%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET883+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 : 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 08:37:13 AM UTC 2026
% Result : Theorem 0.11s 10.56s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t24_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t24_zfmisc_1) ).
fof(t24_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
inference(assume_negation,[status(cth)],[t24_zfmisc_1]) ).
cnf(c_9,plain,
( B = A
| ~ subset(singleton(A),singleton(B)) ),
inference(clausify,[status(thm)],[t6_zfmisc_1]) ).
fof(nnf_5,plain,
? [A,B] :
( B != A
& subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t24_zfmisc_1_neg]) ).
fof(sk_t24_zfmisc_1_neg,plain,
( sK1 != sK0
& subset(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_5]) ).
cnf(c_10,negated_conjecture,
subset(singleton(sK0),singleton(sK1)),
inference(split_conjunct,[status(thm)],[sk_t24_zfmisc_1_neg]) ).
cnf(c_11,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t24_zfmisc_1_neg]) ).
cnf(c_12,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET883+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.54 % Computer : n013.cluster.edu
% 0.11/10.54 % Model : x86_64 x86_64
% 0.11/10.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.54 % Memory : 8046.5625MB
% 0.11/10.54 % OS : Linux 6.8.0-71-generic
% 0.11/10.54 % CPULimit : 300
% 0.11/10.54 % WCLimit : 300
% 0.11/10.54 % DateTime : Sat Sep 26 08:23:48 UTC 2026
% 0.11/10.54 % CPUTime :
% 0.11/10.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.55 % Process 2323053 was started by sandbox2 on n013,
% 0.11/10.55 % Sat Sep 26 08:23:48 2026
% 0.11/10.55 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/10.55
% 0.11/10.55 % From the command line: assign(max_seconds, 300).
% 0.11/10.56
% 0.11/10.56 % SZS status Theorem for theBenchmark
% 0.11/10.56
% 0.11/10.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/10.56 % Length of proof is 7.
% 0.11/10.56 % Level of proof is 3.
% 0.11/10.56 % Maximum clause weight is 8.000.
% 0.11/10.56 % Given clauses 5.
% 0.11/10.56
% 0.11/10.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------