TSTP Solution File: SET949+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:38:34 EDT 2022
% Result : Theorem 0.85s 1.05s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 85 ( 46 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 100 ( 44 ~; 32 |; 16 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 81 ( 4 sgn 43 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ) ).
fof(t102_zfmisc_1,conjecture,
! [A,B,C] :
~ ( in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( in(A,cartesian_product2(B,C))
=> ~ ! [D,E] : ordered_pair(D,E) != A ),
inference(strip,[],[t102_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( in(A,cartesian_product2(B,C))
=> ~ ! [D,E] : ordered_pair(D,E) != A ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ? [B,C] : in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [B,C] : in(skolemFOFtoCNF_A_2,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != skolemFOFtoCNF_A_2 ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B,C] : in(skolemFOFtoCNF_A_2,cartesian_product2(B,C)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != cartesian_product2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(E,A)
& in(F,B) ) ) ),
inference(canonicalize,[],[d2_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != cartesian_product2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(E,A)
& in(F,B) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D,E,F] :
( ( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) )
& ( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_E_1(A,B,D),A) )
& ( C != cartesian_product2(A,B)
| ~ in(D,C)
| in(skolemFOFtoCNF_F_1(A,B,D),B) )
& ( C = cartesian_product2(A,B)
| skolemFOFtoCNF_D(A,B,C) = ordered_pair(skolemFOFtoCNF_E(A,B,C),skolemFOFtoCNF_F(A,B,C))
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = cartesian_product2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C)
| in(skolemFOFtoCNF_E(A,B,C),A) )
& ( C = cartesian_product2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C)
| in(skolemFOFtoCNF_F(A,B,C),B) )
& ( C != cartesian_product2(A,B)
| D != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| in(D,C) )
& ( skolemFOFtoCNF_D(A,B,C) != ordered_pair(E,F)
| ~ in(E,A)
| ~ in(F,B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = cartesian_product2(A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [D,E] : ordered_pair(D,E) != skolemFOFtoCNF_A_2,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [D,E] : ordered_pair(D,E) != skolemFOFtoCNF_A_2,
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( C != cartesian_product2(A,B)
| ~ in(D,C)
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( cartesian_product2(A,B) != cartesian_product2(A,B)
| ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(subst,[],[refute_0_1:[bind(C,$fot(cartesian_product2(A,B)))]]) ).
cnf(refute_0_3,plain,
cartesian_product2(A,B) = cartesian_product2(A,B),
introduced(tautology,[refl,[$fot(cartesian_product2(A,B))]]) ).
cnf(refute_0_4,plain,
( ~ in(D,cartesian_product2(A,B))
| D = ordered_pair(skolemFOFtoCNF_E_1(A,B,D),skolemFOFtoCNF_F_1(A,B,D)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(A,B),cartesian_product2(A,B)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_A_2 = ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
ordered_pair(D,E) != skolemFOFtoCNF_A_2,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_A_2 != ordered_pair(D,E)
| ordered_pair(D,E) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(ordered_pair(D,E)))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_A_2 != ordered_pair(D,E),
inference(resolve,[$cnf( $equal(ordered_pair(D,E),skolemFOFtoCNF_A_2) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_A_2 != ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_12:[bind(D,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))),bind(E,$fot(skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,ordered_pair(skolemFOFtoCNF_E_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2),skolemFOFtoCNF_F_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C,skolemFOFtoCNF_A_2))) )],[refute_0_6,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.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 : Sun Jul 10 13:04:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.85/1.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/1.05
% 0.85/1.05 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.85/1.06
%------------------------------------------------------------------------------