%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN367+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 09:37:43 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 45 ( 16 ~; 11 |; 16 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 2 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2118,conjecture,
( ! [X] :
( ( big_r(X)
& ~ p )
| ( big_q(X)
& p ) )
=> ( ! [X] : big_r(X)
| ! [X] : big_q(X) ) ),
file('theBenchmark.p',x2118) ).
fof(x2118_neg,negated_conjecture,
~ ( ! [X] :
( ( big_r(X)
& ~ p )
| ( big_q(X)
& p ) )
=> ( ! [X] : big_r(X)
| ! [X] : big_q(X) ) ),
inference(assume_negation,[status(cth)],[x2118]) ).
fof(nnf_1,plain,
( ? [X] : ~ big_r(X)
& ? [X1] : ~ big_q(X1)
& ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) ) ),
inference(fof_nnf,[status(thm)],[x2118_neg]) ).
fof(sk_x2118_neg_sk,plain,
( ~ big_r(sK1)
& ~ big_q(sK0)
& ! [X0] :
( ( big_r(X0)
& ~ p )
| ( big_q(X0)
& p ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X,sK1)],[nnf_1]) ).
fof(sk_x2118_neg,plain,
( ~ big_r(sK1)
& ~ big_q(sK0)
& ! [VAR_0] :
( big_r(VAR_0)
| big_q(VAR_0) )
& ! [VAR_0] :
( ~ p
| big_q(VAR_0) )
& ! [VAR_0] :
( big_r(VAR_0)
| p ) ),
inference(cnf_transformation,[status(thm)],[sk_x2118_neg_sk]) ).
cnf(c_2,negated_conjecture,
~ big_q(sK0),
inference(split_conjunct,[status(thm)],[sk_x2118_neg]) ).
cnf(c_4,negated_conjecture,
( ~ p
| big_q(A) ),
inference(split_conjunct,[status(thm)],[sk_x2118_neg]) ).
cnf(c_5,negated_conjecture,
~ big_r(sK1),
inference(split_conjunct,[status(thm)],[sk_x2118_neg]) ).
cnf(c_7,negated_conjecture,
( big_r(A)
| p ),
inference(split_conjunct,[status(thm)],[sk_x2118_neg]) ).
cnf(c_8,negated_conjecture,
p,
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_9,negated_conjecture,
~ p,
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_10,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN367+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:38:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 737062 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 17:38:44 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 8.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 1.000.
% 0.10/0.39 % Given clauses 0.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------