TSTP Solution File: SEU157+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:38:51 EDT 2022
% Result : Theorem 43.44s 43.66s
% Output : CNFRefutation 43.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 123 ( 39 unt; 0 def)
% Number of atoms : 355 ( 168 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 394 ( 162 ~; 153 |; 57 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-3 aty)
% Number of variables : 264 ( 8 sgn 126 !; 34 ?)
% 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(l55_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ) ).
fof(t33_zfmisc_1,axiom,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( A = C
& B = D ) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(A,C) ),
inference(strip,[],[l55_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C) )
=> in(B,D) ),
inference(strip,[],[l55_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C,D] :
( ( in(A,C)
& in(B,D) )
=> in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(strip,[],[l55_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( ~ in(A,C)
& ? [D] : in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& ? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_5,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_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| ( A = C
& B = D ) ),
inference(canonicalize,[],[t33_zfmisc_1]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| ( A = C
& B = D ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( ordered_pair(A,B) != ordered_pair(C,D)
| A = C )
& ( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| A = C ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,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_6]) ).
fof(normalize_0_13,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,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_1:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_3,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_0_4,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ordered_pair(A,B) != ordered_pair(C,D)
| A = C ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| A = skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))),bind(D,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))))]]) ).
cnf(refute_0_9,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_11,plain,
( ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_3,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_13,plain,
ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) = ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))))]]) ).
cnf(refute_0_18,plain,
ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) = ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) != ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))) ),[1],$fot(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_20,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| A = skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))) )],[refute_0_20,refute_0_8]) ).
cnf(refute_0_22,plain,
( ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_23,plain,
ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))))]]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != skolemFOFtoCNF_A_2
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_28,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_A_2) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1,ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_C) )],[refute_0_6,refute_0_28]) ).
cnf(refute_0_30,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_29,refute_0_30]) ).
fof(negate_1_0,plain,
~ ! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C) )
=> in(B,D) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C,D] :
( ~ in(B,D)
& in(A,C)
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2)
& in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
& in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,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_1_4,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_1_3]) ).
fof(normalize_1_5,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_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| ( A = C
& B = D ) ),
inference(canonicalize,[],[t33_zfmisc_1]) ).
fof(normalize_1_8,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| ( A = C
& B = D ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C,D] :
( ( ordered_pair(A,B) != ordered_pair(C,D)
| A = C )
& ( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,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_1_5]) ).
fof(normalize_1_12,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,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_1_1:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_1_3,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_1_4,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_6,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_1_0,refute_1_5]) ).
cnf(refute_1_7,plain,
( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_8,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))
| B = skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_1_7:[bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))),bind(D,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_1_9,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_10,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(subst,[],[refute_1_9:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_1_11,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( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_1_3,refute_1_10]) ).
cnf(refute_1_12,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_1_11:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_13,plain,
ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_1_0,refute_1_12]) ).
cnf(refute_1_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
( ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) = ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_16:[bind(X,$fot(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))))]]) ).
cnf(refute_1_18,plain,
ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) = ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))) )],[refute_1_13,refute_1_17]) ).
cnf(refute_1_19,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) != ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))) ),[1],$fot(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_20,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| B = skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))) )],[refute_1_20,refute_1_8]) ).
cnf(refute_1_22,plain,
( ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_1_21:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_23,plain,
ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
introduced(tautology,[refl,[$fot(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_24,plain,
skolemFOFtoCNF_B_1 = skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_23,refute_1_22]) ).
cnf(refute_1_25,plain,
( skolemFOFtoCNF_B_1 != skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_16:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_1_26,plain,
skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) )],[refute_1_24,refute_1_25]) ).
cnf(refute_1_27,plain,
( skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_B_1
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2)
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_28,plain,
( ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2)
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_B_1) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2,ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_D_2) )],[refute_1_6,refute_1_28]) ).
cnf(refute_1_30,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_2) )],[refute_1_29,refute_1_30]) ).
fof(negate_2_0,plain,
~ ! [A,B,C,D] :
( ( in(A,C)
& in(B,D) )
=> in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C)
& in(B,D) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3))
& in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
& in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_3) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_3),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_4,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_2_5,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_2_4]) ).
fof(normalize_2_6,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_2_5]) ).
fof(normalize_2_7,plain,
! [A,B,C,D,E,F] :
( C != cartesian_product2(A,B)
| D != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(D,C) ),
inference(conjunct,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3)),
inference(conjunct,[],[normalize_2_1]) ).
cnf(refute_2_0,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_3),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_2,plain,
( C != cartesian_product2(A,B)
| D != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ordered_pair(E,F) != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(ordered_pair(E,F),cartesian_product2(A,B)) ),
inference(subst,[],[refute_2_2:[bind(C,$fot(cartesian_product2(A,B))),bind(D,$fot(ordered_pair(E,F)))]]) ).
cnf(refute_2_4,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_2_5,plain,
( ordered_pair(E,F) != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(ordered_pair(E,F),cartesian_product2(A,B)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_2_4,refute_2_3]) ).
cnf(refute_2_6,plain,
ordered_pair(E,F) = ordered_pair(E,F),
introduced(tautology,[refl,[$fot(ordered_pair(E,F))]]) ).
cnf(refute_2_7,plain,
( ~ in(E,A)
| ~ in(F,B)
| in(ordered_pair(E,F),cartesian_product2(A,B)) ),
inference(resolve,[$cnf( $equal(ordered_pair(E,F),ordered_pair(E,F)) )],[refute_2_6,refute_2_5]) ).
cnf(refute_2_8,plain,
( ~ in(X_377,X_375)
| ~ in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
| in(ordered_pair(skolemFOFtoCNF_A_4,X_377),cartesian_product2(skolemFOFtoCNF_C_2,X_375)) ),
inference(subst,[],[refute_2_7:[bind(A,$fot(skolemFOFtoCNF_C_2)),bind(B,$fot(X_375)),bind(E,$fot(skolemFOFtoCNF_A_4)),bind(F,$fot(X_377))]]) ).
cnf(refute_2_9,plain,
( ~ in(X_377,X_375)
| in(ordered_pair(skolemFOFtoCNF_A_4,X_377),cartesian_product2(skolemFOFtoCNF_C_2,X_375)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2) )],[refute_2_1,refute_2_8]) ).
cnf(refute_2_10,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_3)
| in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3)) ),
inference(subst,[],[refute_2_9:[bind(X_375,$fot(skolemFOFtoCNF_D_3)),bind(X_377,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_11,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_3) )],[refute_2_0,refute_2_10]) ).
cnf(refute_2_12,plain,
~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3)),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_13,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_3)) )],[refute_2_11,refute_2_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 11:28:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 43.44/43.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.44/43.66
% 43.44/43.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.44/43.67
%------------------------------------------------------------------------------