%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET924+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 : n026.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 02:44:18 PM UTC 2026
% Result : Theorem 3.90s 1.08s
% Output : Proof 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 36 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 11 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c8,plain,
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f3,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
fof(f3_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [A,B] :
( ( ~ in(A,B)
& set_difference(singleton(A),B) != singleton(A) )
| ( in(A,B)
& set_difference(singleton(A),B) = singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ( ~ in(sk2,sk3)
& set_difference(singleton(sk2),sk3) != singleton(sk2) )
| ( in(sk2,sk3)
& set_difference(singleton(sk2),sk3) = singleton(sk2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f3_nnf]) ).
cnf(c5,plain,
( set_difference(singleton(sk2),sk3) != singleton(sk2)
| in(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p10,plain,
( in(sk2,sk3)
| in(sk2,sk3) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(p11,plain,
in(sk2,sk3),
inference(factoring,[status(thm)],[p10]) ).
cnf(c4,plain,
( ~ in(sk2,sk3)
| set_difference(singleton(sk2),sk3) = singleton(sk2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p13,plain,
set_difference(singleton(sk2),sk3) = singleton(sk2),
inference(resolution,[status(thm)],[p11,c4]) ).
cnf(c7,plain,
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p14,plain,
~ in(sk2,sk3),
inference(resolution,[status(thm)],[p13,c7]) ).
cnf(p15,plain,
$false,
inference(resolution,[status(thm)],[p14,p11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:25:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.90/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------