%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN058+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 : n007.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 09:36:54 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 54 ( 20 ~; 14 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 4 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel28_1,axiom,
! [X] :
( big_p(X)
=> ! [Z] : big_q(Z) ),
file('theBenchmark.p',pel28_1) ).
fof(pel28_2,axiom,
( ! [X] :
( big_r(X)
| big_q(X) )
=> ? [X1] :
( big_s(X1)
& big_q(X1) ) ),
file('theBenchmark.p',pel28_2) ).
fof(pel28_3,axiom,
( ? [X] : big_s(X)
=> ! [X1] :
( big_f(X1)
=> big_g(X1) ) ),
file('theBenchmark.p',pel28_3) ).
fof(pel28,conjecture,
! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
file('theBenchmark.p',pel28) ).
fof(pel28_neg,negated_conjecture,
~ ! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
inference(assume_negation,[status(cth)],[pel28]) ).
fof(nnf_4,plain,
? [X] :
( ~ big_g(X)
& big_f(X)
& big_p(X) ),
inference(fof_nnf,[status(thm)],[pel28_neg]) ).
fof(sk_pel28_neg,plain,
( ~ big_g(sK0)
& big_f(sK0)
& big_p(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_4]) ).
cnf(c_5,negated_conjecture,
big_p(sK0),
inference(split_conjunct,[status(thm)],[sk_pel28_neg]) ).
cnf(c_6,plain,
( big_q(B)
| ~ big_p(A) ),
inference(clausify,[status(thm)],[pel28_1]) ).
cnf(c_7,plain,
( big_g(B)
| ~ big_f(B)
| ~ big_s(A) ),
inference(clausify,[status(thm)],[pel28_3]) ).
fof(nnf_2,plain,
( ? [X1] :
( big_s(X1)
& big_q(X1) )
| ? [X] :
( ~ big_r(X)
& ~ big_q(X) ) ),
inference(fof_nnf,[status(thm)],[pel28_2]) ).
fof(sk_pel28_2_sk,plain,
( ( big_s(sK2)
& big_q(sK2) )
| ( ~ big_r(sK1)
& ~ big_q(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X,sK1),skolemize(X1,sK2)],[nnf_2]) ).
fof(sk_pel28_2,plain,
( ( big_s(sK2)
| ~ big_r(sK1) )
& ( big_q(sK2)
| ~ big_r(sK1) )
& ( big_s(sK2)
| ~ big_q(sK1) )
& ( big_q(sK2)
| ~ big_q(sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel28_2_sk]) ).
cnf(c_8,plain,
( big_s(sK2)
| ~ big_q(sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel28_2]) ).
cnf(c_9,negated_conjecture,
big_f(sK0),
inference(split_conjunct,[status(thm)],[sk_pel28_neg]) ).
cnf(c_10,plain,
( ~ big_q(sK1)
| big_g(A)
| ~ big_f(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_11,negated_conjecture,
~ big_g(sK0),
inference(split_conjunct,[status(thm)],[sk_pel28_neg]) ).
cnf(c_12,negated_conjecture,
( ~ big_q(sK1)
| big_g(sK0) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_13,negated_conjecture,
~ big_q(sK1),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_14,negated_conjecture,
big_q(A),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN058+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.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 17:05:40 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 36867 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 17:05:40 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % 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 15.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 2.000.
% 0.10/0.39 % Given clauses 0.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------