TSTP Solution File: SET971+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:38:42 EDT 2022
% Result : Theorem 0.11s 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 33 unt; 0 def)
% Number of atoms : 110 ( 89 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 42 ~; 35 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(t123_zfmisc_1,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ).
fof(t124_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(strip,[],[t124_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D] :
( set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C)
& subset(A,B)
& subset(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(canonicalize,[],[t123_zfmisc_1]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[t28_xboole_1]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
set_intersection2(A,B) = set_intersection2(B,A),
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_6,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C) = set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_8,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),
introduced(tautology,[refl,[$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_9,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))
| set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C) != set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))) ),[1,1],$fot(set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))]]) ).
cnf(refute_0_10,plain,
( set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C) != set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_13,plain,
( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) != set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))
| set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),bind(Y,$fot(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))))]]) ).
cnf(refute_0_14,plain,
set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))),bind(Y,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)))),bind(Z,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))))]]) ).
cnf(refute_0_19,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) ),[1],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_22,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_25,plain,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_26,plain,
( ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D)
| set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D) = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_27,plain,
set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D) = skolemFOFtoCNF_C,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_29,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D) != skolemFOFtoCNF_C
| cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) ),[1,1],$fot(skolemFOFtoCNF_C)]]) ).
cnf(refute_0_30,plain,
( set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D) != skolemFOFtoCNF_C
| cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D),skolemFOFtoCNF_C) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_33,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_34,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
introduced(tautology,[refl,[$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_36,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_A_2
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_37,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_A_2
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),bind(Y,$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))),bind(Z,$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_40,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_31,refute_0_40]) ).
cnf(refute_0_42,plain,
( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_43,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_43,refute_0_23]) ).
cnf(refute_0_45,plain,
cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_45,refute_0_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 08:19:37 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35
% 0.11/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.11/0.35
%------------------------------------------------------------------------------