TSTP Solution File: GRP519-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP519-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of clauses : 83 ( 46 unt; 0 nHn; 41 RR)
% Number of literals : 137 ( 136 equ; 56 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 255 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
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( $equal(multiply(A,multiply(multiply(inverse(multiply(A,multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C),multiply(multiply(inverse(multiply(A,X_1)),X_2),X_1))),C) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))) = X_4,
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(C,$fot(X_4)),bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(inverse(X_6),X_4))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_7,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_8,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( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5)),X_6) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(multiply(inverse(X_6),X_4),X_6) = X_4,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(X_6),X_4),multiply(multiply(inverse(multiply(multiply(inverse(X_6),X_4),X_5)),X_6),X_5))),X_4) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(subst,[],[refute_0_9:[bind(X_4,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B))),bind(X_6,$fot(X_8))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_8)))]]) ).
cnf(refute_0_12,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_13,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( $equal(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),C) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)),X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(multiply(A,B),X_14) = multiply(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),X_12),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_12)),bind(C,$fot(multiply(A,B))),bind(X_8,$fot(X_14))]]) ).
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),
inference(subst,[],[single_axiom:[bind(C,$fot(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)))]]) ).
cnf(refute_0_17,plain,
multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) = X_2,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(multiply(A,B)))),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_18,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_19,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( $equal(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),X_2) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(A,multiply(X_2,B)) = multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),
inference(resolve,[$cnf( $equal(multiply(A,multiply(multiply(inverse(multiply(A,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)),B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_22,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_23,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(C,X_8) != multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(C,X_8))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)))]]) ).
cnf(refute_0_25,plain,
multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B) = multiply(C,X_8),
inference(resolve,[$cnf( $equal(multiply(C,X_8),multiply(multiply(inverse(multiply(inverse(X_8),B)),C),B)) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1) = multiply(X_2,multiply(A,B)),
inference(subst,[],[refute_0_25:[bind(B,$fot(X_1)),bind(C,$fot(X_2)),bind(X_8,$fot(multiply(A,B)))]]) ).
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(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_28,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( $equal(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1),multiply(X_2,multiply(A,B))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(A,multiply(X_2,B)) = multiply(X_2,multiply(A,B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(X_2,B)),multiply(multiply(inverse(multiply(inverse(multiply(A,B)),X_1)),X_2),X_1)) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) = multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),
inference(subst,[],[refute_0_29:[bind(X_2,$fot(inverse(multiply(inverse(X_14),X_12))))]]) ).
cnf(refute_0_31,plain,
( multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) != multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B))
| multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)) = multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)))),bind(Y,$fot(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B))))]]) ).
cnf(refute_0_32,plain,
multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)) = multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),
inference(resolve,[$cnf( $equal(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiply(multiply(A,B),X_14) != multiply(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),X_12)
| multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)) != multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B))
| multiply(multiply(A,B),X_14) = multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(A,B),X_14),multiply(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),X_12)) ),[1,0],$fot(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)))]]) ).
cnf(refute_0_34,plain,
( multiply(multiply(A,B),X_14) != multiply(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),X_12)
| multiply(multiply(A,B),X_14) = multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(multiply(A,B),X_14) = multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),X_14),multiply(multiply(inverse(multiply(inverse(X_14),X_12)),multiply(A,B)),X_12)) )],[refute_0_15,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) = multiply(X_11,X_10),
inference(subst,[],[refute_0_9:[bind(X_4,$fot(multiply(X_11,X_10)))]]) ).
cnf(refute_0_37,plain,
multiply(inverse(X_6),multiply(X_11,X_10)) = multiply(X_11,multiply(inverse(X_6),X_10)),
inference(subst,[],[refute_0_29:[bind(A,$fot(inverse(X_6))),bind(B,$fot(X_10)),bind(X_2,$fot(X_11))]]) ).
cnf(refute_0_38,plain,
( multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6) != multiply(X_11,X_10)
| multiply(inverse(X_6),multiply(X_11,X_10)) != multiply(X_11,multiply(inverse(X_6),X_10))
| multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$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_39,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( $equal(multiply(inverse(X_6),multiply(X_11,X_10)),multiply(X_11,multiply(inverse(X_6),X_10))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(multiply(X_11,multiply(inverse(X_6),X_10)),X_6) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_6),multiply(X_11,X_10)),X_6),multiply(X_11,X_10)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12) = multiply(A,multiply(B,X_14)),
inference(subst,[],[refute_0_40:[bind(X_10,$fot(multiply(B,X_14))),bind(X_11,$fot(A)),bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_42,plain,
multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(inverse(X_14)))]]) ).
cnf(refute_0_43,plain,
multiply(C,X_14) = multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B),
inference(subst,[],[refute_0_14:[bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
( multiply(C,X_14) != multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)
| multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) = multiply(C,X_14) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(C,X_14))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)))]]) ).
cnf(refute_0_45,plain,
multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) = multiply(C,X_14),
inference(resolve,[$cnf( $equal(multiply(C,X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B) != multiply(C,X_14)
| multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) != C
| multiply(inverse(X_14),multiply(C,X_14)) = C ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),C) ),[0,1],$fot(multiply(C,X_14))]]) ).
cnf(refute_0_47,plain,
( multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)) != C
| multiply(inverse(X_14),multiply(C,X_14)) = C ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B),multiply(C,X_14)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(inverse(X_14),multiply(C,X_14)) = C,
inference(resolve,[$cnf( $equal(multiply(inverse(X_14),multiply(multiply(inverse(multiply(inverse(X_14),B)),C),B)),C) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(inverse(X_16),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)) = multiply(inverse(multiply(inverse(X_8),X_16)),C),
inference(subst,[],[refute_0_48:[bind(C,$fot(multiply(inverse(multiply(inverse(X_8),X_16)),C))),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_50,plain,
multiply(C,X_8) = multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_16))]]) ).
cnf(refute_0_51,plain,
( multiply(C,X_8) != multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)
| multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16) = multiply(C,X_8) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(C,X_8))),bind(Y,$fot(multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)))]]) ).
cnf(refute_0_52,plain,
multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16) = multiply(C,X_8),
inference(resolve,[$cnf( $equal(multiply(C,X_8),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16) != multiply(C,X_8)
| multiply(inverse(X_16),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)) != multiply(inverse(multiply(inverse(X_8),X_16)),C)
| multiply(inverse(X_16),multiply(C,X_8)) = multiply(inverse(multiply(inverse(X_8),X_16)),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_16),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)),multiply(inverse(multiply(inverse(X_8),X_16)),C)) ),[0,1],$fot(multiply(C,X_8))]]) ).
cnf(refute_0_54,plain,
( multiply(inverse(X_16),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)) != multiply(inverse(multiply(inverse(X_8),X_16)),C)
| multiply(inverse(X_16),multiply(C,X_8)) = multiply(inverse(multiply(inverse(X_8),X_16)),C) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16),multiply(C,X_8)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(inverse(X_16),multiply(C,X_8)) = multiply(inverse(multiply(inverse(X_8),X_16)),C),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),multiply(multiply(inverse(multiply(inverse(X_8),X_16)),C),X_16)),multiply(inverse(multiply(inverse(X_8),X_16)),C)) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(inverse(X_16),multiply(C,X_8)) != multiply(inverse(multiply(inverse(X_8),X_16)),C)
| multiply(inverse(multiply(inverse(X_8),X_16)),C) = multiply(inverse(X_16),multiply(C,X_8)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(inverse(X_16),multiply(C,X_8)))),bind(Y,$fot(multiply(inverse(multiply(inverse(X_8),X_16)),C)))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(multiply(inverse(X_8),X_16)),C) = multiply(inverse(X_16),multiply(C,X_8)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),multiply(C,X_8)),multiply(inverse(multiply(inverse(X_8),X_16)),C)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(multiply(inverse(X_14),X_12)),B) = multiply(inverse(X_12),multiply(B,X_14)),
inference(subst,[],[refute_0_57:[bind(C,$fot(B)),bind(X_16,$fot(X_12)),bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_59,plain,
multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) = multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),
introduced(tautology,[refl,[$fot(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)))]]) ).
cnf(refute_0_60,plain,
( multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) != multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B))
| multiply(inverse(multiply(inverse(X_14),X_12)),B) != multiply(inverse(X_12),multiply(B,X_14))
| multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) = multiply(A,multiply(inverse(X_12),multiply(B,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B))) ),[1,1],$fot(multiply(inverse(X_12),multiply(B,X_14)))]]) ).
cnf(refute_0_61,plain,
( multiply(inverse(multiply(inverse(X_14),X_12)),B) != multiply(inverse(X_12),multiply(B,X_14))
| multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) = multiply(A,multiply(inverse(X_12),multiply(B,X_14))) ),
inference(resolve,[$cnf( $equal(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) = multiply(A,multiply(inverse(X_12),multiply(B,X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_14),X_12)),B),multiply(inverse(X_12),multiply(B,X_14))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),
introduced(tautology,[refl,[$fot(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12))]]) ).
cnf(refute_0_64,plain,
( multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) != multiply(A,multiply(inverse(X_12),multiply(B,X_14)))
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) != multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)) ),[1,0],$fot(multiply(A,multiply(inverse(X_12),multiply(B,X_14))))]]) ).
cnf(refute_0_65,plain,
( multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)) != multiply(A,multiply(inverse(X_12),multiply(B,X_14)))
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12),
inference(resolve,[$cnf( $equal(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),multiply(A,multiply(inverse(X_12),multiply(B,X_14)))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_68,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_23,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12) != multiply(A,multiply(B,X_14))
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) != multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12)
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(A,multiply(B,X_14)) ),
inference(subst,[],[refute_0_68:[bind(X,$fot(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12))),bind(Y,$fot(multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12))),bind(Z,$fot(multiply(A,multiply(B,X_14))))]]) ).
cnf(refute_0_70,plain,
( multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12) != multiply(A,multiply(B,X_14))
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(A,multiply(B,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) = multiply(A,multiply(B,X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(X_12),multiply(B,X_14))),X_12),multiply(A,multiply(B,X_14))) )],[refute_0_41,refute_0_70]) ).
cnf(refute_0_72,plain,
( multiply(multiply(A,B),X_14) != multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)
| multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12) != multiply(A,multiply(B,X_14))
| multiply(multiply(A,B),X_14) = multiply(A,multiply(B,X_14)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(A,B),X_14),multiply(A,multiply(B,X_14))) ),[0],$fot(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12))]]) ).
cnf(refute_0_73,plain,
( multiply(multiply(A,B),X_14) != multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)
| multiply(multiply(A,B),X_14) = multiply(A,multiply(B,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12),multiply(A,multiply(B,X_14))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(multiply(A,B),X_14) = multiply(A,multiply(B,X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),X_14),multiply(multiply(A,multiply(inverse(multiply(inverse(X_14),X_12)),B)),X_12)) )],[refute_0_35,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_74:[bind(A,$fot(a3)),bind(B,$fot(b3)),bind(X_14,$fot(c3))]]) ).
cnf(refute_0_76,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_77,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_77,prove_these_axioms_3]) ).
cnf(refute_0_79,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_80,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_79,refute_0_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP519-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 06:10:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.39
% 0.19/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.41
%------------------------------------------------------------------------------