TSTP Solution File: GRP656-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:44:35 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 25
% Syntax : Number of clauses : 81 ( 46 unt; 0 nHn; 37 RR)
% Number of literals : 133 ( 132 equ; 56 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 : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 179 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B ).
cnf(f02,axiom,
ld(A,mult(A,B)) = B ).
cnf(f04,axiom,
rd(mult(A,B),B) = A ).
cnf(f05,axiom,
mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ).
cnf(goal,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)) ).
cnf(refute_0_0,plain,
tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),
inference(subst,[],[goal:[bind(X0,$fot(rd(X_43,X_43)))]]) ).
cnf(refute_0_1,plain,
mult(B,ld(B,B)) = B,
inference(subst,[],[f01:[bind(A,$fot(B))]]) ).
cnf(refute_0_2,plain,
rd(mult(ld(X_29,X_29),B),B) = ld(X_29,X_29),
inference(subst,[],[f04:[bind(A,$fot(ld(X_29,X_29)))]]) ).
cnf(refute_0_3,plain,
ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)) = B,
inference(subst,[],[f02:[bind(A,$fot(mult(B,mult(X_14,X_15))))]]) ).
cnf(refute_0_4,plain,
mult(mult(B,X_14),mult(X_15,B)) = mult(mult(B,mult(X_14,X_15)),B),
inference(subst,[],[f05:[bind(A,$fot(B)),bind(B,$fot(X_14)),bind(C,$fot(X_15))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( mult(mult(B,X_14),mult(X_15,B)) != mult(mult(B,mult(X_14,X_15)),B)
| mult(mult(B,mult(X_14,X_15)),B) = mult(mult(B,X_14),mult(X_15,B)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(mult(B,X_14),mult(X_15,B)))),bind(Y,$fot(mult(mult(B,mult(X_14,X_15)),B)))]]) ).
cnf(refute_0_9,plain,
mult(mult(B,mult(X_14,X_15)),B) = mult(mult(B,X_14),mult(X_15,B)),
inference(resolve,[$cnf( $equal(mult(mult(B,X_14),mult(X_15,B)),mult(mult(B,mult(X_14,X_15)),B)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)) != B
| mult(mult(B,mult(X_14,X_15)),B) != mult(mult(B,X_14),mult(X_15,B))
| ld(mult(B,mult(X_14,X_15)),mult(mult(B,X_14),mult(X_15,B))) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)),B) ),[0,1],$fot(mult(mult(B,X_14),mult(X_15,B)))]]) ).
cnf(refute_0_11,plain,
( ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)) != B
| ld(mult(B,mult(X_14,X_15)),mult(mult(B,X_14),mult(X_15,B))) = B ),
inference(resolve,[$cnf( $equal(mult(mult(B,mult(X_14,X_15)),B),mult(mult(B,X_14),mult(X_15,B))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
ld(mult(B,mult(X_14,X_15)),mult(mult(B,X_14),mult(X_15,B))) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)),B) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_14),mult(ld(X_14,X_25),B))) = B,
inference(subst,[],[refute_0_12:[bind(X_15,$fot(ld(X_14,X_25)))]]) ).
cnf(refute_0_14,plain,
mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) = mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13),
inference(subst,[],[f05:[bind(A,$fot(X_13)),bind(B,$fot(X_14)),bind(C,$fot(ld(X_14,B)))]]) ).
cnf(refute_0_15,plain,
mult(X_14,ld(X_14,B)) = B,
inference(subst,[],[f01:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_16,plain,
( mult(X_14,ld(X_14,B)) != B
| mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) != mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13)
| mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) = mult(mult(X_13,B),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)),mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13)) ),[1,0,1],$fot(B)]]) ).
cnf(refute_0_17,plain,
( mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) != mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13)
| mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) = mult(mult(X_13,B),X_13) ),
inference(resolve,[$cnf( $equal(mult(X_14,ld(X_14,B)),B) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) = mult(mult(X_13,B),X_13),
inference(resolve,[$cnf( $equal(mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)),mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(mult(B,X_14),mult(ld(X_14,X_25),B)) = mult(mult(B,X_25),B),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_25)),bind(X_13,$fot(B))]]) ).
cnf(refute_0_20,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_14),mult(ld(X_14,X_25),B))) != B
| mult(mult(B,X_14),mult(ld(X_14,X_25),B)) != mult(mult(B,X_25),B)
| ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_14),mult(ld(X_14,X_25),B))),B) ),[0,1],$fot(mult(mult(B,X_25),B))]]) ).
cnf(refute_0_21,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_14),mult(ld(X_14,X_25),B))) != B
| ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = B ),
inference(resolve,[$cnf( $equal(mult(mult(B,X_14),mult(ld(X_14,X_25),B)),mult(mult(B,X_25),B)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_14),mult(ld(X_14,X_25),B))),B) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(X_14,ld(X_14,X_25)) = X_25,
inference(subst,[],[f01:[bind(A,$fot(X_14)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_24,plain,
ld(mult(X_14,ld(X_14,X_25)),X_25) = ld(mult(X_14,ld(X_14,X_25)),X_25),
introduced(tautology,[refl,[$fot(ld(mult(X_14,ld(X_14,X_25)),X_25))]]) ).
cnf(refute_0_25,plain,
( ld(mult(X_14,ld(X_14,X_25)),X_25) != ld(mult(X_14,ld(X_14,X_25)),X_25)
| mult(X_14,ld(X_14,X_25)) != X_25
| ld(mult(X_14,ld(X_14,X_25)),X_25) = ld(X_25,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_25)),X_25),ld(mult(X_14,ld(X_14,X_25)),X_25)) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_26,plain,
( mult(X_14,ld(X_14,X_25)) != X_25
| ld(mult(X_14,ld(X_14,X_25)),X_25) = ld(X_25,X_25) ),
inference(resolve,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_25)),X_25),ld(mult(X_14,ld(X_14,X_25)),X_25)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
ld(mult(X_14,ld(X_14,X_25)),X_25) = ld(X_25,X_25),
inference(resolve,[$cnf( $equal(mult(X_14,ld(X_14,X_25)),X_25) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) = mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B),
introduced(tautology,[refl,[$fot(mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B))]]) ).
cnf(refute_0_29,plain,
( ld(mult(X_14,ld(X_14,X_25)),X_25) != ld(X_25,X_25)
| mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) != mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B)
| mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) = mult(ld(X_25,X_25),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B),mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B)) ),[1,0],$fot(ld(X_25,X_25))]]) ).
cnf(refute_0_30,plain,
( ld(mult(X_14,ld(X_14,X_25)),X_25) != ld(X_25,X_25)
| mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) = mult(ld(X_25,X_25),B) ),
inference(resolve,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B),mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) = mult(ld(X_25,X_25),B),
inference(resolve,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_25)),X_25),ld(X_25,X_25)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
ld(mult(X_26,X_27),mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26))) = mult(ld(X_27,X_25),X_26),
inference(subst,[],[f02:[bind(A,$fot(mult(X_26,X_27))),bind(B,$fot(mult(ld(X_27,X_25),X_26)))]]) ).
cnf(refute_0_33,plain,
mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26)) = mult(mult(X_26,X_25),X_26),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_25)),bind(X_13,$fot(X_26)),bind(X_14,$fot(X_27))]]) ).
cnf(refute_0_34,plain,
( ld(mult(X_26,X_27),mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26))) != mult(ld(X_27,X_25),X_26)
| mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26)) != mult(mult(X_26,X_25),X_26)
| ld(mult(X_26,X_27),mult(mult(X_26,X_25),X_26)) = mult(ld(X_27,X_25),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_26,X_27),mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26))),mult(ld(X_27,X_25),X_26)) ),[0,1],$fot(mult(mult(X_26,X_25),X_26))]]) ).
cnf(refute_0_35,plain,
( ld(mult(X_26,X_27),mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26))) != mult(ld(X_27,X_25),X_26)
| ld(mult(X_26,X_27),mult(mult(X_26,X_25),X_26)) = mult(ld(X_27,X_25),X_26) ),
inference(resolve,[$cnf( $equal(mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26)),mult(mult(X_26,X_25),X_26)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
ld(mult(X_26,X_27),mult(mult(X_26,X_25),X_26)) = mult(ld(X_27,X_25),X_26),
inference(resolve,[$cnf( $equal(ld(mult(X_26,X_27),mult(mult(X_26,X_27),mult(ld(X_27,X_25),X_26))),mult(ld(X_27,X_25),X_26)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B),
inference(subst,[],[refute_0_36:[bind(X_26,$fot(B)),bind(X_27,$fot(mult(X_14,ld(X_14,X_25))))]]) ).
cnf(refute_0_38,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_39,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_38]) ).
cnf(refute_0_40,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) != mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B)
| mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) != mult(ld(X_25,X_25),B)
| ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = mult(ld(X_25,X_25),B) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)))),bind(Y,$fot(mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B))),bind(Z,$fot(mult(ld(X_25,X_25),B)))]]) ).
cnf(refute_0_41,plain,
( mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B) != mult(ld(X_25,X_25),B)
| ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = mult(ld(X_25,X_25),B) ),
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)),mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) = mult(ld(X_25,X_25),B),
inference(resolve,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_25)),X_25),B),mult(ld(X_25,X_25),B)) )],[refute_0_31,refute_0_41]) ).
cnf(refute_0_43,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) != B
| ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) != mult(ld(X_25,X_25),B)
| mult(ld(X_25,X_25),B) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)),B) ),[0],$fot(mult(ld(X_25,X_25),B))]]) ).
cnf(refute_0_44,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)) != B
| mult(ld(X_25,X_25),B) = B ),
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)),mult(ld(X_25,X_25),B)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
mult(ld(X_25,X_25),B) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_25))),mult(mult(B,X_25),B)),B) )],[refute_0_22,refute_0_44]) ).
cnf(refute_0_46,plain,
mult(ld(X_29,X_29),B) = B,
inference(subst,[],[refute_0_45:[bind(X_25,$fot(X_29))]]) ).
cnf(refute_0_47,plain,
( mult(ld(X_29,X_29),B) != B
| rd(mult(ld(X_29,X_29),B),B) != ld(X_29,X_29)
| rd(B,B) = ld(X_29,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(ld(X_29,X_29),B),B),ld(X_29,X_29)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_48,plain,
( rd(mult(ld(X_29,X_29),B),B) != ld(X_29,X_29)
| rd(B,B) = ld(X_29,X_29) ),
inference(resolve,[$cnf( $equal(mult(ld(X_29,X_29),B),B) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
rd(B,B) = ld(X_29,X_29),
inference(resolve,[$cnf( $equal(rd(mult(ld(X_29,X_29),B),B),ld(X_29,X_29)) )],[refute_0_2,refute_0_48]) ).
cnf(refute_0_50,plain,
rd(X_32,X_32) = ld(B,B),
inference(subst,[],[refute_0_49:[bind(B,$fot(X_32)),bind(X_29,$fot(B))]]) ).
cnf(refute_0_51,plain,
( rd(X_32,X_32) != ld(B,B)
| ld(B,B) = rd(X_32,X_32) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(rd(X_32,X_32))),bind(Y,$fot(ld(B,B)))]]) ).
cnf(refute_0_52,plain,
ld(B,B) = rd(X_32,X_32),
inference(resolve,[$cnf( $equal(rd(X_32,X_32),ld(B,B)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ld(B,B) != rd(X_32,X_32)
| mult(B,ld(B,B)) != B
| mult(B,rd(X_32,X_32)) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(B,ld(B,B)),B) ),[0,1],$fot(rd(X_32,X_32))]]) ).
cnf(refute_0_54,plain,
( mult(B,ld(B,B)) != B
| mult(B,rd(X_32,X_32)) = B ),
inference(resolve,[$cnf( $equal(ld(B,B),rd(X_32,X_32)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
mult(B,rd(X_32,X_32)) = B,
inference(resolve,[$cnf( $equal(mult(B,ld(B,B)),B) )],[refute_0_1,refute_0_54]) ).
cnf(refute_0_56,plain,
mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43)) = x1_2(rd(X_43,X_43)),
inference(subst,[],[refute_0_55:[bind(B,$fot(x1_2(rd(X_43,X_43)))),bind(X_32,$fot(X_43))]]) ).
cnf(refute_0_57,plain,
( mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43)) != x1_2(rd(X_43,X_43))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) ),[0,1],$fot(x1_2(rd(X_43,X_43)))]]) ).
cnf(refute_0_58,plain,
( tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
inference(resolve,[$cnf( $equal(mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43)),x1_2(rd(X_43,X_43))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),
inference(resolve,[$cnf( $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),mult(x1_2(rd(X_43,X_43)),rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) )],[refute_0_58,refute_0_0]) ).
cnf(refute_0_60,plain,
rd(X_32,X_32) = ld(X_25,X_25),
inference(subst,[],[refute_0_49:[bind(B,$fot(X_32)),bind(X_29,$fot(X_25))]]) ).
cnf(refute_0_61,plain,
( rd(X_32,X_32) != ld(X_25,X_25)
| ld(X_25,X_25) = rd(X_32,X_32) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(rd(X_32,X_32))),bind(Y,$fot(ld(X_25,X_25)))]]) ).
cnf(refute_0_62,plain,
ld(X_25,X_25) = rd(X_32,X_32),
inference(resolve,[$cnf( $equal(rd(X_32,X_32),ld(X_25,X_25)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( ld(X_25,X_25) != rd(X_32,X_32)
| mult(ld(X_25,X_25),B) != B
| mult(rd(X_32,X_32),B) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(ld(X_25,X_25),B),B) ),[0,0],$fot(rd(X_32,X_32))]]) ).
cnf(refute_0_64,plain,
( mult(ld(X_25,X_25),B) != B
| mult(rd(X_32,X_32),B) = B ),
inference(resolve,[$cnf( $equal(ld(X_25,X_25),rd(X_32,X_32)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
mult(rd(X_32,X_32),B) = B,
inference(resolve,[$cnf( $equal(mult(ld(X_25,X_25),B),B) )],[refute_0_45,refute_0_64]) ).
cnf(refute_0_66,plain,
mult(rd(X_43,X_43),x1(rd(X_43,X_43))) = x1(rd(X_43,X_43)),
inference(subst,[],[refute_0_65:[bind(B,$fot(x1(rd(X_43,X_43)))),bind(X_32,$fot(X_43))]]) ).
cnf(refute_0_67,plain,
tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),
introduced(tautology,[refl,[$fot(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))))]]) ).
cnf(refute_0_68,plain,
( mult(rd(X_43,X_43),x1(rd(X_43,X_43))) != x1(rd(X_43,X_43))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) != tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43)))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43)))) ),[1,0],$fot(x1(rd(X_43,X_43)))]]) ).
cnf(refute_0_69,plain,
( mult(rd(X_43,X_43),x1(rd(X_43,X_43))) != x1(rd(X_43,X_43))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
inference(resolve,[$cnf( $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),
inference(resolve,[$cnf( $equal(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1(rd(X_43,X_43))) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))
| tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) ),[0],$fot(tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))))]]) ).
cnf(refute_0_72,plain,
( tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))
| tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) ),
inference(resolve,[$cnf( $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) != tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),
inference(resolve,[$cnf( $equal(tuple(mult(rd(X_43,X_43),x1(rd(X_43,X_43))),x1_2(rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) )],[refute_0_72,refute_0_59]) ).
cnf(refute_0_74,plain,
tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))) = tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),
introduced(tautology,[refl,[$fot(tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))))]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( $equal(tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43))),tuple(x1(rd(X_43,X_43)),x1_2(rd(X_43,X_43)))) )],[refute_0_74,refute_0_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 08:21:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.41
% 0.21/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.43
%------------------------------------------------------------------------------