TSTP Solution File: SET951+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET951+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:38:35 EDT 2022
% Result : Theorem 73.45s 73.67s
% Output : CNFRefutation 73.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 125 ( 33 unt; 0 def)
% Number of atoms : 327 ( 149 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 369 ( 167 ~; 153 |; 34 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 229 ( 12 sgn 113 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
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_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ) ).
fof(t104_zfmisc_1,conjecture,
! [A,B,C,D,E] :
~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
& ! [F,G] :
~ ( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ) ).
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,E] :
( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
=> ~ ! [F,G] :
~ ( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
inference(strip,[],[t104_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D,E] :
( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
=> ~ ! [F,G] :
~ ( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D,E] :
( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
& ! [F,G] :
( A != ordered_pair(F,G)
| ~ in(F,set_intersection2(B,D))
| ~ in(G,set_intersection2(C,E)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)))
& ! [F,G] :
( skolemFOFtoCNF_A_2 != ordered_pair(F,G)
| ~ in(F,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(G,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_1(A,B,C),A)
| in(skolemFOFtoCNF_D_1(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| in(skolemFOFtoCNF_D_1(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D_1(A,B,C),A)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),B)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_13,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_14,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| ( A = C
& B = D ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| A = C ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,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_9]) ).
fof(normalize_0_18,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_19,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [F,G] :
( skolemFOFtoCNF_A_2 != ordered_pair(F,G)
| ~ in(F,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(G,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_21,plain,
! [F,G] :
( skolemFOFtoCNF_A_2 != ordered_pair(F,G)
| ~ in(F,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(G,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,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_9]) ).
fof(normalize_0_23,plain,
! [A,B,C,D] :
( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_1:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_3,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_4,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)))
| in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_9,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_0_10,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_E_1(A,B,D),A) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_12,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_15,plain,
( ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),X_108)
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(X_108,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_108)),bind(B,$fot(skolemFOFtoCNF_B)),bind(D,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_17,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),X_108)
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(X_108,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2)
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_17:[bind(X_108,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_19,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_20,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,B) ),
inference(subst,[],[refute_0_19:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_21,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,B) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_3,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)))
| in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_23,plain,
in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,set_intersection2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))) )],[refute_0_0,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_D_2)),bind(B,$fot(skolemFOFtoCNF_E_2)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_25,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ordered_pair(A,B) != ordered_pair(C,D)
| A = C ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_27,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))
| A = skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_26:[bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))),bind(D,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_28,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(subst,[],[refute_0_28:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_30,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( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_9,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))
| skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_D_2)),bind(B,$fot(skolemFOFtoCNF_E_2)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_32,plain,
skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)) )],[refute_0_23,refute_0_31]) ).
cnf(refute_0_33,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_34,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_35,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_A_2 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_37,plain,
ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( ordered_pair(A,B) != skolemFOFtoCNF_A_2
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_39,plain,
( ordered_pair(A,B) != skolemFOFtoCNF_A_2
| ordered_pair(A,B) = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ordered_pair(A,B) != skolemFOFtoCNF_A_2
| A = skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))) )],[refute_0_39,refute_0_27]) ).
cnf(refute_0_41,plain,
( ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_42,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_43,plain,
skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_6,refute_0_42]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_A_2 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_45,plain,
ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_47,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_47,refute_0_41]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_A_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_50,plain,
skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_49,refute_0_48]) ).
cnf(refute_0_51,plain,
( skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(Y,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_52,plain,
skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2)
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) ),[0],$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_54,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2)
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) )],[refute_0_25,refute_0_54]) ).
cnf(refute_0_56,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_D_2) )],[refute_0_55,refute_0_18]) ).
cnf(refute_0_57,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_58,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_59,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) = set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_59:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_61,plain,
( set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B) != set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B)) ),[1],$fot(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_62,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_B)) )],[refute_0_56,refute_0_62]) ).
cnf(refute_0_64,plain,
( skolemFOFtoCNF_A_2 != ordered_pair(F,G)
| ~ in(F,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(G,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_65,plain,
( skolemFOFtoCNF_A_2 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_64:[bind(F,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(G,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_66,plain,
( ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_A_2,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_67,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_45,refute_0_66]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))) )],[refute_0_67,refute_0_65]) ).
cnf(refute_0_69,plain,
( ~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_49,refute_0_68]) ).
cnf(refute_0_70,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_71,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(subst,[],[refute_0_70:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_72,plain,
( ~ in(D,cartesian_product2(A,B))
| in(skolemFOFtoCNF_F_1(A,B,D),B) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_9,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_74,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_6,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),X_109)
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,X_109)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(X_109)),bind(D,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_76,plain,
( ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),X_109)
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,X_109)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2)
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_76:[bind(X_109,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_78,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2))
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_72:[bind(A,$fot(skolemFOFtoCNF_D_2)),bind(B,$fot(skolemFOFtoCNF_E_2)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_79,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2)) )],[refute_0_23,refute_0_78]) ).
cnf(refute_0_80,plain,
( ordered_pair(A,B) != ordered_pair(C,D)
| B = D ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_81,plain,
( ordered_pair(A,B) != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))
| B = skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_80:[bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))),bind(D,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_82,plain,
( ordered_pair(A,B) != skolemFOFtoCNF_A_2
| B = skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(ordered_pair(A,B),ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2))) )],[refute_0_39,refute_0_81]) ).
cnf(refute_0_83,plain,
( ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_82:[bind(A,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_84,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_47,refute_0_83]) ).
cnf(refute_0_85,plain,
skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_49,refute_0_84]) ).
cnf(refute_0_86,plain,
( skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(Y,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_87,plain,
skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2)
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) ),[0],$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_89,plain,
( ~ in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2)
| in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_D_2,skolemFOFtoCNF_E_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) )],[refute_0_79,refute_0_89]) ).
cnf(refute_0_91,plain,
in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_E_2) )],[refute_0_90,refute_0_77]) ).
cnf(refute_0_92,plain,
~ in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_E_2)) )],[refute_0_91,refute_0_69]) ).
cnf(refute_0_93,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) )],[refute_0_63,refute_0_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET951+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 00:00:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 73.45/73.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.45/73.67
% 73.45/73.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 73.45/73.67
%------------------------------------------------------------------------------