TSTP Solution File: GRP704-11 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP704-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 10:50:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.38s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of clauses : 94 ( 50 unt; 0 nHn; 64 RR)
% Number of literals : 159 ( 158 equ; 67 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f02,axiom,
ld(A,mult(A,B)) = B ).
cnf(f06,axiom,
mult(unit,A) = A ).
cnf(f08,axiom,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ).
cnf(f10,axiom,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ).
cnf(f11,axiom,
op_d = ld(A,mult(op_c,A)) ).
cnf(f13,axiom,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ).
cnf(goal,negated_conjecture,
mult(x4,mult(x5,op_f)) != mult(mult(x4,x5),op_f) ).
cnf(refute_0_0,plain,
mult(X_13,mult(op_c,X_14)) = mult(mult(X_13,op_c),X_14),
inference(subst,[],[f10:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_1,plain,
mult(X_8,ld(X_8,mult(op_c,X_8))) = mult(op_c,X_8),
inference(subst,[],[f01:[bind(A,$fot(X_8)),bind(B,$fot(mult(op_c,X_8)))]]) ).
cnf(refute_0_2,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(subst,[],[f11:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_3,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(subst,[],[f02:[bind(A,$fot(op_c)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_4,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_5,plain,
( op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,op_c)),op_c) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
op_d = op_c,
inference(resolve,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( op_d != ld(A,mult(op_c,A))
| op_d != op_c
| op_c = ld(A,mult(op_c,A)) ),
introduced(tautology,[equality,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) ),[0],$fot(op_c)]]) ).
cnf(refute_0_8,plain,
( op_d != ld(A,mult(op_c,A))
| op_c = ld(A,mult(op_c,A)) ),
inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
op_c = ld(A,mult(op_c,A)),
inference(resolve,[$cnf( $equal(op_d,ld(A,mult(op_c,A))) )],[f11,refute_0_8]) ).
cnf(refute_0_10,plain,
op_c = ld(X_8,mult(op_c,X_8)),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_8))]]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( op_c != ld(X_8,mult(op_c,X_8))
| ld(X_8,mult(op_c,X_8)) = op_c ),
inference(subst,[],[refute_0_13:[bind(X,$fot(op_c)),bind(Y,$fot(ld(X_8,mult(op_c,X_8))))]]) ).
cnf(refute_0_15,plain,
ld(X_8,mult(op_c,X_8)) = op_c,
inference(resolve,[$cnf( $equal(op_c,ld(X_8,mult(op_c,X_8))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( ld(X_8,mult(op_c,X_8)) != op_c
| mult(X_8,ld(X_8,mult(op_c,X_8))) != mult(op_c,X_8)
| mult(X_8,op_c) = mult(op_c,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_8,ld(X_8,mult(op_c,X_8))),mult(op_c,X_8)) ),[0,1],$fot(op_c)]]) ).
cnf(refute_0_17,plain,
( mult(X_8,ld(X_8,mult(op_c,X_8))) != mult(op_c,X_8)
| mult(X_8,op_c) = mult(op_c,X_8) ),
inference(resolve,[$cnf( $equal(ld(X_8,mult(op_c,X_8)),op_c) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(X_8,op_c) = mult(op_c,X_8),
inference(resolve,[$cnf( $equal(mult(X_8,ld(X_8,mult(op_c,X_8))),mult(op_c,X_8)) )],[refute_0_1,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(X_13,op_c) = mult(op_c,X_13),
inference(subst,[],[refute_0_18:[bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_20,plain,
( mult(X_13,mult(op_c,X_14)) != mult(mult(X_13,op_c),X_14)
| mult(X_13,op_c) != mult(op_c,X_13)
| mult(X_13,mult(op_c,X_14)) = mult(mult(op_c,X_13),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_13,mult(op_c,X_14)),mult(mult(X_13,op_c),X_14)) ),[1,0],$fot(mult(op_c,X_13))]]) ).
cnf(refute_0_21,plain,
( mult(X_13,mult(op_c,X_14)) != mult(mult(X_13,op_c),X_14)
| mult(X_13,mult(op_c,X_14)) = mult(mult(op_c,X_13),X_14) ),
inference(resolve,[$cnf( $equal(mult(X_13,op_c),mult(op_c,X_13)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
mult(X_13,mult(op_c,X_14)) = mult(mult(op_c,X_13),X_14),
inference(resolve,[$cnf( $equal(mult(X_13,mult(op_c,X_14)),mult(mult(X_13,op_c),X_14)) )],[refute_0_0,refute_0_21]) ).
cnf(refute_0_23,plain,
( mult(op_c,mult(A,B)) != mult(mult(op_c,A),B)
| mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(mult(op_c,mult(A,B)))),bind(Y,$fot(mult(mult(op_c,A),B)))]]) ).
cnf(refute_0_24,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(resolve,[$cnf( $equal(mult(op_c,mult(A,B)),mult(mult(op_c,A),B)) )],[f08,refute_0_23]) ).
cnf(refute_0_25,plain,
mult(mult(op_c,X_13),X_14) = mult(op_c,mult(X_13,X_14)),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_26,plain,
( mult(X_13,mult(op_c,X_14)) != mult(mult(op_c,X_13),X_14)
| mult(mult(op_c,X_13),X_14) != mult(op_c,mult(X_13,X_14))
| mult(X_13,mult(op_c,X_14)) = mult(op_c,mult(X_13,X_14)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_13,mult(op_c,X_14)),mult(op_c,mult(X_13,X_14))) ),[0],$fot(mult(mult(op_c,X_13),X_14))]]) ).
cnf(refute_0_27,plain,
( mult(X_13,mult(op_c,X_14)) != mult(mult(op_c,X_13),X_14)
| mult(X_13,mult(op_c,X_14)) = mult(op_c,mult(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(mult(mult(op_c,X_13),X_14),mult(op_c,mult(X_13,X_14))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(X_13,mult(op_c,X_14)) = mult(op_c,mult(X_13,X_14)),
inference(resolve,[$cnf( $equal(mult(X_13,mult(op_c,X_14)),mult(mult(op_c,X_13),X_14)) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
mult(x4,mult(op_c,x5)) = mult(op_c,mult(x4,x5)),
inference(subst,[],[refute_0_28:[bind(X_13,$fot(x4)),bind(X_14,$fot(x5))]]) ).
cnf(refute_0_30,plain,
mult(x5,op_c) = mult(op_c,x5),
inference(subst,[],[refute_0_18:[bind(X_8,$fot(x5))]]) ).
cnf(refute_0_31,plain,
mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) = mult(X_18,ld(mult(unit,X_18),op_c)),
inference(subst,[],[f06:[bind(A,$fot(mult(X_18,ld(mult(unit,X_18),op_c))))]]) ).
cnf(refute_0_32,plain,
op_f = mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))),
inference(subst,[],[f13:[bind(A,$fot(unit)),bind(B,$fot(X_18))]]) ).
cnf(refute_0_33,plain,
( op_f != mult(unit,mult(X_18,ld(mult(unit,X_18),op_c)))
| mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) = op_f ),
inference(subst,[],[refute_0_13:[bind(X,$fot(op_f)),bind(Y,$fot(mult(unit,mult(X_18,ld(mult(unit,X_18),op_c)))))]]) ).
cnf(refute_0_34,plain,
mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) = op_f,
inference(resolve,[$cnf( $equal(op_f,mult(unit,mult(X_18,ld(mult(unit,X_18),op_c)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) != mult(X_18,ld(mult(unit,X_18),op_c))
| mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) != op_f
| op_f = mult(X_18,ld(mult(unit,X_18),op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))),mult(X_18,ld(mult(unit,X_18),op_c))) ),[0],$fot(op_f)]]) ).
cnf(refute_0_36,plain,
( mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))) != mult(X_18,ld(mult(unit,X_18),op_c))
| op_f = mult(X_18,ld(mult(unit,X_18),op_c)) ),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))),op_f) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
op_f = mult(X_18,ld(mult(unit,X_18),op_c)),
inference(resolve,[$cnf( $equal(mult(unit,mult(X_18,ld(mult(unit,X_18),op_c))),mult(X_18,ld(mult(unit,X_18),op_c))) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
mult(X_18,ld(X_18,op_c)) = op_c,
inference(subst,[],[f01:[bind(A,$fot(X_18)),bind(B,$fot(op_c))]]) ).
cnf(refute_0_39,plain,
mult(unit,X_18) = X_18,
inference(subst,[],[f06:[bind(A,$fot(X_18))]]) ).
cnf(refute_0_40,plain,
ld(mult(unit,X_18),op_c) = ld(mult(unit,X_18),op_c),
introduced(tautology,[refl,[$fot(ld(mult(unit,X_18),op_c))]]) ).
cnf(refute_0_41,plain,
( ld(mult(unit,X_18),op_c) != ld(mult(unit,X_18),op_c)
| mult(unit,X_18) != X_18
| ld(mult(unit,X_18),op_c) = ld(X_18,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(unit,X_18),op_c),ld(mult(unit,X_18),op_c)) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_42,plain,
( mult(unit,X_18) != X_18
| ld(mult(unit,X_18),op_c) = ld(X_18,op_c) ),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_18),op_c),ld(mult(unit,X_18),op_c)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ld(mult(unit,X_18),op_c) = ld(X_18,op_c),
inference(resolve,[$cnf( $equal(mult(unit,X_18),X_18) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(X_18,ld(mult(unit,X_18),op_c)) = mult(X_18,ld(mult(unit,X_18),op_c)),
introduced(tautology,[refl,[$fot(mult(X_18,ld(mult(unit,X_18),op_c)))]]) ).
cnf(refute_0_45,plain,
( ld(mult(unit,X_18),op_c) != ld(X_18,op_c)
| mult(X_18,ld(mult(unit,X_18),op_c)) != mult(X_18,ld(mult(unit,X_18),op_c))
| mult(X_18,ld(mult(unit,X_18),op_c)) = mult(X_18,ld(X_18,op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_18,ld(mult(unit,X_18),op_c)),mult(X_18,ld(mult(unit,X_18),op_c))) ),[1,1],$fot(ld(X_18,op_c))]]) ).
cnf(refute_0_46,plain,
( ld(mult(unit,X_18),op_c) != ld(X_18,op_c)
| mult(X_18,ld(mult(unit,X_18),op_c)) = mult(X_18,ld(X_18,op_c)) ),
inference(resolve,[$cnf( $equal(mult(X_18,ld(mult(unit,X_18),op_c)),mult(X_18,ld(mult(unit,X_18),op_c))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
mult(X_18,ld(mult(unit,X_18),op_c)) = mult(X_18,ld(X_18,op_c)),
inference(resolve,[$cnf( $equal(ld(mult(unit,X_18),op_c),ld(X_18,op_c)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_49,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_13,refute_0_48]) ).
cnf(refute_0_50,plain,
( mult(X_18,ld(X_18,op_c)) != op_c
| mult(X_18,ld(mult(unit,X_18),op_c)) != mult(X_18,ld(X_18,op_c))
| mult(X_18,ld(mult(unit,X_18),op_c)) = op_c ),
inference(subst,[],[refute_0_49:[bind(X,$fot(mult(X_18,ld(mult(unit,X_18),op_c)))),bind(Y,$fot(mult(X_18,ld(X_18,op_c)))),bind(Z,$fot(op_c))]]) ).
cnf(refute_0_51,plain,
( mult(X_18,ld(X_18,op_c)) != op_c
| mult(X_18,ld(mult(unit,X_18),op_c)) = op_c ),
inference(resolve,[$cnf( $equal(mult(X_18,ld(mult(unit,X_18),op_c)),mult(X_18,ld(X_18,op_c))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(X_18,ld(mult(unit,X_18),op_c)) = op_c,
inference(resolve,[$cnf( $equal(mult(X_18,ld(X_18,op_c)),op_c) )],[refute_0_38,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(X_18,ld(mult(unit,X_18),op_c)) != op_c
| op_f != mult(X_18,ld(mult(unit,X_18),op_c))
| op_f = op_c ),
introduced(tautology,[equality,[$cnf( $equal(op_f,mult(X_18,ld(mult(unit,X_18),op_c))) ),[1],$fot(op_c)]]) ).
cnf(refute_0_54,plain,
( op_f != mult(X_18,ld(mult(unit,X_18),op_c))
| op_f = op_c ),
inference(resolve,[$cnf( $equal(mult(X_18,ld(mult(unit,X_18),op_c)),op_c) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
op_f = op_c,
inference(resolve,[$cnf( $equal(op_f,mult(X_18,ld(mult(unit,X_18),op_c))) )],[refute_0_37,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(x5,op_f) = mult(x5,op_f),
introduced(tautology,[refl,[$fot(mult(x5,op_f))]]) ).
cnf(refute_0_57,plain,
( mult(x5,op_f) != mult(x5,op_f)
| op_f != op_c
| mult(x5,op_f) = mult(x5,op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x5,op_f),mult(x5,op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_58,plain,
( op_f != op_c
| mult(x5,op_f) = mult(x5,op_c) ),
inference(resolve,[$cnf( $equal(mult(x5,op_f),mult(x5,op_f)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
mult(x5,op_f) = mult(x5,op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( mult(x5,op_c) != mult(op_c,x5)
| mult(x5,op_f) != mult(x5,op_c)
| mult(x5,op_f) = mult(op_c,x5) ),
inference(subst,[],[refute_0_49:[bind(X,$fot(mult(x5,op_f))),bind(Y,$fot(mult(x5,op_c))),bind(Z,$fot(mult(op_c,x5)))]]) ).
cnf(refute_0_61,plain,
( mult(x5,op_c) != mult(op_c,x5)
| mult(x5,op_f) = mult(op_c,x5) ),
inference(resolve,[$cnf( $equal(mult(x5,op_f),mult(x5,op_c)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
mult(x5,op_f) = mult(op_c,x5),
inference(resolve,[$cnf( $equal(mult(x5,op_c),mult(op_c,x5)) )],[refute_0_30,refute_0_61]) ).
cnf(refute_0_63,plain,
mult(x4,mult(x5,op_f)) = mult(x4,mult(x5,op_f)),
introduced(tautology,[refl,[$fot(mult(x4,mult(x5,op_f)))]]) ).
cnf(refute_0_64,plain,
( mult(x4,mult(x5,op_f)) != mult(x4,mult(x5,op_f))
| mult(x5,op_f) != mult(op_c,x5)
| mult(x4,mult(x5,op_f)) = mult(x4,mult(op_c,x5)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(x4,mult(x5,op_f))) ),[1,1],$fot(mult(op_c,x5))]]) ).
cnf(refute_0_65,plain,
( mult(x5,op_f) != mult(op_c,x5)
| mult(x4,mult(x5,op_f)) = mult(x4,mult(op_c,x5)) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(x4,mult(x5,op_f))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
mult(x4,mult(x5,op_f)) = mult(x4,mult(op_c,x5)),
inference(resolve,[$cnf( $equal(mult(x5,op_f),mult(op_c,x5)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( mult(x4,mult(op_c,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(x5,op_f)) != mult(x4,mult(op_c,x5))
| mult(x4,mult(x5,op_f)) = mult(op_c,mult(x4,x5)) ),
inference(subst,[],[refute_0_49:[bind(X,$fot(mult(x4,mult(x5,op_f)))),bind(Y,$fot(mult(x4,mult(op_c,x5)))),bind(Z,$fot(mult(op_c,mult(x4,x5))))]]) ).
cnf(refute_0_68,plain,
( mult(x4,mult(op_c,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(x5,op_f)) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(x4,mult(op_c,x5))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
mult(x4,mult(x5,op_f)) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(x4,mult(op_c,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_29,refute_0_68]) ).
cnf(refute_0_70,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(x4,x5),op_f)
| mult(x4,mult(x5,op_f)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(x5,op_f)) = mult(mult(x4,x5),op_f) ),
introduced(tautology,[equality,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(op_c,mult(x4,x5))) ),[1],$fot(mult(mult(x4,x5),op_f))]]) ).
cnf(refute_0_71,plain,
( mult(op_c,mult(x4,x5)) != mult(mult(x4,x5),op_f)
| mult(x4,mult(x5,op_f)) = mult(mult(x4,x5),op_f) ),
inference(resolve,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(op_c,mult(x4,x5))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
mult(mult(x4,x5),op_c) = mult(op_c,mult(x4,x5)),
inference(subst,[],[refute_0_18:[bind(X_8,$fot(mult(x4,x5)))]]) ).
cnf(refute_0_73,plain,
mult(mult(x4,x5),op_f) = mult(mult(x4,x5),op_f),
introduced(tautology,[refl,[$fot(mult(mult(x4,x5),op_f))]]) ).
cnf(refute_0_74,plain,
( mult(mult(x4,x5),op_f) != mult(mult(x4,x5),op_f)
| op_f != op_c
| mult(mult(x4,x5),op_f) = mult(mult(x4,x5),op_c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(x4,x5),op_f),mult(mult(x4,x5),op_f)) ),[1,1],$fot(op_c)]]) ).
cnf(refute_0_75,plain,
( op_f != op_c
| mult(mult(x4,x5),op_f) = mult(mult(x4,x5),op_c) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,x5),op_f),mult(mult(x4,x5),op_f)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
mult(mult(x4,x5),op_f) = mult(mult(x4,x5),op_c),
inference(resolve,[$cnf( $equal(op_f,op_c) )],[refute_0_55,refute_0_75]) ).
cnf(refute_0_77,plain,
( mult(mult(x4,x5),op_c) != mult(op_c,mult(x4,x5))
| mult(mult(x4,x5),op_f) != mult(mult(x4,x5),op_c)
| mult(mult(x4,x5),op_f) = mult(op_c,mult(x4,x5)) ),
inference(subst,[],[refute_0_49:[bind(X,$fot(mult(mult(x4,x5),op_f))),bind(Y,$fot(mult(mult(x4,x5),op_c))),bind(Z,$fot(mult(op_c,mult(x4,x5))))]]) ).
cnf(refute_0_78,plain,
( mult(mult(x4,x5),op_c) != mult(op_c,mult(x4,x5))
| mult(mult(x4,x5),op_f) = mult(op_c,mult(x4,x5)) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,x5),op_f),mult(mult(x4,x5),op_c)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
mult(mult(x4,x5),op_f) = mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(mult(x4,x5),op_c),mult(op_c,mult(x4,x5))) )],[refute_0_72,refute_0_78]) ).
cnf(refute_0_80,plain,
( mult(mult(x4,x5),op_f) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(x4,x5),op_f) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(op_c,mult(x4,x5)),mult(mult(x4,x5),op_f)) ),[1],$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_81,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(op_c,mult(x4,x5)) = mult(mult(x4,x5),op_f) ),
inference(resolve,[$cnf( $equal(mult(mult(x4,x5),op_f),mult(op_c,mult(x4,x5))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5))
| mult(x4,mult(x5,op_f)) = mult(mult(x4,x5),op_f) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(mult(x4,x5),op_f)) )],[refute_0_81,refute_0_71]) ).
cnf(refute_0_83,plain,
mult(op_c,mult(x4,x5)) != mult(op_c,mult(x4,x5)),
inference(resolve,[$cnf( $equal(mult(x4,mult(x5,op_f)),mult(mult(x4,x5),op_f)) )],[refute_0_82,goal]) ).
cnf(refute_0_84,plain,
mult(op_c,mult(x4,x5)) = mult(op_c,mult(x4,x5)),
introduced(tautology,[refl,[$fot(mult(op_c,mult(x4,x5)))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(mult(op_c,mult(x4,x5)),mult(op_c,mult(x4,x5))) )],[refute_0_84,refute_0_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP704-11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.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 : Tue Jun 14 05:54:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.38
% 0.20/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40
%------------------------------------------------------------------------------