TSTP Solution File: GRP698-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP698-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 10:50:02 EDT 2022
% Result : Unsatisfiable 4.24s 4.41s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 32
% Syntax : Number of clauses : 90 ( 50 unt; 0 nHn; 49 RR)
% Number of literals : 150 ( 149 equ; 62 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(A,ld(A,B)) = B ).
cnf(c02,axiom,
ld(A,mult(A,B)) = B ).
cnf(c03,axiom,
mult(rd(A,B),B) = A ).
cnf(c05,axiom,
mult(A,unit) = A ).
cnf(c07,axiom,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)) ).
cnf(refute_0_0,plain,
ld(a,mult(a,b)) = b,
inference(subst,[],[c02:[bind(A,$fot(a)),bind(B,$fot(b))]]) ).
cnf(refute_0_1,plain,
mult(ld(a,mult(a,b)),c) = mult(ld(a,mult(a,b)),c),
introduced(tautology,[refl,[$fot(mult(ld(a,mult(a,b)),c))]]) ).
cnf(refute_0_2,plain,
( ld(a,mult(a,b)) != b
| mult(ld(a,mult(a,b)),c) != mult(ld(a,mult(a,b)),c)
| mult(ld(a,mult(a,b)),c) = mult(b,c) ),
introduced(tautology,[equality,[$cnf( $equal(mult(ld(a,mult(a,b)),c),mult(ld(a,mult(a,b)),c)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_3,plain,
( ld(a,mult(a,b)) != b
| mult(ld(a,mult(a,b)),c) = mult(b,c) ),
inference(resolve,[$cnf( $equal(mult(ld(a,mult(a,b)),c),mult(ld(a,mult(a,b)),c)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(ld(a,mult(a,b)),c) = mult(b,c),
inference(resolve,[$cnf( $equal(ld(a,mult(a,b)),b) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(a,mult(ld(a,mult(a,b)),c)) = mult(a,mult(ld(a,mult(a,b)),c)),
introduced(tautology,[refl,[$fot(mult(a,mult(ld(a,mult(a,b)),c)))]]) ).
cnf(refute_0_6,plain,
( mult(a,mult(ld(a,mult(a,b)),c)) != mult(a,mult(ld(a,mult(a,b)),c))
| mult(ld(a,mult(a,b)),c) != mult(b,c)
| mult(a,mult(ld(a,mult(a,b)),c)) = mult(a,mult(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(a,mult(ld(a,mult(a,b)),c)),mult(a,mult(ld(a,mult(a,b)),c))) ),[1,1],$fot(mult(b,c))]]) ).
cnf(refute_0_7,plain,
( mult(ld(a,mult(a,b)),c) != mult(b,c)
| mult(a,mult(ld(a,mult(a,b)),c)) = mult(a,mult(b,c)) ),
inference(resolve,[$cnf( $equal(mult(a,mult(ld(a,mult(a,b)),c)),mult(a,mult(ld(a,mult(a,b)),c))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
mult(a,mult(ld(a,mult(a,b)),c)) = mult(a,mult(b,c)),
inference(resolve,[$cnf( $equal(mult(ld(a,mult(a,b)),c),mult(b,c)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
mult(mult(mult(X_18,ld(X_18,B)),X_18),mult(X_18,X_20)) = mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),
inference(subst,[],[c07:[bind(A,$fot(X_18)),bind(B,$fot(ld(X_18,B))),bind(C,$fot(X_20))]]) ).
cnf(refute_0_10,plain,
mult(X_18,ld(X_18,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(X_18))]]) ).
cnf(refute_0_11,plain,
( mult(X_18,ld(X_18,B)) != B
| mult(mult(mult(X_18,ld(X_18,B)),X_18),mult(X_18,X_20)) != mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))
| mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_18,ld(X_18,B)),X_18),mult(X_18,X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) ),[0,0,0],$fot(B)]]) ).
cnf(refute_0_12,plain,
( mult(mult(mult(X_18,ld(X_18,B)),X_18),mult(X_18,X_20)) != mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))
| mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) ),
inference(resolve,[$cnf( $equal(mult(X_18,ld(X_18,B)),B) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,ld(X_18,B)),X_18),mult(X_18,X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
ld(A,mult(A,mult(mult(ld(A,X_37),A),A))) = mult(mult(ld(A,X_37),A),A),
inference(subst,[],[c02:[bind(B,$fot(mult(mult(ld(A,X_37),A),A)))]]) ).
cnf(refute_0_15,plain,
mult(mult(mult(X_18,X_19),X_18),mult(X_18,unit)) = mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),
inference(subst,[],[c07:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(unit))]]) ).
cnf(refute_0_16,plain,
mult(X_18,unit) = X_18,
inference(subst,[],[c05:[bind(A,$fot(X_18))]]) ).
cnf(refute_0_17,plain,
( mult(X_18,unit) != X_18
| mult(mult(mult(X_18,X_19),X_18),mult(X_18,unit)) != mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))
| mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),mult(X_18,unit)),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) ),[0,1],$fot(X_18)]]) ).
cnf(refute_0_18,plain,
( mult(mult(mult(X_18,X_19),X_18),mult(X_18,unit)) != mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))
| mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) ),
inference(resolve,[$cnf( $equal(mult(X_18,unit),X_18) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),mult(X_18,unit)),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(mult(mult(X_19,X_18),X_18),unit) = mult(mult(X_19,X_18),X_18),
inference(subst,[],[c05:[bind(A,$fot(mult(mult(X_19,X_18),X_18)))]]) ).
cnf(refute_0_21,plain,
mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) = mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),
introduced(tautology,[refl,[$fot(mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)))]]) ).
cnf(refute_0_22,plain,
( mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) != mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))
| mult(mult(mult(X_19,X_18),X_18),unit) != mult(mult(X_19,X_18),X_18)
| mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) = mult(X_18,mult(mult(X_19,X_18),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) ),[1,1],$fot(mult(mult(X_19,X_18),X_18))]]) ).
cnf(refute_0_23,plain,
( mult(mult(mult(X_19,X_18),X_18),unit) != mult(mult(X_19,X_18),X_18)
| mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) = mult(X_18,mult(mult(X_19,X_18),X_18)) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) = mult(X_18,mult(mult(X_19,X_18),X_18)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_19,X_18),X_18),unit),mult(mult(X_19,X_18),X_18)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)) != mult(X_18,mult(mult(X_19,X_18),X_18))
| mult(mult(mult(X_18,X_19),X_18),X_18) != mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))
| mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(X_19,X_18),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),X_18),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) ),[1],$fot(mult(X_18,mult(mult(X_19,X_18),X_18)))]]) ).
cnf(refute_0_26,plain,
( mult(mult(mult(X_18,X_19),X_18),X_18) != mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))
| mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(X_19,X_18),X_18)) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit)),mult(X_18,mult(mult(X_19,X_18),X_18))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
mult(mult(mult(X_18,X_19),X_18),X_18) = mult(X_18,mult(mult(X_19,X_18),X_18)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),X_18),mult(X_18,mult(mult(mult(X_19,X_18),X_18),unit))) )],[refute_0_19,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(mult(mult(X_21,ld(X_21,B)),X_21),X_21) = mult(X_21,mult(mult(ld(X_21,B),X_21),X_21)),
inference(subst,[],[refute_0_27:[bind(X_18,$fot(X_21)),bind(X_19,$fot(ld(X_21,B)))]]) ).
cnf(refute_0_29,plain,
mult(X_21,ld(X_21,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_30,plain,
( mult(X_21,ld(X_21,B)) != B
| mult(mult(mult(X_21,ld(X_21,B)),X_21),X_21) != mult(X_21,mult(mult(ld(X_21,B),X_21),X_21))
| mult(mult(B,X_21),X_21) = mult(X_21,mult(mult(ld(X_21,B),X_21),X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_21,ld(X_21,B)),X_21),X_21),mult(X_21,mult(mult(ld(X_21,B),X_21),X_21))) ),[0,0,0],$fot(B)]]) ).
cnf(refute_0_31,plain,
( mult(mult(mult(X_21,ld(X_21,B)),X_21),X_21) != mult(X_21,mult(mult(ld(X_21,B),X_21),X_21))
| mult(mult(B,X_21),X_21) = mult(X_21,mult(mult(ld(X_21,B),X_21),X_21)) ),
inference(resolve,[$cnf( $equal(mult(X_21,ld(X_21,B)),B) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(mult(B,X_21),X_21) = mult(X_21,mult(mult(ld(X_21,B),X_21),X_21)),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_21,ld(X_21,B)),X_21),X_21),mult(X_21,mult(mult(ld(X_21,B),X_21),X_21))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(mult(X_37,A),A) = mult(A,mult(mult(ld(A,X_37),A),A)),
inference(subst,[],[refute_0_32:[bind(B,$fot(X_37)),bind(X_21,$fot(A))]]) ).
cnf(refute_0_34,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( mult(mult(X_37,A),A) != mult(A,mult(mult(ld(A,X_37),A),A))
| mult(A,mult(mult(ld(A,X_37),A),A)) = mult(mult(X_37,A),A) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(mult(mult(X_37,A),A))),bind(Y,$fot(mult(A,mult(mult(ld(A,X_37),A),A))))]]) ).
cnf(refute_0_38,plain,
mult(A,mult(mult(ld(A,X_37),A),A)) = mult(mult(X_37,A),A),
inference(resolve,[$cnf( $equal(mult(mult(X_37,A),A),mult(A,mult(mult(ld(A,X_37),A),A))) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( ld(A,mult(A,mult(mult(ld(A,X_37),A),A))) != mult(mult(ld(A,X_37),A),A)
| mult(A,mult(mult(ld(A,X_37),A),A)) != mult(mult(X_37,A),A)
| ld(A,mult(mult(X_37,A),A)) = mult(mult(ld(A,X_37),A),A) ),
introduced(tautology,[equality,[$cnf( $equal(ld(A,mult(A,mult(mult(ld(A,X_37),A),A))),mult(mult(ld(A,X_37),A),A)) ),[0,1],$fot(mult(mult(X_37,A),A))]]) ).
cnf(refute_0_40,plain,
( ld(A,mult(A,mult(mult(ld(A,X_37),A),A))) != mult(mult(ld(A,X_37),A),A)
| ld(A,mult(mult(X_37,A),A)) = mult(mult(ld(A,X_37),A),A) ),
inference(resolve,[$cnf( $equal(mult(A,mult(mult(ld(A,X_37),A),A)),mult(mult(X_37,A),A)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
ld(A,mult(mult(X_37,A),A)) = mult(mult(ld(A,X_37),A),A),
inference(resolve,[$cnf( $equal(ld(A,mult(A,mult(mult(ld(A,X_37),A),A))),mult(mult(ld(A,X_37),A),A)) )],[refute_0_14,refute_0_40]) ).
cnf(refute_0_42,plain,
( ld(A,mult(mult(X_37,A),A)) != mult(mult(ld(A,X_37),A),A)
| mult(mult(ld(A,X_37),A),A) = ld(A,mult(mult(X_37,A),A)) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(ld(A,mult(mult(X_37,A),A)))),bind(Y,$fot(mult(mult(ld(A,X_37),A),A)))]]) ).
cnf(refute_0_43,plain,
mult(mult(ld(A,X_37),A),A) = ld(A,mult(mult(X_37,A),A)),
inference(resolve,[$cnf( $equal(ld(A,mult(mult(X_37,A),A)),mult(mult(ld(A,X_37),A),A)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(mult(ld(X_18,B),X_18),X_18) = ld(X_18,mult(mult(B,X_18),X_18)),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_18)),bind(X_37,$fot(B))]]) ).
cnf(refute_0_45,plain,
mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) = mult(mult(mult(ld(X_18,B),X_18),X_18),X_20),
introduced(tautology,[refl,[$fot(mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))]]) ).
cnf(refute_0_46,plain,
( mult(mult(ld(X_18,B),X_18),X_18) != ld(X_18,mult(mult(B,X_18),X_18))
| mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) != mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)
| mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) = mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(ld(X_18,B),X_18),X_18),X_20),mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) ),[1,0],$fot(ld(X_18,mult(mult(B,X_18),X_18)))]]) ).
cnf(refute_0_47,plain,
( mult(mult(ld(X_18,B),X_18),X_18) != ld(X_18,mult(mult(B,X_18),X_18))
| mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) = mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(ld(X_18,B),X_18),X_18),X_20),mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) = mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20),
inference(resolve,[$cnf( $equal(mult(mult(ld(X_18,B),X_18),X_18),ld(X_18,mult(mult(B,X_18),X_18))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) = mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),
introduced(tautology,[refl,[$fot(mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)))]]) ).
cnf(refute_0_50,plain,
( mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) != mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))
| mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) != mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)
| mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) ),[1,1],$fot(mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20))]]) ).
cnf(refute_0_51,plain,
( mult(mult(mult(ld(X_18,B),X_18),X_18),X_20) != mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)
| mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)),
inference(resolve,[$cnf( $equal(mult(mult(mult(ld(X_18,B),X_18),X_18),X_20),mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)) != mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20))
| mult(mult(B,X_18),mult(X_18,X_20)) != mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))
| mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(B,X_18),mult(X_18,X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) ),[1],$fot(mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)))]]) ).
cnf(refute_0_54,plain,
( mult(mult(B,X_18),mult(X_18,X_20)) != mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))
| mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20)),mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
mult(mult(B,X_18),mult(X_18,X_20)) = mult(X_18,mult(ld(X_18,mult(mult(B,X_18),X_18)),X_20)),
inference(resolve,[$cnf( $equal(mult(mult(B,X_18),mult(X_18,X_20)),mult(X_18,mult(mult(mult(ld(X_18,B),X_18),X_18),X_20))) )],[refute_0_13,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(mult(rd(A,X_154),X_154),X_154)),X_155)),
inference(subst,[],[refute_0_55:[bind(B,$fot(rd(A,X_154))),bind(X_18,$fot(X_154)),bind(X_20,$fot(X_155))]]) ).
cnf(refute_0_57,plain,
mult(rd(A,X_154),X_154) = A,
inference(subst,[],[c03:[bind(B,$fot(X_154))]]) ).
cnf(refute_0_58,plain,
( mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(X_154,mult(ld(X_154,mult(mult(rd(A,X_154),X_154),X_154)),X_155))
| mult(rd(A,X_154),X_154) != A
| mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(X_154,mult(ld(X_154,mult(mult(rd(A,X_154),X_154),X_154)),X_155))) ),[1,1,0,1,0],$fot(A)]]) ).
cnf(refute_0_59,plain,
( mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(X_154,mult(ld(X_154,mult(mult(rd(A,X_154),X_154),X_154)),X_155))
| mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_154),X_154),A) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(X_154,mult(ld(X_154,mult(mult(rd(A,X_154),X_154),X_154)),X_155))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),
introduced(tautology,[refl,[$fot(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)))]]) ).
cnf(refute_0_62,plain,
( mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(mult(rd(A,X_154),X_154),mult(X_154,X_155))
| mult(rd(A,X_154),X_154) != A
| mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(A,mult(X_154,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(mult(rd(A,X_154),X_154),mult(X_154,X_155))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_63,plain,
( mult(rd(A,X_154),X_154) != A
| mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(A,mult(X_154,X_155)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(mult(rd(A,X_154),X_154),mult(X_154,X_155))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) = mult(A,mult(X_154,X_155)),
inference(resolve,[$cnf( $equal(mult(rd(A,X_154),X_154),A) )],[refute_0_57,refute_0_63]) ).
cnf(refute_0_65,plain,
( mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(A,mult(X_154,X_155))
| mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155))
| mult(A,mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155))) ),[0],$fot(mult(A,mult(X_154,X_155)))]]) ).
cnf(refute_0_66,plain,
( mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)) != mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155))
| mult(A,mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)) ),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(A,mult(X_154,X_155))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
mult(A,mult(X_154,X_155)) = mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155)),
inference(resolve,[$cnf( $equal(mult(mult(rd(A,X_154),X_154),mult(X_154,X_155)),mult(X_154,mult(ld(X_154,mult(A,X_154)),X_155))) )],[refute_0_60,refute_0_66]) ).
cnf(refute_0_68,plain,
mult(rd(A,X_251),mult(X_251,X_252)) = mult(X_251,mult(ld(X_251,mult(rd(A,X_251),X_251)),X_252)),
inference(subst,[],[refute_0_67:[bind(A,$fot(rd(A,X_251))),bind(X_154,$fot(X_251)),bind(X_155,$fot(X_252))]]) ).
cnf(refute_0_69,plain,
mult(rd(A,X_251),X_251) = A,
inference(subst,[],[c03:[bind(B,$fot(X_251))]]) ).
cnf(refute_0_70,plain,
( mult(rd(A,X_251),X_251) != A
| mult(rd(A,X_251),mult(X_251,X_252)) != mult(X_251,mult(ld(X_251,mult(rd(A,X_251),X_251)),X_252))
| mult(rd(A,X_251),mult(X_251,X_252)) = mult(X_251,mult(ld(X_251,A),X_252)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(A,X_251),mult(X_251,X_252)),mult(X_251,mult(ld(X_251,mult(rd(A,X_251),X_251)),X_252))) ),[1,1,0,1],$fot(A)]]) ).
cnf(refute_0_71,plain,
( mult(rd(A,X_251),mult(X_251,X_252)) != mult(X_251,mult(ld(X_251,mult(rd(A,X_251),X_251)),X_252))
| mult(rd(A,X_251),mult(X_251,X_252)) = mult(X_251,mult(ld(X_251,A),X_252)) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_251),X_251),A) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
mult(rd(A,X_251),mult(X_251,X_252)) = mult(X_251,mult(ld(X_251,A),X_252)),
inference(resolve,[$cnf( $equal(mult(rd(A,X_251),mult(X_251,X_252)),mult(X_251,mult(ld(X_251,mult(rd(A,X_251),X_251)),X_252))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(rd(mult(a,b),a),mult(a,c)) = mult(a,mult(ld(a,mult(a,b)),c)),
inference(subst,[],[refute_0_72:[bind(A,$fot(mult(a,b))),bind(X_251,$fot(a)),bind(X_252,$fot(c))]]) ).
cnf(refute_0_74,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_75,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_36,refute_0_74]) ).
cnf(refute_0_76,plain,
( mult(a,mult(ld(a,mult(a,b)),c)) != mult(a,mult(b,c))
| mult(rd(mult(a,b),a),mult(a,c)) != mult(a,mult(ld(a,mult(a,b)),c))
| mult(rd(mult(a,b),a),mult(a,c)) = mult(a,mult(b,c)) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(mult(rd(mult(a,b),a),mult(a,c)))),bind(Y,$fot(mult(a,mult(ld(a,mult(a,b)),c)))),bind(Z,$fot(mult(a,mult(b,c))))]]) ).
cnf(refute_0_77,plain,
( mult(a,mult(ld(a,mult(a,b)),c)) != mult(a,mult(b,c))
| mult(rd(mult(a,b),a),mult(a,c)) = mult(a,mult(b,c)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(a,b),a),mult(a,c)),mult(a,mult(ld(a,mult(a,b)),c))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
mult(rd(mult(a,b),a),mult(a,c)) = mult(a,mult(b,c)),
inference(resolve,[$cnf( $equal(mult(a,mult(ld(a,mult(a,b)),c)),mult(a,mult(b,c))) )],[refute_0_8,refute_0_77]) ).
cnf(refute_0_79,plain,
( mult(a,mult(b,c)) != mult(a,mult(b,c))
| mult(rd(mult(a,b),a),mult(a,c)) != mult(a,mult(b,c))
| mult(a,mult(b,c)) = mult(rd(mult(a,b),a),mult(a,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(a,mult(b,c)),mult(rd(mult(a,b),a),mult(a,c))) ),[1],$fot(mult(a,mult(b,c)))]]) ).
cnf(refute_0_80,plain,
( mult(a,mult(b,c)) != mult(a,mult(b,c))
| mult(a,mult(b,c)) = mult(rd(mult(a,b),a),mult(a,c)) ),
inference(resolve,[$cnf( $equal(mult(rd(mult(a,b),a),mult(a,c)),mult(a,mult(b,c))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(resolve,[$cnf( $equal(mult(a,mult(b,c)),mult(rd(mult(a,b),a),mult(a,c))) )],[refute_0_80,goals]) ).
cnf(refute_0_82,plain,
mult(a,mult(b,c)) = mult(a,mult(b,c)),
introduced(tautology,[refl,[$fot(mult(a,mult(b,c)))]]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( $equal(mult(a,mult(b,c)),mult(a,mult(b,c))) )],[refute_0_82,refute_0_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP698-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 09:35:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.24/4.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.24/4.41
% 4.24/4.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.24/4.42
%------------------------------------------------------------------------------