%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:37:44 AM UTC 2026
% Result : Theorem 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 31 ( 13 ~; 8 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 15 ( 2 sgn 8 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2127,conjecture,
( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
file('theBenchmark.p',x2127) ).
fof(x2127_neg,negated_conjecture,
~ ( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
inference(assume_negation,[status(cth)],[x2127]) ).
fof(nnf_1,plain,
( ? [X] : big_p(X)
& ? [X1] : ~ big_p(X1)
& ? [X0] :
! [Y] :
( ( ~ big_p(X0)
| big_p(Y) )
& ( big_p(X0)
| ~ big_p(Y) ) ) ),
inference(fof_nnf,[status(thm)],[x2127_neg]) ).
fof(sk_x2127_neg,plain,
( big_p(sK2)
& ~ big_p(sK1)
& ! [Y] :
( ( ~ big_p(sK0)
| big_p(Y) )
& ( big_p(sK0)
| ~ big_p(Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X,sK2)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( big_p(sK0)
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2127_neg]) ).
cnf(c_3,negated_conjecture,
( ~ big_p(sK0)
| big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2127_neg]) ).
cnf(c_4,negated_conjecture,
~ big_p(sK1),
inference(split_conjunct,[status(thm)],[sk_x2127_neg]) ).
cnf(c_5,negated_conjecture,
big_p(sK2),
inference(split_conjunct,[status(thm)],[sk_x2127_neg]) ).
cnf(c_6,plain,
~ big_p(sK0),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_7,negated_conjecture,
big_p(sK0),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n020.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 17:39:40 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.39 % Process 2139389 was started by sandbox on n020,
% 0.09/5.39 % Sat Sep 26 17:39:40 2026
% 0.09/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Theorem for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 8.
% 0.15/5.40 % Level of proof is 3.
% 0.15/5.40 % Maximum clause weight is 4.000.
% 0.15/5.40 % Given clauses 4.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------