%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 : Theorem 0.11s 0.29s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of formulae : 97 ( 55 unt; 0 def)
% Number of atoms : 155 ( 154 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 122 ( 64 ~; 55 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 217 ( 0 sgn 33 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(f05,axiom,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ).
fof(goals,conjecture,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ) ).
fof(subgoal_0,plain,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] :
( mult(X0,skolemFOFtoCNF_X1(X0)) != skolemFOFtoCNF_X1(X0)
| mult(skolemFOFtoCNF_X1_1(X0),X0) != skolemFOFtoCNF_X1_1(X0) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(canonicalize,[],[f01]) ).
fof(normalize_0_4,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(canonicalize,[],[f04]) ).
fof(normalize_0_6,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_0_8,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(canonicalize,[],[f05]) ).
fof(normalize_0_10,plain,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( mult(X0,skolemFOFtoCNF_X1(X0)) != skolemFOFtoCNF_X1(X0)
| mult(skolemFOFtoCNF_X1_1(X0),X0) != skolemFOFtoCNF_X1_1(X0) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) != skolemFOFtoCNF_X1(rd(X_36,X_36))
| mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)) != skolemFOFtoCNF_X1_1(rd(X_36,X_36)) ),
inference(subst,[],[refute_0_0:[bind(X0,$fot(rd(X_36,X_36)))]]) ).
cnf(refute_0_2,plain,
mult(A,ld(A,B)) = B,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
mult(B,ld(B,B)) = B,
inference(subst,[],[refute_0_2:[bind(A,$fot(B))]]) ).
cnf(refute_0_4,plain,
rd(mult(A,B),B) = A,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
rd(mult(ld(X_26,X_26),B),B) = ld(X_26,X_26),
inference(subst,[],[refute_0_4:[bind(A,$fot(ld(X_26,X_26)))]]) ).
cnf(refute_0_6,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)) = B,
inference(subst,[],[refute_0_6:[bind(A,$fot(mult(B,mult(X_14,X_15))))]]) ).
cnf(refute_0_8,plain,
mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
mult(mult(B,X_14),mult(X_15,B)) = mult(mult(B,mult(X_14,X_15)),B),
inference(subst,[],[refute_0_8:[bind(A,$fot(B)),bind(B,$fot(X_14)),bind(C,$fot(X_15))]]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( mult(mult(B,X_14),mult(X_15,B)) != mult(mult(B,mult(X_14,X_15)),B)
| mult(mult(B,mult(X_14,X_15)),B) = mult(mult(B,X_14),mult(X_15,B)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(mult(mult(B,X_14),mult(X_15,B)))),bind(Y,$fot(mult(mult(B,mult(X_14,X_15)),B)))]]) ).
cnf(refute_0_14,plain,
mult(mult(B,mult(X_14,X_15)),B) = mult(mult(B,X_14),mult(X_15,B)),
inference(resolve,[$cnf( $equal(mult(mult(B,X_14),mult(X_15,B)),mult(mult(B,mult(X_14,X_15)),B)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)) != B
| mult(mult(B,mult(X_14,X_15)),B) != mult(mult(B,X_14),mult(X_15,B))
| ld(mult(B,mult(X_14,X_15)),mult(mult(B,X_14),mult(X_15,B))) = B ),
introduced(tautology,[equality,[$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_16,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( $equal(mult(mult(B,mult(X_14,X_15)),B),mult(mult(B,X_14),mult(X_15,B))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
ld(mult(B,mult(X_14,X_15)),mult(mult(B,X_14),mult(X_15,B))) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,X_15)),mult(mult(B,mult(X_14,X_15)),B)),B) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_14),mult(ld(X_14,X_22),B))) = B,
inference(subst,[],[refute_0_17:[bind(X_15,$fot(ld(X_14,X_22)))]]) ).
cnf(refute_0_19,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,[],[refute_0_8:[bind(A,$fot(X_13)),bind(B,$fot(X_14)),bind(C,$fot(ld(X_14,B)))]]) ).
cnf(refute_0_20,plain,
mult(X_14,ld(X_14,B)) = B,
inference(subst,[],[refute_0_2:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_21,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_22,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( $equal(mult(X_14,ld(X_14,B)),B) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)) = mult(mult(X_13,B),X_13),
inference(resolve,[$cnf( $equal(mult(mult(X_13,X_14),mult(ld(X_14,B),X_13)),mult(mult(X_13,mult(X_14,ld(X_14,B))),X_13)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(mult(B,X_14),mult(ld(X_14,X_22),B)) = mult(mult(B,X_22),B),
inference(subst,[],[refute_0_23:[bind(B,$fot(X_22)),bind(X_13,$fot(B))]]) ).
cnf(refute_0_25,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_14),mult(ld(X_14,X_22),B))) != B
| mult(mult(B,X_14),mult(ld(X_14,X_22),B)) != mult(mult(B,X_22),B)
| ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_14),mult(ld(X_14,X_22),B))),B) ),[0,1],$fot(mult(mult(B,X_22),B))]]) ).
cnf(refute_0_26,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_14),mult(ld(X_14,X_22),B))) != B
| ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = B ),
inference(resolve,[$cnf( $equal(mult(mult(B,X_14),mult(ld(X_14,X_22),B)),mult(mult(B,X_22),B)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_14),mult(ld(X_14,X_22),B))),B) )],[refute_0_18,refute_0_26]) ).
cnf(refute_0_28,plain,
mult(X_14,ld(X_14,X_22)) = X_22,
inference(subst,[],[refute_0_2:[bind(A,$fot(X_14)),bind(B,$fot(X_22))]]) ).
cnf(refute_0_29,plain,
ld(mult(X_14,ld(X_14,X_22)),X_22) = ld(mult(X_14,ld(X_14,X_22)),X_22),
introduced(tautology,[refl,[$fot(ld(mult(X_14,ld(X_14,X_22)),X_22))]]) ).
cnf(refute_0_30,plain,
( ld(mult(X_14,ld(X_14,X_22)),X_22) != ld(mult(X_14,ld(X_14,X_22)),X_22)
| mult(X_14,ld(X_14,X_22)) != X_22
| ld(mult(X_14,ld(X_14,X_22)),X_22) = ld(X_22,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_22)),X_22),ld(mult(X_14,ld(X_14,X_22)),X_22)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_31,plain,
( mult(X_14,ld(X_14,X_22)) != X_22
| ld(mult(X_14,ld(X_14,X_22)),X_22) = ld(X_22,X_22) ),
inference(resolve,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_22)),X_22),ld(mult(X_14,ld(X_14,X_22)),X_22)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
ld(mult(X_14,ld(X_14,X_22)),X_22) = ld(X_22,X_22),
inference(resolve,[$cnf( $equal(mult(X_14,ld(X_14,X_22)),X_22) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) = mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B),
introduced(tautology,[refl,[$fot(mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B))]]) ).
cnf(refute_0_34,plain,
( ld(mult(X_14,ld(X_14,X_22)),X_22) != ld(X_22,X_22)
| mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) != mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B)
| mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) = mult(ld(X_22,X_22),B) ),
introduced(tautology,[equality,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B),mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B)) ),[1,0],$fot(ld(X_22,X_22))]]) ).
cnf(refute_0_35,plain,
( ld(mult(X_14,ld(X_14,X_22)),X_22) != ld(X_22,X_22)
| mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) = mult(ld(X_22,X_22),B) ),
inference(resolve,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B),mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) = mult(ld(X_22,X_22),B),
inference(resolve,[$cnf( $equal(ld(mult(X_14,ld(X_14,X_22)),X_22),ld(X_22,X_22)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
ld(mult(X_23,X_24),mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23))) = mult(ld(X_24,X_22),X_23),
inference(subst,[],[refute_0_6:[bind(A,$fot(mult(X_23,X_24))),bind(B,$fot(mult(ld(X_24,X_22),X_23)))]]) ).
cnf(refute_0_38,plain,
mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23)) = mult(mult(X_23,X_22),X_23),
inference(subst,[],[refute_0_23:[bind(B,$fot(X_22)),bind(X_13,$fot(X_23)),bind(X_14,$fot(X_24))]]) ).
cnf(refute_0_39,plain,
( ld(mult(X_23,X_24),mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23))) != mult(ld(X_24,X_22),X_23)
| mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23)) != mult(mult(X_23,X_22),X_23)
| ld(mult(X_23,X_24),mult(mult(X_23,X_22),X_23)) = mult(ld(X_24,X_22),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(X_23,X_24),mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23))),mult(ld(X_24,X_22),X_23)) ),[0,1],$fot(mult(mult(X_23,X_22),X_23))]]) ).
cnf(refute_0_40,plain,
( ld(mult(X_23,X_24),mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23))) != mult(ld(X_24,X_22),X_23)
| ld(mult(X_23,X_24),mult(mult(X_23,X_22),X_23)) = mult(ld(X_24,X_22),X_23) ),
inference(resolve,[$cnf( $equal(mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23)),mult(mult(X_23,X_22),X_23)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
ld(mult(X_23,X_24),mult(mult(X_23,X_22),X_23)) = mult(ld(X_24,X_22),X_23),
inference(resolve,[$cnf( $equal(ld(mult(X_23,X_24),mult(mult(X_23,X_24),mult(ld(X_24,X_22),X_23))),mult(ld(X_24,X_22),X_23)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B),
inference(subst,[],[refute_0_41:[bind(X_23,$fot(B)),bind(X_24,$fot(mult(X_14,ld(X_14,X_22))))]]) ).
cnf(refute_0_43,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_44,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_43]) ).
cnf(refute_0_45,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) != mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B)
| mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) != mult(ld(X_22,X_22),B)
| ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = mult(ld(X_22,X_22),B) ),
inference(subst,[],[refute_0_44:[bind(X,$fot(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)))),bind(Y,$fot(mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B))),bind(Z,$fot(mult(ld(X_22,X_22),B)))]]) ).
cnf(refute_0_46,plain,
( mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B) != mult(ld(X_22,X_22),B)
| ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = mult(ld(X_22,X_22),B) ),
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)),mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) = mult(ld(X_22,X_22),B),
inference(resolve,[$cnf( $equal(mult(ld(mult(X_14,ld(X_14,X_22)),X_22),B),mult(ld(X_22,X_22),B)) )],[refute_0_36,refute_0_46]) ).
cnf(refute_0_48,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) != B
| ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) != mult(ld(X_22,X_22),B)
| mult(ld(X_22,X_22),B) = B ),
introduced(tautology,[equality,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)),B) ),[0],$fot(mult(ld(X_22,X_22),B))]]) ).
cnf(refute_0_49,plain,
( ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)) != B
| mult(ld(X_22,X_22),B) = B ),
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)),mult(ld(X_22,X_22),B)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
mult(ld(X_22,X_22),B) = B,
inference(resolve,[$cnf( $equal(ld(mult(B,mult(X_14,ld(X_14,X_22))),mult(mult(B,X_22),B)),B) )],[refute_0_27,refute_0_49]) ).
cnf(refute_0_51,plain,
mult(ld(X_26,X_26),B) = B,
inference(subst,[],[refute_0_50:[bind(X_22,$fot(X_26))]]) ).
cnf(refute_0_52,plain,
( mult(ld(X_26,X_26),B) != B
| rd(mult(ld(X_26,X_26),B),B) != ld(X_26,X_26)
| rd(B,B) = ld(X_26,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(ld(X_26,X_26),B),B),ld(X_26,X_26)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_53,plain,
( rd(mult(ld(X_26,X_26),B),B) != ld(X_26,X_26)
| rd(B,B) = ld(X_26,X_26) ),
inference(resolve,[$cnf( $equal(mult(ld(X_26,X_26),B),B) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
rd(B,B) = ld(X_26,X_26),
inference(resolve,[$cnf( $equal(rd(mult(ld(X_26,X_26),B),B),ld(X_26,X_26)) )],[refute_0_5,refute_0_53]) ).
cnf(refute_0_55,plain,
rd(X_29,X_29) = ld(B,B),
inference(subst,[],[refute_0_54:[bind(B,$fot(X_29)),bind(X_26,$fot(B))]]) ).
cnf(refute_0_56,plain,
( rd(X_29,X_29) != ld(B,B)
| ld(B,B) = rd(X_29,X_29) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(rd(X_29,X_29))),bind(Y,$fot(ld(B,B)))]]) ).
cnf(refute_0_57,plain,
ld(B,B) = rd(X_29,X_29),
inference(resolve,[$cnf( $equal(rd(X_29,X_29),ld(B,B)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( ld(B,B) != rd(X_29,X_29)
| mult(B,ld(B,B)) != B
| mult(B,rd(X_29,X_29)) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(B,ld(B,B)),B) ),[0,1],$fot(rd(X_29,X_29))]]) ).
cnf(refute_0_59,plain,
( mult(B,ld(B,B)) != B
| mult(B,rd(X_29,X_29)) = B ),
inference(resolve,[$cnf( $equal(ld(B,B),rd(X_29,X_29)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
mult(B,rd(X_29,X_29)) = B,
inference(resolve,[$cnf( $equal(mult(B,ld(B,B)),B) )],[refute_0_3,refute_0_59]) ).
cnf(refute_0_61,plain,
mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)) = skolemFOFtoCNF_X1_1(rd(X_36,X_36)),
inference(subst,[],[refute_0_60:[bind(B,$fot(skolemFOFtoCNF_X1_1(rd(X_36,X_36)))),bind(X_29,$fot(X_36))]]) ).
cnf(refute_0_62,plain,
( mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)) != skolemFOFtoCNF_X1_1(rd(X_36,X_36))
| skolemFOFtoCNF_X1_1(rd(X_36,X_36)) != skolemFOFtoCNF_X1_1(rd(X_36,X_36))
| mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)) = skolemFOFtoCNF_X1_1(rd(X_36,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)),skolemFOFtoCNF_X1_1(rd(X_36,X_36))) ),[0],$fot(skolemFOFtoCNF_X1_1(rd(X_36,X_36)))]]) ).
cnf(refute_0_63,plain,
( skolemFOFtoCNF_X1_1(rd(X_36,X_36)) != skolemFOFtoCNF_X1_1(rd(X_36,X_36))
| mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)) = skolemFOFtoCNF_X1_1(rd(X_36,X_36)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)),skolemFOFtoCNF_X1_1(rd(X_36,X_36))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) != skolemFOFtoCNF_X1(rd(X_36,X_36))
| skolemFOFtoCNF_X1_1(rd(X_36,X_36)) != skolemFOFtoCNF_X1_1(rd(X_36,X_36)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),rd(X_36,X_36)),skolemFOFtoCNF_X1_1(rd(X_36,X_36))) )],[refute_0_63,refute_0_1]) ).
cnf(refute_0_65,plain,
skolemFOFtoCNF_X1_1(rd(X_36,X_36)) = skolemFOFtoCNF_X1_1(rd(X_36,X_36)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1_1(rd(X_36,X_36)))]]) ).
cnf(refute_0_66,plain,
mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) != skolemFOFtoCNF_X1(rd(X_36,X_36)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1_1(rd(X_36,X_36)),skolemFOFtoCNF_X1_1(rd(X_36,X_36))) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
rd(X_29,X_29) = ld(X_22,X_22),
inference(subst,[],[refute_0_54:[bind(B,$fot(X_29)),bind(X_26,$fot(X_22))]]) ).
cnf(refute_0_68,plain,
( rd(X_29,X_29) != ld(X_22,X_22)
| ld(X_22,X_22) = rd(X_29,X_29) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(rd(X_29,X_29))),bind(Y,$fot(ld(X_22,X_22)))]]) ).
cnf(refute_0_69,plain,
ld(X_22,X_22) = rd(X_29,X_29),
inference(resolve,[$cnf( $equal(rd(X_29,X_29),ld(X_22,X_22)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ld(X_22,X_22) != rd(X_29,X_29)
| mult(ld(X_22,X_22),B) != B
| mult(rd(X_29,X_29),B) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(ld(X_22,X_22),B),B) ),[0,0],$fot(rd(X_29,X_29))]]) ).
cnf(refute_0_71,plain,
( mult(ld(X_22,X_22),B) != B
| mult(rd(X_29,X_29),B) = B ),
inference(resolve,[$cnf( $equal(ld(X_22,X_22),rd(X_29,X_29)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
mult(rd(X_29,X_29),B) = B,
inference(resolve,[$cnf( $equal(mult(ld(X_22,X_22),B),B) )],[refute_0_50,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) = skolemFOFtoCNF_X1(rd(X_36,X_36)),
inference(subst,[],[refute_0_72:[bind(B,$fot(skolemFOFtoCNF_X1(rd(X_36,X_36)))),bind(X_29,$fot(X_36))]]) ).
cnf(refute_0_74,plain,
( mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) != skolemFOFtoCNF_X1(rd(X_36,X_36))
| skolemFOFtoCNF_X1(rd(X_36,X_36)) != skolemFOFtoCNF_X1(rd(X_36,X_36))
| mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) = skolemFOFtoCNF_X1(rd(X_36,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))),skolemFOFtoCNF_X1(rd(X_36,X_36))) ),[0],$fot(skolemFOFtoCNF_X1(rd(X_36,X_36)))]]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_X1(rd(X_36,X_36)) != skolemFOFtoCNF_X1(rd(X_36,X_36))
| mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))) = skolemFOFtoCNF_X1(rd(X_36,X_36)) ),
inference(resolve,[$cnf( $equal(mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))),skolemFOFtoCNF_X1(rd(X_36,X_36))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
skolemFOFtoCNF_X1(rd(X_36,X_36)) != skolemFOFtoCNF_X1(rd(X_36,X_36)),
inference(resolve,[$cnf( $equal(mult(rd(X_36,X_36),skolemFOFtoCNF_X1(rd(X_36,X_36))),skolemFOFtoCNF_X1(rd(X_36,X_36))) )],[refute_0_75,refute_0_66]) ).
cnf(refute_0_77,plain,
skolemFOFtoCNF_X1(rd(X_36,X_36)) = skolemFOFtoCNF_X1(rd(X_36,X_36)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1(rd(X_36,X_36)))]]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(rd(X_36,X_36)),skolemFOFtoCNF_X1(rd(X_36,X_36))) )],[refute_0_77,refute_0_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.08 % Command : metis --show proof --show saturation %s
% 0.07/0.26 % Computer : n011.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Tue Jun 14 08:45:19 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.29
% 0.11/0.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.11/0.30
%------------------------------------------------------------------------------