%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU152+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 : n015.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 08:45:12 AM UTC 2026
% Result : Theorem 0.19s 5.78s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 21 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 2 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(t12_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(l23_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l23_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(assume_negation,[status(cth)],[l23_zfmisc_1]) ).
cnf(c_132,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_143,plain,
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t12_xboole_1]) ).
fof(nnf_73,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1_neg]) ).
fof(sk_l23_zfmisc_1_neg,plain,
( set_union2(singleton(sK0),sK1) != sK1
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_73]) ).
cnf(c_183,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l23_zfmisc_1_neg]) ).
cnf(c_184,negated_conjecture,
set_union2(singleton(sK0),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_l23_zfmisc_1_neg]) ).
cnf(c_1131,plain,
subset(singleton(sK0),sK1),
inference(resolve,[status(thm)],[c_183,c_132]) ).
cnf(c_1893,plain,
set_union2(singleton(sK0),sK1) = sK1,
inference(resolve,[status(thm)],[c_1131,c_143]) ).
cnf(c_1892,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_184,c_1893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.63 % Computer : n015.cluster.edu
% 0.16/5.63 % Model : x86_64 x86_64
% 0.16/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.63 % Memory : 8046.5625MB
% 0.16/5.63 % OS : Linux 6.8.0-71-generic
% 0.16/5.63 % CPULimit : 300
% 0.16/5.63 % WCLimit : 300
% 0.16/5.63 % DateTime : Sat Sep 26 08:44:35 UTC 2026
% 0.16/5.64 % CPUTime :
% 0.16/5.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.64 % Process 3611349 was started by sandbox2 on n015,
% 0.16/5.64 % Sat Sep 26 08:44:35 2026
% 0.16/5.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.66
% 0.16/5.66 % From the command line: assign(max_seconds, 300).
% 0.19/5.78
% 0.19/5.78 % SZS status Theorem for theBenchmark
% 0.19/5.78
% 0.19/5.78 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.19/5.78 % Length of proof is 9.
% 0.19/5.78 % Level of proof is 3.
% 0.19/5.78 % Maximum clause weight is 21.000.
% 0.19/5.78 % Given clauses 197.
% 0.19/5.78
% 0.19/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------