%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET924+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 : 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 : Sun Sep 27 08:37:18 AM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 31 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 10 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 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(t67_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',t67_zfmisc_1) ).
fof(t67_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
inference(assume_negation,[status(cth)],[t67_zfmisc_1]) ).
cnf(c_9,plain,
( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ),
inference(clausify,[status(thm)],[l34_zfmisc_1]) ).
cnf(c_10,plain,
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) ),
inference(clausify,[status(thm)],[l34_zfmisc_1]) ).
fof(nnf_5,plain,
? [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) != singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) = singleton(A) ) ),
inference(fof_nnf,[status(thm)],[t67_zfmisc_1_neg]) ).
fof(sk_t67_zfmisc_1_neg,plain,
( ( in(sK0,sK1)
| set_difference(singleton(sK0),sK1) != singleton(sK0) )
& ( ~ in(sK0,sK1)
| set_difference(singleton(sK0),sK1) = singleton(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_5]) ).
cnf(c_11,negated_conjecture,
( ~ in(sK0,sK1)
| set_difference(singleton(sK0),sK1) = singleton(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t67_zfmisc_1_neg]) ).
cnf(c_12,negated_conjecture,
( in(sK0,sK1)
| set_difference(singleton(sK0),sK1) != singleton(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t67_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
( set_difference(singleton(sK0),sK1) = singleton(sK0)
| set_difference(singleton(sK0),sK1) = singleton(sK0) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_15,negated_conjecture,
set_difference(singleton(sK0),sK1) = singleton(sK0),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_22,negated_conjecture,
( in(sK0,sK1)
| singleton(sK0) != singleton(sK0) ),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_16,negated_conjecture,
in(sK0,sK1),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_23,negated_conjecture,
set_difference(singleton(sK0),sK1) != singleton(sK0),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_24,negated_conjecture,
singleton(sK0) != singleton(sK0),
inference(paramod,[status(thm)],[c_15,c_23]) ).
cnf(c_20,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 08:26:34 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 1081233 was started by sandbox2 on n020,
% 0.16/0.42 % Sat Sep 26 08:26:34 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 9.
% 0.16/0.44 % Level of proof is 4.
% 0.16/0.44 % Maximum clause weight is 10.000.
% 0.16/0.44 % Given clauses 9.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------