TSTP Solution File: SET046+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET046+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:31:47 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 54 ( 24 ~; 16 |; 8 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 14 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel42,conjecture,
~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(X,Z)
& element(Z,X) ) ) ).
fof(subgoal_0,plain,
! [Y] :
~ ! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(X,Z)
& element(Z,X) ) ),
inference(strip,[],[pel42]) ).
fof(negate_0_0,plain,
~ ! [Y] :
~ ! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(X,Z)
& element(Z,X) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Y] :
! [X] :
( ~ element(X,Y)
<=> ? [Z] :
( element(X,Z)
& element(Z,X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ element(X,skolemFOFtoCNF_Y)
<=> ? [Z] :
( element(X,Z)
& element(Z,X) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ element(X,skolemFOFtoCNF_Y)
<=> ? [Z] :
( element(X,Z)
& element(Z,X) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Z] :
( ( element(X,skolemFOFtoCNF_Y)
| element(X,skolemFOFtoCNF_Z(X)) )
& ( element(X,skolemFOFtoCNF_Y)
| element(skolemFOFtoCNF_Z(X),X) )
& ( ~ element(X,Z)
| ~ element(X,skolemFOFtoCNF_Y)
| ~ element(Z,X) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Z] :
( ~ element(X,Z)
| ~ element(X,skolemFOFtoCNF_Y)
| ~ element(Z,X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( element(X,skolemFOFtoCNF_Y)
| element(skolemFOFtoCNF_Z(X),X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [X] :
( element(X,skolemFOFtoCNF_Y)
| element(X,skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ element(X,Z)
| ~ element(X,skolemFOFtoCNF_Y)
| ~ element(Z,X) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z(skolemFOFtoCNF_Y))
| ~ element(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y))),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( element(X,skolemFOFtoCNF_Y)
| element(skolemFOFtoCNF_Z(X),X) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y)
| element(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
( ~ element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z(skolemFOFtoCNF_Y))
| element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
~ element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
~ element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z(skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( element(X,skolemFOFtoCNF_Y)
| element(X,skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y)
| element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z(skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_9,plain,
element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z(skolemFOFtoCNF_Y)) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( element(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_9,refute_0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET046+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.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 : Sat Jul 9 18:20:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------