%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:37:18 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 21 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 4 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l34_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',l34_zfmisc_1) ).
fof(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('theBenchmark.p',l36_zfmisc_1) ).
fof(t69_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
file('theBenchmark.p',t69_zfmisc_1) ).
fof(t69_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).
cnf(c_10,plain,
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) ),
inference(clausify,[status(thm)],[l34_zfmisc_1]) ).
cnf(c_12,plain,
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ),
inference(clausify,[status(thm)],[l36_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B] :
( set_difference(singleton(A),B) != singleton(A)
& set_difference(singleton(A),B) != empty_set ),
inference(fof_nnf,[status(thm)],[t69_zfmisc_1_neg]) ).
fof(sk_t69_zfmisc_1_neg,plain,
( set_difference(singleton(sK0),sK1) != singleton(sK0)
& set_difference(singleton(sK0),sK1) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_6]) ).
cnf(c_15,negated_conjecture,
set_difference(singleton(sK0),sK1) != empty_set,
inference(split_conjunct,[status(thm)],[sk_t69_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
set_difference(singleton(sK0),sK1) != singleton(sK0),
inference(split_conjunct,[status(thm)],[sk_t69_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
~ in(sK0,sK1),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_26,plain,
set_difference(singleton(sK0),sK1) = singleton(sK0),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_25,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_16,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n019.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 08:26:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 851213 was started by sandbox2 on n019,
% 0.10/0.36 % Sat Sep 26 08:26:18 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 9.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 10.000.
% 0.13/0.37 % Given clauses 13.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------