%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG036+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 : n019.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 06:49:19 AM UTC 2026
% Result : Theorem 0.21s 0.48s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 258 ( 257 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 293 ( 90 ~; 95 |; 108 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
( ( unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('theBenchmark.p',ax2) ).
fof(ax5,axiom,
( op(e3,e2) != op(e3,e3)
& op(e3,e1) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e1)
& op(e2,e2) != op(e2,e3)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e1)
& op(e1,e2) != op(e1,e3)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e1)
& op(e0,e2) != op(e0,e3)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e1)
& op(e2,e3) != op(e3,e3)
& op(e1,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e1,e3)
& op(e2,e2) != op(e3,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e1,e2)
& op(e2,e1) != op(e3,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e1,e1)
& op(e2,e0) != op(e3,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e1,e0) ),
file('theBenchmark.p',ax5) ).
fof(ax6,axiom,
( e2 != e3
& e1 != e3
& e1 != e2
& e0 != e3
& e0 != e2
& e0 != 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_24,plain,
op(e0,unit) = e0,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_26,plain,
op(e1,unit) = e1,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_28,plain,
op(e2,unit) = e2,
inference(clausify,[status(thm)],[ax2]) ).
fof(ax4,axiom,
unit = e0,
file('theBenchmark.p',ax4) ).
cnf(c_64,plain,
unit = e0,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_95,plain,
op(e1,e1) != op(e1,e0),
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_102,plain,
op(e2,e2) != op(e2,e0),
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_113,plain,
e1 != e0,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_114,plain,
e2 != e0,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_115,plain,
e3 != e0,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_119,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_245,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_308,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_336,negated_conjecture,
( op(e0,e0) = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_377,plain,
op(e2,e0) = e2,
inference(paramod,[status(thm)],[c_64,c_28]) ).
cnf(c_379,plain,
op(e1,e0) = e1,
inference(paramod,[status(thm)],[c_64,c_26]) ).
cnf(c_381,plain,
op(e0,e0) = e0,
inference(paramod,[status(thm)],[c_64,c_24]) ).
cnf(c_394,plain,
op(e2,e2) != e2,
inference(paramod,[status(thm)],[c_377,c_102]) ).
cnf(c_406,plain,
op(e1,e1) != e1,
inference(paramod,[status(thm)],[c_379,c_95]) ).
cnf(c_424,negated_conjecture,
( e0 = e3
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0 ),
inference(paramod,[status(thm)],[c_381,c_336]) ).
cnf(c_425,negated_conjecture,
( e3 = e0
| op(e2,e2) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0 ),
inference(copy,[status(thm)],[c_424]) ).
cnf(c_426,negated_conjecture,
( e3 = e0
| op(e2,e2) = e2
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_406,c_425]) ).
cnf(c_427,negated_conjecture,
( e3 = e0
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_394,c_426]) ).
cnf(c_420,negated_conjecture,
op(e3,e3) = e0,
inference(resolve,[status(thm)],[c_115,c_427]) ).
cnf(c_428,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2
| e0 = e1
| op(e2,e2) = e0 ),
inference(paramod,[status(thm)],[c_420,c_308]) ).
cnf(c_429,negated_conjecture,
( op(e0,e0) = e3
| e0 = e2
| e0 = e1
| op(e2,e2) = e0 ),
inference(paramod,[status(thm)],[c_420,c_428]) ).
cnf(c_430,negated_conjecture,
( e0 = e3
| e0 = e2
| e0 = e1
| op(e2,e2) = e0 ),
inference(paramod,[status(thm)],[c_381,c_429]) ).
cnf(c_431,negated_conjecture,
( e0 = e3
| e0 = e2
| e1 = e0
| op(e2,e2) = e0 ),
inference(copy,[status(thm)],[c_430]) ).
cnf(c_432,negated_conjecture,
( e0 = e3
| e2 = e0
| e1 = e0
| op(e2,e2) = e0 ),
inference(copy,[status(thm)],[c_431]) ).
cnf(c_433,negated_conjecture,
( e3 = e0
| e2 = e0
| e1 = e0
| op(e2,e2) = e0 ),
inference(copy,[status(thm)],[c_432]) ).
cnf(c_434,negated_conjecture,
( e3 = e0
| e2 = e0
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_113,c_433]) ).
cnf(c_435,negated_conjecture,
( e3 = e0
| op(e2,e2) = e0 ),
inference(resolve,[status(thm)],[c_114,c_434]) ).
cnf(c_421,negated_conjecture,
op(e2,e2) = e0,
inference(resolve,[status(thm)],[c_115,c_435]) ).
cnf(c_436,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2
| e0 = e1
| op(e1,e1) = e0 ),
inference(paramod,[status(thm)],[c_420,c_245]) ).
cnf(c_437,negated_conjecture,
( op(e0,e0) = e3
| e0 = e2
| e0 = e1
| op(e1,e1) = e0 ),
inference(paramod,[status(thm)],[c_420,c_436]) ).
cnf(c_438,negated_conjecture,
( e0 = e3
| e0 = e2
| e0 = e1
| op(e1,e1) = e0 ),
inference(paramod,[status(thm)],[c_381,c_437]) ).
cnf(c_439,negated_conjecture,
( e0 = e3
| e0 = e2
| e1 = e0
| op(e1,e1) = e0 ),
inference(copy,[status(thm)],[c_438]) ).
cnf(c_440,negated_conjecture,
( e0 = e3
| e2 = e0
| e1 = e0
| op(e1,e1) = e0 ),
inference(copy,[status(thm)],[c_439]) ).
cnf(c_441,negated_conjecture,
( e3 = e0
| e2 = e0
| e1 = e0
| op(e1,e1) = e0 ),
inference(copy,[status(thm)],[c_440]) ).
cnf(c_442,negated_conjecture,
( e3 = e0
| e2 = e0
| op(e1,e1) = e0 ),
inference(resolve,[status(thm)],[c_113,c_441]) ).
cnf(c_443,negated_conjecture,
( e3 = e0
| op(e1,e1) = e0 ),
inference(resolve,[status(thm)],[c_114,c_442]) ).
cnf(c_422,negated_conjecture,
op(e1,e1) = e0,
inference(resolve,[status(thm)],[c_115,c_443]) ).
cnf(c_444,negated_conjecture,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| e0 != e0 ),
inference(paramod,[status(thm)],[c_381,c_119]) ).
cnf(c_445,negated_conjecture,
( op(e3,e3) != e0
| op(e2,e2) != e0
| e0 != e0
| e0 != e0 ),
inference(paramod,[status(thm)],[c_422,c_444]) ).
cnf(c_446,negated_conjecture,
( op(e3,e3) != e0
| e0 != e0
| e0 != e0
| e0 != e0 ),
inference(paramod,[status(thm)],[c_421,c_445]) ).
cnf(c_447,negated_conjecture,
( e0 != e0
| e0 != e0
| e0 != e0
| e0 != e0 ),
inference(paramod,[status(thm)],[c_420,c_446]) ).
cnf(c_448,negated_conjecture,
( e0 != e0
| e0 != e0
| e0 != e0 ),
inference(copy,[status(thm)],[c_447]) ).
cnf(c_449,negated_conjecture,
( e0 != e0
| e0 != e0 ),
inference(copy,[status(thm)],[c_448]) ).
cnf(c_450,negated_conjecture,
e0 != e0,
inference(copy,[status(thm)],[c_449]) ).
cnf(c_423,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 21:00:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2191318 was started by sandbox on n019,
% 0.10/0.36 % Sat Sep 26 21:00:48 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.44
% 0.14/0.44 % From the command line: assign(max_seconds, 300).
% 0.21/0.48
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48
% 0.21/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.21/0.48 % Length of proof is 26.
% 0.21/0.48 % Level of proof is 6.
% 0.21/0.48 % Maximum clause weight is 30.000.
% 0.21/0.48 % Given clauses 0.
% 0.21/0.48
% 0.21/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------