TSTP Solution File: SET968+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:38:40 EDT 2022
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 51 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 92 ( 48 ~; 42 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(t120_zfmisc_1,axiom,
! [A,B,C] :
( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C))
& cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ).
fof(t121_zfmisc_1,conjecture,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)) ).
fof(t4_xboole_1,axiom,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)) ).
fof(subgoal_0,plain,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(strip,[],[t121_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) != set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& ! [A,B,C] : cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(canonicalize,[],[t120_zfmisc_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(canonicalize,[],[t4_xboole_1]) ).
fof(normalize_0_6,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] : cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [A,B,C] : cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_10,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( cartesian_product2(C,set_union2(A,B)) != set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
| set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) = cartesian_product2(C,set_union2(A,B)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(cartesian_product2(C,set_union2(A,B)))),bind(Y,$fot(set_union2(cartesian_product2(C,A),cartesian_product2(C,B))))]]) ).
cnf(refute_0_6,plain,
set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) = cartesian_product2(C,set_union2(A,B)),
inference(resolve,[$cnf( $equal(cartesian_product2(C,set_union2(A,B)),set_union2(cartesian_product2(C,A),cartesian_product2(C,B))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),
introduced(tautology,[refl,[$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_9,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))
| set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) ),[1,1],$fot(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_10,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),
introduced(tautology,[refl,[$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))))]]) ).
cnf(refute_0_13,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))) ),[1,1],$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_14,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_17,plain,
set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),
inference(subst,[],[refute_0_16:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D))),bind(C,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_18,plain,
set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),
inference(subst,[],[refute_0_16:[bind(A,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))),bind(C,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_19,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),bind(Y,$fot(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))),bind(Z,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))))]]) ).
cnf(refute_0_22,plain,
( set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) ),
inference(resolve,[$cnf( $equal(set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),
inference(resolve,[$cnf( $equal(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),bind(Y,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))))),bind(Z,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))))]]) ).
cnf(refute_0_25,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
inference(resolve,[$cnf( $equal(set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),set_union2(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))) )],[refute_0_15,refute_0_25]) ).
cnf(refute_0_27,plain,
( cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))
| set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))
| cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) ),[1],$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))))]]) ).
cnf(refute_0_28,plain,
( cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))
| cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),set_union2(set_union2(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) )],[refute_0_28,refute_0_0]) ).
cnf(refute_0_30,plain,
cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_31,plain,
( cartesian_product2(set_union2(A,B),C) != set_union2(cartesian_product2(A,C),cartesian_product2(B,C))
| set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) = cartesian_product2(set_union2(A,B),C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(cartesian_product2(set_union2(A,B),C))),bind(Y,$fot(set_union2(cartesian_product2(A,C),cartesian_product2(B,C))))]]) ).
cnf(refute_0_32,plain,
set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) = cartesian_product2(set_union2(A,B),C),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(A,B),C),set_union2(cartesian_product2(A,C),cartesian_product2(B,C))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(subst,[],[refute_0_32:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_34,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_35,plain,
set_union2(X_8,X_7) = set_union2(X_7,X_8),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_8)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_36,plain,
( set_union2(X_8,X_7) != set_union2(X_7,X_8)
| set_union2(X_7,X_8) = set_union2(X_8,X_7) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(set_union2(X_8,X_7))),bind(Y,$fot(set_union2(X_7,X_8)))]]) ).
cnf(refute_0_37,plain,
set_union2(X_7,X_8) = set_union2(X_8,X_7),
inference(resolve,[$cnf( $equal(set_union2(X_8,X_7),set_union2(X_7,X_8)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),
inference(subst,[],[refute_0_37:[bind(X_7,$fot(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),bind(X_8,$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_39,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) != set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))
| set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))),bind(Y,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))),bind(Z,$fot(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_40,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
set_union2(A,set_union2(X_7,X_8)) = set_union2(set_union2(X_7,X_8),A),
inference(subst,[],[refute_0_34:[bind(B,$fot(set_union2(X_7,X_8)))]]) ).
cnf(refute_0_43,plain,
set_union2(set_union2(X_7,X_8),A) = set_union2(X_7,set_union2(X_8,A)),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_7)),bind(B,$fot(X_8)),bind(C,$fot(A))]]) ).
cnf(refute_0_44,plain,
( set_union2(A,set_union2(X_7,X_8)) != set_union2(set_union2(X_7,X_8),A)
| set_union2(set_union2(X_7,X_8),A) != set_union2(X_7,set_union2(X_8,A))
| set_union2(A,set_union2(X_7,X_8)) = set_union2(X_7,set_union2(X_8,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_union2(A,set_union2(X_7,X_8)),set_union2(X_7,set_union2(X_8,A))) ),[0],$fot(set_union2(set_union2(X_7,X_8),A))]]) ).
cnf(refute_0_45,plain,
( set_union2(A,set_union2(X_7,X_8)) != set_union2(set_union2(X_7,X_8),A)
| set_union2(A,set_union2(X_7,X_8)) = set_union2(X_7,set_union2(X_8,A)) ),
inference(resolve,[$cnf( $equal(set_union2(set_union2(X_7,X_8),A),set_union2(X_7,set_union2(X_8,A))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
set_union2(A,set_union2(X_7,X_8)) = set_union2(X_7,set_union2(X_8,A)),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(X_7,X_8)),set_union2(set_union2(X_7,X_8),A)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
set_union2(A,set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))) = set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)),
inference(subst,[],[refute_0_46:[bind(X_7,$fot(cartesian_product2(X_22,X_20))),bind(X_8,$fot(cartesian_product2(X_22,X_21)))]]) ).
cnf(refute_0_48,plain,
cartesian_product2(X_22,set_union2(X_20,X_21)) = set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21)),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_20)),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_49,plain,
( cartesian_product2(X_22,set_union2(X_20,X_21)) != set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))
| set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21)) = cartesian_product2(X_22,set_union2(X_20,X_21)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(cartesian_product2(X_22,set_union2(X_20,X_21)))),bind(Y,$fot(set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))))]]) ).
cnf(refute_0_50,plain,
set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21)) = cartesian_product2(X_22,set_union2(X_20,X_21)),
inference(resolve,[$cnf( $equal(cartesian_product2(X_22,set_union2(X_20,X_21)),set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( set_union2(A,set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))) != set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))
| set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21)) != cartesian_product2(X_22,set_union2(X_20,X_21))
| set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))) = set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))),set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))) ),[0,1],$fot(cartesian_product2(X_22,set_union2(X_20,X_21)))]]) ).
cnf(refute_0_52,plain,
( set_union2(A,set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))) != set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))
| set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))) = set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21)),cartesian_product2(X_22,set_union2(X_20,X_21))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))) = set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)),
inference(resolve,[$cnf( $equal(set_union2(A,set_union2(cartesian_product2(X_22,X_20),cartesian_product2(X_22,X_21))),set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
( set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))) != set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))
| set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)) = set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))))),bind(Y,$fot(set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))))]]) ).
cnf(refute_0_55,plain,
set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A)) = set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))),
inference(resolve,[$cnf( $equal(set_union2(A,cartesian_product2(X_22,set_union2(X_20,X_21))),set_union2(cartesian_product2(X_22,X_20),set_union2(cartesian_product2(X_22,X_21),A))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) = set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),
inference(subst,[],[refute_0_55:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),bind(X_20,$fot(skolemFOFtoCNF_C)),bind(X_21,$fot(skolemFOFtoCNF_D)),bind(X_22,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_57,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) != set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))
| set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))))),bind(Y,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))),bind(Z,$fot(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_58,plain,
( set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))),cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_41,refute_0_58]) ).
cnf(refute_0_60,plain,
( cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))) ),[1],$fot(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_61,plain,
( cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_union2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))) )],[refute_0_61,refute_0_29]) ).
cnf(refute_0_63,plain,
cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
introduced(tautology,[refl,[$fot(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_64,plain,
$false,
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_63,refute_0_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 02:55:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45
% 0.18/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.46
%------------------------------------------------------------------------------