%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET933+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 : n012.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 08:37:19 AM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 4 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 17 ( 1 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t80_zfmisc_1,conjecture,
! [A] : subset(singleton(A),powerset(A)),
file('theBenchmark.p',t80_zfmisc_1) ).
fof(t80_zfmisc_1_neg,negated_conjecture,
~ ! [A] : subset(singleton(A),powerset(A)),
inference(assume_negation,[status(cth)],[t80_zfmisc_1]) ).
cnf(c_10,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_14,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_17,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
fof(nnf_7,plain,
? [A] : ~ subset(singleton(A),powerset(A)),
inference(fof_nnf,[status(thm)],[t80_zfmisc_1_neg]) ).
fof(sk_t80_zfmisc_1_neg,plain,
~ subset(singleton(sK0),powerset(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_7]) ).
cnf(c_18,negated_conjecture,
~ subset(singleton(sK0),powerset(sK0)),
inference(split_conjunct,[status(thm)],[sk_t80_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
~ in(sK0,powerset(sK0)),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_32,plain,
( ~ subset(sK0,A)
| powerset(A) != powerset(sK0) ),
inference(resolve,[status(thm)],[c_10,c_25]) ).
cnf(c_33,plain,
powerset(sK0) != powerset(sK0),
inference(resolve,[status(thm)],[c_32,c_17]) ).
cnf(c_31,plain,
$false,
inference(copy,[status(thm)],[c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 08:26:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 134401 was started by sandbox on n012,
% 0.03/0.30 % Sat Sep 26 08:26:04 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.03/0.32
% 0.03/0.32 % SZS status Theorem for theBenchmark
% 0.03/0.32
% 0.03/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.32 % Length of proof is 10.
% 0.03/0.32 % Level of proof is 3.
% 0.03/0.32 % Maximum clause weight is 10.000.
% 0.03/0.32 % Given clauses 14.
% 0.03/0.32
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------