%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN393+1.003 : 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 : n003.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 09:37:47 AM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 20 ~; 34 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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(pel12,conjecture,
( ( ( p1
<=> p2 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
file('theBenchmark.p',pel12) ).
fof(pel12_neg,negated_conjecture,
~ ( ( ( p1
<=> p2 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(assume_negation,[status(cth)],[pel12]) ).
cnf(c_2,negated_conjecture,
( p3
| p2
| p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_3,negated_conjecture,
( p3
| ~ p2
| ~ p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_4,negated_conjecture,
( ~ p3
| p2
| ~ p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_5,negated_conjecture,
( ~ p3
| ~ p2
| p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_6,negated_conjecture,
( p3
| p2
| ~ p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_7,negated_conjecture,
( p3
| ~ p2
| p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_8,negated_conjecture,
( ~ p3
| p2
| p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_9,negated_conjecture,
( ~ p3
| ~ p2
| ~ p1 ),
inference(clausify,[status(thm)],[pel12_neg]) ).
cnf(c_21,negated_conjecture,
( p2
| p1
| p2
| p1 ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_22,negated_conjecture,
( p2
| p2
| p1 ),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_10,negated_conjecture,
( p2
| p1 ),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_23,negated_conjecture,
( p3
| p1
| p1 ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_11,negated_conjecture,
( p3
| p1 ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_24,negated_conjecture,
( ~ p2
| p1
| p1 ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_12,negated_conjecture,
( ~ p2
| p1 ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,plain,
( p1
| p1 ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_13,plain,
p1,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_14,negated_conjecture,
( ~ p3
| ~ p2 ),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_15,negated_conjecture,
( p3
| p2 ),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_16,negated_conjecture,
( ~ p3
| p2 ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_17,negated_conjecture,
( p3
| ~ p2 ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_26,negated_conjecture,
( p2
| p2 ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_18,negated_conjecture,
p2,
inference(copy,[status(thm)],[c_26]) ).
cnf(c_19,negated_conjecture,
p3,
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_27,negated_conjecture,
~ p3,
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_20,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN393+1.003 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 17:41:59 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3422354 was started by sandbox on n003,
% 0.09/5.37 % Sat Sep 26 17:41:59 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 20.
% 0.09/5.39 % Level of proof is 9.
% 0.09/5.39 % Maximum clause weight is 3.000.
% 0.09/5.39 % Given clauses 15.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------