TSTP Solution File: SET978+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:38:44 EDT 2022
% Result : Theorem 0.22s 0.39s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 93 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 43 ~; 25 |; 15 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 106 ( 12 sgn 66 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t127_zfmisc_1,axiom,
! [A,B,C,D] :
( ( disjoint(A,B)
| disjoint(C,D) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
fof(t131_zfmisc_1,conjecture,
! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))
& disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ) ).
fof(t17_zfmisc_1,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( A != B
=> disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
inference(strip,[],[t131_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C,D] :
( ( A != B
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
=> disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ),
inference(strip,[],[t131_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( A != B
=> disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( A != B
& ? [C,D] : ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
& ? [C,D] : ~ disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),C),cartesian_product2(singleton(skolemFOFtoCNF_B),D)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [C,D] : ~ disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),C),cartesian_product2(singleton(skolemFOFtoCNF_B),D)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_D)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(canonicalize,[],[t17_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(A,B)
& ~ disjoint(C,D) ) ),
inference(canonicalize,[],[t127_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(A,B)
& ~ disjoint(C,D) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ( ~ disjoint(A,B)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) )
& ( ~ disjoint(C,D)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ~ disjoint(A,B)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_D)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ disjoint(A,B)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( ~ disjoint(singleton(A),singleton(B))
| disjoint(cartesian_product2(singleton(A),X_6),cartesian_product2(singleton(B),X_7)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(singleton(A))),bind(B,$fot(singleton(B))),bind(C,$fot(X_6)),bind(D,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
( A = B
| disjoint(cartesian_product2(singleton(A),X_6),cartesian_product2(singleton(B),X_7)) ),
inference(resolve,[$cnf( disjoint(singleton(A),singleton(B)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B
| disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(X_6,$fot(skolemFOFtoCNF_C)),bind(X_7,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),cartesian_product2(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_D)) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_6,refute_0_7]) ).
fof(negate_1_0,plain,
~ ! [A,B,C,D] :
( ( A != B
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
=> disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C,D] :
( A != B
& ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1
& ~ disjoint(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_D_1,singleton(skolemFOFtoCNF_B_1)))
& disjoint(cartesian_product2(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_C_1),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_D_1)) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ disjoint(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_D_1,singleton(skolemFOFtoCNF_B_1))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(canonicalize,[],[t17_zfmisc_1]) ).
fof(normalize_1_4,plain,
! [A,B] :
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(A,B)
& ~ disjoint(C,D) ) ),
inference(canonicalize,[],[t127_zfmisc_1]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(A,B)
& ~ disjoint(C,D) ) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( ( ~ disjoint(A,B)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) )
& ( ~ disjoint(C,D)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ),
inference(clausify,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B,C,D] :
( ~ disjoint(C,D)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
~ disjoint(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_D_1,singleton(skolemFOFtoCNF_B_1))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( A = B
| disjoint(singleton(A),singleton(B)) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ disjoint(C,D)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_3,plain,
( ~ disjoint(singleton(A),singleton(B))
| disjoint(cartesian_product2(X_32,singleton(A)),cartesian_product2(X_33,singleton(B))) ),
inference(subst,[],[refute_1_2:[bind(A,$fot(X_32)),bind(B,$fot(X_33)),bind(C,$fot(singleton(A))),bind(D,$fot(singleton(B)))]]) ).
cnf(refute_1_4,plain,
( A = B
| disjoint(cartesian_product2(X_32,singleton(A)),cartesian_product2(X_33,singleton(B))) ),
inference(resolve,[$cnf( disjoint(singleton(A),singleton(B)) )],[refute_1_1,refute_1_3]) ).
cnf(refute_1_5,plain,
( skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1
| disjoint(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_D_1,singleton(skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(X_32,$fot(skolemFOFtoCNF_C_1)),bind(X_33,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( disjoint(cartesian_product2(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)),cartesian_product2(skolemFOFtoCNF_D_1,singleton(skolemFOFtoCNF_B_1))) )],[refute_1_5,refute_1_0]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_8,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) )],[refute_1_6,refute_1_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jul 9 16:22:25 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.39
% 0.22/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.39
%------------------------------------------------------------------------------