TSTP Solution File: GRP518-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 10:42:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 65
% Syntax : Number of clauses : 254 ( 136 unt; 0 nHn; 124 RR)
% Number of literals : 427 ( 426 equ; 176 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 : 656 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,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,$fot(multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)))]]) ).
cnf(refute_0_1,plain,
multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)) != X_2
| multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) != C
| multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C ),
introduced(tautology,[equality,[$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_3,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( $equal(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1)),X_2) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(A,multiply(multiply(inverse(X_2),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))) = C,
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12))) = X_11,
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(inverse(X_13),X_11))),bind(C,$fot(X_11)),bind(X_1,$fot(X_12)),bind(X_2,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12)) = X_13,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(inverse(X_13),X_11))),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_7,plain,
( multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12))) != X_11
| multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12)) != X_13
| multiply(multiply(inverse(X_13),X_11),X_13) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12))),X_11) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_8,plain,
( multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12))) != X_11
| multiply(multiply(inverse(X_13),X_11),X_13) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12)),X_13) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(multiply(inverse(X_13),X_11),X_13) = X_11,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(X_13),X_11),multiply(multiply(inverse(multiply(multiply(inverse(X_13),X_11),X_12)),X_13),X_12))),X_11) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_13) = multiply(inverse(inverse(X_13)),X_25),
inference(subst,[],[refute_0_9:[bind(X_11,$fot(multiply(inverse(inverse(X_13)),X_25)))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(inverse(multiply(X_20,X_11)),X_11),multiply(X_20,X_11)) = X_11,
inference(subst,[],[refute_0_9:[bind(X_13,$fot(multiply(X_20,X_11)))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(multiply(X_3,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(multiply(X_3,X_4))))]]) ).
cnf(refute_0_13,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,$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)))]]) ).
cnf(refute_0_14,plain,
multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(multiply(A,B)))),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_15,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_16,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( $equal(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),X_2) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(X_3,multiply(C,X_4)) = multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_3)),bind(B,$fot(X_4)),bind(X_1,$fot(B)),bind(X_2,$fot(C))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_3,multiply(C,X_4)) != multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B) = multiply(X_3,multiply(C,X_4)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(X_3,multiply(C,X_4)))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)))]]) ).
cnf(refute_0_23,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B) = multiply(X_3,multiply(C,X_4)),
inference(resolve,[$cnf( $equal(multiply(X_3,multiply(C,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B) != multiply(X_3,multiply(C,X_4))
| multiply(inverse(multiply(X_3,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)) != C
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)),C) ),[0,1],$fot(multiply(X_3,multiply(C,X_4)))]]) ).
cnf(refute_0_25,plain,
( multiply(inverse(multiply(X_3,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)) != C
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) = C ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B),multiply(X_3,multiply(C,X_4))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(multiply(inverse(multiply(inverse(multiply(X_3,X_4)),B)),C),B)),C) )],[refute_0_12,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9)))) = C,
inference(subst,[],[refute_0_26:[bind(X_3,$fot(inverse(multiply(C,X_9)))),bind(X_4,$fot(multiply(X_7,X_9)))]]) ).
cnf(refute_0_28,plain,
multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9))) = X_7,
inference(subst,[],[refute_0_26:[bind(C,$fot(X_7)),bind(X_3,$fot(C)),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_29,plain,
( multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9))) != X_7
| multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9)))) != C
| multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9)))),C) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_30,plain,
( multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9)))) != C
| multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) = C ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9))),X_7) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),multiply(inverse(multiply(C,X_9)),multiply(C,multiply(X_7,X_9)))),C) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))))) = inverse(multiply(X_8,X_9)),
inference(subst,[],[refute_0_26:[bind(C,$fot(inverse(multiply(X_8,X_9)))),bind(X_4,$fot(multiply(X_8,multiply(X_7,X_9))))]]) ).
cnf(refute_0_33,plain,
multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))) = X_7,
inference(subst,[],[refute_0_26:[bind(C,$fot(X_7)),bind(X_3,$fot(X_8)),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_34,plain,
( multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))))) != inverse(multiply(X_8,X_9))
| multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))) != X_7
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = inverse(multiply(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))))),inverse(multiply(X_8,X_9))) ),[0,1,1],$fot(X_7)]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))))) != inverse(multiply(X_8,X_9))
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = inverse(multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))),X_7) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = inverse(multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,multiply(inverse(multiply(X_8,X_9)),multiply(X_8,multiply(X_7,X_9))))),inverse(multiply(X_8,X_9))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(multiply(inverse(X_4),X_14),X_4))) = multiply(inverse(X_4),X_14),
inference(subst,[],[refute_0_26:[bind(C,$fot(multiply(inverse(X_4),X_14)))]]) ).
cnf(refute_0_38,plain,
multiply(multiply(inverse(X_4),X_14),X_4) = X_14,
inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_14)),bind(X_13,$fot(X_4))]]) ).
cnf(refute_0_39,plain,
( multiply(multiply(inverse(X_4),X_14),X_4) != X_14
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(multiply(inverse(X_4),X_14),X_4))) != multiply(inverse(X_4),X_14)
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) = multiply(inverse(X_4),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(multiply(inverse(X_4),X_14),X_4))),multiply(inverse(X_4),X_14)) ),[0,1,1],$fot(X_14)]]) ).
cnf(refute_0_40,plain,
( multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(multiply(inverse(X_4),X_14),X_4))) != multiply(inverse(X_4),X_14)
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) = multiply(inverse(X_4),X_14) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_4),X_14),X_4),X_14) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) = multiply(inverse(X_4),X_14),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(multiply(inverse(X_4),X_14),X_4))),multiply(inverse(X_4),X_14)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),multiply(X_3,X_4)) = multiply(X_3,multiply(C,X_4)),
inference(subst,[],[refute_0_9:[bind(X_11,$fot(multiply(X_3,multiply(C,X_4)))),bind(X_13,$fot(multiply(X_3,X_4)))]]) ).
cnf(refute_0_43,plain,
( multiply(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),multiply(X_3,X_4)) != multiply(X_3,multiply(C,X_4))
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) != C
| multiply(C,multiply(X_3,X_4)) = multiply(X_3,multiply(C,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) ),[0,0],$fot(C)]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),multiply(X_3,X_4)) != multiply(X_3,multiply(C,X_4))
| multiply(C,multiply(X_3,X_4)) = multiply(X_3,multiply(C,X_4)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),C) )],[refute_0_26,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(C,multiply(X_3,X_4)) = multiply(X_3,multiply(C,X_4)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))),multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( multiply(C,multiply(X_3,X_4)) != multiply(X_3,multiply(C,X_4))
| multiply(X_3,multiply(C,X_4)) = multiply(C,multiply(X_3,X_4)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(C,multiply(X_3,X_4)))),bind(Y,$fot(multiply(X_3,multiply(C,X_4))))]]) ).
cnf(refute_0_47,plain,
multiply(X_3,multiply(C,X_4)) = multiply(C,multiply(X_3,X_4)),
inference(resolve,[$cnf( $equal(multiply(C,multiply(X_3,X_4)),multiply(X_3,multiply(C,X_4))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) = multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14)),
inference(subst,[],[refute_0_47:[bind(C,$fot(X_3)),bind(X_3,$fot(inverse(multiply(X_3,X_4)))),bind(X_4,$fot(X_14))]]) ).
cnf(refute_0_49,plain,
( multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) != multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14))
| multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) != multiply(inverse(X_4),X_14)
| multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14)) = multiply(inverse(X_4),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)),multiply(inverse(X_4),X_14)) ),[0],$fot(multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14)))]]) ).
cnf(refute_0_50,plain,
( multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)) != multiply(inverse(X_4),X_14)
| multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14)) = multiply(inverse(X_4),X_14) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)),multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(X_3,multiply(inverse(multiply(X_3,X_4)),X_14)) = multiply(inverse(X_4),X_14),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,X_4)),multiply(X_3,X_14)),multiply(inverse(X_4),X_14)) )],[refute_0_41,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)) = multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7),
inference(subst,[],[refute_0_51:[bind(X_14,$fot(X_7)),bind(X_4,$fot(multiply(X_8,multiply(X_7,X_9))))]]) ).
cnf(refute_0_53,plain,
multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)),
inference(subst,[],[refute_0_47:[bind(C,$fot(X_3)),bind(X_3,$fot(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))))),bind(X_4,$fot(X_7))]]) ).
cnf(refute_0_54,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_55,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_21,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)) != multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) != multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7))
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)))),bind(Y,$fot(multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)))),bind(Z,$fot(multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)))]]) ).
cnf(refute_0_57,plain,
( multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)) != multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)),multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) = multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7),
inference(resolve,[$cnf( $equal(multiply(X_3,multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),X_7)),multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
( multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) != multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)
| multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) != inverse(multiply(X_8,X_9))
| multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7) = inverse(multiply(X_8,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)),inverse(multiply(X_8,X_9))) ),[0],$fot(multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7))]]) ).
cnf(refute_0_60,plain,
( multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)) != inverse(multiply(X_8,X_9))
| multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7) = inverse(multiply(X_8,X_9)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)),multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(inverse(multiply(X_8,multiply(X_7,X_9))),X_7) = inverse(multiply(X_8,X_9)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_3,multiply(X_8,multiply(X_7,X_9)))),multiply(X_3,X_7)),inverse(multiply(X_8,X_9))) )],[refute_0_36,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) = inverse(multiply(inverse(multiply(C,X_9)),X_9)),
inference(subst,[],[refute_0_61:[bind(X_8,$fot(inverse(multiply(C,X_9))))]]) ).
cnf(refute_0_63,plain,
( multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) != C
| multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) != inverse(multiply(inverse(multiply(C,X_9)),X_9))
| inverse(multiply(inverse(multiply(C,X_9)),X_9)) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7),C) ),[0],$fot(inverse(multiply(inverse(multiply(C,X_9)),X_9)))]]) ).
cnf(refute_0_64,plain,
( multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7) != C
| inverse(multiply(inverse(multiply(C,X_9)),X_9)) = C ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7),inverse(multiply(inverse(multiply(C,X_9)),X_9))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
inverse(multiply(inverse(multiply(C,X_9)),X_9)) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(C,X_9)),multiply(X_7,X_9))),X_7),C) )],[refute_0_31,refute_0_64]) ).
cnf(refute_0_66,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X_17),X_11),X_17)),X_17)) = multiply(inverse(X_17),X_11),
inference(subst,[],[refute_0_65:[bind(C,$fot(multiply(inverse(X_17),X_11))),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_67,plain,
multiply(multiply(inverse(X_17),X_11),X_17) = X_11,
inference(subst,[],[refute_0_9:[bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_68,plain,
( multiply(multiply(inverse(X_17),X_11),X_17) != X_11
| inverse(multiply(inverse(multiply(multiply(inverse(X_17),X_11),X_17)),X_17)) != multiply(inverse(X_17),X_11)
| inverse(multiply(inverse(X_11),X_17)) = multiply(inverse(X_17),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(multiply(inverse(X_17),X_11),X_17)),X_17)),multiply(inverse(X_17),X_11)) ),[0,0,0,0],$fot(X_11)]]) ).
cnf(refute_0_69,plain,
( inverse(multiply(inverse(multiply(multiply(inverse(X_17),X_11),X_17)),X_17)) != multiply(inverse(X_17),X_11)
| inverse(multiply(inverse(X_11),X_17)) = multiply(inverse(X_17),X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_17),X_11),X_17),X_11) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
inverse(multiply(inverse(X_11),X_17)) = multiply(inverse(X_17),X_11),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(multiply(inverse(X_17),X_11),X_17)),X_17)),multiply(inverse(X_17),X_11)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
inverse(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))) = multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(X_18)),bind(X_17,$fot(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)))]]) ).
cnf(refute_0_72,plain,
multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_18)))]]) ).
cnf(refute_0_73,plain,
( multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) != C
| inverse(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))) != multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)
| inverse(C) = multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) ),[0,0],$fot(C)]]) ).
cnf(refute_0_74,plain,
( inverse(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))) != multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)
| inverse(C) = multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),C) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
inverse(C) = multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_18),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(multiply(inverse(B),X_14),multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(B),X_14),B)),X_1)),X_2),X_1),
inference(subst,[],[refute_0_17:[bind(A,$fot(multiply(inverse(B),X_14)))]]) ).
cnf(refute_0_77,plain,
multiply(multiply(inverse(B),X_14),B) = X_14,
inference(subst,[],[refute_0_9:[bind(X_11,$fot(X_14)),bind(X_13,$fot(B))]]) ).
cnf(refute_0_78,plain,
( multiply(multiply(inverse(B),X_14),B) != X_14
| multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(B),X_14),B)),X_1)),X_2),X_1)
| multiply(multiply(inverse(B),X_14),multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(B),X_14),B)),X_1)),X_2),X_1)) ),[1,0,0,0,0,0],$fot(X_14)]]) ).
cnf(refute_0_79,plain,
( multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(B),X_14),B)),X_1)),X_2),X_1)
| multiply(multiply(inverse(B),X_14),multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_14),B),X_14) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(multiply(inverse(B),X_14),multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(B),X_14),B)),X_1)),X_2),X_1)) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),X_15) = multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B),
inference(subst,[],[refute_0_9:[bind(X_11,$fot(multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B))),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_82,plain,
multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_15)))]]) ).
cnf(refute_0_83,plain,
( multiply(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),X_15) != multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)
| multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)) != C
| multiply(C,X_15) = multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)) ),[0,0],$fot(C)]]) ).
cnf(refute_0_84,plain,
( multiply(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),X_15) != multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)
| multiply(C,X_15) = multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),C) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(C,X_15) = multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)),X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(inverse(B),X_14),multiply(X_2,B)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(multiply(inverse(B),X_14),multiply(X_2,B)))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)))]]) ).
cnf(refute_0_87,plain,
multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(inverse(B),X_14),multiply(X_2,B)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) )],[refute_0_80,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B) = multiply(multiply(inverse(B),X_15),multiply(C,B)),
inference(subst,[],[refute_0_87:[bind(X_1,$fot(B)),bind(X_14,$fot(X_15)),bind(X_2,$fot(C))]]) ).
cnf(refute_0_89,plain,
( multiply(C,X_15) != multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B) != multiply(multiply(inverse(B),X_15),multiply(C,B))
| multiply(C,X_15) = multiply(multiply(inverse(B),X_15),multiply(C,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(C,X_15),multiply(multiply(inverse(B),X_15),multiply(C,B))) ),[0],$fot(multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B))]]) ).
cnf(refute_0_90,plain,
( multiply(C,X_15) != multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)
| multiply(C,X_15) = multiply(multiply(inverse(B),X_15),multiply(C,B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B),multiply(multiply(inverse(B),X_15),multiply(C,B))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(C,X_15) = multiply(multiply(inverse(B),X_15),multiply(C,B)),
inference(resolve,[$cnf( $equal(multiply(C,X_15),multiply(multiply(inverse(multiply(inverse(X_15),B)),C),B)) )],[refute_0_85,refute_0_90]) ).
cnf(refute_0_92,plain,
( multiply(C,X_15) != multiply(multiply(inverse(B),X_15),multiply(C,B))
| multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(C,X_15) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(C,X_15))),bind(Y,$fot(multiply(multiply(inverse(B),X_15),multiply(C,B))))]]) ).
cnf(refute_0_93,plain,
multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(C,X_15),
inference(resolve,[$cnf( $equal(multiply(C,X_15),multiply(multiply(inverse(B),X_15),multiply(C,B))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(multiply(inverse(B),X_14),multiply(X_2,B)) = multiply(X_2,X_14),
inference(subst,[],[refute_0_93:[bind(C,$fot(X_2)),bind(X_15,$fot(X_14))]]) ).
cnf(refute_0_95,plain,
( multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(X_2,X_14)
| multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(X_2,X_14) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) ),[0],$fot(multiply(X_2,X_14))]]) ).
cnf(refute_0_96,plain,
( multiply(multiply(inverse(B),X_14),multiply(X_2,B)) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(X_2,X_14) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(X_2,X_14)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(X_2,X_14) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_14),multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) )],[refute_0_80,refute_0_96]) ).
cnf(refute_0_98,plain,
inverse(multiply(inverse(X_14),X_1)) = multiply(inverse(X_1),X_14),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(X_14)),bind(X_17,$fot(X_1))]]) ).
cnf(refute_0_99,plain,
multiply(inverse(multiply(inverse(X_14),X_1)),X_2) = multiply(inverse(multiply(inverse(X_14),X_1)),X_2),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(X_14),X_1)),X_2))]]) ).
cnf(refute_0_100,plain,
( multiply(inverse(multiply(inverse(X_14),X_1)),X_2) != multiply(inverse(multiply(inverse(X_14),X_1)),X_2)
| inverse(multiply(inverse(X_14),X_1)) != multiply(inverse(X_1),X_14)
| multiply(inverse(multiply(inverse(X_14),X_1)),X_2) = multiply(multiply(inverse(X_1),X_14),X_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),multiply(inverse(multiply(inverse(X_14),X_1)),X_2)) ),[1,0],$fot(multiply(inverse(X_1),X_14))]]) ).
cnf(refute_0_101,plain,
( inverse(multiply(inverse(X_14),X_1)) != multiply(inverse(X_1),X_14)
| multiply(inverse(multiply(inverse(X_14),X_1)),X_2) = multiply(multiply(inverse(X_1),X_14),X_2) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),multiply(inverse(multiply(inverse(X_14),X_1)),X_2)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(inverse(multiply(inverse(X_14),X_1)),X_2) = multiply(multiply(inverse(X_1),X_14),X_2),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_14),X_1)),multiply(inverse(X_1),X_14)) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1))]]) ).
cnf(refute_0_104,plain,
( multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(inverse(multiply(inverse(X_14),X_1)),X_2) != multiply(multiply(inverse(X_1),X_14),X_2)
| multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) ),[1,0],$fot(multiply(multiply(inverse(X_1),X_14),X_2))]]) ).
cnf(refute_0_105,plain,
( multiply(inverse(multiply(inverse(X_14),X_1)),X_2) != multiply(multiply(inverse(X_1),X_14),X_2)
| multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),multiply(multiply(inverse(X_1),X_14),X_2)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( multiply(X_2,X_14) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1) != multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)
| multiply(X_2,X_14) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_2,X_14),multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)) ),[0],$fot(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1))]]) ).
cnf(refute_0_108,plain,
( multiply(X_2,X_14) != multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)
| multiply(X_2,X_14) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1),multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(X_2,X_14) = multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(X_2,X_14),multiply(multiply(inverse(multiply(inverse(X_14),X_1)),X_2),X_1)) )],[refute_0_97,refute_0_108]) ).
cnf(refute_0_110,plain,
( multiply(X_2,X_14) != multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)
| multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) = multiply(X_2,X_14) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(X_2,X_14))),bind(Y,$fot(multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)))]]) ).
cnf(refute_0_111,plain,
multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1) = multiply(X_2,X_14),
inference(resolve,[$cnf( $equal(multiply(X_2,X_14),multiply(multiply(multiply(inverse(X_1),X_14),X_2),X_1)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(multiply(multiply(inverse(B),X_18),C),B) = multiply(C,X_18),
inference(subst,[],[refute_0_111:[bind(X_1,$fot(B)),bind(X_14,$fot(X_18)),bind(X_2,$fot(C))]]) ).
cnf(refute_0_113,plain,
inverse(multiply(inverse(X_18),B)) = multiply(inverse(B),X_18),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(X_18)),bind(X_17,$fot(B))]]) ).
cnf(refute_0_114,plain,
multiply(inverse(multiply(inverse(X_18),B)),C) = multiply(inverse(multiply(inverse(X_18),B)),C),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(X_18),B)),C))]]) ).
cnf(refute_0_115,plain,
( multiply(inverse(multiply(inverse(X_18),B)),C) != multiply(inverse(multiply(inverse(X_18),B)),C)
| inverse(multiply(inverse(X_18),B)) != multiply(inverse(B),X_18)
| multiply(inverse(multiply(inverse(X_18),B)),C) = multiply(multiply(inverse(B),X_18),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_18),B)),C),multiply(inverse(multiply(inverse(X_18),B)),C)) ),[1,0],$fot(multiply(inverse(B),X_18))]]) ).
cnf(refute_0_116,plain,
( inverse(multiply(inverse(X_18),B)) != multiply(inverse(B),X_18)
| multiply(inverse(multiply(inverse(X_18),B)),C) = multiply(multiply(inverse(B),X_18),C) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_18),B)),C),multiply(inverse(multiply(inverse(X_18),B)),C)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(inverse(multiply(inverse(X_18),B)),C) = multiply(multiply(inverse(B),X_18),C),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_18),B)),multiply(inverse(B),X_18)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))]]) ).
cnf(refute_0_119,plain,
( multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) != multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)
| multiply(inverse(multiply(inverse(X_18),B)),C) != multiply(multiply(inverse(B),X_18),C)
| multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(multiply(multiply(inverse(B),X_18),C),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) ),[1,0],$fot(multiply(multiply(inverse(B),X_18),C))]]) ).
cnf(refute_0_120,plain,
( multiply(inverse(multiply(inverse(X_18),B)),C) != multiply(multiply(inverse(B),X_18),C)
| multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(multiply(multiply(inverse(B),X_18),C),B) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B),multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(multiply(multiply(inverse(B),X_18),C),B),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_18),B)),C),multiply(multiply(inverse(B),X_18),C)) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( multiply(multiply(multiply(inverse(B),X_18),C),B) != multiply(C,X_18)
| multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) != multiply(multiply(multiply(inverse(B),X_18),C),B)
| multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(C,X_18) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))),bind(Y,$fot(multiply(multiply(multiply(inverse(B),X_18),C),B))),bind(Z,$fot(multiply(C,X_18)))]]) ).
cnf(refute_0_123,plain,
( multiply(multiply(multiply(inverse(B),X_18),C),B) != multiply(C,X_18)
| multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(C,X_18) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B),multiply(multiply(multiply(inverse(B),X_18),C),B)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) = multiply(C,X_18),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(inverse(B),X_18),C),B),multiply(C,X_18)) )],[refute_0_112,refute_0_123]) ).
cnf(refute_0_125,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) = inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)))]]) ).
cnf(refute_0_126,plain,
( multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) != multiply(C,X_18)
| inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) != inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))
| inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) = inverse(multiply(C,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))) ),[1,0],$fot(multiply(C,X_18))]]) ).
cnf(refute_0_127,plain,
( multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B) != multiply(C,X_18)
| inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) = inverse(multiply(C,X_18)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) = inverse(multiply(C,X_18)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B),multiply(C,X_18)) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) = multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18))]]) ).
cnf(refute_0_130,plain,
( multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) != multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)
| inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) != inverse(multiply(C,X_18))
| multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) = multiply(inverse(multiply(C,X_18)),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) ),[1,0],$fot(inverse(multiply(C,X_18)))]]) ).
cnf(refute_0_131,plain,
( inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)) != inverse(multiply(C,X_18))
| multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) = multiply(inverse(multiply(C,X_18)),X_18) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) = multiply(inverse(multiply(C,X_18)),X_18),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),inverse(multiply(C,X_18))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18) != multiply(inverse(multiply(C,X_18)),X_18)
| inverse(C) != multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)
| inverse(C) = multiply(inverse(multiply(C,X_18)),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(C),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) ),[1],$fot(multiply(inverse(multiply(C,X_18)),X_18))]]) ).
cnf(refute_0_134,plain,
( inverse(C) != multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)
| inverse(C) = multiply(inverse(multiply(C,X_18)),X_18) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18),multiply(inverse(multiply(C,X_18)),X_18)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
inverse(C) = multiply(inverse(multiply(C,X_18)),X_18),
inference(resolve,[$cnf( $equal(inverse(C),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X_18),B)),C),B)),X_18)) )],[refute_0_75,refute_0_134]) ).
cnf(refute_0_136,plain,
inverse(X_20) = multiply(inverse(multiply(X_20,X_11)),X_11),
inference(subst,[],[refute_0_135:[bind(C,$fot(X_20)),bind(X_18,$fot(X_11))]]) ).
cnf(refute_0_137,plain,
( inverse(X_20) != multiply(inverse(multiply(X_20,X_11)),X_11)
| multiply(inverse(multiply(X_20,X_11)),X_11) = inverse(X_20) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(inverse(X_20))),bind(Y,$fot(multiply(inverse(multiply(X_20,X_11)),X_11)))]]) ).
cnf(refute_0_138,plain,
multiply(inverse(multiply(X_20,X_11)),X_11) = inverse(X_20),
inference(resolve,[$cnf( $equal(inverse(X_20),multiply(inverse(multiply(X_20,X_11)),X_11)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( multiply(multiply(inverse(multiply(X_20,X_11)),X_11),multiply(X_20,X_11)) != X_11
| multiply(inverse(multiply(X_20,X_11)),X_11) != inverse(X_20)
| multiply(inverse(X_20),multiply(X_20,X_11)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(X_20,X_11)),X_11),multiply(X_20,X_11)),X_11) ),[0,0],$fot(inverse(X_20))]]) ).
cnf(refute_0_140,plain,
( multiply(multiply(inverse(multiply(X_20,X_11)),X_11),multiply(X_20,X_11)) != X_11
| multiply(inverse(X_20),multiply(X_20,X_11)) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_20,X_11)),X_11),inverse(X_20)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(inverse(X_20),multiply(X_20,X_11)) = X_11,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(X_20,X_11)),X_11),multiply(X_20,X_11)),X_11) )],[refute_0_11,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(inverse(X_20),multiply(X_20,X_11)) = multiply(X_20,multiply(inverse(X_20),X_11)),
inference(subst,[],[refute_0_47:[bind(C,$fot(X_20)),bind(X_3,$fot(inverse(X_20))),bind(X_4,$fot(X_11))]]) ).
cnf(refute_0_143,plain,
( multiply(inverse(X_20),multiply(X_20,X_11)) != X_11
| multiply(inverse(X_20),multiply(X_20,X_11)) != multiply(X_20,multiply(inverse(X_20),X_11))
| multiply(X_20,multiply(inverse(X_20),X_11)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_20),multiply(X_20,X_11)),X_11) ),[0],$fot(multiply(X_20,multiply(inverse(X_20),X_11)))]]) ).
cnf(refute_0_144,plain,
( multiply(inverse(X_20),multiply(X_20,X_11)) != X_11
| multiply(X_20,multiply(inverse(X_20),X_11)) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(X_20,X_11)),multiply(X_20,multiply(inverse(X_20),X_11))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(X_20,multiply(inverse(X_20),X_11)) = X_11,
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(X_20,X_11)),X_11) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)) = X_25,
inference(subst,[],[refute_0_145:[bind(X_11,$fot(X_25)),bind(X_20,$fot(inverse(X_13)))]]) ).
cnf(refute_0_147,plain,
( multiply(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_13) != multiply(inverse(inverse(X_13)),X_25)
| multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)) != X_25
| multiply(X_25,X_13) = multiply(inverse(inverse(X_13)),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_13),multiply(inverse(inverse(X_13)),X_25)) ),[0,0],$fot(X_25)]]) ).
cnf(refute_0_148,plain,
( multiply(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_13) != multiply(inverse(inverse(X_13)),X_25)
| multiply(X_25,X_13) = multiply(inverse(inverse(X_13)),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_25) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(X_25,X_13) = multiply(inverse(inverse(X_13)),X_25),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_13),multiply(inverse(inverse(X_13)),X_25)),X_13),multiply(inverse(inverse(X_13)),X_25)) )],[refute_0_10,refute_0_148]) ).
cnf(refute_0_150,plain,
inverse(multiply(inverse(multiply(X_20,X_17)),X_17)) = multiply(inverse(X_17),multiply(X_20,X_17)),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(multiply(X_20,X_17)))]]) ).
cnf(refute_0_151,plain,
inverse(X_20) = multiply(inverse(multiply(X_20,X_17)),X_17),
inference(subst,[],[refute_0_135:[bind(C,$fot(X_20)),bind(X_18,$fot(X_17))]]) ).
cnf(refute_0_152,plain,
( inverse(X_20) != multiply(inverse(multiply(X_20,X_17)),X_17)
| multiply(inverse(multiply(X_20,X_17)),X_17) = inverse(X_20) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(inverse(X_20))),bind(Y,$fot(multiply(inverse(multiply(X_20,X_17)),X_17)))]]) ).
cnf(refute_0_153,plain,
multiply(inverse(multiply(X_20,X_17)),X_17) = inverse(X_20),
inference(resolve,[$cnf( $equal(inverse(X_20),multiply(inverse(multiply(X_20,X_17)),X_17)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( multiply(inverse(multiply(X_20,X_17)),X_17) != inverse(X_20)
| inverse(multiply(inverse(multiply(X_20,X_17)),X_17)) != multiply(inverse(X_17),multiply(X_20,X_17))
| inverse(inverse(X_20)) = multiply(inverse(X_17),multiply(X_20,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(X_20,X_17)),X_17)),multiply(inverse(X_17),multiply(X_20,X_17))) ),[0,0],$fot(inverse(X_20))]]) ).
cnf(refute_0_155,plain,
( inverse(multiply(inverse(multiply(X_20,X_17)),X_17)) != multiply(inverse(X_17),multiply(X_20,X_17))
| inverse(inverse(X_20)) = multiply(inverse(X_17),multiply(X_20,X_17)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_20,X_17)),X_17),inverse(X_20)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
inverse(inverse(X_20)) = multiply(inverse(X_17),multiply(X_20,X_17)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(X_20,X_17)),X_17)),multiply(inverse(X_17),multiply(X_20,X_17))) )],[refute_0_150,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(inverse(multiply(multiply(inverse(X_4),X_14),X_4)),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = C,
inference(subst,[],[refute_0_26:[bind(X_3,$fot(multiply(inverse(X_4),X_14)))]]) ).
cnf(refute_0_158,plain,
( multiply(multiply(inverse(X_4),X_14),X_4) != X_14
| multiply(inverse(multiply(multiply(inverse(X_4),X_14),X_4)),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != C
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(multiply(inverse(X_4),X_14),X_4)),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),C) ),[0,0,0],$fot(X_14)]]) ).
cnf(refute_0_159,plain,
( multiply(inverse(multiply(multiply(inverse(X_4),X_14),X_4)),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != C
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = C ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_4),X_14),X_4),X_14) )],[refute_0_38,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(multiply(inverse(X_4),X_14),X_4)),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),C) )],[refute_0_157,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)) = multiply(C,X_14),
inference(subst,[],[refute_0_93:[bind(B,$fot(X_4)),bind(X_15,$fot(X_14))]]) ).
cnf(refute_0_162,plain,
multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))))]]) ).
cnf(refute_0_163,plain,
( multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)) != multiply(C,X_14)
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)))
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = multiply(inverse(X_14),multiply(C,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)))) ),[1,1],$fot(multiply(C,X_14))]]) ).
cnf(refute_0_164,plain,
( multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)) != multiply(C,X_14)
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = multiply(inverse(X_14),multiply(C,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) = multiply(inverse(X_14),multiply(C,X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_4),X_14),multiply(C,X_4)),multiply(C,X_14)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != C
| multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != multiply(inverse(X_14),multiply(C,X_14))
| multiply(inverse(X_14),multiply(C,X_14)) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),C) ),[0],$fot(multiply(inverse(X_14),multiply(C,X_14)))]]) ).
cnf(refute_0_167,plain,
( multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))) != C
| multiply(inverse(X_14),multiply(C,X_14)) = C ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),multiply(inverse(X_14),multiply(C,X_14))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(inverse(X_14),multiply(C,X_14)) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(X_4),X_14),multiply(C,X_4))),C) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(inverse(X_17),multiply(X_20,X_17)) = X_20,
inference(subst,[],[refute_0_168:[bind(C,$fot(X_20)),bind(X_14,$fot(X_17))]]) ).
cnf(refute_0_170,plain,
( multiply(inverse(X_17),multiply(X_20,X_17)) != X_20
| inverse(inverse(X_20)) != multiply(inverse(X_17),multiply(X_20,X_17))
| inverse(inverse(X_20)) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_20)),multiply(inverse(X_17),multiply(X_20,X_17))) ),[1],$fot(X_20)]]) ).
cnf(refute_0_171,plain,
( inverse(inverse(X_20)) != multiply(inverse(X_17),multiply(X_20,X_17))
| inverse(inverse(X_20)) = X_20 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_17),multiply(X_20,X_17)),X_20) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
inverse(inverse(X_20)) = X_20,
inference(resolve,[$cnf( $equal(inverse(inverse(X_20)),multiply(inverse(X_17),multiply(X_20,X_17))) )],[refute_0_156,refute_0_171]) ).
cnf(refute_0_173,plain,
inverse(inverse(X_13)) = X_13,
inference(subst,[],[refute_0_172:[bind(X_20,$fot(X_13))]]) ).
cnf(refute_0_174,plain,
multiply(inverse(inverse(X_13)),X_25) = multiply(inverse(inverse(X_13)),X_25),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_13)),X_25))]]) ).
cnf(refute_0_175,plain,
( multiply(inverse(inverse(X_13)),X_25) != multiply(inverse(inverse(X_13)),X_25)
| inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),X_25) = multiply(X_13,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_13)),X_25),multiply(inverse(inverse(X_13)),X_25)) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_176,plain,
( inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),X_25) = multiply(X_13,X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),X_25),multiply(inverse(inverse(X_13)),X_25)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(inverse(inverse(X_13)),X_25) = multiply(X_13,X_25),
inference(resolve,[$cnf( $equal(inverse(inverse(X_13)),X_13) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
( multiply(X_25,X_13) != multiply(inverse(inverse(X_13)),X_25)
| multiply(inverse(inverse(X_13)),X_25) != multiply(X_13,X_25)
| multiply(X_25,X_13) = multiply(X_13,X_25) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_25,X_13),multiply(X_13,X_25)) ),[0],$fot(multiply(inverse(inverse(X_13)),X_25))]]) ).
cnf(refute_0_179,plain,
( multiply(X_25,X_13) != multiply(inverse(inverse(X_13)),X_25)
| multiply(X_25,X_13) = multiply(X_13,X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),X_25),multiply(X_13,X_25)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(X_25,X_13) = multiply(X_13,X_25),
inference(resolve,[$cnf( $equal(multiply(X_25,X_13),multiply(inverse(inverse(X_13)),X_25)) )],[refute_0_149,refute_0_179]) ).
cnf(refute_0_181,plain,
( multiply(X_25,X_13) != multiply(X_13,X_25)
| multiply(X_13,X_25) = multiply(X_25,X_13) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(X_25,X_13))),bind(Y,$fot(multiply(X_13,X_25)))]]) ).
cnf(refute_0_182,plain,
multiply(X_13,X_25) = multiply(X_25,X_13),
inference(resolve,[$cnf( $equal(multiply(X_25,X_13),multiply(X_13,X_25)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(inverse(b2),b2) = multiply(b2,inverse(b2)),
inference(subst,[],[refute_0_182:[bind(X_13,$fot(inverse(b2))),bind(X_25,$fot(b2))]]) ).
cnf(refute_0_184,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(inverse(b2),b2)),
introduced(tautology,[refl,[$fot(multiply(a2,multiply(inverse(b2),b2)))]]) ).
cnf(refute_0_185,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_186,plain,
( multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),multiply(b2,inverse(b2))) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(inverse(b2),b2)),
inference(subst,[],[refute_0_182:[bind(X_13,$fot(multiply(inverse(b2),b2))),bind(X_25,$fot(a2))]]) ).
cnf(refute_0_189,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(inverse(b2),b2))
| multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Z,$fot(multiply(a2,multiply(b2,inverse(b2)))))]]) ).
cnf(refute_0_190,plain,
( multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(multiply(a2,multiply(b2,inverse(b2))))]]) ).
cnf(refute_0_193,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_193,prove_these_axioms_2]) ).
cnf(refute_0_195,plain,
multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) = inverse(inverse(X_20)),
inference(subst,[],[refute_0_145:[bind(X_11,$fot(inverse(inverse(X_20))))]]) ).
cnf(refute_0_196,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),B)) = multiply(inverse(inverse(multiply(A,B))),X_25),
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(inverse(inverse(multiply(A,B))),X_25)))]]) ).
cnf(refute_0_197,plain,
multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)) = X_25,
inference(subst,[],[refute_0_145:[bind(X_11,$fot(X_25)),bind(X_20,$fot(inverse(multiply(A,B))))]]) ).
cnf(refute_0_198,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),B)) != multiply(inverse(inverse(multiply(A,B))),X_25)
| multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)) != X_25
| multiply(A,multiply(X_25,B)) = multiply(inverse(inverse(multiply(A,B))),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),B)),multiply(inverse(inverse(multiply(A,B))),X_25)) ),[0,1,0],$fot(X_25)]]) ).
cnf(refute_0_199,plain,
( multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),B)) != multiply(inverse(inverse(multiply(A,B))),X_25)
| multiply(A,multiply(X_25,B)) = multiply(inverse(inverse(multiply(A,B))),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),X_25) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(A,multiply(X_25,B)) = multiply(inverse(inverse(multiply(A,B))),X_25),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(inverse(inverse(multiply(A,B))),X_25)),B)),multiply(inverse(inverse(multiply(A,B))),X_25)) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
inverse(inverse(multiply(A,B))) = multiply(A,B),
inference(subst,[],[refute_0_172:[bind(X_20,$fot(multiply(A,B)))]]) ).
cnf(refute_0_202,plain,
multiply(inverse(inverse(multiply(A,B))),X_25) = multiply(inverse(inverse(multiply(A,B))),X_25),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(multiply(A,B))),X_25))]]) ).
cnf(refute_0_203,plain,
( multiply(inverse(inverse(multiply(A,B))),X_25) != multiply(inverse(inverse(multiply(A,B))),X_25)
| inverse(inverse(multiply(A,B))) != multiply(A,B)
| multiply(inverse(inverse(multiply(A,B))),X_25) = multiply(multiply(A,B),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(A,B))),X_25),multiply(inverse(inverse(multiply(A,B))),X_25)) ),[1,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_204,plain,
( inverse(inverse(multiply(A,B))) != multiply(A,B)
| multiply(inverse(inverse(multiply(A,B))),X_25) = multiply(multiply(A,B),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(A,B))),X_25),multiply(inverse(inverse(multiply(A,B))),X_25)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
multiply(inverse(inverse(multiply(A,B))),X_25) = multiply(multiply(A,B),X_25),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(A,B))),multiply(A,B)) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( multiply(A,multiply(X_25,B)) != multiply(inverse(inverse(multiply(A,B))),X_25)
| multiply(inverse(inverse(multiply(A,B))),X_25) != multiply(multiply(A,B),X_25)
| multiply(A,multiply(X_25,B)) = multiply(multiply(A,B),X_25) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,multiply(X_25,B)),multiply(multiply(A,B),X_25)) ),[0],$fot(multiply(inverse(inverse(multiply(A,B))),X_25))]]) ).
cnf(refute_0_207,plain,
( multiply(A,multiply(X_25,B)) != multiply(inverse(inverse(multiply(A,B))),X_25)
| multiply(A,multiply(X_25,B)) = multiply(multiply(A,B),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(A,B))),X_25),multiply(multiply(A,B),X_25)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(A,multiply(X_25,B)) = multiply(multiply(A,B),X_25),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_25,B)),multiply(inverse(inverse(multiply(A,B))),X_25)) )],[refute_0_200,refute_0_207]) ).
cnf(refute_0_209,plain,
( multiply(A,multiply(X_25,B)) != multiply(multiply(A,B),X_25)
| multiply(multiply(A,B),X_25) = multiply(A,multiply(X_25,B)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(A,multiply(X_25,B)))),bind(Y,$fot(multiply(multiply(A,B),X_25)))]]) ).
cnf(refute_0_210,plain,
multiply(multiply(A,B),X_25) = multiply(A,multiply(X_25,B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_25,B)),multiply(multiply(A,B),X_25)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(multiply(C,B),X_15) = multiply(C,multiply(X_15,B)),
inference(subst,[],[refute_0_210:[bind(A,$fot(C)),bind(X_25,$fot(X_15))]]) ).
cnf(refute_0_212,plain,
multiply(inverse(B),multiply(multiply(C,B),X_15)) = multiply(inverse(B),multiply(multiply(C,B),X_15)),
introduced(tautology,[refl,[$fot(multiply(inverse(B),multiply(multiply(C,B),X_15)))]]) ).
cnf(refute_0_213,plain,
( multiply(multiply(C,B),X_15) != multiply(C,multiply(X_15,B))
| multiply(inverse(B),multiply(multiply(C,B),X_15)) != multiply(inverse(B),multiply(multiply(C,B),X_15))
| multiply(inverse(B),multiply(multiply(C,B),X_15)) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),multiply(multiply(C,B),X_15)),multiply(inverse(B),multiply(multiply(C,B),X_15))) ),[1,1],$fot(multiply(C,multiply(X_15,B)))]]) ).
cnf(refute_0_214,plain,
( multiply(multiply(C,B),X_15) != multiply(C,multiply(X_15,B))
| multiply(inverse(B),multiply(multiply(C,B),X_15)) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(B),multiply(multiply(C,B),X_15)),multiply(inverse(B),multiply(multiply(C,B),X_15))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(inverse(B),multiply(multiply(C,B),X_15)) = multiply(inverse(B),multiply(C,multiply(X_15,B))),
inference(resolve,[$cnf( $equal(multiply(multiply(C,B),X_15),multiply(C,multiply(X_15,B))) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(inverse(B),multiply(multiply(C,B),X_15)),
inference(subst,[],[refute_0_210:[bind(A,$fot(inverse(B))),bind(B,$fot(X_15)),bind(X_25,$fot(multiply(C,B)))]]) ).
cnf(refute_0_217,plain,
( multiply(multiply(inverse(B),X_15),multiply(C,B)) != multiply(inverse(B),multiply(multiply(C,B),X_15))
| multiply(inverse(B),multiply(multiply(C,B),X_15)) != multiply(inverse(B),multiply(C,multiply(X_15,B)))
| multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
inference(subst,[],[refute_0_55:[bind(X,$fot(multiply(multiply(inverse(B),X_15),multiply(C,B)))),bind(Y,$fot(multiply(inverse(B),multiply(multiply(C,B),X_15)))),bind(Z,$fot(multiply(inverse(B),multiply(C,multiply(X_15,B)))))]]) ).
cnf(refute_0_218,plain,
( multiply(inverse(B),multiply(multiply(C,B),X_15)) != multiply(inverse(B),multiply(C,multiply(X_15,B)))
| multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_15),multiply(C,B)),multiply(inverse(B),multiply(multiply(C,B),X_15))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(multiply(inverse(B),X_15),multiply(C,B)) = multiply(inverse(B),multiply(C,multiply(X_15,B))),
inference(resolve,[$cnf( $equal(multiply(inverse(B),multiply(multiply(C,B),X_15)),multiply(inverse(B),multiply(C,multiply(X_15,B)))) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( multiply(C,X_15) != multiply(multiply(inverse(B),X_15),multiply(C,B))
| multiply(multiply(inverse(B),X_15),multiply(C,B)) != multiply(inverse(B),multiply(C,multiply(X_15,B)))
| multiply(C,X_15) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(C,X_15),multiply(inverse(B),multiply(C,multiply(X_15,B)))) ),[0],$fot(multiply(multiply(inverse(B),X_15),multiply(C,B)))]]) ).
cnf(refute_0_221,plain,
( multiply(C,X_15) != multiply(multiply(inverse(B),X_15),multiply(C,B))
| multiply(C,X_15) = multiply(inverse(B),multiply(C,multiply(X_15,B))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_15),multiply(C,B)),multiply(inverse(B),multiply(C,multiply(X_15,B)))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(C,X_15) = multiply(inverse(B),multiply(C,multiply(X_15,B))),
inference(resolve,[$cnf( $equal(multiply(C,X_15),multiply(multiply(inverse(B),X_15),multiply(C,B))) )],[refute_0_91,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(X_40,inverse(X_40)) = multiply(inverse(X_39),multiply(X_40,multiply(inverse(X_40),X_39))),
inference(subst,[],[refute_0_222:[bind(B,$fot(X_39)),bind(C,$fot(X_40)),bind(X_15,$fot(inverse(X_40)))]]) ).
cnf(refute_0_224,plain,
multiply(X_40,multiply(inverse(X_40),X_39)) = X_39,
inference(subst,[],[refute_0_145:[bind(X_11,$fot(X_39)),bind(X_20,$fot(X_40))]]) ).
cnf(refute_0_225,plain,
( multiply(X_40,multiply(inverse(X_40),X_39)) != X_39
| multiply(X_40,inverse(X_40)) != multiply(inverse(X_39),multiply(X_40,multiply(inverse(X_40),X_39)))
| multiply(X_40,inverse(X_40)) = multiply(inverse(X_39),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_40,inverse(X_40)),multiply(inverse(X_39),multiply(X_40,multiply(inverse(X_40),X_39)))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_226,plain,
( multiply(X_40,inverse(X_40)) != multiply(inverse(X_39),multiply(X_40,multiply(inverse(X_40),X_39)))
| multiply(X_40,inverse(X_40)) = multiply(inverse(X_39),X_39) ),
inference(resolve,[$cnf( $equal(multiply(X_40,multiply(inverse(X_40),X_39)),X_39) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
multiply(X_40,inverse(X_40)) = multiply(inverse(X_39),X_39),
inference(resolve,[$cnf( $equal(multiply(X_40,inverse(X_40)),multiply(inverse(X_39),multiply(X_40,multiply(inverse(X_40),X_39)))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(X_20,multiply(inverse(X_20),multiply(X_33,X_20))) = multiply(X_33,X_20),
inference(subst,[],[refute_0_145:[bind(X_11,$fot(multiply(X_33,X_20)))]]) ).
cnf(refute_0_229,plain,
multiply(inverse(X_20),multiply(X_33,X_20)) = X_33,
inference(subst,[],[refute_0_168:[bind(C,$fot(X_33)),bind(X_14,$fot(X_20))]]) ).
cnf(refute_0_230,plain,
( multiply(X_20,multiply(inverse(X_20),multiply(X_33,X_20))) != multiply(X_33,X_20)
| multiply(inverse(X_20),multiply(X_33,X_20)) != X_33
| multiply(X_20,X_33) = multiply(X_33,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),multiply(X_33,X_20))),multiply(X_33,X_20)) ),[0,1],$fot(X_33)]]) ).
cnf(refute_0_231,plain,
( multiply(X_20,multiply(inverse(X_20),multiply(X_33,X_20))) != multiply(X_33,X_20)
| multiply(X_20,X_33) = multiply(X_33,X_20) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),multiply(X_33,X_20)),X_33) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(X_20,X_33) = multiply(X_33,X_20),
inference(resolve,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),multiply(X_33,X_20))),multiply(X_33,X_20)) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( multiply(X_20,X_33) != multiply(X_33,X_20)
| multiply(X_33,X_20) = multiply(X_20,X_33) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiply(X_20,X_33))),bind(Y,$fot(multiply(X_33,X_20)))]]) ).
cnf(refute_0_234,plain,
multiply(X_33,X_20) = multiply(X_20,X_33),
inference(resolve,[$cnf( $equal(multiply(X_20,X_33),multiply(X_33,X_20)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(inverse(X_39),X_39) = multiply(X_39,inverse(X_39)),
inference(subst,[],[refute_0_234:[bind(X_20,$fot(X_39)),bind(X_33,$fot(inverse(X_39)))]]) ).
cnf(refute_0_236,plain,
( multiply(X_40,inverse(X_40)) != multiply(inverse(X_39),X_39)
| multiply(inverse(X_39),X_39) != multiply(X_39,inverse(X_39))
| multiply(X_40,inverse(X_40)) = multiply(X_39,inverse(X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_40,inverse(X_40)),multiply(X_39,inverse(X_39))) ),[0],$fot(multiply(inverse(X_39),X_39))]]) ).
cnf(refute_0_237,plain,
( multiply(X_40,inverse(X_40)) != multiply(inverse(X_39),X_39)
| multiply(X_40,inverse(X_40)) = multiply(X_39,inverse(X_39)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),X_39),multiply(X_39,inverse(X_39))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
multiply(X_40,inverse(X_40)) = multiply(X_39,inverse(X_39)),
inference(resolve,[$cnf( $equal(multiply(X_40,inverse(X_40)),multiply(inverse(X_39),X_39)) )],[refute_0_227,refute_0_237]) ).
cnf(refute_0_239,plain,
multiply(inverse(X_20),inverse(inverse(X_20))) = multiply(X_42,inverse(X_42)),
inference(subst,[],[refute_0_238:[bind(X_39,$fot(X_42)),bind(X_40,$fot(inverse(X_20)))]]) ).
cnf(refute_0_240,plain,
( multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) != inverse(inverse(X_20))
| multiply(inverse(X_20),inverse(inverse(X_20))) != multiply(X_42,inverse(X_42))
| multiply(X_20,multiply(X_42,inverse(X_42))) = inverse(inverse(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))),inverse(inverse(X_20))) ),[0,1],$fot(multiply(X_42,inverse(X_42)))]]) ).
cnf(refute_0_241,plain,
( multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) != inverse(inverse(X_20))
| multiply(X_20,multiply(X_42,inverse(X_42))) = inverse(inverse(X_20)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),inverse(inverse(X_20))),multiply(X_42,inverse(X_42))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(X_20,multiply(X_42,inverse(X_42))) = inverse(inverse(X_20)),
inference(resolve,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))),inverse(inverse(X_20))) )],[refute_0_195,refute_0_241]) ).
cnf(refute_0_243,plain,
( multiply(X_20,multiply(X_42,inverse(X_42))) != inverse(inverse(X_20))
| inverse(inverse(X_20)) != X_20
| multiply(X_20,multiply(X_42,inverse(X_42))) = X_20 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_20,multiply(X_42,inverse(X_42))),X_20) ),[0],$fot(inverse(inverse(X_20)))]]) ).
cnf(refute_0_244,plain,
( multiply(X_20,multiply(X_42,inverse(X_42))) != inverse(inverse(X_20))
| multiply(X_20,multiply(X_42,inverse(X_42))) = X_20 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_20)),X_20) )],[refute_0_172,refute_0_243]) ).
cnf(refute_0_245,plain,
multiply(X_20,multiply(X_42,inverse(X_42))) = X_20,
inference(resolve,[$cnf( $equal(multiply(X_20,multiply(X_42,inverse(X_42))),inverse(inverse(X_20))) )],[refute_0_242,refute_0_244]) ).
cnf(refute_0_246,plain,
multiply(a2,multiply(b2,inverse(b2))) = a2,
inference(subst,[],[refute_0_245:[bind(X_20,$fot(a2)),bind(X_42,$fot(b2))]]) ).
cnf(refute_0_247,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| a2 != a2
| multiply(a2,multiply(b2,inverse(b2))) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_248,plain,
( a2 != a2
| multiply(a2,multiply(b2,inverse(b2))) = a2 ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_248,refute_0_194]) ).
cnf(refute_0_250,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_251,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_250,refute_0_249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 12:49:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51
% 0.19/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.37/0.54
%------------------------------------------------------------------------------