%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN044+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 : n012.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 09:36:49 AM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 12 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 4 ( 3 usr; 4 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel10_1,axiom,
( q
=> r ),
file('theBenchmark.p',pel10_1) ).
fof(pel10_2,axiom,
( r
=> ( q
& p ) ),
file('theBenchmark.p',pel10_2) ).
fof(pel10_3,axiom,
( p
=> ( r
| q ) ),
file('theBenchmark.p',pel10_3) ).
fof(pel10,conjecture,
( p
<=> q ),
file('theBenchmark.p',pel10) ).
fof(pel10_neg,negated_conjecture,
~ ( p
<=> q ),
inference(assume_negation,[status(cth)],[pel10]) ).
cnf(c_5,plain,
( r
| ~ q ),
inference(clausify,[status(thm)],[pel10_1]) ).
cnf(c_6,plain,
( p
| ~ r ),
inference(clausify,[status(thm)],[pel10_2]) ).
cnf(c_7,plain,
( q
| ~ r ),
inference(clausify,[status(thm)],[pel10_2]) ).
cnf(c_8,plain,
( r
| q
| ~ p ),
inference(clausify,[status(thm)],[pel10_3]) ).
cnf(c_9,negated_conjecture,
( q
| p ),
inference(clausify,[status(thm)],[pel10_neg]) ).
cnf(c_10,negated_conjecture,
( ~ q
| ~ p ),
inference(clausify,[status(thm)],[pel10_neg]) ).
cnf(c_16,negated_conjecture,
( r
| q
| q ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_11,negated_conjecture,
( r
| q ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_17,plain,
( q
| q ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_12,plain,
q,
inference(copy,[status(thm)],[c_17]) ).
cnf(c_13,negated_conjecture,
~ p,
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_14,plain,
r,
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_18,plain,
p,
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_15,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN044+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 17:05:50 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 1103796 was started by sandbox2 on n012,
% 0.03/0.31 % Sat Sep 26 17:05:50 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.03/0.32
% 0.03/0.32 % SZS status Theorem for theBenchmark
% 0.03/0.32
% 0.03/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.32 % Length of proof is 15.
% 0.03/0.32 % Level of proof is 5.
% 0.03/0.32 % Maximum clause weight is 3.000.
% 0.03/0.32 % Given clauses 7.
% 0.03/0.32
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------