%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET926+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 2.45s 0.79s
% Output : Proof 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 38 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 18 ~; 12 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c3,plain,
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f6,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( set_difference(singleton(A),B) != singleton(A)
& set_difference(singleton(A),B) != empty_set ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( set_difference(singleton(sk2),sk3) != singleton(sk2)
& set_difference(singleton(sk2),sk3) != empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f6_nnf]) ).
cnf(c9,plain,
set_difference(singleton(sk2),sk3) != singleton(sk2),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p12,plain,
in(sk2,sk3),
inference(resolution,[status(thm)],[c3,c9]) ).
fof(f3,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p15,plain,
set_difference(singleton(sk2),sk3) = empty_set,
inference(resolution,[status(thm)],[p12,c5]) ).
cnf(c8,plain,
set_difference(singleton(sk2),sk3) != empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p16,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p15,c8]) ).
cnf(p18,plain,
$false,
inference(equality_resolution,[status(thm)],[p16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:26:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.45/0.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.45/0.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------