%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN051+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 : n016.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 09:36:51 AM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 3 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 12 ~; 10 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 8 ( 2 sgn 0 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel21_1,axiom,
? [X] :
( p
=> big_f(X) ),
file('theBenchmark.p',pel21_1) ).
fof(pel21_2,axiom,
? [X] :
( big_f(X)
=> p ),
file('theBenchmark.p',pel21_2) ).
fof(pel21,conjecture,
? [X] :
( p
<=> big_f(X) ),
file('theBenchmark.p',pel21) ).
fof(pel21_neg,negated_conjecture,
~ ? [X] :
( p
<=> big_f(X) ),
inference(assume_negation,[status(cth)],[pel21]) ).
fof(nnf_2,plain,
? [X] :
( p
| ~ big_f(X) ),
inference(fof_nnf,[status(thm)],[pel21_2]) ).
fof(sk_pel21_2,plain,
( p
| ~ big_f(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_2]) ).
cnf(c_4,plain,
( p
| ~ big_f(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel21_2]) ).
fof(nnf_1,plain,
? [X] :
( big_f(X)
| ~ p ),
inference(fof_nnf,[status(thm)],[pel21_1]) ).
fof(sk_pel21_1,plain,
( big_f(sK1)
| ~ p ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1)],[nnf_1]) ).
cnf(c_5,plain,
( big_f(sK1)
| ~ p ),
inference(split_conjunct,[status(thm)],[sk_pel21_1]) ).
cnf(c_6,negated_conjecture,
( big_f(A)
| p ),
inference(clausify,[status(thm)],[pel21_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_f(A)
| ~ p ),
inference(clausify,[status(thm)],[pel21_neg]) ).
cnf(c_8,negated_conjecture,
( ~ p
| ~ p ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_9,negated_conjecture,
~ p,
inference(copy,[status(thm)],[c_8]) ).
cnf(c_10,negated_conjecture,
( p
| p ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_12,negated_conjecture,
p,
inference(copy,[status(thm)],[c_10]) ).
cnf(c_11,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN051+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n016.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 17:11:46 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.47 % Process 1357419 was started by sandbox2 on n016,
% 0.20/0.47 % Sat Sep 26 17:11:46 2026
% 0.20/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.20/0.49
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49
% 0.20/0.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.49 % Length of proof is 11.
% 0.20/0.49 % Level of proof is 4.
% 0.20/0.49 % Maximum clause weight is 1.000.
% 0.20/0.49 % Given clauses 0.
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------