TSTP Solution File: GRP710-11 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 54
% Syntax : Number of clauses : 190 ( 103 unt; 0 nHn; 104 RR)
% Number of literals : 316 ( 315 equ; 141 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 : 252 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,unit) = A ).
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(X5,x4) != x3 ).
cnf(refute_0_0,plain,
mult(mult(mult(X_5,X_6),X_6),x4) != x3,
inference(subst,[],[goal:[bind(X5,$fot(mult(mult(X_5,X_6),X_6)))]]) ).
cnf(refute_0_1,plain,
mult(X_5,mult(X_6,mult(X_6,x4))) = mult(mult(mult(X_5,X_6),X_6),x4),
inference(subst,[],[f03:[bind(A,$fot(X_5)),bind(B,$fot(X_6)),bind(C,$fot(x4))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( mult(X_5,mult(X_6,mult(X_6,x4))) != mult(mult(mult(X_5,X_6),X_6),x4)
| mult(mult(mult(X_5,X_6),X_6),x4) = mult(X_5,mult(X_6,mult(X_6,x4))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_5,mult(X_6,mult(X_6,x4))))),bind(Y,$fot(mult(mult(mult(X_5,X_6),X_6),x4)))]]) ).
cnf(refute_0_6,plain,
mult(mult(mult(X_5,X_6),X_6),x4) = mult(X_5,mult(X_6,mult(X_6,x4))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,x4))),mult(mult(mult(X_5,X_6),X_6),x4)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( mult(X_5,mult(X_6,mult(X_6,x4))) != x3
| mult(mult(mult(X_5,X_6),X_6),x4) != mult(X_5,mult(X_6,mult(X_6,x4)))
| mult(mult(mult(X_5,X_6),X_6),x4) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),x4),mult(X_5,mult(X_6,mult(X_6,x4)))) ),[1],$fot(x3)]]) ).
cnf(refute_0_8,plain,
( mult(X_5,mult(X_6,mult(X_6,x4))) != x3
| mult(mult(mult(X_5,X_6),X_6),x4) = x3 ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),x4),mult(X_5,mult(X_6,mult(X_6,x4)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(X_5,mult(X_6,mult(X_6,x4))) != x3,
inference(resolve,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),x4),x3) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
mult(X_26,mult(i(x4),mult(i(x4),x4))) != x3,
inference(subst,[],[refute_0_9:[bind(X_5,$fot(X_26)),bind(X_6,$fot(i(x4)))]]) ).
cnf(refute_0_11,plain,
mult(i(x4),x4) = unit,
inference(subst,[],[f05:[bind(A,$fot(x4))]]) ).
cnf(refute_0_12,plain,
( mult(X_26,mult(i(x4),unit)) != x3
| mult(i(x4),x4) != unit
| mult(X_26,mult(i(x4),mult(i(x4),x4))) = x3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_26,mult(i(x4),mult(i(x4),x4))),x3) ),[0,1,1],$fot(unit)]]) ).
cnf(refute_0_13,plain,
( mult(X_26,mult(i(x4),unit)) != x3
| mult(X_26,mult(i(x4),mult(i(x4),x4))) = x3 ),
inference(resolve,[$cnf( $equal(mult(i(x4),x4),unit) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(X_26,mult(i(x4),unit)) != x3,
inference(resolve,[$cnf( $equal(mult(X_26,mult(i(x4),mult(i(x4),x4))),x3) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
mult(i(x4),unit) = i(x4),
inference(subst,[],[f01:[bind(A,$fot(i(x4)))]]) ).
cnf(refute_0_16,plain,
mult(X_26,mult(i(x4),unit)) = mult(X_26,mult(i(x4),unit)),
introduced(tautology,[refl,[$fot(mult(X_26,mult(i(x4),unit)))]]) ).
cnf(refute_0_17,plain,
( mult(X_26,mult(i(x4),unit)) != mult(X_26,mult(i(x4),unit))
| mult(i(x4),unit) != i(x4)
| mult(X_26,mult(i(x4),unit)) = mult(X_26,i(x4)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_26,mult(i(x4),unit)),mult(X_26,mult(i(x4),unit))) ),[1,1],$fot(i(x4))]]) ).
cnf(refute_0_18,plain,
( mult(i(x4),unit) != i(x4)
| mult(X_26,mult(i(x4),unit)) = mult(X_26,i(x4)) ),
inference(resolve,[$cnf( $equal(mult(X_26,mult(i(x4),unit)),mult(X_26,mult(i(x4),unit))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(X_26,mult(i(x4),unit)) = mult(X_26,i(x4)),
inference(resolve,[$cnf( $equal(mult(i(x4),unit),i(x4)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( mult(X_26,i(x4)) != x3
| mult(X_26,mult(i(x4),unit)) != mult(X_26,i(x4))
| mult(X_26,mult(i(x4),unit)) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_26,mult(i(x4),unit)),mult(X_26,i(x4))) ),[1],$fot(x3)]]) ).
cnf(refute_0_21,plain,
( mult(X_26,i(x4)) != x3
| mult(X_26,mult(i(x4),unit)) = x3 ),
inference(resolve,[$cnf( $equal(mult(X_26,mult(i(x4),unit)),mult(X_26,i(x4))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
mult(X_26,i(x4)) != x3,
inference(resolve,[$cnf( $equal(mult(X_26,mult(i(x4),unit)),x3) )],[refute_0_21,refute_0_14]) ).
cnf(refute_0_23,plain,
mult(mult(X_5,i(x4)),i(x4)) != x3,
inference(subst,[],[refute_0_22:[bind(X_26,$fot(mult(X_5,i(x4))))]]) ).
cnf(refute_0_24,plain,
mult(mult(mult(X_5,X_6),X_6),unit) = mult(mult(X_5,X_6),X_6),
inference(subst,[],[f01:[bind(A,$fot(mult(mult(X_5,X_6),X_6)))]]) ).
cnf(refute_0_25,plain,
mult(X_5,mult(X_6,mult(X_6,unit))) = mult(mult(mult(X_5,X_6),X_6),unit),
inference(subst,[],[f03:[bind(A,$fot(X_5)),bind(B,$fot(X_6)),bind(C,$fot(unit))]]) ).
cnf(refute_0_26,plain,
( mult(X_5,mult(X_6,mult(X_6,unit))) != mult(mult(mult(X_5,X_6),X_6),unit)
| mult(mult(mult(X_5,X_6),X_6),unit) = mult(X_5,mult(X_6,mult(X_6,unit))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_5,mult(X_6,mult(X_6,unit))))),bind(Y,$fot(mult(mult(mult(X_5,X_6),X_6),unit)))]]) ).
cnf(refute_0_27,plain,
mult(mult(mult(X_5,X_6),X_6),unit) = mult(X_5,mult(X_6,mult(X_6,unit))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(mult(mult(X_5,X_6),X_6),unit)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( mult(mult(mult(X_5,X_6),X_6),unit) != mult(X_5,mult(X_6,mult(X_6,unit)))
| mult(mult(mult(X_5,X_6),X_6),unit) != mult(mult(X_5,X_6),X_6)
| mult(X_5,mult(X_6,mult(X_6,unit))) = mult(mult(X_5,X_6),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),unit),mult(mult(X_5,X_6),X_6)) ),[0],$fot(mult(X_5,mult(X_6,mult(X_6,unit))))]]) ).
cnf(refute_0_29,plain,
( mult(mult(mult(X_5,X_6),X_6),unit) != mult(mult(X_5,X_6),X_6)
| mult(X_5,mult(X_6,mult(X_6,unit))) = mult(mult(X_5,X_6),X_6) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),unit),mult(X_5,mult(X_6,mult(X_6,unit)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(X_5,mult(X_6,mult(X_6,unit))) = mult(mult(X_5,X_6),X_6),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_5,X_6),X_6),unit),mult(mult(X_5,X_6),X_6)) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(X_6,unit) = X_6,
inference(subst,[],[f01:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_32,plain,
mult(X_6,mult(X_6,unit)) = mult(X_6,mult(X_6,unit)),
introduced(tautology,[refl,[$fot(mult(X_6,mult(X_6,unit)))]]) ).
cnf(refute_0_33,plain,
( mult(X_6,mult(X_6,unit)) != mult(X_6,mult(X_6,unit))
| mult(X_6,unit) != X_6
| mult(X_6,mult(X_6,unit)) = mult(X_6,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_6,mult(X_6,unit)),mult(X_6,mult(X_6,unit))) ),[1,1],$fot(X_6)]]) ).
cnf(refute_0_34,plain,
( mult(X_6,unit) != X_6
| mult(X_6,mult(X_6,unit)) = mult(X_6,X_6) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_6,unit)),mult(X_6,mult(X_6,unit))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(X_6,mult(X_6,unit)) = mult(X_6,X_6),
inference(resolve,[$cnf( $equal(mult(X_6,unit),X_6) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(X_5,mult(X_6,mult(X_6,unit))) = mult(X_5,mult(X_6,mult(X_6,unit))),
introduced(tautology,[refl,[$fot(mult(X_5,mult(X_6,mult(X_6,unit))))]]) ).
cnf(refute_0_37,plain,
( mult(X_5,mult(X_6,mult(X_6,unit))) != mult(X_5,mult(X_6,mult(X_6,unit)))
| mult(X_6,mult(X_6,unit)) != mult(X_6,X_6)
| mult(X_5,mult(X_6,mult(X_6,unit))) = mult(X_5,mult(X_6,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(X_5,mult(X_6,mult(X_6,unit)))) ),[1,1],$fot(mult(X_6,X_6))]]) ).
cnf(refute_0_38,plain,
( mult(X_6,mult(X_6,unit)) != mult(X_6,X_6)
| mult(X_5,mult(X_6,mult(X_6,unit))) = mult(X_5,mult(X_6,X_6)) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(X_5,mult(X_6,mult(X_6,unit)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
mult(X_5,mult(X_6,mult(X_6,unit))) = mult(X_5,mult(X_6,X_6)),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_6,unit)),mult(X_6,X_6)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( mult(X_5,mult(X_6,mult(X_6,unit))) != mult(X_5,mult(X_6,X_6))
| mult(X_5,mult(X_6,mult(X_6,unit))) != mult(mult(X_5,X_6),X_6)
| mult(X_5,mult(X_6,X_6)) = mult(mult(X_5,X_6),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(mult(X_5,X_6),X_6)) ),[0],$fot(mult(X_5,mult(X_6,X_6)))]]) ).
cnf(refute_0_41,plain,
( mult(X_5,mult(X_6,mult(X_6,unit))) != mult(mult(X_5,X_6),X_6)
| mult(X_5,mult(X_6,X_6)) = mult(mult(X_5,X_6),X_6) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(X_5,mult(X_6,X_6))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
mult(X_5,mult(X_6,X_6)) = mult(mult(X_5,X_6),X_6),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_6,unit))),mult(mult(X_5,X_6),X_6)) )],[refute_0_30,refute_0_41]) ).
cnf(refute_0_43,plain,
mult(X_5,mult(i(x4),i(x4))) = mult(mult(X_5,i(x4)),i(x4)),
inference(subst,[],[refute_0_42:[bind(X_6,$fot(i(x4)))]]) ).
cnf(refute_0_44,plain,
( mult(X_5,mult(i(x4),i(x4))) != mult(mult(X_5,i(x4)),i(x4))
| mult(mult(X_5,i(x4)),i(x4)) = mult(X_5,mult(i(x4),i(x4))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_5,mult(i(x4),i(x4))))),bind(Y,$fot(mult(mult(X_5,i(x4)),i(x4))))]]) ).
cnf(refute_0_45,plain,
mult(mult(X_5,i(x4)),i(x4)) = mult(X_5,mult(i(x4),i(x4))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),mult(mult(X_5,i(x4)),i(x4))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( mult(X_5,mult(i(x4),i(x4))) != x3
| mult(mult(X_5,i(x4)),i(x4)) != mult(X_5,mult(i(x4),i(x4)))
| mult(mult(X_5,i(x4)),i(x4)) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_5,i(x4)),i(x4)),mult(X_5,mult(i(x4),i(x4)))) ),[1],$fot(x3)]]) ).
cnf(refute_0_47,plain,
( mult(X_5,mult(i(x4),i(x4))) != x3
| mult(mult(X_5,i(x4)),i(x4)) = x3 ),
inference(resolve,[$cnf( $equal(mult(mult(X_5,i(x4)),i(x4)),mult(X_5,mult(i(x4),i(x4)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(X_5,mult(i(x4),i(x4))) != x3,
inference(resolve,[$cnf( $equal(mult(mult(X_5,i(x4)),i(x4)),x3) )],[refute_0_47,refute_0_23]) ).
cnf(refute_0_49,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(mult(i(X_6),X_6),X_6),X_7),
inference(subst,[],[f03:[bind(A,$fot(i(X_6))),bind(B,$fot(X_6)),bind(C,$fot(X_7))]]) ).
cnf(refute_0_50,plain,
mult(i(X_6),X_6) = unit,
inference(subst,[],[f05:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_51,plain,
( mult(i(X_6),X_6) != unit
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(mult(i(X_6),X_6),X_6),X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(unit,X_6),X_7) ),
introduced(tautology,[equality,[$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_52,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( $equal(mult(i(X_6),X_6),unit) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(mult(unit,X_6),X_7),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(mult(mult(i(X_6),X_6),X_6),X_7)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
mult(unit,X_6) = X_6,
inference(subst,[],[f02:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_55,plain,
mult(mult(unit,X_6),X_7) = mult(mult(unit,X_6),X_7),
introduced(tautology,[refl,[$fot(mult(mult(unit,X_6),X_7))]]) ).
cnf(refute_0_56,plain,
( mult(mult(unit,X_6),X_7) != mult(mult(unit,X_6),X_7)
| mult(unit,X_6) != X_6
| mult(mult(unit,X_6),X_7) = mult(X_6,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(unit,X_6),X_7),mult(mult(unit,X_6),X_7)) ),[1,0],$fot(X_6)]]) ).
cnf(refute_0_57,plain,
( mult(unit,X_6) != X_6
| mult(mult(unit,X_6),X_7) = mult(X_6,X_7) ),
inference(resolve,[$cnf( $equal(mult(mult(unit,X_6),X_7),mult(mult(unit,X_6),X_7)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
mult(mult(unit,X_6),X_7) = mult(X_6,X_7),
inference(resolve,[$cnf( $equal(mult(unit,X_6),X_6) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( mult(i(X_6),mult(X_6,mult(X_6,X_7))) != mult(mult(unit,X_6),X_7)
| mult(mult(unit,X_6),X_7) != mult(X_6,X_7)
| mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(X_6,X_7) ),
introduced(tautology,[equality,[$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_60,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( $equal(mult(mult(unit,X_6),X_7),mult(X_6,X_7)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
mult(i(X_6),mult(X_6,mult(X_6,X_7))) = mult(X_6,X_7),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,X_7))),mult(mult(unit,X_6),X_7)) )],[refute_0_53,refute_0_60]) ).
cnf(refute_0_62,plain,
mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))))) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))),
inference(subst,[],[refute_0_61:[bind(X_7,$fot(mult(i(X_6),i(mult(X_6,X_6)))))]]) ).
cnf(refute_0_63,plain,
mult(X_8,mult(i(X_8),i(X_8))) = mult(mult(X_8,i(X_8)),i(X_8)),
inference(subst,[],[refute_0_42:[bind(X_5,$fot(X_8)),bind(X_6,$fot(i(X_8)))]]) ).
cnf(refute_0_64,plain,
mult(X_8,i(X_8)) = unit,
inference(subst,[],[f04:[bind(A,$fot(X_8))]]) ).
cnf(refute_0_65,plain,
( mult(X_8,i(X_8)) != unit
| mult(X_8,mult(i(X_8),i(X_8))) != mult(mult(X_8,i(X_8)),i(X_8))
| mult(X_8,mult(i(X_8),i(X_8))) = mult(unit,i(X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_8,mult(i(X_8),i(X_8))),mult(mult(X_8,i(X_8)),i(X_8))) ),[1,0],$fot(unit)]]) ).
cnf(refute_0_66,plain,
( mult(X_8,mult(i(X_8),i(X_8))) != mult(mult(X_8,i(X_8)),i(X_8))
| mult(X_8,mult(i(X_8),i(X_8))) = mult(unit,i(X_8)) ),
inference(resolve,[$cnf( $equal(mult(X_8,i(X_8)),unit) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
mult(X_8,mult(i(X_8),i(X_8))) = mult(unit,i(X_8)),
inference(resolve,[$cnf( $equal(mult(X_8,mult(i(X_8),i(X_8))),mult(mult(X_8,i(X_8)),i(X_8))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
mult(unit,i(X_8)) = i(X_8),
inference(subst,[],[f02:[bind(A,$fot(i(X_8)))]]) ).
cnf(refute_0_69,plain,
( mult(X_8,mult(i(X_8),i(X_8))) != mult(unit,i(X_8))
| mult(unit,i(X_8)) != i(X_8)
| mult(X_8,mult(i(X_8),i(X_8))) = i(X_8) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_8,mult(i(X_8),i(X_8))),i(X_8)) ),[0],$fot(mult(unit,i(X_8)))]]) ).
cnf(refute_0_70,plain,
( mult(X_8,mult(i(X_8),i(X_8))) != mult(unit,i(X_8))
| mult(X_8,mult(i(X_8),i(X_8))) = i(X_8) ),
inference(resolve,[$cnf( $equal(mult(unit,i(X_8)),i(X_8)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
mult(X_8,mult(i(X_8),i(X_8))) = i(X_8),
inference(resolve,[$cnf( $equal(mult(X_8,mult(i(X_8),i(X_8))),mult(unit,i(X_8))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) = i(mult(X_12,X_12)),
inference(subst,[],[refute_0_71:[bind(X_8,$fot(mult(X_12,X_12)))]]) ).
cnf(refute_0_73,plain,
mult(unit,mult(X_6,mult(X_6,X_7))) = mult(mult(mult(unit,X_6),X_6),X_7),
inference(subst,[],[f03:[bind(A,$fot(unit)),bind(B,$fot(X_6)),bind(C,$fot(X_7))]]) ).
cnf(refute_0_74,plain,
( mult(unit,X_6) != X_6
| mult(unit,mult(X_6,mult(X_6,X_7))) != mult(mult(mult(unit,X_6),X_6),X_7)
| mult(unit,mult(X_6,mult(X_6,X_7))) = mult(mult(X_6,X_6),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_6,mult(X_6,X_7))),mult(mult(mult(unit,X_6),X_6),X_7)) ),[1,0,0],$fot(X_6)]]) ).
cnf(refute_0_75,plain,
( mult(unit,mult(X_6,mult(X_6,X_7))) != mult(mult(mult(unit,X_6),X_6),X_7)
| mult(unit,mult(X_6,mult(X_6,X_7))) = mult(mult(X_6,X_6),X_7) ),
inference(resolve,[$cnf( $equal(mult(unit,X_6),X_6) )],[refute_0_54,refute_0_74]) ).
cnf(refute_0_76,plain,
mult(unit,mult(X_6,mult(X_6,X_7))) = mult(mult(X_6,X_6),X_7),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_6,mult(X_6,X_7))),mult(mult(mult(unit,X_6),X_6),X_7)) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(unit,mult(X_6,mult(X_6,X_7))) = mult(X_6,mult(X_6,X_7)),
inference(subst,[],[f02:[bind(A,$fot(mult(X_6,mult(X_6,X_7))))]]) ).
cnf(refute_0_78,plain,
( mult(unit,mult(X_6,mult(X_6,X_7))) != mult(X_6,mult(X_6,X_7))
| mult(unit,mult(X_6,mult(X_6,X_7))) != mult(mult(X_6,X_6),X_7)
| mult(X_6,mult(X_6,X_7)) = mult(mult(X_6,X_6),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_6,mult(X_6,X_7))),mult(mult(X_6,X_6),X_7)) ),[0],$fot(mult(X_6,mult(X_6,X_7)))]]) ).
cnf(refute_0_79,plain,
( mult(unit,mult(X_6,mult(X_6,X_7))) != mult(mult(X_6,X_6),X_7)
| mult(X_6,mult(X_6,X_7)) = mult(mult(X_6,X_6),X_7) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_6,mult(X_6,X_7))),mult(X_6,mult(X_6,X_7))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
mult(X_6,mult(X_6,X_7)) = mult(mult(X_6,X_6),X_7),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_6,mult(X_6,X_7))),mult(mult(X_6,X_6),X_7)) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))),
inference(subst,[],[refute_0_80:[bind(X_6,$fot(X_12)),bind(X_7,$fot(mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))]]) ).
cnf(refute_0_82,plain,
( mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) != mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))
| mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) = mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))))),bind(Y,$fot(mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))))]]) ).
cnf(refute_0_83,plain,
mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) = mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),
inference(resolve,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) != i(mult(X_12,X_12))
| mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) != mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))
| mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = i(mult(X_12,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))),i(mult(X_12,X_12))) ),[0],$fot(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))))]]) ).
cnf(refute_0_85,plain,
( mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) != i(mult(X_12,X_12))
| mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = i(mult(X_12,X_12)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))),mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = i(mult(X_12,X_12)),
inference(resolve,[$cnf( $equal(mult(mult(X_12,X_12),mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))),i(mult(X_12,X_12))) )],[refute_0_72,refute_0_85]) ).
cnf(refute_0_87,plain,
mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) = mult(mult(X_5,i(mult(X_5,X_5))),i(mult(X_5,X_5))),
inference(subst,[],[refute_0_42:[bind(X_6,$fot(i(mult(X_5,X_5))))]]) ).
cnf(refute_0_88,plain,
mult(i(X_16),mult(X_16,mult(X_16,i(mult(X_16,X_16))))) = mult(X_16,i(mult(X_16,X_16))),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(X_16)),bind(X_7,$fot(i(mult(X_16,X_16))))]]) ).
cnf(refute_0_89,plain,
mult(mult(X_12,X_12),i(mult(X_12,X_12))) = unit,
inference(subst,[],[f04:[bind(A,$fot(mult(X_12,X_12)))]]) ).
cnf(refute_0_90,plain,
mult(X_12,mult(X_12,i(mult(X_12,X_12)))) = mult(mult(X_12,X_12),i(mult(X_12,X_12))),
inference(subst,[],[refute_0_80:[bind(X_6,$fot(X_12)),bind(X_7,$fot(i(mult(X_12,X_12))))]]) ).
cnf(refute_0_91,plain,
( mult(X_12,mult(X_12,i(mult(X_12,X_12)))) != mult(mult(X_12,X_12),i(mult(X_12,X_12)))
| mult(mult(X_12,X_12),i(mult(X_12,X_12))) = mult(X_12,mult(X_12,i(mult(X_12,X_12)))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_12,mult(X_12,i(mult(X_12,X_12)))))),bind(Y,$fot(mult(mult(X_12,X_12),i(mult(X_12,X_12)))))]]) ).
cnf(refute_0_92,plain,
mult(mult(X_12,X_12),i(mult(X_12,X_12))) = mult(X_12,mult(X_12,i(mult(X_12,X_12)))),
inference(resolve,[$cnf( $equal(mult(X_12,mult(X_12,i(mult(X_12,X_12)))),mult(mult(X_12,X_12),i(mult(X_12,X_12)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( mult(mult(X_12,X_12),i(mult(X_12,X_12))) != mult(X_12,mult(X_12,i(mult(X_12,X_12))))
| mult(mult(X_12,X_12),i(mult(X_12,X_12))) != unit
| mult(X_12,mult(X_12,i(mult(X_12,X_12)))) = unit ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_12,X_12),i(mult(X_12,X_12))),unit) ),[0],$fot(mult(X_12,mult(X_12,i(mult(X_12,X_12)))))]]) ).
cnf(refute_0_94,plain,
( mult(mult(X_12,X_12),i(mult(X_12,X_12))) != unit
| mult(X_12,mult(X_12,i(mult(X_12,X_12)))) = unit ),
inference(resolve,[$cnf( $equal(mult(mult(X_12,X_12),i(mult(X_12,X_12))),mult(X_12,mult(X_12,i(mult(X_12,X_12))))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
mult(X_12,mult(X_12,i(mult(X_12,X_12)))) = unit,
inference(resolve,[$cnf( $equal(mult(mult(X_12,X_12),i(mult(X_12,X_12))),unit) )],[refute_0_89,refute_0_94]) ).
cnf(refute_0_96,plain,
mult(X_16,mult(X_16,i(mult(X_16,X_16)))) = unit,
inference(subst,[],[refute_0_95:[bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_97,plain,
( mult(X_16,mult(X_16,i(mult(X_16,X_16)))) != unit
| mult(i(X_16),mult(X_16,mult(X_16,i(mult(X_16,X_16))))) != mult(X_16,i(mult(X_16,X_16)))
| mult(i(X_16),unit) = mult(X_16,i(mult(X_16,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_16),mult(X_16,mult(X_16,i(mult(X_16,X_16))))),mult(X_16,i(mult(X_16,X_16)))) ),[0,1],$fot(unit)]]) ).
cnf(refute_0_98,plain,
( mult(i(X_16),mult(X_16,mult(X_16,i(mult(X_16,X_16))))) != mult(X_16,i(mult(X_16,X_16)))
| mult(i(X_16),unit) = mult(X_16,i(mult(X_16,X_16))) ),
inference(resolve,[$cnf( $equal(mult(X_16,mult(X_16,i(mult(X_16,X_16)))),unit) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
mult(i(X_16),unit) = mult(X_16,i(mult(X_16,X_16))),
inference(resolve,[$cnf( $equal(mult(i(X_16),mult(X_16,mult(X_16,i(mult(X_16,X_16))))),mult(X_16,i(mult(X_16,X_16)))) )],[refute_0_88,refute_0_98]) ).
cnf(refute_0_100,plain,
mult(i(X_16),unit) = i(X_16),
inference(subst,[],[f01:[bind(A,$fot(i(X_16)))]]) ).
cnf(refute_0_101,plain,
( mult(i(X_16),unit) != i(X_16)
| mult(i(X_16),unit) != mult(X_16,i(mult(X_16,X_16)))
| i(X_16) = mult(X_16,i(mult(X_16,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_16),unit),mult(X_16,i(mult(X_16,X_16)))) ),[0],$fot(i(X_16))]]) ).
cnf(refute_0_102,plain,
( mult(i(X_16),unit) != mult(X_16,i(mult(X_16,X_16)))
| i(X_16) = mult(X_16,i(mult(X_16,X_16))) ),
inference(resolve,[$cnf( $equal(mult(i(X_16),unit),i(X_16)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
i(X_16) = mult(X_16,i(mult(X_16,X_16))),
inference(resolve,[$cnf( $equal(mult(i(X_16),unit),mult(X_16,i(mult(X_16,X_16)))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
i(X_5) = mult(X_5,i(mult(X_5,X_5))),
inference(subst,[],[refute_0_103:[bind(X_16,$fot(X_5))]]) ).
cnf(refute_0_105,plain,
( i(X_5) != mult(X_5,i(mult(X_5,X_5)))
| mult(X_5,i(mult(X_5,X_5))) = i(X_5) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i(X_5))),bind(Y,$fot(mult(X_5,i(mult(X_5,X_5)))))]]) ).
cnf(refute_0_106,plain,
mult(X_5,i(mult(X_5,X_5))) = i(X_5),
inference(resolve,[$cnf( $equal(i(X_5),mult(X_5,i(mult(X_5,X_5)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( mult(X_5,i(mult(X_5,X_5))) != i(X_5)
| mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) != mult(mult(X_5,i(mult(X_5,X_5))),i(mult(X_5,X_5)))
| mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) = mult(i(X_5),i(mult(X_5,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))),mult(mult(X_5,i(mult(X_5,X_5))),i(mult(X_5,X_5)))) ),[1,0],$fot(i(X_5))]]) ).
cnf(refute_0_108,plain,
( mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) != mult(mult(X_5,i(mult(X_5,X_5))),i(mult(X_5,X_5)))
| mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) = mult(i(X_5),i(mult(X_5,X_5))) ),
inference(resolve,[$cnf( $equal(mult(X_5,i(mult(X_5,X_5))),i(X_5)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))) = mult(i(X_5),i(mult(X_5,X_5))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(mult(X_5,X_5)),i(mult(X_5,X_5)))),mult(mult(X_5,i(mult(X_5,X_5))),i(mult(X_5,X_5)))) )],[refute_0_87,refute_0_108]) ).
cnf(refute_0_110,plain,
mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) = mult(i(X_12),i(mult(X_12,X_12))),
inference(subst,[],[refute_0_109:[bind(X_5,$fot(X_12))]]) ).
cnf(refute_0_111,plain,
mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),
introduced(tautology,[refl,[$fot(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))))]]) ).
cnf(refute_0_112,plain,
( mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) != mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))
| mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) != mult(i(X_12),i(mult(X_12,X_12)))
| mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))) ),[1,1],$fot(mult(i(X_12),i(mult(X_12,X_12))))]]) ).
cnf(refute_0_113,plain,
( mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))) != mult(i(X_12),i(mult(X_12,X_12)))
| mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))) ),
inference(resolve,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) = mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))),
inference(resolve,[$cnf( $equal(mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12)))),mult(i(X_12),i(mult(X_12,X_12)))) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) != i(mult(X_12,X_12))
| mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) != mult(X_12,mult(i(X_12),i(mult(X_12,X_12))))
| mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))) = i(mult(X_12,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),i(mult(X_12,X_12))) ),[0],$fot(mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))))]]) ).
cnf(refute_0_116,plain,
( mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))) != i(mult(X_12,X_12))
| mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))) = i(mult(X_12,X_12)) ),
inference(resolve,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),mult(X_12,mult(i(X_12),i(mult(X_12,X_12))))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
mult(X_12,mult(i(X_12),i(mult(X_12,X_12)))) = i(mult(X_12,X_12)),
inference(resolve,[$cnf( $equal(mult(X_12,mult(X_12,mult(i(mult(X_12,X_12)),i(mult(X_12,X_12))))),i(mult(X_12,X_12))) )],[refute_0_86,refute_0_116]) ).
cnf(refute_0_118,plain,
mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) = i(mult(X_6,X_6)),
inference(subst,[],[refute_0_117:[bind(X_12,$fot(X_6))]]) ).
cnf(refute_0_119,plain,
( mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) != i(mult(X_6,X_6))
| mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))))) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))))),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) ),[0,1,1],$fot(i(mult(X_6,X_6)))]]) ).
cnf(refute_0_120,plain,
( mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))))) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))),i(mult(X_6,X_6))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))))),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) )],[refute_0_62,refute_0_120]) ).
cnf(refute_0_122,plain,
( i(X_16) != mult(X_16,i(mult(X_16,X_16)))
| mult(X_16,i(mult(X_16,X_16))) = i(X_16) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i(X_16))),bind(Y,$fot(mult(X_16,i(mult(X_16,X_16)))))]]) ).
cnf(refute_0_123,plain,
mult(X_16,i(mult(X_16,X_16))) = i(X_16),
inference(resolve,[$cnf( $equal(i(X_16),mult(X_16,i(mult(X_16,X_16)))) )],[refute_0_103,refute_0_122]) ).
cnf(refute_0_124,plain,
mult(X_6,i(mult(X_6,X_6))) = i(X_6),
inference(subst,[],[refute_0_123:[bind(X_16,$fot(X_6))]]) ).
cnf(refute_0_125,plain,
mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),
introduced(tautology,[refl,[$fot(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))))]]) ).
cnf(refute_0_126,plain,
( mult(X_6,i(mult(X_6,X_6))) != i(X_6)
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) != mult(i(X_6),mult(X_6,i(mult(X_6,X_6))))
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(i(X_6),i(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),mult(i(X_6),mult(X_6,i(mult(X_6,X_6))))) ),[1,1],$fot(i(X_6))]]) ).
cnf(refute_0_127,plain,
( mult(X_6,i(mult(X_6,X_6))) != i(X_6)
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(i(X_6),i(X_6)) ),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),mult(i(X_6),mult(X_6,i(mult(X_6,X_6))))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) = mult(i(X_6),i(X_6)),
inference(resolve,[$cnf( $equal(mult(X_6,i(mult(X_6,X_6))),i(X_6)) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
( mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) != mult(i(X_6),i(X_6))
| mult(i(X_6),i(X_6)) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) ),[0],$fot(mult(i(X_6),i(X_6)))]]) ).
cnf(refute_0_130,plain,
( mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),i(X_6)) = mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) ),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),mult(i(X_6),i(X_6))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))) != i(mult(X_6,X_6))
| mult(i(X_6),i(X_6)) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),i(X_6)) = i(mult(X_6,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_6),i(X_6)),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) ),[1],$fot(i(mult(X_6,X_6)))]]) ).
cnf(refute_0_132,plain,
( mult(i(X_6),i(X_6)) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),i(X_6)) = i(mult(X_6,X_6)) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(i(X_6),i(mult(X_6,X_6)))),i(mult(X_6,X_6))) )],[refute_0_118,refute_0_131]) ).
cnf(refute_0_133,plain,
( mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))) != mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))
| mult(i(X_6),i(X_6)) = i(mult(X_6,X_6)) ),
inference(resolve,[$cnf( $equal(mult(i(X_6),i(X_6)),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) )],[refute_0_130,refute_0_132]) ).
cnf(refute_0_134,plain,
mult(i(X_6),i(X_6)) = i(mult(X_6,X_6)),
inference(resolve,[$cnf( $equal(mult(i(X_6),mult(X_6,i(mult(X_6,X_6)))),mult(X_6,mult(i(X_6),i(mult(X_6,X_6))))) )],[refute_0_121,refute_0_133]) ).
cnf(refute_0_135,plain,
mult(i(x4),i(x4)) = i(mult(x4,x4)),
inference(subst,[],[refute_0_134:[bind(X_6,$fot(x4))]]) ).
cnf(refute_0_136,plain,
mult(X_5,mult(i(x4),i(x4))) = mult(X_5,mult(i(x4),i(x4))),
introduced(tautology,[refl,[$fot(mult(X_5,mult(i(x4),i(x4))))]]) ).
cnf(refute_0_137,plain,
( mult(X_5,mult(i(x4),i(x4))) != mult(X_5,mult(i(x4),i(x4)))
| mult(i(x4),i(x4)) != i(mult(x4,x4))
| mult(X_5,mult(i(x4),i(x4))) = mult(X_5,i(mult(x4,x4))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),mult(X_5,mult(i(x4),i(x4)))) ),[1,1],$fot(i(mult(x4,x4)))]]) ).
cnf(refute_0_138,plain,
( mult(i(x4),i(x4)) != i(mult(x4,x4))
| mult(X_5,mult(i(x4),i(x4))) = mult(X_5,i(mult(x4,x4))) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),mult(X_5,mult(i(x4),i(x4)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
mult(X_5,mult(i(x4),i(x4))) = mult(X_5,i(mult(x4,x4))),
inference(resolve,[$cnf( $equal(mult(i(x4),i(x4)),i(mult(x4,x4))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( mult(X_5,i(mult(x4,x4))) != x3
| mult(X_5,mult(i(x4),i(x4))) != mult(X_5,i(mult(x4,x4)))
| mult(X_5,mult(i(x4),i(x4))) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),mult(X_5,i(mult(x4,x4)))) ),[1],$fot(x3)]]) ).
cnf(refute_0_141,plain,
( mult(X_5,i(mult(x4,x4))) != x3
| mult(X_5,mult(i(x4),i(x4))) = x3 ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),mult(X_5,i(mult(x4,x4)))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
mult(X_5,i(mult(x4,x4))) != x3,
inference(resolve,[$cnf( $equal(mult(X_5,mult(i(x4),i(x4))),x3) )],[refute_0_141,refute_0_48]) ).
cnf(refute_0_143,plain,
mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) != x3,
inference(subst,[],[refute_0_142:[bind(X_5,$fot(mult(X_52,mult(X_53,X_53))))]]) ).
cnf(refute_0_144,plain,
( mult(X_5,mult(X_6,X_6)) != mult(mult(X_5,X_6),X_6)
| mult(mult(X_5,X_6),X_6) = mult(X_5,mult(X_6,X_6)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_5,mult(X_6,X_6)))),bind(Y,$fot(mult(mult(X_5,X_6),X_6)))]]) ).
cnf(refute_0_145,plain,
mult(mult(X_5,X_6),X_6) = mult(X_5,mult(X_6,X_6)),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,X_6)),mult(mult(X_5,X_6),X_6)) )],[refute_0_42,refute_0_144]) ).
cnf(refute_0_146,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(subst,[],[refute_0_145:[bind(X_5,$fot(A)),bind(X_6,$fot(B))]]) ).
cnf(refute_0_147,plain,
mult(mult(mult(A,B),B),C) = mult(mult(mult(A,B),B),C),
introduced(tautology,[refl,[$fot(mult(mult(mult(A,B),B),C))]]) ).
cnf(refute_0_148,plain,
( mult(mult(A,B),B) != mult(A,mult(B,B))
| mult(mult(mult(A,B),B),C) != mult(mult(mult(A,B),B),C)
| mult(mult(mult(A,B),B),C) = mult(mult(A,mult(B,B)),C) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(A,B),B),C),mult(mult(mult(A,B),B),C)) ),[1,0],$fot(mult(A,mult(B,B)))]]) ).
cnf(refute_0_149,plain,
( mult(mult(A,B),B) != mult(A,mult(B,B))
| mult(mult(mult(A,B),B),C) = mult(mult(A,mult(B,B)),C) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(A,B),B),C),mult(mult(mult(A,B),B),C)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
mult(mult(mult(A,B),B),C) = mult(mult(A,mult(B,B)),C),
inference(resolve,[$cnf( $equal(mult(mult(A,B),B),mult(A,mult(B,B))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( mult(A,mult(B,mult(B,C))) != mult(mult(mult(A,B),B),C)
| mult(mult(mult(A,B),B),C) != mult(mult(A,mult(B,B)),C)
| mult(A,mult(B,mult(B,C))) = mult(mult(A,mult(B,B)),C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(A,mult(B,mult(B,C))),mult(mult(A,mult(B,B)),C)) ),[0],$fot(mult(mult(mult(A,B),B),C))]]) ).
cnf(refute_0_152,plain,
( mult(A,mult(B,mult(B,C))) != mult(mult(mult(A,B),B),C)
| mult(A,mult(B,mult(B,C))) = mult(mult(A,mult(B,B)),C) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(A,B),B),C),mult(mult(A,mult(B,B)),C)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(A,mult(B,B)),C),
inference(resolve,[$cnf( $equal(mult(A,mult(B,mult(B,C))),mult(mult(mult(A,B),B),C)) )],[f03,refute_0_152]) ).
cnf(refute_0_154,plain,
mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) = mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))),
inference(subst,[],[refute_0_153:[bind(A,$fot(X_52)),bind(B,$fot(X_53)),bind(C,$fot(i(mult(x4,x4))))]]) ).
cnf(refute_0_155,plain,
( mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) != mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4)))
| mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) = mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))))),bind(Y,$fot(mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4)))))]]) ).
cnf(refute_0_156,plain,
mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) = mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))),
inference(resolve,[$cnf( $equal(mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))),mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
( mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) != x3
| mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) != mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4)))))
| mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))),mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4)))))) ),[1],$fot(x3)]]) ).
cnf(refute_0_158,plain,
( mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) != x3
| mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))) = x3 ),
inference(resolve,[$cnf( $equal(mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))),mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4)))))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
mult(X_52,mult(X_53,mult(X_53,i(mult(x4,x4))))) != x3,
inference(resolve,[$cnf( $equal(mult(mult(X_52,mult(X_53,X_53)),i(mult(x4,x4))),x3) )],[refute_0_158,refute_0_143]) ).
cnf(refute_0_160,plain,
mult(X_55,mult(x4,mult(x4,i(mult(x4,x4))))) != x3,
inference(subst,[],[refute_0_159:[bind(X_52,$fot(X_55)),bind(X_53,$fot(x4))]]) ).
cnf(refute_0_161,plain,
i(x4) = mult(x4,i(mult(x4,x4))),
inference(subst,[],[refute_0_103:[bind(X_16,$fot(x4))]]) ).
cnf(refute_0_162,plain,
( i(x4) != mult(x4,i(mult(x4,x4)))
| mult(x4,i(mult(x4,x4))) = i(x4) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i(x4))),bind(Y,$fot(mult(x4,i(mult(x4,x4)))))]]) ).
cnf(refute_0_163,plain,
mult(x4,i(mult(x4,x4))) = i(x4),
inference(resolve,[$cnf( $equal(i(x4),mult(x4,i(mult(x4,x4)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( mult(X_55,mult(x4,i(x4))) != x3
| mult(x4,i(mult(x4,x4))) != i(x4)
| mult(X_55,mult(x4,mult(x4,i(mult(x4,x4))))) = x3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_55,mult(x4,mult(x4,i(mult(x4,x4))))),x3) ),[0,1,1],$fot(i(x4))]]) ).
cnf(refute_0_165,plain,
( mult(X_55,mult(x4,i(x4))) != x3
| mult(X_55,mult(x4,mult(x4,i(mult(x4,x4))))) = x3 ),
inference(resolve,[$cnf( $equal(mult(x4,i(mult(x4,x4))),i(x4)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
mult(X_55,mult(x4,i(x4))) != x3,
inference(resolve,[$cnf( $equal(mult(X_55,mult(x4,mult(x4,i(mult(x4,x4))))),x3) )],[refute_0_165,refute_0_160]) ).
cnf(refute_0_167,plain,
mult(X_55,unit) = X_55,
inference(subst,[],[f01:[bind(A,$fot(X_55))]]) ).
cnf(refute_0_168,plain,
mult(x4,i(x4)) = unit,
inference(subst,[],[f04:[bind(A,$fot(x4))]]) ).
cnf(refute_0_169,plain,
mult(X_55,mult(x4,i(x4))) = mult(X_55,mult(x4,i(x4))),
introduced(tautology,[refl,[$fot(mult(X_55,mult(x4,i(x4))))]]) ).
cnf(refute_0_170,plain,
( mult(X_55,mult(x4,i(x4))) != mult(X_55,mult(x4,i(x4)))
| mult(x4,i(x4)) != unit
| mult(X_55,mult(x4,i(x4))) = mult(X_55,unit) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),mult(X_55,mult(x4,i(x4)))) ),[1,1],$fot(unit)]]) ).
cnf(refute_0_171,plain,
( mult(x4,i(x4)) != unit
| mult(X_55,mult(x4,i(x4))) = mult(X_55,unit) ),
inference(resolve,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),mult(X_55,mult(x4,i(x4)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
mult(X_55,mult(x4,i(x4))) = mult(X_55,unit),
inference(resolve,[$cnf( $equal(mult(x4,i(x4)),unit) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_174,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_173]) ).
cnf(refute_0_175,plain,
( mult(X_55,mult(x4,i(x4))) != mult(X_55,unit)
| mult(X_55,unit) != X_55
| mult(X_55,mult(x4,i(x4))) = X_55 ),
inference(subst,[],[refute_0_174:[bind(X,$fot(mult(X_55,mult(x4,i(x4))))),bind(Y,$fot(mult(X_55,unit))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_176,plain,
( mult(X_55,unit) != X_55
| mult(X_55,mult(x4,i(x4))) = X_55 ),
inference(resolve,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),mult(X_55,unit)) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
mult(X_55,mult(x4,i(x4))) = X_55,
inference(resolve,[$cnf( $equal(mult(X_55,unit),X_55) )],[refute_0_167,refute_0_176]) ).
cnf(refute_0_178,plain,
( X_55 != x3
| mult(X_55,mult(x4,i(x4))) != X_55
| mult(X_55,mult(x4,i(x4))) = x3 ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),X_55) ),[1],$fot(x3)]]) ).
cnf(refute_0_179,plain,
( X_55 != x3
| mult(X_55,mult(x4,i(x4))) = x3 ),
inference(resolve,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),X_55) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
X_55 != x3,
inference(resolve,[$cnf( $equal(mult(X_55,mult(x4,i(x4))),x3) )],[refute_0_179,refute_0_166]) ).
cnf(refute_0_181,plain,
x3 != x3,
inference(subst,[],[refute_0_180:[bind(X_55,$fot(x3))]]) ).
cnf(refute_0_182,plain,
x3 = x3,
introduced(tautology,[refl,[$fot(x3)]]) ).
cnf(refute_0_183,plain,
$false,
inference(resolve,[$cnf( $equal(x3,x3) )],[refute_0_182,refute_0_181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 10:32:07 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50
% 0.21/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.52
%------------------------------------------------------------------------------