%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 02:51:09 PM UTC 2026
% Result : Theorem 29.67s 4.58s
% Output : Proof 29.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 12 unt; 0 def)
% Number of atoms : 177 ( 80 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 177 ( 59 ~; 82 |; 27 &)
% ( 8 <=>; 1 =>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 3 sgn 48 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f12_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk10(A,B),B)
& in(sk10(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f12_nnf]) ).
cnf(c52,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f69,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f69_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f69]) ).
fof(f69_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)],[f69_neg]) ).
fof(f69_sk,plain,
( ( ( sk19 = singleton(sk20)
| sk19 = empty_set )
& ~ subset(sk19,singleton(sk20)) )
| ( sk19 != singleton(sk20)
& sk19 != empty_set
& subset(sk19,singleton(sk20)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20])],[f69_nnf]) ).
cnf(c153,plain,
( sk19 = singleton(sk20)
| sk19 = empty_set
| subset(sk19,singleton(sk20)) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(p703,plain,
( sk19 = singleton(sk20)
| sk19 = empty_set
| in(X0,singleton(sk20))
| ~ in(X0,sk19) ),
inference(resolution,[status(thm)],[c52,c153]) ).
fof(f7,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( in(sk1(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c15,plain,
( in(sk1(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p730,plain,
( sk19 = empty_set
| sk19 = singleton(sk20)
| sk19 = empty_set
| in(sk1(sk19),singleton(sk20)) ),
inference(resolution,[status(thm)],[p703,c15]) ).
cnf(p764,plain,
( sk19 = singleton(sk20)
| sk19 = empty_set
| in(sk1(sk19),singleton(sk20)) ),
inference(factoring,[status(thm)],[p730]) ).
fof(f6,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c8,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p199,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p769,plain,
( sk1(sk19) = sk20
| sk19 = singleton(sk20)
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p764,p199]) ).
cnf(p777,plain,
( in(sk20,sk19)
| sk19 = empty_set
| sk19 = singleton(sk20)
| sk19 = empty_set ),
inference(superposition,[status(thm)],[p769,c15]) ).
cnf(p936,plain,
( in(sk20,sk19)
| sk19 = singleton(sk20)
| sk19 = empty_set ),
inference(factoring,[status(thm)],[p777]) ).
fof(f40,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f40_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c109,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f48,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f48_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c123,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(p238,plain,
in(X0,singleton(X0)),
inference(resolution,[status(thm)],[c109,c123]) ).
cnf(p950,plain,
( in(sk20,sk19)
| in(sk20,sk19)
| sk19 = empty_set ),
inference(superposition,[status(thm)],[p936,p238]) ).
cnf(p1002,plain,
( in(sk20,sk19)
| sk19 = empty_set ),
inference(factoring,[status(thm)],[p950]) ).
cnf(c110,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p1004,plain,
( subset(singleton(sk20),sk19)
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p1002,c110]) ).
fof(f5,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f5_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p193,plain,
( sk19 = singleton(sk20)
| sk19 = empty_set
| ~ subset(singleton(sk20),sk19)
| sk19 = singleton(sk20) ),
inference(resolution,[status(thm)],[c7,c153]) ).
cnf(p197,plain,
( sk19 = empty_set
| ~ subset(singleton(sk20),sk19)
| sk19 = singleton(sk20) ),
inference(factoring,[status(thm)],[p193]) ).
cnf(p1011,plain,
( sk19 = empty_set
| sk19 = singleton(sk20)
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p1004,p197]) ).
cnf(p1166,plain,
( sk19 = singleton(sk20)
| sk19 = empty_set ),
inference(factoring,[status(thm)],[p1011]) ).
cnf(c5,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p1194,plain,
( subset(sk19,singleton(sk20))
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p1166,c5]) ).
cnf(c156,plain,
( ~ subset(sk19,singleton(sk20))
| sk19 != singleton(sk20) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(p1193,plain,
( ~ subset(sk19,singleton(sk20))
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p1166,c156]) ).
cnf(p1238,plain,
( sk19 = empty_set
| sk19 = empty_set ),
inference(resolution,[status(thm)],[p1194,p1193]) ).
cnf(p1240,plain,
sk19 = empty_set,
inference(factoring,[status(thm)],[p1238]) ).
cnf(c154,plain,
( ~ subset(sk19,singleton(sk20))
| sk19 != empty_set ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(p1241,plain,
( ~ subset(empty_set,singleton(sk20))
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p1240,c154]) ).
cnf(p1243,plain,
~ subset(empty_set,singleton(sk20)),
inference(equality_resolution,[status(thm)],[p1241]) ).
fof(f61,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f61_nnf,plain,
! [A] : subset(empty_set,A),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [A] : subset(empty_set,A),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c139,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(p1244,plain,
$false,
inference(resolution,[status(thm)],[p1243,c139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.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 12:59:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.67/4.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.67/4.58 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------