TSTP Solution File: SET086+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 03:32:25 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 57 ( 36 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 29 ~; 20 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 2 sgn 13 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_of_substitution,conjecture,
! [X] :
? [U] :
( ( member(U,universal_class)
& X = singleton(U) )
| ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& U = X ) ) ).
fof(subgoal_0,plain,
! [X] :
? [U] :
( ( member(U,universal_class)
& X = singleton(U) )
| ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& U = X ) ),
inference(strip,[],[member_of_substitution]) ).
fof(negate_0_0,plain,
~ ! [X] :
? [U] :
( ( member(U,universal_class)
& X = singleton(U) )
| ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& U = X ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ( ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) )
| ! [U] : U != X )
& ! [U] :
( X != singleton(U)
| ~ member(U,universal_class) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ( ? [Y] :
( skolemFOFtoCNF_X_2 = singleton(Y)
& member(Y,universal_class) )
| ! [U] : U != skolemFOFtoCNF_X_2 )
& ! [U] :
( skolemFOFtoCNF_X_2 != singleton(U)
| ~ member(U,universal_class) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ? [Y] :
( skolemFOFtoCNF_X_2 = singleton(Y)
& member(Y,universal_class) )
| ! [U] : U != skolemFOFtoCNF_X_2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U] :
( ( U != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = singleton(skolemFOFtoCNF_Y_1) )
& ( U != skolemFOFtoCNF_X_2
| member(skolemFOFtoCNF_Y_1,universal_class) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [U] :
( U != skolemFOFtoCNF_X_2
| member(skolemFOFtoCNF_Y_1,universal_class) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U] :
( skolemFOFtoCNF_X_2 != singleton(U)
| ~ member(U,universal_class) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [U] :
( skolemFOFtoCNF_X_2 != singleton(U)
| ~ member(U,universal_class) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [U] :
( U != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = singleton(skolemFOFtoCNF_Y_1) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( U != skolemFOFtoCNF_X_2
| member(skolemFOFtoCNF_Y_1,universal_class) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2
| member(skolemFOFtoCNF_Y_1,universal_class) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_X_2 = skolemFOFtoCNF_X_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_Y_1,universal_class),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( skolemFOFtoCNF_X_2 != singleton(U)
| ~ member(U,universal_class) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_X_2 != singleton(skolemFOFtoCNF_Y_1)
| ~ member(skolemFOFtoCNF_Y_1,universal_class) ),
inference(subst,[],[refute_0_4:[bind(U,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_X_2 != singleton(skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,universal_class) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( U != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = singleton(skolemFOFtoCNF_Y_1) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = singleton(skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_7:[bind(U,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_Y_1)) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_0_2,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.08/0.12 % 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 : Sun Jul 10 11:00:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.42
%------------------------------------------------------------------------------