%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 08:45:14 AM UTC 2026
% Result : Theorem 1.74s 0.64s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 10 ~; 10 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(t37_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t37_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(assume_negation,[status(cth)],[t37_zfmisc_1]) ).
cnf(c_164,plain,
( in(A,B)
| ~ subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_165,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
fof(nnf_86,plain,
? [A,B] :
( ( ~ in(A,B)
| ~ subset(singleton(A),B) )
& ( in(A,B)
| subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[t37_zfmisc_1_neg]) ).
fof(sk_t37_zfmisc_1_neg,plain,
( ( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) )
& ( in(sK0,sK1)
| subset(singleton(sK0),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_86]) ).
cnf(c_223,negated_conjecture,
( in(sK0,sK1)
| subset(singleton(sK0),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t37_zfmisc_1_neg]) ).
cnf(c_224,negated_conjecture,
( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t37_zfmisc_1_neg]) ).
cnf(c_2636,negated_conjecture,
( in(sK0,sK1)
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_223,c_164]) ).
cnf(c_2629,negated_conjecture,
in(sK0,sK1),
inference(copy,[status(thm)],[c_2636]) ).
cnf(c_2637,negated_conjecture,
( subset(singleton(sK0),sK1)
| subset(singleton(sK0),sK1) ),
inference(resolve,[status(thm)],[c_223,c_165]) ).
cnf(c_2634,negated_conjecture,
subset(singleton(sK0),sK1),
inference(copy,[status(thm)],[c_2637]) ).
cnf(c_2638,negated_conjecture,
~ in(sK0,sK1),
inference(resolve,[status(thm)],[c_2634,c_224]) ).
cnf(c_2635,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2629,c_2638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:44:06 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 33697 was started by sandbox2 on n018,
% 0.10/0.35 % Sat Sep 26 08:44:06 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 1.74/0.64
% 1.74/0.64 % SZS status Theorem for theBenchmark
% 1.74/0.64
% 1.74/0.64 % Proof 1 at 0.20 (+ 0.05) seconds.
% 1.74/0.64 % Length of proof is 9.
% 1.74/0.64 % Level of proof is 3.
% 1.74/0.64 % Maximum clause weight is 17.000.
% 1.74/0.64 % Given clauses 133.
% 1.74/0.64
% 1.74/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------