TSTP Solution File: SET950+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 : Tue Jul 19 03:38:34 EDT 2022
% Result : Theorem 1.46s 1.67s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 14 unt; 0 def)
% Number of atoms : 179 ( 59 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 216 ( 95 ~; 78 |; 31 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 125 ( 0 sgn 67 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t103_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( ( subset(A,cartesian_product2(B,C))
& in(D,A) )
=> ~ ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(strip,[],[t103_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( ( subset(A,cartesian_product2(B,C))
& in(D,A) )
=> ~ ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D] :
( in(D,A)
& subset(A,cartesian_product2(B,C))
& ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(E,B)
| ~ in(F,C) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( in(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2)
& subset(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
& ! [E,F] :
( skolemFOFtoCNF_D_1 != ordered_pair(E,F)
| ~ in(E,skolemFOFtoCNF_B)
| ~ in(F,skolemFOFtoCNF_C_1) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [E,F] :
( skolemFOFtoCNF_D_1 != ordered_pair(E,F)
| ~ in(E,skolemFOFtoCNF_B)
| ~ in(F,skolemFOFtoCNF_C_1) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,F] :
( skolemFOFtoCNF_D_1 != ordered_pair(E,F)
| ~ in(E,skolemFOFtoCNF_B)
| ~ in(F,skolemFOFtoCNF_C_1) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
in(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
subset(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( C != cartesian_product2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(E,A)
& in(F,B) ) ) ),
inference(canonicalize,[],[d2_zfmisc_1]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( C != cartesian_product2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(E,A)
& in(F,B) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C,D,E,F] :
( ( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) )
& ( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) )
& ( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) )
& ( C = cartesian_product2(A,B)
| skolemFOFtoCNF_D(A,B,C) = ordered_pair(skolemFOFtoCNF_E(A,B,C),skolemFOFtoCNF_F(A,B,C))
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = cartesian_product2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C)
| in(skolemFOFtoCNF_E(A,B,C),A) )
& ( C = cartesian_product2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C)
| in(skolemFOFtoCNF_F(A,B,C),B) )
& ( C != cartesian_product2(A,B)
| D != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(D,C) )
& ( skolemFOFtoCNF_D(A,B,C) != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = cartesian_product2(A,B) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_D_1 != ordered_pair(E,F)
| ~ in(E,skolemFOFtoCNF_B)
| ~ in(F,skolemFOFtoCNF_C_1) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_D_1 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_0:[bind(E,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))),bind(F,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_0_2,plain,
in(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
subset(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ in(X_64,skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| in(X_64,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))),bind(C,$fot(X_64))]]) ).
cnf(refute_0_6,plain,
( ~ in(X_64,skolemFOFtoCNF_A_2)
| in(X_64,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ in(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_6:[bind(X_64,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_8,plain,
in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_11,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_0_12,plain,
( ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_D_1 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_D_1 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_D_1 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) = skolemFOFtoCNF_D_1 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_D_1)),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))))]]) ).
cnf(refute_0_19,plain,
ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) = skolemFOFtoCNF_D_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) != skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D_1 != skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D_1 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))) ),[1],$fot(skolemFOFtoCNF_D_1)]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_D_1 != skolemFOFtoCNF_D_1
| skolemFOFtoCNF_D_1 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),skolemFOFtoCNF_D_1) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_D_1 != skolemFOFtoCNF_D_1
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
skolemFOFtoCNF_D_1 = skolemFOFtoCNF_D_1,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_D_1)]]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1,skolemFOFtoCNF_D_1) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_26,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(subst,[],[refute_0_25:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_27,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_11,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_29,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_8,refute_0_28]) ).
cnf(refute_0_30,plain,
~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B) )],[refute_0_29,refute_0_24]) ).
cnf(refute_0_31,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_32,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(subst,[],[refute_0_31:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_33,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_11,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_35,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_8,refute_0_34]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_C_1) )],[refute_0_35,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 03:09:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.46/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.46/1.67
% 1.46/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.46/1.67
%------------------------------------------------------------------------------