%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 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 10:44:52 EDT 2022
% Result : Unsatisfiable 3.76s 3.97s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of clauses : 90 ( 52 unt; 0 nHn; 44 RR)
% Number of literals : 146 ( 145 equ; 59 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(A,ld(A,B)) = B ).
cnf(c02,axiom,
ld(A,mult(A,B)) = B ).
cnf(c05,axiom,
mult(A,unit) = A ).
cnf(c07,axiom,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ).
cnf(c08,axiom,
mult(i(A),mult(A,B)) = B ).
cnf(c09,axiom,
mult(op_c,A) = mult(A,op_c) ).
cnf(goals,negated_conjecture,
mult(i(op_c),a) != mult(a,i(op_c)) ).
cnf(refute_0_0,plain,
mult(i(A),mult(A,ld(A,X_9))) = ld(A,X_9),
inference(subst,[],[c08:[bind(B,$fot(ld(A,X_9)))]]) ).
cnf(refute_0_1,plain,
mult(A,ld(A,X_9)) = X_9,
inference(subst,[],[c01:[bind(B,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( mult(A,ld(A,X_9)) != X_9
| mult(i(A),mult(A,ld(A,X_9))) != ld(A,X_9)
| mult(i(A),X_9) = ld(A,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(A),mult(A,ld(A,X_9))),ld(A,X_9)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_3,plain,
( mult(i(A),mult(A,ld(A,X_9))) != ld(A,X_9)
| mult(i(A),X_9) = ld(A,X_9) ),
inference(resolve,[$cnf( $equal(mult(A,ld(A,X_9)),X_9) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(i(A),X_9) = ld(A,X_9),
inference(resolve,[$cnf( $equal(mult(i(A),mult(A,ld(A,X_9))),ld(A,X_9)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(i(op_c),a) = ld(op_c,a),
inference(subst,[],[refute_0_4:[bind(A,$fot(op_c)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_6,plain,
( ld(op_c,a) != mult(a,i(op_c))
| mult(i(op_c),a) != ld(op_c,a)
| mult(i(op_c),a) = mult(a,i(op_c)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(op_c),a),ld(op_c,a)) ),[1],$fot(mult(a,i(op_c)))]]) ).
cnf(refute_0_7,plain,
( ld(op_c,a) != mult(a,i(op_c))
| mult(i(op_c),a) = mult(a,i(op_c)) ),
inference(resolve,[$cnf( $equal(mult(i(op_c),a),ld(op_c,a)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
ld(op_c,a) != mult(a,i(op_c)),
inference(resolve,[$cnf( $equal(mult(i(op_c),a),mult(a,i(op_c))) )],[refute_0_7,goals]) ).
cnf(refute_0_9,plain,
mult(mult(op_c,B),ld(mult(op_c,B),B)) = B,
inference(subst,[],[c01:[bind(A,$fot(mult(op_c,B)))]]) ).
cnf(refute_0_10,plain,
ld(mult(X_59,mult(X_60,X_59)),mult(mult(X_59,mult(X_60,X_59)),B)) = B,
inference(subst,[],[c02:[bind(A,$fot(mult(X_59,mult(X_60,X_59))))]]) ).
cnf(refute_0_11,plain,
mult(X_59,mult(X_60,mult(X_59,B))) = mult(mult(X_59,mult(X_60,X_59)),B),
inference(subst,[],[c07:[bind(A,$fot(X_59)),bind(B,$fot(X_60)),bind(C,$fot(B))]]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( mult(X_59,mult(X_60,mult(X_59,B))) != mult(mult(X_59,mult(X_60,X_59)),B)
| mult(mult(X_59,mult(X_60,X_59)),B) = mult(X_59,mult(X_60,mult(X_59,B))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(mult(X_59,mult(X_60,mult(X_59,B))))),bind(Y,$fot(mult(mult(X_59,mult(X_60,X_59)),B)))]]) ).
cnf(refute_0_16,plain,
mult(mult(X_59,mult(X_60,X_59)),B) = mult(X_59,mult(X_60,mult(X_59,B))),
inference(resolve,[$cnf( $equal(mult(X_59,mult(X_60,mult(X_59,B))),mult(mult(X_59,mult(X_60,X_59)),B)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( ld(mult(X_59,mult(X_60,X_59)),mult(mult(X_59,mult(X_60,X_59)),B)) != B
| mult(mult(X_59,mult(X_60,X_59)),B) != mult(X_59,mult(X_60,mult(X_59,B)))
| ld(mult(X_59,mult(X_60,X_59)),mult(X_59,mult(X_60,mult(X_59,B)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_59,mult(X_60,X_59)),mult(mult(X_59,mult(X_60,X_59)),B)),B) ),[0,1],$fot(mult(X_59,mult(X_60,mult(X_59,B))))]]) ).
cnf(refute_0_18,plain,
( ld(mult(X_59,mult(X_60,X_59)),mult(mult(X_59,mult(X_60,X_59)),B)) != B
| ld(mult(X_59,mult(X_60,X_59)),mult(X_59,mult(X_60,mult(X_59,B)))) = B ),
inference(resolve,[$cnf( $equal(mult(mult(X_59,mult(X_60,X_59)),B),mult(X_59,mult(X_60,mult(X_59,B)))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
ld(mult(X_59,mult(X_60,X_59)),mult(X_59,mult(X_60,mult(X_59,B)))) = B,
inference(resolve,[$cnf( $equal(ld(mult(X_59,mult(X_60,X_59)),mult(mult(X_59,mult(X_60,X_59)),B)),B) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,mult(X_180,i(X_180))))) = i(X_180),
inference(subst,[],[refute_0_19:[bind(B,$fot(i(X_180))),bind(X_59,$fot(X_180)),bind(X_60,$fot(X_181))]]) ).
cnf(refute_0_21,plain,
mult(A,ld(A,unit)) = unit,
inference(subst,[],[c01:[bind(B,$fot(unit))]]) ).
cnf(refute_0_22,plain,
mult(i(X_31),unit) = i(X_31),
inference(subst,[],[c05:[bind(A,$fot(i(X_31)))]]) ).
cnf(refute_0_23,plain,
mult(i(X_31),unit) = ld(X_31,unit),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_31)),bind(X_9,$fot(unit))]]) ).
cnf(refute_0_24,plain,
( mult(i(X_31),unit) != i(X_31)
| mult(i(X_31),unit) != ld(X_31,unit)
| ld(X_31,unit) = i(X_31) ),
introduced(tautology,[equality,[$cnf( $equal(mult(i(X_31),unit),i(X_31)) ),[0],$fot(ld(X_31,unit))]]) ).
cnf(refute_0_25,plain,
( mult(i(X_31),unit) != i(X_31)
| ld(X_31,unit) = i(X_31) ),
inference(resolve,[$cnf( $equal(mult(i(X_31),unit),ld(X_31,unit)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
ld(X_31,unit) = i(X_31),
inference(resolve,[$cnf( $equal(mult(i(X_31),unit),i(X_31)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
ld(A,unit) = i(A),
inference(subst,[],[refute_0_26:[bind(X_31,$fot(A))]]) ).
cnf(refute_0_28,plain,
( ld(A,unit) != i(A)
| mult(A,ld(A,unit)) != unit
| mult(A,i(A)) = unit ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,ld(A,unit)),unit) ),[0,1],$fot(i(A))]]) ).
cnf(refute_0_29,plain,
( mult(A,ld(A,unit)) != unit
| mult(A,i(A)) = unit ),
inference(resolve,[$cnf( $equal(ld(A,unit),i(A)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
mult(A,i(A)) = unit,
inference(resolve,[$cnf( $equal(mult(A,ld(A,unit)),unit) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(X_180,i(X_180)) = unit,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_180))]]) ).
cnf(refute_0_32,plain,
( ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,mult(X_180,i(X_180))))) != i(X_180)
| mult(X_180,i(X_180)) != unit
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = i(X_180) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,mult(X_180,i(X_180))))),i(X_180)) ),[0,1,1,1],$fot(unit)]]) ).
cnf(refute_0_33,plain,
( ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,mult(X_180,i(X_180))))) != i(X_180)
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = i(X_180) ),
inference(resolve,[$cnf( $equal(mult(X_180,i(X_180)),unit) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = i(X_180),
inference(resolve,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,mult(X_180,i(X_180))))),i(X_180)) )],[refute_0_20,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(X_181,unit) = X_181,
inference(subst,[],[c05:[bind(A,$fot(X_181))]]) ).
cnf(refute_0_36,plain,
mult(X_180,mult(X_181,unit)) = mult(X_180,mult(X_181,unit)),
introduced(tautology,[refl,[$fot(mult(X_180,mult(X_181,unit)))]]) ).
cnf(refute_0_37,plain,
( mult(X_180,mult(X_181,unit)) != mult(X_180,mult(X_181,unit))
| mult(X_181,unit) != X_181
| mult(X_180,mult(X_181,unit)) = mult(X_180,X_181) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_180,mult(X_181,unit)),mult(X_180,mult(X_181,unit))) ),[1,1],$fot(X_181)]]) ).
cnf(refute_0_38,plain,
( mult(X_181,unit) != X_181
| mult(X_180,mult(X_181,unit)) = mult(X_180,X_181) ),
inference(resolve,[$cnf( $equal(mult(X_180,mult(X_181,unit)),mult(X_180,mult(X_181,unit))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
mult(X_180,mult(X_181,unit)) = mult(X_180,X_181),
inference(resolve,[$cnf( $equal(mult(X_181,unit),X_181) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),
introduced(tautology,[refl,[$fot(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))))]]) ).
cnf(refute_0_41,plain,
( ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) != ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit)))
| mult(X_180,mult(X_181,unit)) != mult(X_180,X_181)
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit)))) ),[1,1],$fot(mult(X_180,X_181))]]) ).
cnf(refute_0_42,plain,
( mult(X_180,mult(X_181,unit)) != mult(X_180,X_181)
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)) ),
inference(resolve,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) = ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)),
inference(resolve,[$cnf( $equal(mult(X_180,mult(X_181,unit)),mult(X_180,X_181)) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) != i(X_180)
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) != ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181))
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)) = i(X_180) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),i(X_180)) ),[0],$fot(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)))]]) ).
cnf(refute_0_45,plain,
( ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))) != i(X_180)
| ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)) = i(X_180) ),
inference(resolve,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
ld(mult(X_180,mult(X_181,X_180)),mult(X_180,X_181)) = i(X_180),
inference(resolve,[$cnf( $equal(ld(mult(X_180,mult(X_181,X_180)),mult(X_180,mult(X_181,unit))),i(X_180)) )],[refute_0_34,refute_0_45]) ).
cnf(refute_0_47,plain,
ld(mult(op_c,mult(X_204,op_c)),mult(op_c,X_204)) = i(op_c),
inference(subst,[],[refute_0_46:[bind(X_180,$fot(op_c)),bind(X_181,$fot(X_204))]]) ).
cnf(refute_0_48,plain,
mult(op_c,X_204) = mult(X_204,op_c),
inference(subst,[],[c09:[bind(A,$fot(X_204))]]) ).
cnf(refute_0_49,plain,
( mult(op_c,X_204) != mult(X_204,op_c)
| mult(X_204,op_c) = mult(op_c,X_204) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(mult(op_c,X_204))),bind(Y,$fot(mult(X_204,op_c)))]]) ).
cnf(refute_0_50,plain,
mult(X_204,op_c) = mult(op_c,X_204),
inference(resolve,[$cnf( $equal(mult(op_c,X_204),mult(X_204,op_c)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( ld(mult(op_c,mult(X_204,op_c)),mult(op_c,X_204)) != i(op_c)
| mult(X_204,op_c) != mult(op_c,X_204)
| ld(mult(op_c,mult(op_c,X_204)),mult(op_c,X_204)) = i(op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(op_c,mult(X_204,op_c)),mult(op_c,X_204)),i(op_c)) ),[0,0,1],$fot(mult(op_c,X_204))]]) ).
cnf(refute_0_52,plain,
( ld(mult(op_c,mult(X_204,op_c)),mult(op_c,X_204)) != i(op_c)
| ld(mult(op_c,mult(op_c,X_204)),mult(op_c,X_204)) = i(op_c) ),
inference(resolve,[$cnf( $equal(mult(X_204,op_c),mult(op_c,X_204)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ld(mult(op_c,mult(op_c,X_204)),mult(op_c,X_204)) = i(op_c),
inference(resolve,[$cnf( $equal(ld(mult(op_c,mult(X_204,op_c)),mult(op_c,X_204)),i(op_c)) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
ld(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,ld(op_c,B))) = i(op_c),
inference(subst,[],[refute_0_53:[bind(X_204,$fot(ld(op_c,B)))]]) ).
cnf(refute_0_55,plain,
mult(op_c,ld(op_c,B)) = B,
inference(subst,[],[c01:[bind(A,$fot(op_c))]]) ).
cnf(refute_0_56,plain,
( ld(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,ld(op_c,B))) != i(op_c)
| mult(op_c,ld(op_c,B)) != B
| ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = i(op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,ld(op_c,B))),i(op_c)) ),[0,1],$fot(B)]]) ).
cnf(refute_0_57,plain,
( ld(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,ld(op_c,B))) != i(op_c)
| ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = i(op_c) ),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,B)),B) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = i(op_c),
inference(resolve,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,ld(op_c,B))),i(op_c)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
mult(op_c,mult(op_c,ld(op_c,B))) = mult(op_c,mult(op_c,ld(op_c,B))),
introduced(tautology,[refl,[$fot(mult(op_c,mult(op_c,ld(op_c,B))))]]) ).
cnf(refute_0_60,plain,
( mult(op_c,ld(op_c,B)) != B
| mult(op_c,mult(op_c,ld(op_c,B))) != mult(op_c,mult(op_c,ld(op_c,B)))
| mult(op_c,mult(op_c,ld(op_c,B))) = mult(op_c,B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,mult(op_c,ld(op_c,B)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_61,plain,
( mult(op_c,ld(op_c,B)) != B
| mult(op_c,mult(op_c,ld(op_c,B))) = mult(op_c,B) ),
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,mult(op_c,ld(op_c,B)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
mult(op_c,mult(op_c,ld(op_c,B))) = mult(op_c,B),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,B)),B) )],[refute_0_55,refute_0_61]) ).
cnf(refute_0_63,plain,
ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = ld(mult(op_c,mult(op_c,ld(op_c,B))),B),
introduced(tautology,[refl,[$fot(ld(mult(op_c,mult(op_c,ld(op_c,B))),B))]]) ).
cnf(refute_0_64,plain,
( ld(mult(op_c,mult(op_c,ld(op_c,B))),B) != ld(mult(op_c,mult(op_c,ld(op_c,B))),B)
| mult(op_c,mult(op_c,ld(op_c,B))) != mult(op_c,B)
| ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = ld(mult(op_c,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),B),ld(mult(op_c,mult(op_c,ld(op_c,B))),B)) ),[1,0],$fot(mult(op_c,B))]]) ).
cnf(refute_0_65,plain,
( mult(op_c,mult(op_c,ld(op_c,B))) != mult(op_c,B)
| ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = ld(mult(op_c,B),B) ),
inference(resolve,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),B),ld(mult(op_c,mult(op_c,ld(op_c,B))),B)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
ld(mult(op_c,mult(op_c,ld(op_c,B))),B) = ld(mult(op_c,B),B),
inference(resolve,[$cnf( $equal(mult(op_c,mult(op_c,ld(op_c,B))),mult(op_c,B)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( ld(mult(op_c,mult(op_c,ld(op_c,B))),B) != i(op_c)
| ld(mult(op_c,mult(op_c,ld(op_c,B))),B) != ld(mult(op_c,B),B)
| ld(mult(op_c,B),B) = i(op_c) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),B),i(op_c)) ),[0],$fot(ld(mult(op_c,B),B))]]) ).
cnf(refute_0_68,plain,
( ld(mult(op_c,mult(op_c,ld(op_c,B))),B) != i(op_c)
| ld(mult(op_c,B),B) = i(op_c) ),
inference(resolve,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),B),ld(mult(op_c,B),B)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
ld(mult(op_c,B),B) = i(op_c),
inference(resolve,[$cnf( $equal(ld(mult(op_c,mult(op_c,ld(op_c,B))),B),i(op_c)) )],[refute_0_58,refute_0_68]) ).
cnf(refute_0_70,plain,
( ld(mult(op_c,B),B) != i(op_c)
| mult(mult(op_c,B),ld(mult(op_c,B),B)) != B
| mult(mult(op_c,B),i(op_c)) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,B),ld(mult(op_c,B),B)),B) ),[0,1],$fot(i(op_c))]]) ).
cnf(refute_0_71,plain,
( mult(mult(op_c,B),ld(mult(op_c,B),B)) != B
| mult(mult(op_c,B),i(op_c)) = B ),
inference(resolve,[$cnf( $equal(ld(mult(op_c,B),B),i(op_c)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
mult(mult(op_c,B),i(op_c)) = B,
inference(resolve,[$cnf( $equal(mult(mult(op_c,B),ld(mult(op_c,B),B)),B) )],[refute_0_9,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(mult(op_c,ld(op_c,B)),i(op_c)) = ld(op_c,B),
inference(subst,[],[refute_0_72:[bind(B,$fot(ld(op_c,B)))]]) ).
cnf(refute_0_74,plain,
( mult(mult(op_c,ld(op_c,B)),i(op_c)) != ld(op_c,B)
| mult(op_c,ld(op_c,B)) != B
| mult(B,i(op_c)) = ld(op_c,B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(op_c,ld(op_c,B)),i(op_c)),ld(op_c,B)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_75,plain,
( mult(mult(op_c,ld(op_c,B)),i(op_c)) != ld(op_c,B)
| mult(B,i(op_c)) = ld(op_c,B) ),
inference(resolve,[$cnf( $equal(mult(op_c,ld(op_c,B)),B) )],[refute_0_55,refute_0_74]) ).
cnf(refute_0_76,plain,
mult(B,i(op_c)) = ld(op_c,B),
inference(resolve,[$cnf( $equal(mult(mult(op_c,ld(op_c,B)),i(op_c)),ld(op_c,B)) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(a,i(op_c)) = ld(op_c,a),
inference(subst,[],[refute_0_76:[bind(B,$fot(a))]]) ).
cnf(refute_0_78,plain,
( ld(op_c,a) != ld(op_c,a)
| mult(a,i(op_c)) != ld(op_c,a)
| ld(op_c,a) = mult(a,i(op_c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ld(op_c,a),mult(a,i(op_c))) ),[1],$fot(ld(op_c,a))]]) ).
cnf(refute_0_79,plain,
( ld(op_c,a) != ld(op_c,a)
| ld(op_c,a) = mult(a,i(op_c)) ),
inference(resolve,[$cnf( $equal(mult(a,i(op_c)),ld(op_c,a)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
ld(op_c,a) != ld(op_c,a),
inference(resolve,[$cnf( $equal(ld(op_c,a),mult(a,i(op_c))) )],[refute_0_79,refute_0_8]) ).
cnf(refute_0_81,plain,
ld(op_c,a) = ld(op_c,a),
introduced(tautology,[refl,[$fot(ld(op_c,a))]]) ).
cnf(refute_0_82,plain,
$false,
inference(resolve,[$cnf( $equal(ld(op_c,a),ld(op_c,a)) )],[refute_0_81,refute_0_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 07:29:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.76/3.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.76/3.97
% 3.76/3.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/3.97
%------------------------------------------------------------------------------