%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN064+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 : 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 09:36:55 AM UTC 2026
% Result : Theorem 0.14s 5.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% Number of variables : 18 ( 2 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel35,conjecture,
? [X,Y] :
( big_p(X,Y)
=> ! [Z,W] : big_p(Z,W) ),
file('theBenchmark.p',pel35) ).
fof(pel35_neg,negated_conjecture,
~ ? [X,Y] :
( big_p(X,Y)
=> ! [Z,W] : big_p(Z,W) ),
inference(assume_negation,[status(cth)],[pel35]) ).
fof(nnf_1,plain,
! [X,Y] :
( ? [Z,W] : ~ big_p(Z,W)
& big_p(X,Y) ),
inference(fof_nnf,[status(thm)],[pel35_neg]) ).
fof(sk_pel35_neg,plain,
! [X,Y] :
( ~ big_p(sK0(X,Y),sK1(X,Y))
& big_p(X,Y) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Z,sK0(X,Y)),skolemize(W,sK1(X,Y))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
~ big_p(sK0(A,B),sK1(A,B)),
inference(split_conjunct,[status(thm)],[sk_pel35_neg]) ).
cnf(c_3,negated_conjecture,
big_p(A,B),
inference(split_conjunct,[status(thm)],[sk_pel35_neg]) ).
cnf(c_4,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN064+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n020.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 17:09:55 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.42 % Process 2091149 was started by sandbox on n020,
% 0.14/5.42 % Sat Sep 26 17:09:55 2026
% 0.14/5.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.43
% 0.14/5.43 % From the command line: assign(max_seconds, 300).
% 0.14/5.44
% 0.14/5.44 % SZS status Theorem for theBenchmark
% 0.14/5.44
% 0.14/5.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.44 % Length of proof is 4.
% 0.14/5.44 % Level of proof is 2.
% 0.14/5.44 % Maximum clause weight is 0.000.
% 0.14/5.44 % Given clauses 0.
% 0.14/5.44
% 0.14/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------