TSTP Solution File: SET893+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:38:09 EDT 2022
% Result : Theorem 10.77s 10.94s
% Output : CNFRefutation 10.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 138 ( 53 unt; 0 def)
% Number of atoms : 316 ( 176 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 331 ( 153 ~; 119 |; 31 &)
% ( 22 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 197 ( 4 sgn 113 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ) ).
fof(t34_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
<=> ( A = C
& B = D ) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
=> A = C ),
inference(strip,[],[t34_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
& A = C )
=> B = D ),
inference(strip,[],[t34_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C,D] :
( ( A = C
& B = D )
=> in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D))) ),
inference(strip,[],[t34_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
=> A = C ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( A != C
& ? [D] : in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D))) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C_1
& ? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(D))) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(D))),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_D))),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(canonicalize,[],[l55_zfmisc_1]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) )
& ( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C_1,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C_1 ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_D))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_D)))
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(singleton(skolemFOFtoCNF_C_1))),bind(D,$fot(singleton(skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_8,plain,
in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(singleton(skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_D))) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C_1,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_C_1)) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C_1,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) )],[refute_0_9,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
& A = C )
=> B = D ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_1_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C,D] :
( B != D
& A = C
& in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D))) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( skolemFOFtoCNF_B_1 != skolemFOFtoCNF_D_1
& skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2
& in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2,
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_8,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(canonicalize,[],[l55_zfmisc_1]) ).
fof(normalize_1_9,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) )
& ( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
skolemFOFtoCNF_B_1 != skolemFOFtoCNF_D_1,
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_1_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_1_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_1_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
( ~ in(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_D_1))
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_D_1 ),
inference(subst,[],[refute_1_3:[bind(A,$fot(skolemFOFtoCNF_D_1)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_5,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2,
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_C_2
| skolemFOFtoCNF_C_2 = skolemFOFtoCNF_A_3 ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_A_3)),bind(Y,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_11,plain,
skolemFOFtoCNF_C_2 = skolemFOFtoCNF_A_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_C_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_13,plain,
( singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C_2 != skolemFOFtoCNF_A_3
| singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_C_2)) ),[1,0],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_14,plain,
( skolemFOFtoCNF_C_2 != skolemFOFtoCNF_A_3
| singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_C_2)) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_2,skolemFOFtoCNF_A_3) )],[refute_1_11,refute_1_14]) ).
cnf(refute_1_16,plain,
cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) = cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)),
introduced(tautology,[refl,[$fot(cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_1_17,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) != cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))
| singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_A_3)
| cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) = cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))) ),[1,0],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_18,plain,
( singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_A_3)
| cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) = cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) = cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_15,refute_1_18]) ).
cnf(refute_1_20,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)) != cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))
| ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)))
| in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))) ),
introduced(tautology,[equality,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))) ),[1],$fot(cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_1_21,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)))
| in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1)),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_D_1))) )],[refute_1_5,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_24,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1)))
| in(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_D_1)) ),
inference(subst,[],[refute_1_23:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(singleton(skolemFOFtoCNF_A_3))),bind(D,$fot(singleton(skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_1_25,plain,
in(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_D_1))) )],[refute_1_22,refute_1_24]) ).
cnf(refute_1_26,plain,
skolemFOFtoCNF_B_1 = skolemFOFtoCNF_D_1,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_D_1)) )],[refute_1_25,refute_1_4]) ).
cnf(refute_1_27,plain,
skolemFOFtoCNF_B_1 != skolemFOFtoCNF_D_1,
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_28,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )],[refute_1_26,refute_1_27]) ).
fof(negate_2_0,plain,
~ ! [A,B,C,D] :
( ( A = C
& B = D )
=> in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D))) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
& A = C
& B = D ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)))
& skolemFOFtoCNF_A_4 = skolemFOFtoCNF_C_3
& skolemFOFtoCNF_B_2 = skolemFOFtoCNF_D_2 ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
skolemFOFtoCNF_B_2 = skolemFOFtoCNF_D_2,
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_4,plain,
skolemFOFtoCNF_A_4 = skolemFOFtoCNF_C_3,
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_5,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_2_6,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(canonicalize,[],[l55_zfmisc_1]) ).
fof(normalize_2_10,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) )
& ( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(clausify,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [A,B,C,D] :
( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(conjunct,[],[normalize_2_11]) ).
cnf(refute_2_0,plain,
~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
skolemFOFtoCNF_B_2 = skolemFOFtoCNF_D_2,
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_2,refute_2_3]) ).
cnf(refute_2_5,plain,
( skolemFOFtoCNF_B_2 != skolemFOFtoCNF_D_2
| skolemFOFtoCNF_D_2 = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_2_4:[bind(X,$fot(skolemFOFtoCNF_B_2)),bind(Y,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_2_6,plain,
skolemFOFtoCNF_D_2 = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) )],[refute_2_1,refute_2_5]) ).
cnf(refute_2_7,plain,
singleton(skolemFOFtoCNF_D_2) = singleton(skolemFOFtoCNF_D_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_2_8,plain,
( singleton(skolemFOFtoCNF_D_2) != singleton(skolemFOFtoCNF_D_2)
| skolemFOFtoCNF_D_2 != skolemFOFtoCNF_B_2
| singleton(skolemFOFtoCNF_D_2) = singleton(skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_D_2),singleton(skolemFOFtoCNF_D_2)) ),[1,0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_2_9,plain,
( skolemFOFtoCNF_D_2 != skolemFOFtoCNF_B_2
| singleton(skolemFOFtoCNF_D_2) = singleton(skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_D_2),singleton(skolemFOFtoCNF_D_2)) )],[refute_2_7,refute_2_8]) ).
cnf(refute_2_10,plain,
singleton(skolemFOFtoCNF_D_2) = singleton(skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B_2) )],[refute_2_6,refute_2_9]) ).
cnf(refute_2_11,plain,
cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)),
introduced(tautology,[refl,[$fot(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_2_12,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2))
| singleton(skolemFOFtoCNF_D_2) != singleton(skolemFOFtoCNF_B_2)
| cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2))) ),[1,1],$fot(singleton(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_13,plain,
( singleton(skolemFOFtoCNF_D_2) != singleton(skolemFOFtoCNF_B_2)
| cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2))) )],[refute_2_11,refute_2_12]) ).
cnf(refute_2_14,plain,
cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_D_2),singleton(skolemFOFtoCNF_B_2)) )],[refute_2_10,refute_2_13]) ).
cnf(refute_2_15,plain,
skolemFOFtoCNF_A_4 = skolemFOFtoCNF_C_3,
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_16,plain,
( skolemFOFtoCNF_A_4 != skolemFOFtoCNF_C_3
| skolemFOFtoCNF_C_3 = skolemFOFtoCNF_A_4 ),
inference(subst,[],[refute_2_4:[bind(X,$fot(skolemFOFtoCNF_A_4)),bind(Y,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_17,plain,
skolemFOFtoCNF_C_3 = skolemFOFtoCNF_A_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) )],[refute_2_15,refute_2_16]) ).
cnf(refute_2_18,plain,
singleton(skolemFOFtoCNF_C_3) = singleton(skolemFOFtoCNF_C_3),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_19,plain,
( singleton(skolemFOFtoCNF_C_3) != singleton(skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C_3 != skolemFOFtoCNF_A_4
| singleton(skolemFOFtoCNF_C_3) = singleton(skolemFOFtoCNF_A_4) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_C_3)) ),[1,0],$fot(skolemFOFtoCNF_A_4)]]) ).
cnf(refute_2_20,plain,
( skolemFOFtoCNF_C_3 != skolemFOFtoCNF_A_4
| singleton(skolemFOFtoCNF_C_3) = singleton(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_C_3)) )],[refute_2_18,refute_2_19]) ).
cnf(refute_2_21,plain,
singleton(skolemFOFtoCNF_C_3) = singleton(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_3,skolemFOFtoCNF_A_4) )],[refute_2_17,refute_2_20]) ).
cnf(refute_2_22,plain,
cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)),
introduced(tautology,[refl,[$fot(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_2_23,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))
| singleton(skolemFOFtoCNF_C_3) != singleton(skolemFOFtoCNF_A_4)
| cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) ),[1,0],$fot(singleton(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_2_24,plain,
( singleton(skolemFOFtoCNF_C_3) != singleton(skolemFOFtoCNF_A_4)
| cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) )],[refute_2_22,refute_2_23]) ).
cnf(refute_2_25,plain,
cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_A_4)) )],[refute_2_21,refute_2_24]) ).
cnf(refute_2_26,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_27,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_4,refute_2_26]) ).
cnf(refute_2_28,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))
| cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2))
| cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)) ),
inference(subst,[],[refute_2_27:[bind(X,$fot(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)))),bind(Y,$fot(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)))),bind(Z,$fot(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))))]]) ).
cnf(refute_2_29,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))
| cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2))) )],[refute_2_25,refute_2_28]) ).
cnf(refute_2_30,plain,
cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) = cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))) )],[refute_2_14,refute_2_29]) ).
cnf(refute_2_31,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)) != cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))
| ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)))
| in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) ),
introduced(tautology,[equality,[$cnf( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) ),[1],$fot(cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_2_32,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2)))
| in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2)),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))) )],[refute_2_30,refute_2_31]) ).
cnf(refute_2_33,plain,
~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_C_3),singleton(skolemFOFtoCNF_D_2))) )],[refute_2_32,refute_2_0]) ).
cnf(refute_2_34,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_35,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_2_34:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_2_36,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_2_37,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_2_36,refute_2_35]) ).
cnf(refute_2_38,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_2_39,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_2_38,refute_2_37]) ).
cnf(refute_2_40,plain,
in(X_239,singleton(X_239)),
inference(subst,[],[refute_2_39:[bind(A,$fot(X_239))]]) ).
cnf(refute_2_41,plain,
in(X_234,singleton(X_234)),
inference(subst,[],[refute_2_39:[bind(A,$fot(X_234))]]) ).
cnf(refute_2_42,plain,
( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_43,plain,
( ~ in(X_234,singleton(X_234))
| ~ in(X_235,X_237)
| in(ordered_pair(X_234,X_235),cartesian_product2(singleton(X_234),X_237)) ),
inference(subst,[],[refute_2_42:[bind(A,$fot(X_234)),bind(B,$fot(X_235)),bind(C,$fot(singleton(X_234))),bind(D,$fot(X_237))]]) ).
cnf(refute_2_44,plain,
( ~ in(X_235,X_237)
| in(ordered_pair(X_234,X_235),cartesian_product2(singleton(X_234),X_237)) ),
inference(resolve,[$cnf( in(X_234,singleton(X_234)) )],[refute_2_41,refute_2_43]) ).
cnf(refute_2_45,plain,
( ~ in(X_239,singleton(X_239))
| in(ordered_pair(X_238,X_239),cartesian_product2(singleton(X_238),singleton(X_239))) ),
inference(subst,[],[refute_2_44:[bind(X_234,$fot(X_238)),bind(X_235,$fot(X_239)),bind(X_237,$fot(singleton(X_239)))]]) ).
cnf(refute_2_46,plain,
in(ordered_pair(X_238,X_239),cartesian_product2(singleton(X_238),singleton(X_239))),
inference(resolve,[$cnf( in(X_239,singleton(X_239)) )],[refute_2_40,refute_2_45]) ).
cnf(refute_2_47,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))),
inference(subst,[],[refute_2_46:[bind(X_238,$fot(skolemFOFtoCNF_A_4)),bind(X_239,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_48,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(singleton(skolemFOFtoCNF_A_4),singleton(skolemFOFtoCNF_B_2))) )],[refute_2_47,refute_2_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.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 : Mon Jul 11 03:08:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.77/10.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.77/10.94
% 10.77/10.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.77/10.95
%------------------------------------------------------------------------------