%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG031+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 : n005.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 06:49:12 AM UTC 2026
% Result : Theorem 6.53s 1.32s
% Output : CNFRefutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 113
% Number of leaves : 5
% Syntax : Number of formulae : 229 ( 79 unt; 0 def)
% Number of atoms : 1217 (1216 equ)
% Maximal formula atoms : 156 ( 5 avg)
% Number of connectives : 1028 ( 40 ~; 700 |; 286 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 87 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
( e14 != e15
& e13 != e15
& e13 != e14
& e12 != e15
& e12 != e14
& e12 != e13
& e11 != e15
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e15
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('theBenchmark.p',ax1) ).
fof(ax2,axiom,
( e24 != e25
& e23 != e25
& e23 != e24
& e22 != e25
& e22 != e24
& e22 != e23
& e21 != e25
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e25
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('theBenchmark.p',ax2) ).
fof(ax4,axiom,
( op1(e15,e15) = e12
& op1(e15,e14) = e10
& op1(e15,e13) = e14
& op1(e15,e12) = e11
& op1(e15,e11) = e13
& op1(e15,e10) = e15
& op1(e14,e15) = e10
& op1(e14,e14) = e13
& op1(e14,e13) = e11
& op1(e14,e12) = e15
& op1(e14,e11) = e12
& op1(e14,e10) = e14
& op1(e13,e15) = e14
& op1(e13,e14) = e11
& op1(e13,e13) = e12
& op1(e13,e12) = e10
& op1(e13,e11) = e15
& op1(e13,e10) = e13
& op1(e12,e15) = e11
& op1(e12,e14) = e15
& op1(e12,e13) = e10
& op1(e12,e12) = e13
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e15) = e13
& op1(e11,e14) = e12
& op1(e11,e13) = e15
& op1(e11,e12) = e14
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e15) = e15
& 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(e25,e25) = e20
& op2(e25,e24) = e22
& op2(e25,e23) = e21
& op2(e25,e22) = e24
& op2(e25,e21) = e23
& op2(e25,e20) = e25
& op2(e24,e25) = e21
& op2(e24,e24) = e23
& op2(e24,e23) = e20
& op2(e24,e22) = e25
& op2(e24,e21) = e22
& op2(e24,e20) = e24
& op2(e23,e25) = e22
& op2(e23,e24) = e20
& op2(e23,e23) = e24
& op2(e23,e22) = e21
& op2(e23,e21) = e25
& op2(e23,e20) = e23
& op2(e22,e25) = e23
& op2(e22,e24) = e21
& op2(e22,e23) = e25
& op2(e22,e22) = e20
& op2(e22,e21) = e24
& op2(e22,e20) = e22
& op2(e21,e25) = e24
& op2(e21,e24) = e25
& op2(e21,e23) = e22
& op2(e21,e22) = e23
& op2(e21,e21) = e20
& op2(e21,e20) = e21
& op2(e20,e25) = e25
& 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(e25) = e15
| j(e25) = e14
| j(e25) = e13
| j(e25) = e12
| j(e25) = e11
| j(e25) = e10 )
& ( j(e24) = e15
| j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e15
| j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e15
| j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e15
| j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e15
| j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e15) = e25
| h(e15) = e24
| h(e15) = e23
| h(e15) = e22
| h(e15) = e21
| h(e15) = e20 )
& ( h(e14) = e25
| h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e25
| h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e25
| h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e25
| h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e25
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e15)) = e15
& j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e25)) = e25
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e25,e25)) = op1(j(e25),j(e25))
& j(op2(e25,e24)) = op1(j(e25),j(e24))
& j(op2(e25,e23)) = op1(j(e25),j(e23))
& j(op2(e25,e22)) = op1(j(e25),j(e22))
& j(op2(e25,e21)) = op1(j(e25),j(e21))
& j(op2(e25,e20)) = op1(j(e25),j(e20))
& j(op2(e24,e25)) = op1(j(e24),j(e25))
& 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,e25)) = op1(j(e23),j(e25))
& 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,e25)) = op1(j(e22),j(e25))
& 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,e25)) = op1(j(e21),j(e25))
& 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,e25)) = op1(j(e20),j(e25))
& 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(e15,e15)) = op2(h(e15),h(e15))
& h(op1(e15,e14)) = op2(h(e15),h(e14))
& h(op1(e15,e13)) = op2(h(e15),h(e13))
& h(op1(e15,e12)) = op2(h(e15),h(e12))
& h(op1(e15,e11)) = op2(h(e15),h(e11))
& h(op1(e15,e10)) = op2(h(e15),h(e10))
& h(op1(e14,e15)) = op2(h(e14),h(e15))
& 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,e15)) = op2(h(e13),h(e15))
& 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,e15)) = op2(h(e12),h(e15))
& 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,e15)) = op2(h(e11),h(e15))
& 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,e15)) = op2(h(e10),h(e15))
& 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(e25) = e15
| j(e25) = e14
| j(e25) = e13
| j(e25) = e12
| j(e25) = e11
| j(e25) = e10 )
& ( j(e24) = e15
| j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e15
| j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e15
| j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e15
| j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e15
| j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e15) = e25
| h(e15) = e24
| h(e15) = e23
| h(e15) = e22
| h(e15) = e21
| h(e15) = e20 )
& ( h(e14) = e25
| h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e25
| h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e25
| h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e25
| h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e25
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e15)) = e15
& j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e25)) = e25
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e25,e25)) = op1(j(e25),j(e25))
& j(op2(e25,e24)) = op1(j(e25),j(e24))
& j(op2(e25,e23)) = op1(j(e25),j(e23))
& j(op2(e25,e22)) = op1(j(e25),j(e22))
& j(op2(e25,e21)) = op1(j(e25),j(e21))
& j(op2(e25,e20)) = op1(j(e25),j(e20))
& j(op2(e24,e25)) = op1(j(e24),j(e25))
& 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,e25)) = op1(j(e23),j(e25))
& 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,e25)) = op1(j(e22),j(e25))
& 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,e25)) = op1(j(e21),j(e25))
& 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,e25)) = op1(j(e20),j(e25))
& 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(e15,e15)) = op2(h(e15),h(e15))
& h(op1(e15,e14)) = op2(h(e15),h(e14))
& h(op1(e15,e13)) = op2(h(e15),h(e13))
& h(op1(e15,e12)) = op2(h(e15),h(e12))
& h(op1(e15,e11)) = op2(h(e15),h(e11))
& h(op1(e15,e10)) = op2(h(e15),h(e10))
& h(op1(e14,e15)) = op2(h(e14),h(e15))
& 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,e15)) = op2(h(e13),h(e15))
& 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,e15)) = op2(h(e12),h(e15))
& 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,e15)) = op2(h(e11),h(e15))
& 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,e15)) = op2(h(e10),h(e15))
& 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_8,plain,
e12 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_9,plain,
e13 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_22,plain,
e21 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_23,plain,
e22 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_27,plain,
e22 != e21,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_33,plain,
e25 != e22,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_34,plain,
e24 != e23,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_73,plain,
op1(e10,e10) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_81,plain,
op1(e11,e12) = e14,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_82,plain,
op1(e11,e13) = e15,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_84,plain,
op1(e11,e15) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_86,plain,
op1(e12,e11) = e14,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_87,plain,
op1(e12,e12) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_92,plain,
op1(e13,e11) = e15,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_94,plain,
op1(e13,e13) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_98,plain,
op1(e14,e11) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_101,plain,
op1(e14,e14) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_104,plain,
op1(e15,e11) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_108,plain,
op1(e15,e15) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_116,plain,
op2(e21,e21) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_117,plain,
op2(e21,e22) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_119,plain,
op2(e21,e24) = e25,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_122,plain,
op2(e22,e21) = e24,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_123,plain,
op2(e22,e22) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_130,plain,
op2(e23,e23) = e24,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_134,plain,
op2(e24,e21) = e22,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_137,plain,
op2(e24,e24) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_144,plain,
op2(e25,e25) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_145,negated_conjecture,
( h(e10) = e25
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_152,negated_conjecture,
( j(e21) = e15
| j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_153,negated_conjecture,
( j(e22) = e15
| j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_157,negated_conjecture,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2270,negated_conjecture,
h(e10) = op2(h(e10),h(e10)),
inference(paramod,[status(thm)],[c_73,c_157]) ).
cnf(c_158,negated_conjecture,
op2(h(e10),h(e10)) = h(e10),
inference(copy,[status(thm)],[c_2270]) ).
cnf(c_173,negated_conjecture,
h(op1(e11,e12)) = op2(h(e11),h(e12)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2271,negated_conjecture,
h(e14) = op2(h(e11),h(e12)),
inference(paramod,[status(thm)],[c_81,c_173]) ).
cnf(c_174,negated_conjecture,
op2(h(e11),h(e12)) = h(e14),
inference(copy,[status(thm)],[c_2271]) ).
cnf(c_175,negated_conjecture,
h(op1(e11,e13)) = op2(h(e11),h(e13)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2272,negated_conjecture,
h(e15) = op2(h(e11),h(e13)),
inference(paramod,[status(thm)],[c_82,c_175]) ).
cnf(c_176,negated_conjecture,
op2(h(e11),h(e13)) = h(e15),
inference(copy,[status(thm)],[c_2272]) ).
cnf(c_179,negated_conjecture,
h(op1(e11,e15)) = op2(h(e11),h(e15)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2273,negated_conjecture,
h(e13) = op2(h(e11),h(e15)),
inference(paramod,[status(thm)],[c_84,c_179]) ).
cnf(c_180,negated_conjecture,
op2(h(e11),h(e15)) = h(e13),
inference(copy,[status(thm)],[c_2273]) ).
cnf(c_183,negated_conjecture,
h(op1(e12,e11)) = op2(h(e12),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2274,negated_conjecture,
h(e14) = op2(h(e12),h(e11)),
inference(paramod,[status(thm)],[c_86,c_183]) ).
cnf(c_184,negated_conjecture,
op2(h(e12),h(e11)) = h(e14),
inference(copy,[status(thm)],[c_2274]) ).
cnf(c_195,negated_conjecture,
h(op1(e13,e11)) = op2(h(e13),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2275,negated_conjecture,
h(e15) = op2(h(e13),h(e11)),
inference(paramod,[status(thm)],[c_92,c_195]) ).
cnf(c_196,negated_conjecture,
op2(h(e13),h(e11)) = h(e15),
inference(copy,[status(thm)],[c_2275]) ).
cnf(c_207,negated_conjecture,
h(op1(e14,e11)) = op2(h(e14),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2276,negated_conjecture,
h(e12) = op2(h(e14),h(e11)),
inference(paramod,[status(thm)],[c_98,c_207]) ).
cnf(c_208,negated_conjecture,
op2(h(e14),h(e11)) = h(e12),
inference(copy,[status(thm)],[c_2276]) ).
cnf(c_219,negated_conjecture,
h(op1(e15,e11)) = op2(h(e15),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2277,negated_conjecture,
h(e13) = op2(h(e15),h(e11)),
inference(paramod,[status(thm)],[c_104,c_219]) ).
cnf(c_220,negated_conjecture,
op2(h(e15),h(e11)) = h(e13),
inference(copy,[status(thm)],[c_2277]) ).
cnf(c_243,negated_conjecture,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2278,negated_conjecture,
j(e20) = op1(j(e21),j(e21)),
inference(paramod,[status(thm)],[c_116,c_243]) ).
cnf(c_244,negated_conjecture,
op1(j(e21),j(e21)) = j(e20),
inference(copy,[status(thm)],[c_2278]) ).
cnf(c_302,negated_conjecture,
h(j(e21)) = e21,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_303,negated_conjecture,
h(j(e22)) = e22,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_307,negated_conjecture,
j(h(e10)) = e10,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_309,negated_conjecture,
j(h(e12)) = e12,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_310,negated_conjecture,
j(h(e13)) = e13,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_311,negated_conjecture,
j(h(e14)) = e14,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_312,negated_conjecture,
j(h(e15)) = e15,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_313,plain,
( op2(e25,h(e10)) = h(e10)
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_145,c_158]) ).
cnf(c_458,plain,
( h(e15) = e21
| j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_152,c_302]) ).
cnf(c_459,plain,
( h(e15) = e22
| j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(paramod,[status(thm)],[c_153,c_303]) ).
cnf(c_2279,plain,
( op2(e25,e25) = h(e10)
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_145,c_313]) ).
cnf(c_2280,plain,
( e20 = h(e10)
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_144,c_2279]) ).
cnf(c_2281,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2280]) ).
cnf(c_2282,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2281]) ).
cnf(c_2283,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2282]) ).
cnf(c_2284,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2283]) ).
cnf(c_2285,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2284]) ).
cnf(c_2286,plain,
( h(e10) = e20
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2285]) ).
cnf(c_469,plain,
( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2286]) ).
cnf(c_470,plain,
( op2(e24,h(e10)) = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_469,c_158]) ).
cnf(c_520,plain,
( h(e14) = e21
| h(e15) = e21
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_458,c_302]) ).
cnf(c_533,plain,
( h(e14) = e22
| h(e15) = e22
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(paramod,[status(thm)],[c_459,c_303]) ).
cnf(c_672,plain,
( h(e13) = e21
| h(e14) = e21
| h(e15) = e21
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_520,c_302]) ).
cnf(c_685,plain,
( h(e13) = e22
| h(e14) = e22
| h(e15) = e22
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(paramod,[status(thm)],[c_533,c_303]) ).
cnf(c_752,plain,
( h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| h(e15) = e21
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_672,c_302]) ).
cnf(c_765,plain,
( h(e12) = e22
| h(e13) = e22
| h(e14) = e22
| h(e15) = e22
| j(e22) = e11
| j(e22) = e10 ),
inference(paramod,[status(thm)],[c_685,c_303]) ).
cnf(c_832,plain,
( h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| h(e15) = e21
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_752,c_302]) ).
cnf(c_845,plain,
( h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22
| h(e15) = e22
| j(e22) = e10 ),
inference(paramod,[status(thm)],[c_765,c_303]) ).
cnf(c_912,plain,
( h(e10) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| h(e15) = e21 ),
inference(paramod,[status(thm)],[c_832,c_302]) ).
cnf(c_925,plain,
( h(e10) = e22
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22
| h(e15) = e22 ),
inference(paramod,[status(thm)],[c_845,c_303]) ).
cnf(c_991,plain,
( j(e21) = e15
| h(e10) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_912,c_312]) ).
cnf(c_994,plain,
( op2(h(e11),e22) = h(e13)
| h(e10) = e22
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_925,c_180]) ).
cnf(c_999,plain,
( op2(e22,h(e11)) = h(e13)
| h(e10) = e22
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_925,c_220]) ).
cnf(c_1074,plain,
( op1(e15,j(e21)) = j(e20)
| h(e10) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_991,c_244]) ).
cnf(c_2287,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_469,c_470]) ).
cnf(c_2288,plain,
( e23 = 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_137,c_2287]) ).
cnf(c_2289,plain,
( h(e10) = e23
| 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_2288]) ).
cnf(c_2290,plain,
( h(e10) = e23
| 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_2289]) ).
cnf(c_2291,plain,
( h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2290]) ).
cnf(c_2292,plain,
( h(e10) = e23
| h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2291]) ).
cnf(c_2293,plain,
( h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2292]) ).
cnf(c_1158,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2293]) ).
cnf(c_1159,plain,
( op2(e23,h(e10)) = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1158,c_158]) ).
cnf(c_2294,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_1158,c_1159]) ).
cnf(c_2295,plain,
( e24 = 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_130,c_2294]) ).
cnf(c_2296,plain,
( h(e10) = e24
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2295]) ).
cnf(c_2297,plain,
( h(e10) = e24
| h(e10) = e22
| h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2296]) ).
cnf(c_2298,plain,
( h(e10) = e24
| h(e10) = e22
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2297]) ).
cnf(c_1188,plain,
( h(e10) = e24
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2298]) ).
cnf(c_2299,plain,
( e24 = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1188,c_1158]) ).
cnf(c_2300,plain,
( e24 = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2299]) ).
cnf(c_2301,plain,
( e24 = e23
| h(e10) = e22
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2300]) ).
cnf(c_2302,plain,
( e24 = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2301]) ).
cnf(c_1203,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(resolve,[status(thm)],[c_34,c_2302]) ).
cnf(c_1204,plain,
( op2(e22,h(e10)) = h(e10)
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1203,c_158]) ).
cnf(c_2303,plain,
( op2(e22,e22) = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1203,c_1204]) ).
cnf(c_2304,plain,
( e20 = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_123,c_2303]) ).
cnf(c_2305,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2304]) ).
cnf(c_2306,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2305]) ).
cnf(c_2307,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2306]) ).
cnf(c_1233,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2307]) ).
cnf(c_1234,plain,
( op2(e21,h(e10)) = h(e10)
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1233,c_158]) ).
cnf(c_2308,plain,
( op2(e21,e21) = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_1233,c_1234]) ).
cnf(c_2309,plain,
( e20 = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_116,c_2308]) ).
cnf(c_2310,plain,
( h(e10) = e20
| h(e10) = e20
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2309]) ).
cnf(c_2311,plain,
( h(e10) = e20
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2310]) ).
cnf(c_1263,plain,
h(e10) = e20,
inference(copy,[status(thm)],[c_2311]) ).
cnf(c_2312,plain,
( op1(e15,j(e21)) = j(e20)
| e20 = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_1263,c_1074]) ).
cnf(c_2313,plain,
( op1(e15,j(e21)) = j(e20)
| e21 = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2312]) ).
cnf(c_1321,plain,
( op1(e15,j(e21)) = j(e20)
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(resolve,[status(thm)],[c_22,c_2313]) ).
cnf(c_2314,plain,
( op2(e22,h(e11)) = h(e13)
| e20 = e22
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1263,c_999]) ).
cnf(c_2315,plain,
( op2(e22,h(e11)) = h(e13)
| e22 = e20
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2314]) ).
cnf(c_1376,plain,
( op2(e22,h(e11)) = h(e13)
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(resolve,[status(thm)],[c_23,c_2315]) ).
cnf(c_2316,plain,
( op2(h(e11),e22) = h(e13)
| e20 = e22
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1263,c_994]) ).
cnf(c_2317,plain,
( op2(h(e11),e22) = h(e13)
| e22 = e20
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2316]) ).
cnf(c_1381,plain,
( op2(h(e11),e22) = h(e13)
| h(e11) = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(resolve,[status(thm)],[c_23,c_2317]) ).
cnf(c_2318,plain,
( j(e21) = e15
| e20 = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_1263,c_991]) ).
cnf(c_2319,plain,
( j(e21) = e15
| e21 = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2318]) ).
cnf(c_1382,plain,
( j(e21) = e15
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(resolve,[status(thm)],[c_22,c_2319]) ).
cnf(c_1404,negated_conjecture,
j(e20) = e10,
inference(paramod,[status(thm)],[c_1263,c_307]) ).
cnf(c_1420,plain,
( op1(e15,j(e21)) = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_1404,c_1321]) ).
cnf(c_1498,negated_conjecture,
op1(j(e21),j(e21)) = e10,
inference(paramod,[status(thm)],[c_1404,c_244]) ).
cnf(c_2320,plain,
( op1(e15,e15) = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_1382,c_1420]) ).
cnf(c_2321,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_108,c_2320]) ).
cnf(c_2322,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2321]) ).
cnf(c_2323,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2322]) ).
cnf(c_2324,plain,
( e12 = e10
| h(e11) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2323]) ).
cnf(c_2325,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(copy,[status(thm)],[c_2324]) ).
cnf(c_1553,plain,
( h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(resolve,[status(thm)],[c_8,c_2325]) ).
cnf(c_1562,plain,
( j(e21) = e14
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_1553,c_311]) ).
cnf(c_1580,plain,
( op1(e14,j(e21)) = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_1562,c_1498]) ).
cnf(c_2326,plain,
( op1(e14,e14) = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_1562,c_1580]) ).
cnf(c_2327,plain,
( e13 = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_101,c_2326]) ).
cnf(c_2328,plain,
( e13 = e10
| h(e11) = e21
| h(e12) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(copy,[status(thm)],[c_2327]) ).
cnf(c_2329,plain,
( e13 = e10
| h(e11) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(copy,[status(thm)],[c_2328]) ).
cnf(c_2330,plain,
( e13 = e10
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(copy,[status(thm)],[c_2329]) ).
cnf(c_1585,plain,
( h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(resolve,[status(thm)],[c_9,c_2330]) ).
cnf(c_1594,plain,
( j(e21) = e13
| h(e11) = e21
| h(e12) = e21 ),
inference(paramod,[status(thm)],[c_1585,c_310]) ).
cnf(c_1608,plain,
( op1(e13,j(e21)) = e10
| h(e11) = e21
| h(e12) = e21 ),
inference(paramod,[status(thm)],[c_1594,c_1498]) ).
cnf(c_2331,plain,
( op1(e13,e13) = e10
| h(e11) = e21
| h(e12) = e21
| h(e11) = e21
| h(e12) = e21 ),
inference(paramod,[status(thm)],[c_1594,c_1608]) ).
cnf(c_2332,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21
| h(e11) = e21
| h(e12) = e21 ),
inference(paramod,[status(thm)],[c_94,c_2331]) ).
cnf(c_2333,plain,
( e12 = e10
| h(e11) = e21
| h(e11) = e21
| h(e12) = e21 ),
inference(copy,[status(thm)],[c_2332]) ).
cnf(c_2334,plain,
( e12 = e10
| h(e11) = e21
| h(e12) = e21 ),
inference(copy,[status(thm)],[c_2333]) ).
cnf(c_1612,plain,
( h(e11) = e21
| h(e12) = e21 ),
inference(resolve,[status(thm)],[c_8,c_2334]) ).
cnf(c_1621,plain,
( j(e21) = e12
| h(e11) = e21 ),
inference(paramod,[status(thm)],[c_1612,c_309]) ).
cnf(c_1638,plain,
( op1(e12,j(e21)) = e10
| h(e11) = e21 ),
inference(paramod,[status(thm)],[c_1621,c_1498]) ).
cnf(c_2335,plain,
( op1(e12,e12) = e10
| h(e11) = e21
| h(e11) = e21 ),
inference(paramod,[status(thm)],[c_1621,c_1638]) ).
cnf(c_2336,plain,
( e13 = e10
| h(e11) = e21
| h(e11) = e21 ),
inference(paramod,[status(thm)],[c_87,c_2335]) ).
cnf(c_2337,plain,
( e13 = e10
| h(e11) = e21 ),
inference(copy,[status(thm)],[c_2336]) ).
cnf(c_1643,plain,
h(e11) = e21,
inference(resolve,[status(thm)],[c_9,c_2337]) ).
cnf(c_2338,plain,
( op2(h(e11),e22) = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1643,c_1381]) ).
cnf(c_2339,plain,
( op2(e21,e22) = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1643,c_2338]) ).
cnf(c_2340,plain,
( e23 = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_117,c_2339]) ).
cnf(c_2341,plain,
( e23 = h(e13)
| e22 = e21
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2340]) ).
cnf(c_2342,plain,
( h(e13) = e23
| e22 = e21
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2341]) ).
cnf(c_1661,plain,
( h(e13) = e23
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(resolve,[status(thm)],[c_27,c_2342]) ).
cnf(c_2343,plain,
( op2(e22,h(e11)) = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1643,c_1376]) ).
cnf(c_2344,plain,
( op2(e22,e21) = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_1643,c_2343]) ).
cnf(c_2345,plain,
( e24 = h(e13)
| e21 = e22
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(paramod,[status(thm)],[c_122,c_2344]) ).
cnf(c_2346,plain,
( e24 = h(e13)
| e22 = e21
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2345]) ).
cnf(c_2347,plain,
( h(e13) = e24
| e22 = e21
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(copy,[status(thm)],[c_2346]) ).
cnf(c_1666,plain,
( h(e13) = e24
| h(e12) = e22
| h(e13) = e22
| h(e14) = e22 ),
inference(resolve,[status(thm)],[c_27,c_2347]) ).
cnf(c_1759,negated_conjecture,
op2(h(e14),e21) = h(e12),
inference(paramod,[status(thm)],[c_1643,c_208]) ).
cnf(c_1761,negated_conjecture,
op2(h(e13),e21) = h(e15),
inference(paramod,[status(thm)],[c_1643,c_196]) ).
cnf(c_1763,negated_conjecture,
op2(h(e12),e21) = h(e14),
inference(paramod,[status(thm)],[c_1643,c_184]) ).
cnf(c_1766,negated_conjecture,
op2(e21,h(e13)) = h(e15),
inference(paramod,[status(thm)],[c_1643,c_176]) ).
cnf(c_1767,negated_conjecture,
op2(e21,h(e12)) = h(e14),
inference(paramod,[status(thm)],[c_1643,c_174]) ).
cnf(c_2348,plain,
( op2(e22,e21) = h(e12)
| h(e13) = e23
| h(e12) = e22
| h(e13) = e22 ),
inference(paramod,[status(thm)],[c_1661,c_1759]) ).
cnf(c_2349,plain,
( e24 = h(e12)
| h(e13) = e23
| h(e12) = e22
| h(e13) = e22 ),
inference(paramod,[status(thm)],[c_122,c_2348]) ).
cnf(c_1893,plain,
( h(e12) = e24
| h(e13) = e23
| h(e12) = e22
| h(e13) = e22 ),
inference(copy,[status(thm)],[c_2349]) ).
cnf(c_2350,plain,
( op2(e22,e21) = h(e12)
| h(e13) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(paramod,[status(thm)],[c_1666,c_1759]) ).
cnf(c_2351,plain,
( e24 = h(e12)
| h(e13) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(paramod,[status(thm)],[c_122,c_2350]) ).
cnf(c_1905,plain,
( h(e12) = e24
| h(e13) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(copy,[status(thm)],[c_2351]) ).
cnf(c_2352,plain,
( h(e12) = e24
| e24 = e23
| h(e12) = e22
| h(e13) = e22
| h(e12) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(paramod,[status(thm)],[c_1905,c_1893]) ).
cnf(c_2353,plain,
( h(e12) = e24
| e24 = e23
| h(e12) = e22
| h(e12) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(copy,[status(thm)],[c_2352]) ).
cnf(c_2354,plain,
( h(e12) = e24
| e24 = e23
| h(e12) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(copy,[status(thm)],[c_2353]) ).
cnf(c_2355,plain,
( e24 = e23
| h(e12) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(copy,[status(thm)],[c_2354]) ).
cnf(c_2101,plain,
( h(e12) = e24
| h(e12) = e22
| h(e13) = e22 ),
inference(resolve,[status(thm)],[c_34,c_2355]) ).
cnf(c_2356,plain,
( op2(e22,e21) = h(e15)
| h(e12) = e24
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2101,c_1761]) ).
cnf(c_2357,plain,
( e24 = h(e15)
| h(e12) = e24
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_122,c_2356]) ).
cnf(c_2111,plain,
( h(e15) = e24
| h(e12) = e24
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2357]) ).
cnf(c_2358,plain,
( op2(e21,e22) = h(e15)
| h(e12) = e24
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2101,c_1766]) ).
cnf(c_2359,plain,
( e23 = h(e15)
| h(e12) = e24
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_117,c_2358]) ).
cnf(c_2112,plain,
( h(e15) = e23
| h(e12) = e24
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2359]) ).
cnf(c_2360,plain,
( e23 = e24
| h(e12) = e24
| h(e12) = e22
| h(e12) = e24
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2112,c_2111]) ).
cnf(c_2361,plain,
( e24 = e23
| h(e12) = e24
| h(e12) = e22
| h(e12) = e24
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2360]) ).
cnf(c_2362,plain,
( e24 = e23
| h(e12) = e24
| h(e12) = e24
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2361]) ).
cnf(c_2363,plain,
( e24 = e23
| h(e12) = e24
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2362]) ).
cnf(c_2142,plain,
( h(e12) = e24
| h(e12) = e22 ),
inference(resolve,[status(thm)],[c_34,c_2363]) ).
cnf(c_2364,plain,
( op2(e24,e21) = h(e14)
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2142,c_1763]) ).
cnf(c_2365,plain,
( e22 = h(e14)
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_134,c_2364]) ).
cnf(c_2155,plain,
( h(e14) = e22
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2365]) ).
cnf(c_2366,plain,
( op2(e21,e24) = h(e14)
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2142,c_1767]) ).
cnf(c_2367,plain,
( e25 = h(e14)
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_119,c_2366]) ).
cnf(c_2157,plain,
( h(e14) = e25
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2367]) ).
cnf(c_2368,plain,
( e25 = e22
| h(e12) = e22
| h(e12) = e22 ),
inference(paramod,[status(thm)],[c_2157,c_2155]) ).
cnf(c_2369,plain,
( e25 = e22
| h(e12) = e22 ),
inference(copy,[status(thm)],[c_2368]) ).
cnf(c_2194,plain,
h(e12) = e22,
inference(resolve,[status(thm)],[c_33,c_2369]) ).
cnf(c_2370,negated_conjecture,
op2(e21,e22) = h(e14),
inference(paramod,[status(thm)],[c_2194,c_1767]) ).
cnf(c_2371,negated_conjecture,
e23 = h(e14),
inference(paramod,[status(thm)],[c_117,c_2370]) ).
cnf(c_2268,negated_conjecture,
h(e14) = e23,
inference(copy,[status(thm)],[c_2371]) ).
cnf(c_2372,negated_conjecture,
op2(e22,e21) = h(e14),
inference(paramod,[status(thm)],[c_2194,c_1763]) ).
cnf(c_2373,negated_conjecture,
e24 = h(e14),
inference(paramod,[status(thm)],[c_122,c_2372]) ).
cnf(c_2374,negated_conjecture,
e24 = e23,
inference(paramod,[status(thm)],[c_2268,c_2373]) ).
cnf(c_2269,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_34,c_2374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG031+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 20:59:19 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3095076 was started by sandbox2 on n005,
% 0.17/0.44 % Sat Sep 26 20:59:19 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 6.53/1.32
% 6.53/1.32 % SZS status Theorem for theBenchmark
% 6.53/1.32
% 6.53/1.32 % Proof 1 at 0.70 (+ 0.14) seconds.
% 6.53/1.32 % Length of proof is 123.
% 6.53/1.32 % Level of proof is 34.
% 6.53/1.32 % Maximum clause weight is 42.000.
% 6.53/1.32 % Given clauses 463.
% 6.53/1.32
% 6.53/1.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------