%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 06:49:20 AM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 122 ( 30 ~; 36 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
( e2 != e3
& e1 != e3
& e1 != e2
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('theBenchmark.p',ax5) ).
fof(ax6,axiom,
( e2 = op(e3,e1)
& e0 = op(e1,e1) ),
file('theBenchmark.p',ax6) ).
fof(co1,conjecture,
~ ( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ~ ( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_121,plain,
e1 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_122,plain,
e0 != e1,
inference(copy,[status(thm)],[c_121]) ).
cnf(c_123,plain,
e2 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_124,plain,
e3 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_128,plain,
op(e1,e1) = e0,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_129,plain,
e0 = op(e1,e1),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_152,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_279,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_342,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_384,negated_conjecture,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_385,negated_conjecture,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e0,e0) != e0 ),
inference(resolve,[status(thm)],[c_129,c_384]) ).
cnf(c_441,plain,
op(e1,e1) != e1,
inference(paramod,[status(thm)],[c_129,c_122]) ).
cnf(c_489,plain,
e2 != op(e1,e1),
inference(paramod,[status(thm)],[c_129,c_123]) ).
cnf(c_442,plain,
op(e1,e1) != e2,
inference(copy,[status(thm)],[c_489]) ).
cnf(c_490,plain,
e3 != op(e1,e1),
inference(paramod,[status(thm)],[c_129,c_124]) ).
cnf(c_443,plain,
op(e1,e1) != e3,
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_441,c_342]) ).
cnf(c_492,negated_conjecture,
( op(e1,e1) = e3
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_442,c_491]) ).
cnf(c_452,negated_conjecture,
op(e3,e3) = e0,
inference(resolve,[status(thm)],[c_443,c_492]) ).
cnf(c_493,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_441,c_279]) ).
cnf(c_494,negated_conjecture,
( op(e1,e1) = e3
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_442,c_493]) ).
cnf(c_461,negated_conjecture,
op(e2,e2) = e0,
inference(resolve,[status(thm)],[c_443,c_494]) ).
cnf(c_495,negated_conjecture,
( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_441,c_152]) ).
cnf(c_496,negated_conjecture,
( op(e1,e1) = e3
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_442,c_495]) ).
cnf(c_480,negated_conjecture,
op(e0,e0) = e0,
inference(resolve,[status(thm)],[c_443,c_496]) ).
cnf(c_497,negated_conjecture,
( op(e3,e3) != e0
| op(e2,e2) != e0 ),
inference(resolve,[status(thm)],[c_480,c_385]) ).
cnf(c_498,negated_conjecture,
op(e3,e3) != e0,
inference(resolve,[status(thm)],[c_461,c_497]) ).
cnf(c_488,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_452,c_498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 21:01:29 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1533096 was started by sandbox2 on n011,
% 0.12/0.36 % Sat Sep 26 21:01:29 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.43
% 0.12/0.43 % 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 0.04 (+ 0.01) seconds.
% 0.20/0.49 % Length of proof is 21.
% 0.20/0.49 % Level of proof is 5.
% 0.20/0.49 % Maximum clause weight is 30.000.
% 0.20/0.49 % Given clauses 112.
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------