%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG081+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 : n012.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 06:49:26 AM UTC 2026
% Result : Theorem 0.22s 0.44s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 5
% Syntax : Number of formulae : 179 ( 57 unt; 0 def)
% Number of atoms : 898 ( 897 equ)
% Maximal formula atoms : 110 ( 5 avg)
% Number of connectives : 751 ( 32 ~; 515 |; 202 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 5 avg)
% Maximal term depth : 3 ( 1 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(ax1,axiom,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('theBenchmark.p',ax1) ).
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) = e11
& op1(e14,e13) = e12
& op1(e14,e12) = e10
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e12
& op1(e13,e13) = e11
& op1(e13,e12) = e14
& op1(e13,e11) = e10
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e10
& op1(e12,e12) = e11
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e14) = e10
& op1(e11,e13) = e14
& op1(e11,e12) = e13
& op1(e11,e11) = e12
& 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_7,plain,
e11 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_8,plain,
e12 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_17,plain,
e21 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_19,plain,
e23 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_20,plain,
e24 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_21,plain,
e22 != e21,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_23,plain,
e24 != e21,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_24,plain,
e23 != e22,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_25,plain,
e24 != e22,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_52,plain,
op1(e10,e10) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_54,plain,
op1(e10,e12) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_58,plain,
op1(e11,e11) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_61,plain,
op1(e11,e14) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_64,plain,
op1(e12,e12) = e11,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_68,plain,
op1(e13,e11) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_70,plain,
op1(e13,e13) = e11,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_76,plain,
op1(e14,e14) = e11,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_77,plain,
op2(e20,e20) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_83,plain,
op2(e21,e21) = e22,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_86,plain,
op2(e21,e24) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_89,plain,
op2(e22,e22) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_93,plain,
op2(e23,e21) = e24,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_95,plain,
op2(e23,e23) = e21,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_100,plain,
op2(e24,e23) = e22,
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_103,negated_conjecture,
( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_108,negated_conjecture,
( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_111,negated_conjecture,
( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = 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_1215,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_1215]) ).
cnf(c_124,negated_conjecture,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1216,negated_conjecture,
h(e12) = op2(h(e11),h(e11)),
inference(paramod,[status(thm)],[c_58,c_124]) ).
cnf(c_125,negated_conjecture,
op2(h(e11),h(e11)) = h(e12),
inference(copy,[status(thm)],[c_1216]) ).
cnf(c_130,negated_conjecture,
h(op1(e11,e14)) = op2(h(e11),h(e14)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1217,negated_conjecture,
h(e10) = op2(h(e11),h(e14)),
inference(paramod,[status(thm)],[c_61,c_130]) ).
cnf(c_131,negated_conjecture,
op2(h(e11),h(e14)) = h(e10),
inference(copy,[status(thm)],[c_1217]) ).
cnf(c_144,negated_conjecture,
h(op1(e13,e11)) = op2(h(e13),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1218,negated_conjecture,
h(e10) = op2(h(e13),h(e11)),
inference(paramod,[status(thm)],[c_68,c_144]) ).
cnf(c_145,negated_conjecture,
op2(h(e13),h(e11)) = h(e10),
inference(copy,[status(thm)],[c_1218]) ).
cnf(c_162,negated_conjecture,
j(op2(e20,e20)) = op1(j(e20),j(e20)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1219,negated_conjecture,
j(e20) = op1(j(e20),j(e20)),
inference(paramod,[status(thm)],[c_77,c_162]) ).
cnf(c_163,negated_conjecture,
op1(j(e20),j(e20)) = j(e20),
inference(copy,[status(thm)],[c_1219]) ).
cnf(c_210,negated_conjecture,
j(op2(e24,e24)) = op1(j(e24),j(e24)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1220,negated_conjecture,
j(e20) = op1(j(e24),j(e24)),
inference(paramod,[status(thm)],[c_101,c_210]) ).
cnf(c_211,negated_conjecture,
op1(j(e24),j(e24)) = j(e20),
inference(copy,[status(thm)],[c_1220]) ).
cnf(c_213,negated_conjecture,
h(j(e21)) = e21,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_216,negated_conjecture,
h(j(e24)) = e24,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_217,negated_conjecture,
j(h(e10)) = e10,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_219,negated_conjecture,
j(h(e12)) = e12,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_220,negated_conjecture,
j(h(e13)) = e13,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_221,negated_conjecture,
j(h(e14)) = e14,
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_234,plain,
( op2(e24,h(e11)) = h(e12)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_103,c_125]) ).
cnf(c_323,plain,
( h(e14) = e21
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_108,c_213]) ).
cnf(c_326,plain,
( h(e14) = e24
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 ),
inference(paramod,[status(thm)],[c_111,c_216]) ).
cnf(c_1221,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_1222,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_1221]) ).
cnf(c_1223,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_1222]) ).
cnf(c_1224,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_1223]) ).
cnf(c_1225,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_1224]) ).
cnf(c_1226,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1225]) ).
cnf(c_1227,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1226]) ).
cnf(c_332,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1227]) ).
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_375,plain,
( h(e13) = e21
| h(e14) = e21
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_323,c_213]) ).
cnf(c_410,plain,
( h(e13) = e24
| h(e14) = e24
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 ),
inference(paramod,[status(thm)],[c_326,c_216]) ).
cnf(c_480,plain,
( h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_375,c_213]) ).
cnf(c_513,plain,
( h(e12) = e24
| h(e13) = e24
| h(e14) = e24
| j(e24) = e11
| j(e24) = e10 ),
inference(paramod,[status(thm)],[c_410,c_216]) ).
cnf(c_535,plain,
( h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_480,c_213]) ).
cnf(c_570,plain,
( h(e11) = e24
| h(e12) = e24
| h(e13) = e24
| h(e14) = e24
| j(e24) = e10 ),
inference(paramod,[status(thm)],[c_513,c_216]) ).
cnf(c_592,plain,
( h(e10) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e14) = e21 ),
inference(paramod,[status(thm)],[c_535,c_213]) ).
cnf(c_627,plain,
( h(e10) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24
| h(e14) = e24 ),
inference(paramod,[status(thm)],[c_570,c_216]) ).
cnf(c_640,plain,
( op2(h(e11),e21) = h(e10)
| h(e10) = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_592,c_131]) ).
cnf(c_689,plain,
( j(e24) = e14
| h(e10) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_627,c_221]) ).
cnf(c_742,plain,
( op1(e14,j(e24)) = j(e20)
| h(e10) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_689,c_211]) ).
cnf(c_1228,plain,
( op2(e24,e24) = h(e12)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_103,c_234]) ).
cnf(c_1229,plain,
( e20 = h(e12)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_101,c_1228]) ).
cnf(c_1230,plain,
( h(e12) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1229]) ).
cnf(c_1231,plain,
( h(e12) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1230]) ).
cnf(c_1232,plain,
( h(e12) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1231]) ).
cnf(c_1233,plain,
( h(e12) = e20
| h(e11) = e23
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1232]) ).
cnf(c_744,plain,
( h(e12) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1233]) ).
cnf(c_755,plain,
( j(e20) = e12
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_744,c_219]) ).
cnf(c_758,plain,
( op1(j(e20),e12) = j(e20)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_755,c_163]) ).
cnf(c_1234,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_1235,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_1234]) ).
cnf(c_1236,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_1235]) ).
cnf(c_1237,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1236]) ).
cnf(c_1238,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1237]) ).
cnf(c_1239,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1238]) ).
cnf(c_767,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1239]) ).
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_1240,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_1241,plain,
( e23 = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_89,c_1240]) ).
cnf(c_1242,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1241]) ).
cnf(c_1243,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1242]) ).
cnf(c_793,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1243]) ).
cnf(c_1244,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_793,c_767]) ).
cnf(c_1245,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1244]) ).
cnf(c_1246,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1245]) ).
cnf(c_807,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(resolve,[status(thm)],[c_24,c_1246]) ).
cnf(c_808,plain,
( op2(e21,h(e10)) = h(e10)
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_807,c_113]) ).
cnf(c_1247,plain,
( op2(e21,e21) = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_807,c_808]) ).
cnf(c_1248,plain,
( e22 = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_83,c_1247]) ).
cnf(c_1249,plain,
( h(e10) = e22
| h(e10) = e20
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1248]) ).
cnf(c_833,plain,
( h(e10) = e22
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1249]) ).
cnf(c_1250,plain,
( e22 = e21
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_833,c_807]) ).
cnf(c_1251,plain,
( e22 = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_1250]) ).
cnf(c_846,plain,
h(e10) = e20,
inference(resolve,[status(thm)],[c_21,c_1251]) ).
cnf(c_1252,plain,
( op1(e14,j(e24)) = j(e20)
| e20 = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_846,c_742]) ).
cnf(c_1253,plain,
( op1(e14,j(e24)) = j(e20)
| e24 = e20
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(copy,[status(thm)],[c_1252]) ).
cnf(c_850,plain,
( op1(e14,j(e24)) = j(e20)
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(resolve,[status(thm)],[c_20,c_1253]) ).
cnf(c_1254,plain,
( j(e24) = e14
| e20 = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_846,c_689]) ).
cnf(c_1255,plain,
( j(e24) = e14
| e24 = e20
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(copy,[status(thm)],[c_1254]) ).
cnf(c_892,plain,
( j(e24) = e14
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(resolve,[status(thm)],[c_20,c_1255]) ).
cnf(c_1256,plain,
( op2(h(e11),e21) = h(e10)
| e20 = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_846,c_640]) ).
cnf(c_1257,plain,
( op2(h(e11),e21) = e20
| e20 = e21
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(paramod,[status(thm)],[c_846,c_1256]) ).
cnf(c_1258,plain,
( op2(h(e11),e21) = e20
| e21 = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(copy,[status(thm)],[c_1257]) ).
cnf(c_934,plain,
( op2(h(e11),e21) = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21 ),
inference(resolve,[status(thm)],[c_17,c_1258]) ).
cnf(c_943,negated_conjecture,
j(e20) = e10,
inference(paramod,[status(thm)],[c_846,c_217]) ).
cnf(c_946,negated_conjecture,
op2(h(e13),h(e11)) = e20,
inference(paramod,[status(thm)],[c_846,c_145]) ).
cnf(c_962,plain,
( op1(e14,j(e24)) = e10
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_943,c_850]) ).
cnf(c_1259,plain,
( op1(e10,e12) = j(e20)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_943,c_758]) ).
cnf(c_1260,plain,
( e12 = j(e20)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_54,c_1259]) ).
cnf(c_1261,plain,
( e12 = e10
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_943,c_1260]) ).
cnf(c_964,plain,
( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(resolve,[status(thm)],[c_8,c_1261]) ).
cnf(c_1003,negated_conjecture,
op1(j(e24),j(e24)) = e10,
inference(paramod,[status(thm)],[c_943,c_211]) ).
cnf(c_1026,plain,
( op2(h(e11),e23) = h(e12)
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_964,c_125]) ).
cnf(c_1262,plain,
( op2(e23,e21) = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_964,c_934]) ).
cnf(c_1263,plain,
( e24 = e20
| h(e11) = e21
| h(e12) = e21
| h(e13) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_93,c_1262]) ).
cnf(c_1264,plain,
( e24 = e20
| h(e12) = e21
| h(e13) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_1263]) ).
cnf(c_1069,plain,
( h(e12) = e21
| h(e13) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(resolve,[status(thm)],[c_20,c_1264]) ).
cnf(c_1077,plain,
( op2(e21,h(e11)) = e20
| h(e12) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1069,c_946]) ).
cnf(c_1265,plain,
( op1(e14,e14) = e10
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_892,c_962]) ).
cnf(c_1266,plain,
( e11 = e10
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(paramod,[status(thm)],[c_76,c_1265]) ).
cnf(c_1267,plain,
( e11 = e10
| h(e11) = e24
| h(e12) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(copy,[status(thm)],[c_1266]) ).
cnf(c_1268,plain,
( e11 = e10
| h(e11) = e24
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(copy,[status(thm)],[c_1267]) ).
cnf(c_1269,plain,
( e11 = e10
| h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(copy,[status(thm)],[c_1268]) ).
cnf(c_1113,plain,
( h(e11) = e24
| h(e12) = e24
| h(e13) = e24 ),
inference(resolve,[status(thm)],[c_7,c_1269]) ).
cnf(c_1121,plain,
( j(e24) = e13
| h(e11) = e24
| h(e12) = e24 ),
inference(paramod,[status(thm)],[c_1113,c_220]) ).
cnf(c_1133,plain,
( op1(e13,j(e24)) = e10
| h(e11) = e24
| h(e12) = e24 ),
inference(paramod,[status(thm)],[c_1121,c_1003]) ).
cnf(c_1270,plain,
( op1(e13,e13) = e10
| h(e11) = e24
| h(e12) = e24
| h(e11) = e24
| h(e12) = e24 ),
inference(paramod,[status(thm)],[c_1121,c_1133]) ).
cnf(c_1271,plain,
( e11 = e10
| h(e11) = e24
| h(e12) = e24
| h(e11) = e24
| h(e12) = e24 ),
inference(paramod,[status(thm)],[c_70,c_1270]) ).
cnf(c_1272,plain,
( e11 = e10
| h(e11) = e24
| h(e11) = e24
| h(e12) = e24 ),
inference(copy,[status(thm)],[c_1271]) ).
cnf(c_1273,plain,
( e11 = e10
| h(e11) = e24
| h(e12) = e24 ),
inference(copy,[status(thm)],[c_1272]) ).
cnf(c_1139,plain,
( h(e11) = e24
| h(e12) = e24 ),
inference(resolve,[status(thm)],[c_7,c_1273]) ).
cnf(c_1146,plain,
( j(e24) = e12
| h(e11) = e24 ),
inference(paramod,[status(thm)],[c_1139,c_219]) ).
cnf(c_1163,plain,
( op1(e12,j(e24)) = e10
| h(e11) = e24 ),
inference(paramod,[status(thm)],[c_1146,c_1003]) ).
cnf(c_1274,plain,
( op1(e12,e12) = e10
| h(e11) = e24
| h(e11) = e24 ),
inference(paramod,[status(thm)],[c_1146,c_1163]) ).
cnf(c_1275,plain,
( e11 = e10
| h(e11) = e24
| h(e11) = e24 ),
inference(paramod,[status(thm)],[c_64,c_1274]) ).
cnf(c_1276,plain,
( e11 = e10
| h(e11) = e24 ),
inference(copy,[status(thm)],[c_1275]) ).
cnf(c_1168,plain,
h(e11) = e24,
inference(resolve,[status(thm)],[c_7,c_1276]) ).
cnf(c_1277,plain,
( op2(e21,h(e11)) = e20
| h(e12) = e21
| h(e11) = e22
| h(e11) = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1077]) ).
cnf(c_1278,plain,
( op2(e21,h(e11)) = e20
| h(e12) = e21
| h(e11) = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1277]) ).
cnf(c_1279,plain,
( op2(e21,h(e11)) = e20
| h(e12) = e21
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1278]) ).
cnf(c_1280,plain,
( op2(e21,e24) = e20
| h(e12) = e21
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1279]) ).
cnf(c_1281,plain,
( e23 = e20
| h(e12) = e21
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_86,c_1280]) ).
cnf(c_1282,plain,
( e23 = e20
| h(e12) = e21
| e24 = e22
| e24 = e21 ),
inference(resolve,[status(thm)],[c_20,c_1281]) ).
cnf(c_1283,plain,
( e23 = e20
| h(e12) = e21
| e24 = e22 ),
inference(resolve,[status(thm)],[c_23,c_1282]) ).
cnf(c_1284,plain,
( e23 = e20
| h(e12) = e21 ),
inference(resolve,[status(thm)],[c_25,c_1283]) ).
cnf(c_1198,plain,
h(e12) = e21,
inference(resolve,[status(thm)],[c_19,c_1284]) ).
cnf(c_1285,plain,
( op2(h(e11),e23) = h(e12)
| h(e11) = e22
| h(e11) = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1026]) ).
cnf(c_1286,plain,
( op2(h(e11),e23) = h(e12)
| h(e11) = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1285]) ).
cnf(c_1287,plain,
( op2(h(e11),e23) = h(e12)
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1286]) ).
cnf(c_1288,plain,
( op2(e24,e23) = h(e12)
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1168,c_1287]) ).
cnf(c_1289,plain,
( e22 = h(e12)
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_100,c_1288]) ).
cnf(c_1290,plain,
( e22 = e21
| e24 = e22
| e24 = e21
| e24 = e20 ),
inference(paramod,[status(thm)],[c_1198,c_1289]) ).
cnf(c_1291,plain,
( e22 = e21
| e24 = e22
| e24 = e21 ),
inference(resolve,[status(thm)],[c_20,c_1290]) ).
cnf(c_1292,plain,
( e22 = e21
| e24 = e22 ),
inference(resolve,[status(thm)],[c_23,c_1291]) ).
cnf(c_1293,plain,
e22 = e21,
inference(resolve,[status(thm)],[c_25,c_1292]) ).
cnf(c_1214,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_1293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG081+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 21:06:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 1504523 was started by sandbox on n012,
% 0.04/0.30 % Sat Sep 26 21:06:34 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 0.22/0.44
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44
% 0.22/0.44 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.22/0.44 % Length of proof is 99.
% 0.22/0.44 % Level of proof is 23.
% 0.22/0.44 % Maximum clause weight is 38.000.
% 0.22/0.44 % Given clauses 296.
% 0.22/0.44
% 0.22/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------