%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET879+1 : 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 : n005.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 08:37:12 AM UTC 2026
% Result : Theorem 0.10s 5.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 50 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 19 |; 2 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 29 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l34_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',l34_zfmisc_1) ).
fof(t20_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('theBenchmark.p',t20_zfmisc_1) ).
fof(t20_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
inference(assume_negation,[status(cth)],[t20_zfmisc_1]) ).
cnf(c_8,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_9,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_12,plain,
( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ),
inference(clausify,[status(thm)],[l34_zfmisc_1]) ).
cnf(c_13,plain,
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) ),
inference(clausify,[status(thm)],[l34_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B] :
( ( B = A
| set_difference(singleton(A),singleton(B)) != singleton(A) )
& ( B != A
| set_difference(singleton(A),singleton(B)) = singleton(A) ) ),
inference(fof_nnf,[status(thm)],[t20_zfmisc_1_neg]) ).
fof(sk_t20_zfmisc_1_neg,plain,
( ( sK1 = sK0
| set_difference(singleton(sK0),singleton(sK1)) != singleton(sK0) )
& ( sK1 != sK0
| set_difference(singleton(sK0),singleton(sK1)) = singleton(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_6]) ).
cnf(c_16,negated_conjecture,
( sK1 != sK0
| set_difference(singleton(sK0),singleton(sK1)) = singleton(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t20_zfmisc_1_neg]) ).
cnf(c_17,negated_conjecture,
( sK1 = sK0
| set_difference(singleton(sK0),singleton(sK1)) != singleton(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t20_zfmisc_1_neg]) ).
cnf(c_20,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_8]) ).
cnf(c_21,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_9]) ).
cnf(c_31,plain,
( set_difference(singleton(A),singleton(B)) = singleton(A)
| A = B ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_33,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_21]) ).
cnf(c_36,plain,
set_difference(singleton(A),singleton(A)) != singleton(A),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_62,negated_conjecture,
( sK1 = sK0
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_31,c_17]) ).
cnf(c_63,negated_conjecture,
( sK1 = sK0
| sK1 = sK0 ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_53,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,negated_conjecture,
( sK1 != sK0
| set_difference(singleton(sK0),singleton(sK0)) = singleton(sK0) ),
inference(paramod,[status(thm)],[c_53,c_16]) ).
cnf(c_65,negated_conjecture,
( sK0 != sK0
| set_difference(singleton(sK0),singleton(sK0)) = singleton(sK0) ),
inference(paramod,[status(thm)],[c_53,c_64]) ).
cnf(c_66,negated_conjecture,
set_difference(singleton(sK0),singleton(sK0)) = singleton(sK0),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_61,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_36,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n005.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 08:23:52 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.36 % Process 1684801 was started by sandbox on n005,
% 0.10/5.36 % Sat Sep 26 08:23:52 2026
% 0.10/5.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 0.10/5.38
% 0.10/5.38 % SZS status Theorem for theBenchmark
% 0.10/5.38
% 0.10/5.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.10/5.38 % Length of proof is 16.
% 0.10/5.38 % Level of proof is 5.
% 0.10/5.38 % Maximum clause weight is 26.000.
% 0.10/5.38 % Given clauses 32.
% 0.10/5.38
% 0.10/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------