%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:51:10 PM UTC 2026
% Result : Theorem 0.48s 0.80s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 68 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 24 ~; 31 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 19 ( 2 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c10,plain,
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f4,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_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)],[f4_neg]) ).
fof(f4_sk,plain,
( ( ( sk2 = singleton(sk3)
| sk2 = empty_set )
& ~ subset(sk2,singleton(sk3)) )
| ( sk2 != singleton(sk3)
& sk2 != empty_set
& subset(sk2,singleton(sk3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f4_nnf]) ).
cnf(c5,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set
| subset(sk2,singleton(sk3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p20,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(p26,plain,
( sk2 = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p20]) ).
cnf(p27,plain,
( sk2 = singleton(sk3)
| sk2 = empty_set ),
inference(factoring,[status(thm)],[p26]) ).
cnf(c12,plain,
( X0 != singleton(X1)
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p33,plain,
( subset(sk2,singleton(sk3))
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p27,c12]) ).
cnf(c8,plain,
( ~ subset(sk2,singleton(sk3))
| sk2 != singleton(sk3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p32,plain,
( ~ subset(sk2,singleton(sk3))
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p27,c8]) ).
cnf(p40,plain,
( sk2 = empty_set
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p33,p32]) ).
cnf(p41,plain,
sk2 = empty_set,
inference(factoring,[status(thm)],[p40]) ).
cnf(c6,plain,
( ~ subset(sk2,singleton(sk3))
| sk2 != empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p42,plain,
( ~ subset(empty_set,singleton(sk3))
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p41,c6]) ).
cnf(p44,plain,
~ subset(empty_set,singleton(sk3)),
inference(equality_resolution,[status(thm)],[p42]) ).
cnf(c11,plain,
( X0 != empty_set
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p13,plain,
subset(empty_set,singleton(X0)),
inference(equality_resolution,[status(thm)],[c11]) ).
cnf(p45,plain,
$false,
inference(resolution,[status(thm)],[p44,p13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Thu Sep 24 12:59:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.48/0.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------