%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG089+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 : n020.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 06:49:27 AM UTC 2026
% Result : Theorem 2.67s 0.82s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 4
% Syntax : Number of formulae : 117 ( 43 unt; 0 def)
% Number of atoms : 642 ( 641 equ)
% Maximal formula atoms : 110 ( 5 avg)
% Number of connectives : 542 ( 17 ~; 330 |; 193 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
( e23 != e24
& e22 != e24
& e22 != e23
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('theBenchmark.p',ax2) ).
fof(ax4,axiom,
( op1(e14,e14) = e10
& op1(e14,e13) = e12
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e11
& op1(e13,e13) = e10
& op1(e13,e12) = e14
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e14) = e12
& op1(e11,e13) = e14
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e14) = e14
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('theBenchmark.p',ax4) ).
fof(ax5,axiom,
( op2(e24,e24) = e20
& op2(e24,e23) = e22
& op2(e24,e22) = e21
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e22
& op2(e23,e23) = e21
& op2(e23,e22) = e20
& op2(e23,e21) = e24
& op2(e23,e20) = e23
& op2(e22,e24) = e21
& op2(e22,e23) = e24
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e24) = e23
& op2(e21,e23) = e20
& op2(e21,e22) = e24
& op2(e21,e21) = e22
& op2(e21,e20) = e21
& op2(e20,e24) = e24
& op2(e20,e23) = e23
& op2(e20,e22) = e22
& op2(e20,e21) = e21
& op2(e20,e20) = e20 ),
file('theBenchmark.p',ax5) ).
fof(co1,conjecture,
( ( ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ( ( ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_17,plain,
e21 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_19,plain,
e23 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_21,plain,
e22 != e21,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_24,plain,
e23 != e22,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_52,plain,
op1(e10,e10) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_58,plain,
op1(e11,e11) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_64,plain,
op1(e12,e12) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_70,plain,
op1(e13,e13) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_72,plain,
op1(e14,e10) = e14,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_76,plain,
op1(e14,e14) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_83,plain,
op2(e21,e21) = e22,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_89,plain,
op2(e22,e22) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_92,plain,
op2(e23,e20) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_95,plain,
op2(e23,e23) = e21,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_101,plain,
op2(e24,e24) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_102,negated_conjecture,
( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_110,negated_conjecture,
( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_112,negated_conjecture,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1074,negated_conjecture,
h(e10) = op2(h(e10),h(e10)),
inference(paramod,[status(thm)],[c_52,c_112]) ).
cnf(c_113,negated_conjecture,
op2(h(e10),h(e10)) = h(e10),
inference(copy,[status(thm)],[c_1074]) ).
cnf(c_124,negated_conjecture,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1075,negated_conjecture,
h(e10) = op2(h(e11),h(e11)),
inference(paramod,[status(thm)],[c_58,c_124]) ).
cnf(c_125,negated_conjecture,
op2(h(e11),h(e11)) = h(e10),
inference(copy,[status(thm)],[c_1075]) ).
cnf(c_136,negated_conjecture,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1076,negated_conjecture,
h(e10) = op2(h(e12),h(e12)),
inference(paramod,[status(thm)],[c_64,c_136]) ).
cnf(c_137,negated_conjecture,
op2(h(e12),h(e12)) = h(e10),
inference(copy,[status(thm)],[c_1076]) ).
cnf(c_148,negated_conjecture,
h(op1(e13,e13)) = op2(h(e13),h(e13)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1077,negated_conjecture,
h(e10) = op2(h(e13),h(e13)),
inference(paramod,[status(thm)],[c_70,c_148]) ).
cnf(c_149,negated_conjecture,
op2(h(e13),h(e13)) = h(e10),
inference(copy,[status(thm)],[c_1077]) ).
cnf(c_152,negated_conjecture,
h(op1(e14,e10)) = op2(h(e14),h(e10)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1078,negated_conjecture,
h(e14) = op2(h(e14),h(e10)),
inference(paramod,[status(thm)],[c_72,c_152]) ).
cnf(c_153,negated_conjecture,
op2(h(e14),h(e10)) = h(e14),
inference(copy,[status(thm)],[c_1078]) ).
cnf(c_160,negated_conjecture,
h(op1(e14,e14)) = op2(h(e14),h(e14)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1079,negated_conjecture,
h(e10) = op2(h(e14),h(e14)),
inference(paramod,[status(thm)],[c_76,c_160]) ).
cnf(c_161,negated_conjecture,
op2(h(e14),h(e14)) = h(e10),
inference(copy,[status(thm)],[c_1079]) ).
cnf(c_215,negated_conjecture,
h(j(e23)) = e23,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_222,plain,
( op2(e24,h(e10)) = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_102,c_113]) ).
cnf(c_325,plain,
( h(e14) = e23
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 ),
inference(paramod,[status(thm)],[c_110,c_215]) ).
cnf(c_1080,plain,
( op2(e24,e24) = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_102,c_222]) ).
cnf(c_1081,plain,
( e20 = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_101,c_1080]) ).
cnf(c_1082,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1081]) ).
cnf(c_1083,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1082]) ).
cnf(c_1084,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1083]) ).
cnf(c_1085,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1084]) ).
cnf(c_1086,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1085]) ).
cnf(c_332,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1086]) ).
cnf(c_333,plain,
( op2(e23,h(e10)) = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_332,c_113]) ).
cnf(c_397,plain,
( h(e13) = e23
| h(e14) = e23
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 ),
inference(paramod,[status(thm)],[c_325,c_215]) ).
cnf(c_502,plain,
( h(e12) = e23
| h(e13) = e23
| h(e14) = e23
| j(e23) = e11
| j(e23) = e10 ),
inference(paramod,[status(thm)],[c_397,c_215]) ).
cnf(c_559,plain,
( h(e11) = e23
| h(e12) = e23
| h(e13) = e23
| h(e14) = e23
| j(e23) = e10 ),
inference(paramod,[status(thm)],[c_502,c_215]) ).
cnf(c_616,plain,
( h(e10) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23
| h(e14) = e23 ),
inference(paramod,[status(thm)],[c_559,c_215]) ).
cnf(c_668,plain,
( op2(e23,h(e10)) = h(e14)
| h(e10) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_616,c_153]) ).
cnf(c_673,plain,
( op2(h(e14),e23) = h(e10)
| h(e10) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_616,c_161]) ).
cnf(c_1087,plain,
( op2(e23,e23) = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_1088,plain,
( e21 = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_95,c_1087]) ).
cnf(c_1089,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1088]) ).
cnf(c_1090,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1089]) ).
cnf(c_1091,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1090]) ).
cnf(c_1092,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1091]) ).
cnf(c_767,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1092]) ).
cnf(c_768,plain,
( op2(e22,h(e10)) = h(e10)
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_767,c_113]) ).
cnf(c_1093,plain,
( op2(e22,e22) = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_767,c_768]) ).
cnf(c_1094,plain,
( e23 = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_89,c_1093]) ).
cnf(c_1095,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1094]) ).
cnf(c_1096,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1095]) ).
cnf(c_792,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1096]) ).
cnf(c_1097,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_792,c_767]) ).
cnf(c_1098,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1097]) ).
cnf(c_1099,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1098]) ).
cnf(c_805,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(resolve,[status(thm)],[c_24,c_1099]) ).
cnf(c_806,plain,
( op2(e21,h(e10)) = h(e10)
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_805,c_113]) ).
cnf(c_1100,plain,
( op2(e21,e21) = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_805,c_806]) ).
cnf(c_1101,plain,
( e22 = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_83,c_1100]) ).
cnf(c_1102,plain,
( h(e10) = e22
| h(e10) = e20
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1101]) ).
cnf(c_830,plain,
( h(e10) = e22
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1102]) ).
cnf(c_1103,plain,
( e22 = e21
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_830,c_805]) ).
cnf(c_1104,plain,
( e22 = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1103]) ).
cnf(c_843,plain,
h(e10) = e20,
inference(resolve,[status(thm)],[c_21,c_1104]) ).
cnf(c_1105,plain,
( op2(h(e14),e23) = h(e10)
| e20 = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_843,c_673]) ).
cnf(c_1106,plain,
( op2(h(e14),e23) = e20
| e20 = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_843,c_1105]) ).
cnf(c_1107,plain,
( op2(h(e14),e23) = e20
| e23 = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1106]) ).
cnf(c_900,plain,
( op2(h(e14),e23) = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(resolve,[status(thm)],[c_19,c_1107]) ).
cnf(c_1108,plain,
( op2(e23,h(e10)) = h(e14)
| e20 = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_843,c_668]) ).
cnf(c_1109,plain,
( op2(e23,e20) = h(e14)
| e20 = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_843,c_1108]) ).
cnf(c_1110,plain,
( e23 = h(e14)
| e20 = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_92,c_1109]) ).
cnf(c_1111,plain,
( e23 = h(e14)
| e23 = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1110]) ).
cnf(c_1112,plain,
( h(e14) = e23
| e23 = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1111]) ).
cnf(c_905,plain,
( h(e14) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(resolve,[status(thm)],[c_19,c_1112]) ).
cnf(c_941,negated_conjecture,
op2(h(e13),h(e13)) = e20,
inference(paramod,[status(thm)],[c_843,c_149]) ).
cnf(c_943,negated_conjecture,
op2(h(e12),h(e12)) = e20,
inference(paramod,[status(thm)],[c_843,c_137]) ).
cnf(c_945,negated_conjecture,
op2(h(e11),h(e11)) = e20,
inference(paramod,[status(thm)],[c_843,c_125]) ).
cnf(c_1113,plain,
( op2(e23,e23) = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_905,c_900]) ).
cnf(c_1114,plain,
( e21 = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(paramod,[status(thm)],[c_95,c_1113]) ).
cnf(c_1115,plain,
( e21 = e20
| h(e11) = e23
| h(e12) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1114]) ).
cnf(c_1116,plain,
( e21 = e20
| h(e11) = e23
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1115]) ).
cnf(c_1117,plain,
( e21 = e20
| h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(copy,[status(thm)],[c_1116]) ).
cnf(c_1020,plain,
( h(e11) = e23
| h(e12) = e23
| h(e13) = e23 ),
inference(resolve,[status(thm)],[c_17,c_1117]) ).
cnf(c_1031,plain,
( op2(e23,h(e13)) = e20
| h(e11) = e23
| h(e12) = e23 ),
inference(paramod,[status(thm)],[c_1020,c_941]) ).
cnf(c_1118,plain,
( op2(e23,e23) = e20
| h(e11) = e23
| h(e12) = e23
| h(e11) = e23
| h(e12) = e23 ),
inference(paramod,[status(thm)],[c_1020,c_1031]) ).
cnf(c_1119,plain,
( e21 = e20
| h(e11) = e23
| h(e12) = e23
| h(e11) = e23
| h(e12) = e23 ),
inference(paramod,[status(thm)],[c_95,c_1118]) ).
cnf(c_1120,plain,
( e21 = e20
| h(e11) = e23
| h(e11) = e23
| h(e12) = e23 ),
inference(copy,[status(thm)],[c_1119]) ).
cnf(c_1121,plain,
( e21 = e20
| h(e11) = e23
| h(e12) = e23 ),
inference(copy,[status(thm)],[c_1120]) ).
cnf(c_1043,plain,
( h(e11) = e23
| h(e12) = e23 ),
inference(resolve,[status(thm)],[c_17,c_1121]) ).
cnf(c_1052,plain,
( op2(e23,h(e12)) = e20
| h(e11) = e23 ),
inference(paramod,[status(thm)],[c_1043,c_943]) ).
cnf(c_1122,plain,
( op2(e23,e23) = e20
| h(e11) = e23
| h(e11) = e23 ),
inference(paramod,[status(thm)],[c_1043,c_1052]) ).
cnf(c_1123,plain,
( e21 = e20
| h(e11) = e23
| h(e11) = e23 ),
inference(paramod,[status(thm)],[c_95,c_1122]) ).
cnf(c_1124,plain,
( e21 = e20
| h(e11) = e23 ),
inference(copy,[status(thm)],[c_1123]) ).
cnf(c_1065,plain,
h(e11) = e23,
inference(resolve,[status(thm)],[c_17,c_1124]) ).
cnf(c_1125,negated_conjecture,
op2(e23,h(e11)) = e20,
inference(paramod,[status(thm)],[c_1065,c_945]) ).
cnf(c_1126,negated_conjecture,
op2(e23,e23) = e20,
inference(paramod,[status(thm)],[c_1065,c_1125]) ).
cnf(c_1127,negated_conjecture,
e21 = e20,
inference(paramod,[status(thm)],[c_95,c_1126]) ).
cnf(c_1073,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_1127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG089+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n020.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 21:08:03 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2514569 was started by sandbox on n020,
% 0.19/0.46 % Sat Sep 26 21:08:03 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 2.67/0.82
% 2.67/0.82 % SZS status Theorem for theBenchmark
% 2.67/0.82
% 2.67/0.82 % Proof 1 at 0.26 (+ 0.07) seconds.
% 2.67/0.82 % Length of proof is 62.
% 2.67/0.82 % Level of proof is 19.
% 2.67/0.82 % Maximum clause weight is 38.000.
% 2.67/0.82 % Given clauses 270.
% 2.67/0.82
% 2.67/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------