TSTP Solution File: SET979+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:38:45 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 74 ( 42 unt; 0 def)
% Number of atoms : 118 ( 116 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 91 ( 47 ~; 36 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(t132_zfmisc_1,conjecture,
! [A,B,C] :
( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
& cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ).
fof(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ).
fof(subgoal_0,plain,
! [A,B,C] : cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)),
inference(strip,[],[t132_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
=> cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ),
inference(strip,[],[t132_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] : cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] : cartesian_product2(unordered_pair(A,B),C) != set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[t41_enumset1]) ).
fof(normalize_0_3,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(specialize,[],[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))
& ! [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_5,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_4]) ).
fof(normalize_0_6,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_5]) ).
cnf(refute_0_0,plain,
cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[normalize_0_3]) ).
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( unordered_pair(A,B) != set_union2(singleton(A),singleton(B))
| set_union2(singleton(A),singleton(B)) = unordered_pair(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(unordered_pair(A,B))),bind(Y,$fot(set_union2(singleton(A),singleton(B))))]]) ).
cnf(refute_0_6,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),set_union2(singleton(A),singleton(B))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) = cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C))]]) ).
cnf(refute_0_9,plain,
( cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) != cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C),cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C)) ),[1,0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_10,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C),cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_13,plain,
( cartesian_product2(set_union2(A,B),C) != set_union2(cartesian_product2(A,C),cartesian_product2(B,C))
| set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) = cartesian_product2(set_union2(A,B),C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(cartesian_product2(set_union2(A,B),C))),bind(Y,$fot(set_union2(cartesian_product2(A,C),cartesian_product2(B,C))))]]) ).
cnf(refute_0_14,plain,
set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) = cartesian_product2(set_union2(A,B),C),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(A,B),C),set_union2(cartesian_product2(A,C),cartesian_product2(B,C))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) = cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C),
inference(subst,[],[refute_0_14:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(singleton(skolemFOFtoCNF_B))),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) != cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C)
| set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)))),bind(Y,$fot(cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C))),bind(Z,$fot(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_19,plain,
( cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)),cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(cartesian_product2(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_C),cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C))) ),[1],$fot(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C))]]) ).
cnf(refute_0_22,plain,
( cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C)),cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_C))) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),cartesian_product2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)) )],[refute_0_24,refute_0_23]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
=> cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) != set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1)))
& cartesian_product2(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = set_union2(cartesian_product2(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_C_1),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1)) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[t41_enumset1]) ).
fof(normalize_1_4,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,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_1_6,plain,
! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(specialize,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( unordered_pair(A,B) != set_union2(singleton(A),singleton(B))
| set_union2(singleton(A),singleton(B)) = unordered_pair(A,B) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(unordered_pair(A,B))),bind(Y,$fot(set_union2(singleton(A),singleton(B))))]]) ).
cnf(refute_1_6,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),set_union2(singleton(A),singleton(B))) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_1_6:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_8,plain,
cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))),
introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_1_9,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) != cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)))
| set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))),cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)))) ),[1,1],$fot(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_10,plain,
( set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))),cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)))) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)),unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_7,refute_1_10]) ).
cnf(refute_1_12,plain,
cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_13,plain,
( cartesian_product2(C,set_union2(A,B)) != set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
| set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) = cartesian_product2(C,set_union2(A,B)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(cartesian_product2(C,set_union2(A,B)))),bind(Y,$fot(set_union2(cartesian_product2(C,A),cartesian_product2(C,B))))]]) ).
cnf(refute_1_14,plain,
set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) = cartesian_product2(C,set_union2(A,B)),
inference(resolve,[$cnf( $equal(cartesian_product2(C,set_union2(A,B)),set_union2(cartesian_product2(C,A),cartesian_product2(C,B))) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))),
inference(subst,[],[refute_1_14:[bind(A,$fot(singleton(skolemFOFtoCNF_A_3))),bind(B,$fot(singleton(skolemFOFtoCNF_B_1))),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_16]) ).
cnf(refute_1_18,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) != cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)))
| set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))))),bind(Y,$fot(cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))))),bind(Z,$fot(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_1_19,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))),cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)))) )],[refute_1_15,refute_1_18]) ).
cnf(refute_1_20,plain,
set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_C_1,set_union2(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1))),cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) )],[refute_1_11,refute_1_19]) ).
cnf(refute_1_21,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) = set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1)))) ),[1],$fot(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_22,plain,
( cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))
| cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) = set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))) ),
inference(resolve,[$cnf( $equal(set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1))),cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) != cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),set_union2(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_B_1)))) )],[refute_1_22,refute_1_0]) ).
cnf(refute_1_24,plain,
cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) = cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),
introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_25,plain,
$false,
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)),cartesian_product2(skolemFOFtoCNF_C_1,unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))) )],[refute_1_24,refute_1_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 : Sat Jul 9 21:11:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------