%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:51:04 PM UTC 2026
% Result : Theorem 5.61s 1.24s
% Output : Proof 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 88 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 95 ( 36 ~; 37 |; 16 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c8,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f1_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)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c1,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p23,plain,
( sk1(singleton(X0),X1) = X0
| subset(singleton(X0),X1) ),
inference(resolution,[status(thm)],[c8,p17]) ).
cnf(c9,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p35,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1)
| subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[p23,c9]) ).
cnf(p44,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(factoring,[status(thm)],[p35]) ).
cnf(c7,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f4,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B] :
( ( in(A,B)
& ~ subset(singleton(A),B) )
| ( ~ in(A,B)
& subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ( in(sk2,sk3)
& ~ subset(singleton(sk2),sk3) )
| ( ~ in(sk2,sk3)
& subset(singleton(sk2),sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f4_nnf]) ).
cnf(c12,plain,
( in(sk2,sk3)
| subset(singleton(sk2),sk3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p31,plain,
( in(sk2,sk3)
| in(X0,sk3)
| ~ in(X0,singleton(sk2)) ),
inference(resolution,[status(thm)],[c7,c12]) ).
cnf(c2,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p18,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p20,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[p18]) ).
cnf(p37,plain,
( in(sk2,sk3)
| in(sk2,sk3) ),
inference(resolution,[status(thm)],[p31,p20]) ).
cnf(p40,plain,
in(sk2,sk3),
inference(factoring,[status(thm)],[p37]) ).
cnf(p47,plain,
subset(singleton(sk2),sk3),
inference(resolution,[status(thm)],[p44,p40]) ).
cnf(c13,plain,
( ~ subset(singleton(sk2),sk3)
| ~ in(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p42,plain,
~ subset(singleton(sk2),sk3),
inference(resolution,[status(thm)],[p40,c13]) ).
cnf(p50,plain,
$false,
inference(resolution,[status(thm)],[p47,p42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:56:48 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.61/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.61/1.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------