%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET923+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 : n013.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 08:37:17 AM UTC 2026
% Result : Theorem 0.18s 0.64s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 43 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 23 ~; 11 |; 8 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 23 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t66_zfmisc_1,conjecture,
! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
file('theBenchmark.p',t66_zfmisc_1) ).
fof(t66_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(assume_negation,[status(cth)],[t66_zfmisc_1]) ).
cnf(c_8,plain,
( singleton(B) = A
| A = empty_set
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
cnf(c_9,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(copy,[status(thm)],[c_8]) ).
cnf(c_16,plain,
( subset(A,B)
| set_difference(A,B) != empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
fof(nnf_6,plain,
? [A,B] :
( singleton(B) != A
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(fof_nnf,[status(thm)],[t66_zfmisc_1_neg]) ).
fof(sk_t66_zfmisc_1_neg,plain,
( singleton(sK1) != sK0
& sK0 != empty_set
& set_difference(sK0,singleton(sK1)) = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_6]) ).
cnf(c_18,negated_conjecture,
set_difference(sK0,singleton(sK1)) = empty_set,
inference(split_conjunct,[status(thm)],[sk_t66_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
empty_set = set_difference(sK0,singleton(sK1)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,negated_conjecture,
sK0 != empty_set,
inference(split_conjunct,[status(thm)],[sk_t66_zfmisc_1_neg]) ).
cnf(c_32,negated_conjecture,
sK0 != set_difference(sK0,singleton(sK1)),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_21,negated_conjecture,
set_difference(sK0,singleton(sK1)) != sK0,
inference(copy,[status(thm)],[c_32]) ).
cnf(c_22,negated_conjecture,
singleton(sK1) != sK0,
inference(split_conjunct,[status(thm)],[sk_t66_zfmisc_1_neg]) ).
cnf(c_33,plain,
( subset(A,B)
| set_difference(A,B) != set_difference(sK0,singleton(sK1)) ),
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_24,plain,
( subset(A,B)
| set_difference(sK0,singleton(sK1)) != set_difference(A,B) ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_26,plain,
( singleton(B) = A
| set_difference(sK0,singleton(sK1)) = A
| ~ subset(A,singleton(B)) ),
inference(paramod,[status(thm)],[c_19,c_9]) ).
cnf(c_29,plain,
subset(sK0,singleton(sK1)),
inference(xxres,[status(thm)],[c_24]) ).
cnf(c_34,negated_conjecture,
( singleton(A) = sK0
| ~ subset(sK0,singleton(A)) ),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_35,negated_conjecture,
~ subset(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_34,c_22]) ).
cnf(c_31,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_29,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.62 % Computer : n013.cluster.edu
% 0.18/0.62 % Model : x86_64 x86_64
% 0.18/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.62 % Memory : 8046.5625MB
% 0.18/0.62 % OS : Linux 6.8.0-71-generic
% 0.18/0.62 % CPULimit : 300
% 0.18/0.62 % WCLimit : 300
% 0.18/0.62 % DateTime : Sat Sep 26 08:25:06 UTC 2026
% 0.18/0.62 % CPUTime :
% 0.18/0.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.62 % Process 2325425 was started by sandbox on n013,
% 0.18/0.62 % Sat Sep 26 08:25:06 2026
% 0.18/0.62 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.63
% 0.18/0.63 % From the command line: assign(max_seconds, 300).
% 0.18/0.64
% 0.18/0.64 % SZS status Theorem for theBenchmark
% 0.18/0.64
% 0.18/0.64 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.64 % Length of proof is 15.
% 0.18/0.64 % Level of proof is 5.
% 0.18/0.64 % Maximum clause weight is 14.000.
% 0.18/0.64 % Given clauses 11.
% 0.18/0.64
% 0.18/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------