TSTP Solution File: GRP710-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP710-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:50:27 EDT 2022
% Result : Unsatisfiable 0.40s 0.56s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of clauses : 81 ( 47 unt; 0 nHn; 40 RR)
% Number of literals : 131 ( 130 equ; 56 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 138 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
mult(unit,A) = A ).
cnf(f03,axiom,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ).
cnf(f04,axiom,
mult(A,i(A)) = unit ).
cnf(f05,axiom,
mult(i(A),A) = unit ).
cnf(goal,negated_conjecture,
mult(x0,X2) != x1 ).
cnf(refute_0_0,plain,
mult(x0,mult(i(x0),mult(i(x0),X_26))) != x1,
inference(subst,[],[goal:[bind(X2,$fot(mult(i(x0),mult(i(x0),X_26))))]]) ).
cnf(refute_0_1,plain,
mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(mult(mult(X_5,i(X_5)),i(X_5)),X_7),
inference(subst,[],[f03:[bind(A,$fot(X_5)),bind(B,$fot(i(X_5))),bind(C,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
mult(X_5,i(X_5)) = unit,
inference(subst,[],[f04:[bind(A,$fot(X_5))]]) ).
cnf(refute_0_3,plain,
( mult(X_5,i(X_5)) != unit
| mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) != mult(mult(mult(X_5,i(X_5)),i(X_5)),X_7)
| mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(mult(unit,i(X_5)),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(i(X_5),mult(i(X_5),X_7))),mult(mult(mult(X_5,i(X_5)),i(X_5)),X_7)) ),[1,0,0],$fot(unit)]]) ).
cnf(refute_0_4,plain,
( mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) != mult(mult(mult(X_5,i(X_5)),i(X_5)),X_7)
| mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(mult(unit,i(X_5)),X_7) ),
inference(resolve,[$cnf( $equal(mult(X_5,i(X_5)),unit) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(mult(unit,i(X_5)),X_7),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(X_5),mult(i(X_5),X_7))),mult(mult(mult(X_5,i(X_5)),i(X_5)),X_7)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
mult(unit,i(X_5)) = i(X_5),
inference(subst,[],[f02:[bind(A,$fot(i(X_5)))]]) ).
cnf(refute_0_7,plain,
mult(mult(unit,i(X_5)),X_7) = mult(mult(unit,i(X_5)),X_7),
introduced(tautology,[refl,[$fot(mult(mult(unit,i(X_5)),X_7))]]) ).
cnf(refute_0_8,plain,
( mult(mult(unit,i(X_5)),X_7) != mult(mult(unit,i(X_5)),X_7)
| mult(unit,i(X_5)) != i(X_5)
| mult(mult(unit,i(X_5)),X_7) = mult(i(X_5),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(unit,i(X_5)),X_7),mult(mult(unit,i(X_5)),X_7)) ),[1,0],$fot(i(X_5))]]) ).
cnf(refute_0_9,plain,
( mult(unit,i(X_5)) != i(X_5)
| mult(mult(unit,i(X_5)),X_7) = mult(i(X_5),X_7) ),
inference(resolve,[$cnf( $equal(mult(mult(unit,i(X_5)),X_7),mult(mult(unit,i(X_5)),X_7)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(mult(unit,i(X_5)),X_7) = mult(i(X_5),X_7),
inference(resolve,[$cnf( $equal(mult(unit,i(X_5)),i(X_5)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) != mult(mult(unit,i(X_5)),X_7)
| mult(mult(unit,i(X_5)),X_7) != mult(i(X_5),X_7)
| mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(i(X_5),X_7) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_5,mult(i(X_5),mult(i(X_5),X_7))),mult(i(X_5),X_7)) ),[0],$fot(mult(mult(unit,i(X_5)),X_7))]]) ).
cnf(refute_0_12,plain,
( mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) != mult(mult(unit,i(X_5)),X_7)
| mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(i(X_5),X_7) ),
inference(resolve,[$cnf( $equal(mult(mult(unit,i(X_5)),X_7),mult(i(X_5),X_7)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(X_5,mult(i(X_5),mult(i(X_5),X_7))) = mult(i(X_5),X_7),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(X_5),mult(i(X_5),X_7))),mult(mult(unit,i(X_5)),X_7)) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(x0,mult(i(x0),mult(i(x0),X_26))) = mult(i(x0),X_26),
inference(subst,[],[refute_0_13:[bind(X_5,$fot(x0)),bind(X_7,$fot(X_26))]]) ).
cnf(refute_0_15,plain,
( mult(i(x0),X_26) != x1
| mult(x0,mult(i(x0),mult(i(x0),X_26))) != mult(i(x0),X_26)
| mult(x0,mult(i(x0),mult(i(x0),X_26))) = x1 ),
introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(i(x0),mult(i(x0),X_26))),mult(i(x0),X_26)) ),[1],$fot(x1)]]) ).
cnf(refute_0_16,plain,
( mult(i(x0),X_26) != x1
| mult(x0,mult(i(x0),mult(i(x0),X_26))) = x1 ),
inference(resolve,[$cnf( $equal(mult(x0,mult(i(x0),mult(i(x0),X_26))),mult(i(x0),X_26)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
mult(i(x0),X_26) != x1,
inference(resolve,[$cnf( $equal(mult(x0,mult(i(x0),mult(i(x0),X_26))),x1) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
mult(i(x0),mult(i(i(x0)),X_53)) != x1,
inference(subst,[],[refute_0_17:[bind(X_26,$fot(mult(i(i(x0)),X_53)))]]) ).
cnf(refute_0_19,plain,
mult(mult(X_5,B),mult(B,mult(B,C))) = mult(mult(mult(mult(X_5,B),B),B),C),
inference(subst,[],[f03:[bind(A,$fot(mult(X_5,B)))]]) ).
cnf(refute_0_20,plain,
mult(X_5,mult(B,mult(B,B))) = mult(mult(mult(X_5,B),B),B),
inference(subst,[],[f03:[bind(A,$fot(X_5)),bind(C,$fot(B))]]) ).
cnf(refute_0_21,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( mult(X_5,mult(B,mult(B,B))) != mult(mult(mult(X_5,B),B),B)
| mult(mult(mult(X_5,B),B),B) = mult(X_5,mult(B,mult(B,B))) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(mult(X_5,mult(B,mult(B,B))))),bind(Y,$fot(mult(mult(mult(X_5,B),B),B)))]]) ).
cnf(refute_0_25,plain,
mult(mult(mult(X_5,B),B),B) = mult(X_5,mult(B,mult(B,B))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(B,mult(B,B))),mult(mult(mult(X_5,B),B),B)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( mult(mult(X_5,B),mult(B,mult(B,C))) != mult(mult(mult(mult(X_5,B),B),B),C)
| mult(mult(mult(X_5,B),B),B) != mult(X_5,mult(B,mult(B,B)))
| mult(mult(X_5,B),mult(B,mult(B,C))) = mult(mult(X_5,mult(B,mult(B,B))),C) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_5,B),mult(B,mult(B,C))),mult(mult(mult(mult(X_5,B),B),B),C)) ),[1,0],$fot(mult(X_5,mult(B,mult(B,B))))]]) ).
cnf(refute_0_27,plain,
( mult(mult(X_5,B),mult(B,mult(B,C))) != mult(mult(mult(mult(X_5,B),B),B),C)
| mult(mult(X_5,B),mult(B,mult(B,C))) = mult(mult(X_5,mult(B,mult(B,B))),C) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_5,B),B),B),mult(X_5,mult(B,mult(B,B)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(mult(X_5,B),mult(B,mult(B,C))) = mult(mult(X_5,mult(B,mult(B,B))),C),
inference(resolve,[$cnf( $equal(mult(mult(X_5,B),mult(B,mult(B,C))),mult(mult(mult(mult(X_5,B),B),B),C)) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = mult(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),X_36),
inference(subst,[],[refute_0_28:[bind(B,$fot(X_35)),bind(C,$fot(X_36)),bind(X_5,$fot(i(mult(X_35,mult(X_35,X_35)))))]]) ).
cnf(refute_0_30,plain,
mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))) = unit,
inference(subst,[],[f05:[bind(A,$fot(mult(X_35,mult(X_35,X_35))))]]) ).
cnf(refute_0_31,plain,
( mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))) != unit
| mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) != mult(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),X_36)
| mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = mult(unit,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))),mult(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),X_36)) ),[1,0],$fot(unit)]]) ).
cnf(refute_0_32,plain,
( mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) != mult(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),X_36)
| mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = mult(unit,X_36) ),
inference(resolve,[$cnf( $equal(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),unit) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = mult(unit,X_36),
inference(resolve,[$cnf( $equal(mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))),mult(mult(i(mult(X_35,mult(X_35,X_35))),mult(X_35,mult(X_35,X_35))),X_36)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
mult(unit,X_36) = X_36,
inference(subst,[],[f02:[bind(A,$fot(X_36))]]) ).
cnf(refute_0_35,plain,
( mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) != mult(unit,X_36)
| mult(unit,X_36) != X_36
| mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = X_36 ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))),X_36) ),[0],$fot(mult(unit,X_36))]]) ).
cnf(refute_0_36,plain,
( mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) != mult(unit,X_36)
| mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = X_36 ),
inference(resolve,[$cnf( $equal(mult(unit,X_36),X_36) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))) = X_36,
inference(resolve,[$cnf( $equal(mult(mult(i(mult(X_35,mult(X_35,X_35))),X_35),mult(X_35,mult(X_35,X_36))),mult(unit,X_36)) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),mult(X_6,mult(i(X_6),X_26))))) = mult(X_6,mult(i(X_6),X_26)),
inference(subst,[],[refute_0_37:[bind(X_35,$fot(i(X_6))),bind(X_36,$fot(mult(X_6,mult(i(X_6),X_26))))]]) ).
cnf(refute_0_39,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(mult(i(X_6),X_6),X_6),X_7),
inference(subst,[],[f03:[bind(A,$fot(i(X_6))),bind(B,$fot(X_6)),bind(C,$fot(X_7))]]) ).
cnf(refute_0_40,plain,
mult(i(X_6),X_6) = unit,
inference(subst,[],[f05:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_41,plain,
( mult(i(X_6),X_6) != unit
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(mult(i(X_6),X_6),X_6),X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(unit,X_6),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(mult(mult(i(X_6),X_6),X_6),X_7)) ),[1,0,0],$fot(unit)]]) ).
cnf(refute_0_42,plain,
( mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(mult(i(X_6),X_6),X_6),X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(unit,X_6),X_7) ),
inference(resolve,[$cnf( $equal(mult(i(X_6),X_6),unit) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(unit,X_6),X_7),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(mult(mult(i(X_6),X_6),X_6),X_7)) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(unit,X_6) = X_6,
inference(subst,[],[f02:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_45,plain,
mult(mult(unit,X_6),X_7) = mult(mult(unit,X_6),X_7),
introduced(tautology,[refl,[$fot(mult(mult(unit,X_6),X_7))]]) ).
cnf(refute_0_46,plain,
( mult(mult(unit,X_6),X_7) != mult(mult(unit,X_6),X_7)
| mult(unit,X_6) != X_6
| mult(mult(unit,X_6),X_7) = mult(X_6,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(unit,X_6),X_7),mult(mult(unit,X_6),X_7)) ),[1,0],$fot(X_6)]]) ).
cnf(refute_0_47,plain,
( mult(unit,X_6) != X_6
| mult(mult(unit,X_6),X_7) = mult(X_6,X_7) ),
inference(resolve,[$cnf( $equal(mult(mult(unit,X_6),X_7),mult(mult(unit,X_6),X_7)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(mult(unit,X_6),X_7) = mult(X_6,X_7),
inference(resolve,[$cnf( $equal(mult(unit,X_6),X_6) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(unit,X_6),X_7)
| mult(mult(unit,X_6),X_7) != mult(X_6,X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(X_6,X_7) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(X_6,X_7)) ),[0],$fot(mult(mult(unit,X_6),X_7))]]) ).
cnf(refute_0_50,plain,
( mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(unit,X_6),X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(X_6,X_7) ),
inference(resolve,[$cnf( $equal(mult(mult(unit,X_6),X_7),mult(X_6,X_7)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(X_6,X_7),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(mult(unit,X_6),X_7)) )],[refute_0_43,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),mult(i(X_6),X_26))))) = mult(X_6,mult(i(X_6),mult(i(X_6),X_26))),
inference(subst,[],[refute_0_51:[bind(X_7,$fot(mult(i(X_6),mult(i(X_6),X_26))))]]) ).
cnf(refute_0_53,plain,
mult(X_6,mult(i(X_6),mult(i(X_6),X_26))) = mult(i(X_6),X_26),
inference(subst,[],[refute_0_13:[bind(X_5,$fot(X_6)),bind(X_7,$fot(X_26))]]) ).
cnf(refute_0_54,plain,
( mult(X_6,mult(i(X_6),mult(i(X_6),X_26))) != mult(i(X_6),X_26)
| mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),mult(i(X_6),X_26))))) != mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))
| mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),mult(i(X_6),X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),mult(i(X_6),X_26))))),mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))) ),[0,1,1],$fot(mult(i(X_6),X_26))]]) ).
cnf(refute_0_55,plain,
( mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),mult(i(X_6),X_26))))) != mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))
| mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),mult(i(X_6),X_26))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(i(X_6),mult(i(X_6),X_26))),mult(i(X_6),X_26)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),mult(i(X_6),X_26))),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),mult(i(X_6),X_26))))),mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
( mult(X_6,mult(i(X_6),mult(i(X_6),X_26))) != mult(i(X_6),X_26)
| mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) != mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))
| mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(i(X_6),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(i(X_6),X_26))),mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))) ),[1],$fot(mult(i(X_6),X_26))]]) ).
cnf(refute_0_58,plain,
( mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) != mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))
| mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(i(X_6),X_26) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(i(X_6),mult(i(X_6),X_26))),mult(i(X_6),X_26)) )],[refute_0_53,refute_0_57]) ).
cnf(refute_0_59,plain,
mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) = mult(i(X_6),X_26),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(i(X_6),X_26))),mult(X_6,mult(i(X_6),mult(i(X_6),X_26)))) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
( mult(i(X_6),mult(X_6,mult(i(X_6),X_26))) != mult(i(X_6),X_26)
| mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),mult(X_6,mult(i(X_6),X_26))))) != mult(X_6,mult(i(X_6),X_26))
| mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),mult(X_6,mult(i(X_6),X_26))))),mult(X_6,mult(i(X_6),X_26))) ),[0,1,1],$fot(mult(i(X_6),X_26))]]) ).
cnf(refute_0_61,plain,
( mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),mult(X_6,mult(i(X_6),X_26))))) != mult(X_6,mult(i(X_6),X_26))
| mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),X_26)) ),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(i(X_6),X_26))),mult(i(X_6),X_26)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) = mult(X_6,mult(i(X_6),X_26)),
inference(resolve,[$cnf( $equal(mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),mult(X_6,mult(i(X_6),X_26))))),mult(X_6,mult(i(X_6),X_26))) )],[refute_0_38,refute_0_61]) ).
cnf(refute_0_63,plain,
mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) = X_26,
inference(subst,[],[refute_0_37:[bind(X_35,$fot(i(X_6))),bind(X_36,$fot(X_26))]]) ).
cnf(refute_0_64,plain,
( mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) != X_26
| mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) != mult(X_6,mult(i(X_6),X_26))
| X_26 = mult(X_6,mult(i(X_6),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))),mult(X_6,mult(i(X_6),X_26))) ),[0],$fot(X_26)]]) ).
cnf(refute_0_65,plain,
( mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))) != mult(X_6,mult(i(X_6),X_26))
| X_26 = mult(X_6,mult(i(X_6),X_26)) ),
inference(resolve,[$cnf( $equal(mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))),X_26) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
X_26 = mult(X_6,mult(i(X_6),X_26)),
inference(resolve,[$cnf( $equal(mult(mult(i(mult(i(X_6),mult(i(X_6),i(X_6)))),i(X_6)),mult(i(X_6),mult(i(X_6),X_26))),mult(X_6,mult(i(X_6),X_26))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
X_53 = mult(i(x0),mult(i(i(x0)),X_53)),
inference(subst,[],[refute_0_66:[bind(X_26,$fot(X_53)),bind(X_6,$fot(i(x0)))]]) ).
cnf(refute_0_68,plain,
( X_53 != mult(i(x0),mult(i(i(x0)),X_53))
| mult(i(x0),mult(i(i(x0)),X_53)) = X_53 ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_53)),bind(Y,$fot(mult(i(x0),mult(i(i(x0)),X_53))))]]) ).
cnf(refute_0_69,plain,
mult(i(x0),mult(i(i(x0)),X_53)) = X_53,
inference(resolve,[$cnf( $equal(X_53,mult(i(x0),mult(i(i(x0)),X_53))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( X_53 != x1
| mult(i(x0),mult(i(i(x0)),X_53)) != X_53
| mult(i(x0),mult(i(i(x0)),X_53)) = x1 ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(x0),mult(i(i(x0)),X_53)),X_53) ),[1],$fot(x1)]]) ).
cnf(refute_0_71,plain,
( X_53 != x1
| mult(i(x0),mult(i(i(x0)),X_53)) = x1 ),
inference(resolve,[$cnf( $equal(mult(i(x0),mult(i(i(x0)),X_53)),X_53) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
X_53 != x1,
inference(resolve,[$cnf( $equal(mult(i(x0),mult(i(i(x0)),X_53)),x1) )],[refute_0_71,refute_0_18]) ).
cnf(refute_0_73,plain,
x1 != x1,
inference(subst,[],[refute_0_72:[bind(X_53,$fot(x1))]]) ).
cnf(refute_0_74,plain,
x1 = x1,
introduced(tautology,[refl,[$fot(x1)]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( $equal(x1,x1) )],[refute_0_74,refute_0_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP710-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 13:10:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.56
% 0.40/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.57
%------------------------------------------------------------------------------