%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG017+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 06:49:08 AM UTC 2026
% Result : Theorem 0.37s 0.70s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% 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(ax10,axiom,
( e2 != e3
& e1 != e3
& e1 != e2
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('theBenchmark.p',ax10) ).
fof(ax11,axiom,
( e1 = op(e2,e3)
& e0 = op(e3,e3) ),
file('theBenchmark.p',ax11) ).
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_211,plain,
e1 != e0,
inference(clausify,[status(thm)],[ax10]) ).
cnf(c_212,plain,
e2 != e0,
inference(clausify,[status(thm)],[ax10]) ).
cnf(c_213,plain,
e3 != e0,
inference(clausify,[status(thm)],[ax10]) ).
cnf(c_214,plain,
e0 != e3,
inference(copy,[status(thm)],[c_213]) ).
cnf(c_220,plain,
op(e3,e3) = e0,
inference(clausify,[status(thm)],[ax11]) ).
cnf(c_221,plain,
e0 = op(e3,e3),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_286,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_349,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_412,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_476,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_477,negated_conjecture,
( op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(resolve,[status(thm)],[c_221,c_476]) ).
cnf(c_933,plain,
e1 != op(e3,e3),
inference(paramod,[status(thm)],[c_221,c_211]) ).
cnf(c_923,plain,
op(e3,e3) != e1,
inference(copy,[status(thm)],[c_933]) ).
cnf(c_934,plain,
e2 != op(e3,e3),
inference(paramod,[status(thm)],[c_221,c_212]) ).
cnf(c_924,plain,
op(e3,e3) != e2,
inference(copy,[status(thm)],[c_934]) ).
cnf(c_925,plain,
op(e3,e3) != e3,
inference(paramod,[status(thm)],[c_221,c_214]) ).
cnf(c_935,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_923,c_412]) ).
cnf(c_936,negated_conjecture,
( op(e3,e3) = e3
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_924,c_935]) ).
cnf(c_929,negated_conjecture,
op(e2,e2) = e0,
inference(resolve,[status(thm)],[c_925,c_936]) ).
cnf(c_937,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e1,e1) = e0 ),
inference(resolve,[status(thm)],[c_923,c_349]) ).
cnf(c_938,negated_conjecture,
( op(e3,e3) = e3
| op(e1,e1) = e0 ),
inference(resolve,[status(thm)],[c_924,c_937]) ).
cnf(c_930,negated_conjecture,
op(e1,e1) = e0,
inference(resolve,[status(thm)],[c_925,c_938]) ).
cnf(c_939,negated_conjecture,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_923,c_286]) ).
cnf(c_940,negated_conjecture,
( op(e3,e3) = e3
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_924,c_939]) ).
cnf(c_931,negated_conjecture,
op(e0,e0) = e0,
inference(resolve,[status(thm)],[c_925,c_940]) ).
cnf(c_941,negated_conjecture,
( op(e2,e2) != e0
| op(e1,e1) != e0 ),
inference(resolve,[status(thm)],[c_931,c_477]) ).
cnf(c_942,negated_conjecture,
op(e2,e2) != e0,
inference(resolve,[status(thm)],[c_930,c_941]) ).
cnf(c_932,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_929,c_942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG017+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n016.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 21:04:02 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1714801 was started by sandbox on n016,
% 0.17/0.43 % Sat Sep 26 21:04:02 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.36/0.60
% 0.36/0.60 % From the command line: assign(max_seconds, 300).
% 0.37/0.70
% 0.37/0.70 % SZS status Theorem for theBenchmark
% 0.37/0.70
% 0.37/0.70 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.37/0.70 % Length of proof is 21.
% 0.37/0.70 % Level of proof is 5.
% 0.37/0.70 % Maximum clause weight is 30.000.
% 0.37/0.70 % Given clauses 179.
% 0.37/0.70
% 0.37/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------