%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN373+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 61 ( 22 ~; 23 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 6 sgn 16 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2124,conjecture,
( ? [X] :
( big_p(X)
=> big_q(X) )
<=> ( ! [X] : big_p(X)
=> ? [X] : big_q(X) ) ),
file('theBenchmark.p',x2124) ).
fof(x2124_neg,negated_conjecture,
~ ( ? [X] :
( big_p(X)
=> big_q(X) )
<=> ( ! [X] : big_p(X)
=> ? [X] : big_q(X) ) ),
inference(assume_negation,[status(cth)],[x2124]) ).
fof(nnf_1,plain,
( ( ( ! [X] : ~ big_q(X)
& ! [X4] : big_p(X4) )
| ! [X3] :
( ~ big_q(X3)
& big_p(X3) ) )
& ( ? [X2] : big_q(X2)
| ? [X1] : ~ big_p(X1)
| ? [X0] :
( big_q(X0)
| ~ big_p(X0) ) ) ),
inference(fof_nnf,[status(thm)],[x2124_neg]) ).
fof(sk_x2124_neg_sk,plain,
( ( ( ! [X] : ~ big_q(X)
& ! [X4] : big_p(X4) )
| ! [X3] :
( ~ big_q(X3)
& big_p(X3) ) )
& ( big_q(sK2)
| ~ big_p(sK1)
| big_q(sK0)
| ~ big_p(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_1]) ).
fof(sk_x2124_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_q(VAR_1)
| ~ big_q(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_p(VAR_1)
| ~ big_q(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ big_q(VAR_1)
| big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_p(VAR_1)
| big_p(VAR_0) )
& ( big_q(sK2)
| ~ big_p(sK1)
| big_q(sK0)
| ~ big_p(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2124_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_q(sK2)
| ~ big_p(sK1)
| big_q(sK0)
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2124_neg]) ).
cnf(c_3,negated_conjecture,
( big_p(B)
| big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2124_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_q(B)
| ~ big_q(A) ),
inference(split_conjunct,[status(thm)],[sk_x2124_neg]) ).
cnf(c_6,plain,
big_p(A),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_7,plain,
~ big_q(A),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_9,negated_conjecture,
( big_q(sK2)
| ~ big_p(sK1)
| big_q(sK0) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_10,negated_conjecture,
( big_q(sK2)
| ~ big_p(sK1) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_11,negated_conjecture,
big_q(sK2),
inference(resolve,[status(thm)],[c_6,c_10]) ).
cnf(c_8,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN373+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 17:38:53 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2258773 was started by sandbox2 on n004,
% 0.11/0.36 % Sat Sep 26 17:38:53 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 7.
% 0.11/0.38 % Level of proof is 3.
% 0.11/0.38 % Maximum clause weight is 8.000.
% 0.11/0.38 % Given clauses 0.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------