%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:44:19 PM UTC 2026
% Result : Theorem 2.82s 0.78s
% Output : Proof 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 52 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 18 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
& ~ in(C,B) )
| ( ~ subset(C,A)
& in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A,C] :
( ( ( subset(sk0(A,B),A)
& ~ in(sk0(A,B),B) )
| ( ~ subset(sk0(A,B),A)
& in(sk0(A,B),B) )
| B = powerset(A) )
& ( ( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p15,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f5,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f5_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p21,plain,
in(X0,powerset(X0)),
inference(resolution,[status(thm)],[p15,c11]) ).
fof(f2,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c8,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
subset(singleton(X0),powerset(X0)),
inference(resolution,[status(thm)],[p21,c8]) ).
fof(f6,conjecture,
! [A] : subset(singleton(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A] : subset(singleton(A),powerset(A)),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A] : ~ subset(singleton(A),powerset(A)),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
~ subset(singleton(sk3),powerset(sk3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f6_nnf]) ).
cnf(c12,plain,
~ subset(singleton(sk3),powerset(sk3)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p41,plain,
$false,
inference(resolution,[status(thm)],[p30,c12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.32 % Computer : n003.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8046.5625MB
% 0.08/0.32 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Thu Sep 24 12:25:36 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.82/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.82/0.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------