%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG200+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 : n007.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 06:49:43 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 106 ( 45 ~; 45 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
~ ( ( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1
| op(e0,e0) != e0 )
& ( op(e6,e6) = e6
| op(e5,e5) = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 )
& op(e6,e6) = e6
& op(e5,e5) = e5
& op(e4,e4) = e4
& op(e3,e3) = e3
& op(e2,e2) = e2
& op(e1,e1) = e1
& op(e0,e0) = e0 ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ~ ( ( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1
| op(e0,e0) != e0 )
& ( op(e6,e6) = e6
| op(e5,e5) = e5
| op(e4,e4) = e4
| op(e3,e3) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0 )
& op(e6,e6) = e6
& op(e5,e5) = e5
& op(e4,e4) = e4
& op(e3,e3) = e3
& op(e2,e2) = e2
& op(e1,e1) = e1
& op(e0,e0) = e0 ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_584,negated_conjecture,
op(e0,e0) = e0,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_585,negated_conjecture,
op(e1,e1) = e1,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_586,negated_conjecture,
op(e2,e2) = e2,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_587,negated_conjecture,
op(e3,e3) = e3,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_588,negated_conjecture,
op(e4,e4) = e4,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_589,negated_conjecture,
op(e5,e5) = e5,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_590,negated_conjecture,
op(e6,e6) = e6,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_591,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1
| op(e0,e0) != e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_593,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2
| op(e1,e1) != e1 ),
inference(resolve,[status(thm)],[c_584,c_591]) ).
cnf(c_594,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3
| op(e2,e2) != e2 ),
inference(resolve,[status(thm)],[c_585,c_593]) ).
cnf(c_595,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4
| op(e3,e3) != e3 ),
inference(resolve,[status(thm)],[c_586,c_594]) ).
cnf(c_596,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5
| op(e4,e4) != e4 ),
inference(resolve,[status(thm)],[c_587,c_595]) ).
cnf(c_597,negated_conjecture,
( op(e6,e6) != e6
| op(e5,e5) != e5 ),
inference(resolve,[status(thm)],[c_588,c_596]) ).
cnf(c_598,negated_conjecture,
op(e6,e6) != e6,
inference(resolve,[status(thm)],[c_589,c_597]) ).
cnf(c_592,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_590,c_598]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG200+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:22:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 490744 was started by sandbox on n007,
% 0.10/0.37 % Sat Sep 26 21:22:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.43
% 0.10/0.43 % From the command line: assign(max_seconds, 300).
% 0.10/0.46
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46
% 0.10/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.46 % Length of proof is 10.
% 0.10/0.46 % Level of proof is 2.
% 0.10/0.46 % Maximum clause weight is 15.000.
% 0.10/0.46 % Given clauses 0.
% 0.10/0.46
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------