TSTP Solution File: SET095+4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:32:33 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 7 unt; 0 def)
% Number of atoms : 72 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 28 ~; 21 |; 7 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ) ).
fof(thI44,conjecture,
! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ) ).
fof(subgoal_0,plain,
! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
inference(strip,[],[thI44]) ).
fof(negate_0_0,plain,
~ ! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,X] :
( ( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) )
& ( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) )
& ( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,X] :
( ~ subset(singleton(X),A)
& member(X,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A)
& member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,X] :
( X != A
<=> ~ member(X,singleton(A)) ),
inference(canonicalize,[],[singleton]) ).
fof(normalize_0_8,plain,
! [A,X] :
( X != A
<=> ~ member(X,singleton(A)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,X] :
( ( X != A
| member(X,singleton(A)) )
& ( ~ member(X,singleton(A))
| X = A ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,X] :
( ~ member(X,singleton(A))
| X = A ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(singleton(skolemFOFtoCNF_X_1))),bind(B,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_2,plain,
~ subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ member(X,singleton(A))
| X = A ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_X(singleton(A),X_21),singleton(A))
| skolemFOFtoCNF_X(singleton(A),X_21) = A ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X(singleton(A),X_21)))]]) ).
cnf(refute_0_5,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_X(singleton(A),X_21),singleton(A))
| subset(singleton(A),X_21) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(singleton(A))),bind(B,$fot(X_21))]]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_X(singleton(A),X_21) = A
| subset(singleton(A),X_21) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(singleton(A),X_21),singleton(A)) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) = skolemFOFtoCNF_X_1
| subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_X_1)),bind(X_21,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) != skolemFOFtoCNF_X_1
| ~ member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A)
| member(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_A) ),
introduced(tautology,[equality,[$cnf( ~ member(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_A) ),[0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A)
| member(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_X_1) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A)
| subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),skolemFOFtoCNF_A) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_1,skolemFOFtoCNF_A) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_X_1),skolemFOFtoCNF_A) )],[refute_0_14,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 00:22:31 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------