%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 2.61s 0.78s
% Output : Proof 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 51 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 15 |; 14 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 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(f5,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f5_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,conjecture,
! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk2 != singleton(sk3)
& sk2 != empty_set
& set_difference(sk2,singleton(sk3)) = empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f6_nnf]) ).
cnf(c9,plain,
set_difference(sk2,singleton(sk3)) = empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p15,plain,
subset(sk2,singleton(sk3)),
inference(resolution,[status(thm)],[c7,c9]) ).
fof(f1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p16,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p15,c1]) ).
cnf(c11,plain,
sk2 != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p20,plain,
sk2 = empty_set,
inference(resolution,[status(thm)],[p16,c11]) ).
cnf(c10,plain,
sk2 != empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p22,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p20,c10]) ).
cnf(p27,plain,
$false,
inference(equality_resolution,[status(thm)],[p22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:23:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.61/0.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.61/0.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------