%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU158+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 12 ~; 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_7,plain,
( in(A,B)
| ~ subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_9,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
fof(nnf_6,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_6]) ).
cnf(c_10,negated_conjecture,
( in(sK0,sK1)
| subset(singleton(sK0),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t37_zfmisc_1_neg]) ).
cnf(c_11,negated_conjecture,
( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) ),
inference(split_conjunct,[status(thm)],[sk_t37_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
( in(sK0,sK1)
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_17,negated_conjecture,
in(sK0,sK1),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,negated_conjecture,
( ~ in(sK0,sK1)
| ~ in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_20,negated_conjecture,
~ in(sK0,sK1),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_19,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU158+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:40:10 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3321230 was started by sandbox on n007,
% 0.17/0.45 % Sat Sep 26 08:40:10 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 10.
% 0.17/0.47 % Level of proof is 4.
% 0.17/0.47 % Maximum clause weight is 3.000.
% 0.17/0.47 % Given clauses 0.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------