_6),X_10))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6),multiply(X_11,X_10)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(multiply(X_25,multiply(inverse(X_26),X_24)),X_26) = multiply(X_25,X_24),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_24)),bind(X_11,$fot(X_25)),bind(X_6,$fot(X_26))]]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_26),multiply(X_25,X_24)) = multiply(X_25,multiply(inverse(X_26),X_24)),
inference(subst,[],[refute_0_28:[bind(A,$fot(inverse(X_26))),bind(B,$fot(X_24)),bind(X_2,$fot(X_25))]]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_26),multiply(X_25,X_24)) != multiply(X_25,multiply(inverse(X_26),X_24))
| multiply(X_25,multiply(inverse(X_26),X_24)) = multiply(inverse(X_26),multiply(X_25,X_24)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(inverse(X_26),multiply(X_25,X_24)))),bind(Y,$fot(multiply(X_25,multiply(inverse(X_26),X_24))))]]) ).
cnf(refute_0_42,plain,
multiply(X_25,multiply(inverse(X_26),X_24)) = multiply(inverse(X_26),multiply(X_25,X_24)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),multiply(X_25,X_24)),multiply(X_25,multiply(inverse(X_26),X_24))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( multiply(X_25,multiply(inverse(X_26),X_24)) != multiply(inverse(X_26),multiply(X_25,X_24))
| multiply(multiply(X_25,multiply(inverse(X_26),X_24)),X_26) != multiply(X_25,X_24)
| multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(X_25,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_25,multiply(inverse(X_26),X_24)),X_26),multiply(X_25,X_24)) ),[0,0],$fot(multiply(inverse(X_26),multiply(X_25,X_24)))]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(X_25,multiply(inverse(X_26),X_24)),X_26) != multiply(X_25,X_24)
| multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(X_25,X_24) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(inverse(X_26),X_24)),multiply(inverse(X_26),multiply(X_25,X_24))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(X_25,X_24),
inference(resolve,[$cnf( $equal(multiply(multiply(X_25,multiply(inverse(X_26),X_24)),X_26),multiply(X_25,X_24)) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(multiply(X_25,multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),X_26) = multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),bind(X_11,$fot(X_25)),bind(X_6,$fot(X_26))]]) ).
cnf(refute_0_47,plain,
multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_26)))]]) ).
cnf(refute_0_48,plain,
( multiply(multiply(X_25,multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),X_26) != multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))
| multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) != C
| multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_25,multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),X_26),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) ),[0,0,1],$fot(C)]]) ).
cnf(refute_0_49,plain,
( multiply(multiply(X_25,multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),X_26) != multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))
| multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),C) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_25,multiply(inverse(X_26),multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))),X_26),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B) = multiply(C,X_26),
inference(subst,[],[refute_0_24:[bind(X_8,$fot(X_26))]]) ).
cnf(refute_0_52,plain,
multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) = multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),
introduced(tautology,[refl,[$fot(multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)))]]) ).
cnf(refute_0_53,plain,
( multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) != multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))
| multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B) != multiply(C,X_26)
| multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) = multiply(X_25,multiply(C,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) ),[1,1],$fot(multiply(C,X_26))]]) ).
cnf(refute_0_54,plain,
( multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B) != multiply(C,X_26)
| multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) = multiply(X_25,multiply(C,X_26)) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) = multiply(X_25,multiply(C,X_26)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B),multiply(C,X_26)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)) != multiply(X_25,multiply(C,X_26))
| multiply(multiply(X_25,C),X_26) != multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))
| multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(C,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_25,C),X_26),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) ),[1],$fot(multiply(X_25,multiply(C,X_26)))]]) ).
cnf(refute_0_57,plain,
( multiply(multiply(X_25,C),X_26) != multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))
| multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(C,X_26)) ),
inference(resolve,[$cnf( $equal(multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B)),multiply(X_25,multiply(C,X_26))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(multiply(X_25,C),X_26) = multiply(X_25,multiply(C,X_26)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_25,C),X_26),multiply(X_25,multiply(multiply(inverse(multiply(inverse(X_26),B)),C),B))) )],[refute_0_50,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(multiply(X_25,X_24),X_26) = multiply(X_25,multiply(X_24,X_26)),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_24))]]) ).
cnf(refute_0_60,plain,
multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) = multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)),
introduced(tautology,[refl,[$fot(multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)))]]) ).
cnf(refute_0_61,plain,
( multiply(multiply(X_25,X_24),X_26) != multiply(X_25,multiply(X_24,X_26))
| multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) != multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26))
| multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)),multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26))) ),[1,1],$fot(multiply(X_25,multiply(X_24,X_26)))]]) ).
cnf(refute_0_62,plain,
( multiply(multiply(X_25,X_24),X_26) != multiply(X_25,multiply(X_24,X_26))
| multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)),multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_25,X_24),X_26),multiply(X_25,multiply(X_24,X_26))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiply(X_25,X_24))),bind(X_25,$fot(inverse(X_26)))]]) ).
cnf(refute_0_65,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_66,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_22,refute_0_65]) ).
cnf(refute_0_67,plain,
( multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) != multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26))
| multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) != multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))
| multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26))),bind(Y,$fot(multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)))),bind(Z,$fot(multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))))]]) ).
cnf(refute_0_68,plain,
( multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)) != multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))
| multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26),multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) = multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),multiply(multiply(X_25,X_24),X_26)),multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
( multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) != multiply(X_25,X_24)
| multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) != multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))
| multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) = multiply(X_25,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26),multiply(X_25,X_24)) ),[0],$fot(multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))))]]) ).
cnf(refute_0_71,plain,
( multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26) != multiply(X_25,X_24)
| multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) = multiply(X_25,X_24) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26),multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(inverse(X_26),multiply(X_25,multiply(X_24,X_26))) = multiply(X_25,X_24),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_26),multiply(X_25,X_24)),X_26),multiply(X_25,X_24)) )],[refute_0_45,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) = multiply(X_4,X_9),
inference(subst,[],[refute_0_72:[bind(X_24,$fot(X_9)),bind(X_25,$fot(X_4)),bind(X_26,$fot(X_10))]]) ).
cnf(refute_0_74,plain,
multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))),
inference(subst,[],[refute_0_58:[bind(C,$fot(X_4)),bind(X_25,$fot(inverse(X_10))),bind(X_26,$fot(multiply(X_9,X_10)))]]) ).
cnf(refute_0_75,plain,
( multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) != multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10)))
| multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) != multiply(X_4,X_9)
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)))),bind(Y,$fot(multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))))),bind(Z,$fot(multiply(X_4,X_9)))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))) != multiply(X_4,X_9)
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) = multiply(X_4,X_9),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),multiply(X_4,multiply(X_9,X_10))),multiply(X_4,X_9)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( multiply(X_9,X_4) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)) != multiply(X_4,X_9)
| multiply(X_9,X_4) = multiply(X_4,X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_9,X_4),multiply(X_4,X_9)) ),[0],$fot(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)))]]) ).
cnf(refute_0_79,plain,
( multiply(X_9,X_4) != multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))
| multiply(X_9,X_4) = multiply(X_4,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10)),multiply(X_4,X_9)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_9,X_4) = multiply(X_4,X_9),
inference(resolve,[$cnf( $equal(multiply(X_9,X_4),multiply(multiply(inverse(X_10),X_4),multiply(X_9,X_10))) )],[refute_0_33,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(X_9,X_4) != multiply(X_4,X_9)
| multiply(X_4,X_9) = multiply(X_9,X_4) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_9,X_4))),bind(Y,$fot(multiply(X_4,X_9)))]]) ).
cnf(refute_0_82,plain,
multiply(X_4,X_9) = multiply(X_9,X_4),
inference(resolve,[$cnf( $equal(multiply(X_9,X_4),multiply(X_4,X_9)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_82:[bind(X_4,$fot(b)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_84,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_85,plain,
( multiply(a,b) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_85,prove_these_axioms_4]) ).
cnf(refute_0_87,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_88,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_87,refute_0_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.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 : Tue Jun 14 13:06:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54
% 0.18/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.56
%------------------------------------------------------------------------------