TSTP Solution File: ALG115+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:02:30 EDT 2022
% Result : Theorem 0.49s 0.70s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 75
% Syntax : Number of clauses : 203 ( 118 unt; 76 nHn; 203 RR)
% Number of literals : 435 ( 0 equ; 105 neg)
% Maximal clause size : 20 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e11,e10),
file('ALG115+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e12,e10),
file('ALG115+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e13,e10),
file('ALG115+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e12,e11),
file('ALG115+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e13,e11),
file('ALG115+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e13,e12),
file('ALG115+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e21,e20),
file('ALG115+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e22,e20),
file('ALG115+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e23,e20),
file('ALG115+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e22,e21),
file('ALG115+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e23,e21),
file('ALG115+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(e23,e22),
file('ALG115+1.p',unknown),
[] ).
cnf(32,axiom,
equal(h4(e13),e23),
file('ALG115+1.p',unknown),
[] ).
cnf(33,axiom,
equal(op1(e13,e13),e11),
file('ALG115+1.p',unknown),
[] ).
cnf(34,axiom,
equal(op2(e23,e23),e21),
file('ALG115+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ equal(h4(e10),e20)
| skC141 ),
file('ALG115+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ equal(h4(e11),e21)
| skC142 ),
file('ALG115+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ equal(h4(e12),e22)
| skC143 ),
file('ALG115+1.p',unknown),
[] ).
cnf(83,axiom,
equal(op2(e20,e20),h1(e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(84,axiom,
equal(op2(e21,e21),h2(e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(85,axiom,
equal(op2(e22,e22),h3(e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(86,axiom,
equal(op2(e23,e23),h4(e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(525,axiom,
equal(op1(op1(e13,e13),e13),e12),
file('ALG115+1.p',unknown),
[] ).
cnf(526,axiom,
equal(op2(op2(e23,e23),e23),e22),
file('ALG115+1.p',unknown),
[] ).
cnf(529,axiom,
~ equal(op1(e13,e10),op1(e10,e10)),
file('ALG115+1.p',unknown),
[] ).
cnf(536,axiom,
~ equal(op1(e12,e11),op1(e11,e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(537,axiom,
~ equal(op1(e13,e11),op1(e11,e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(542,axiom,
~ equal(op1(e12,e12),op1(e11,e12)),
file('ALG115+1.p',unknown),
[] ).
cnf(543,axiom,
~ equal(op1(e13,e12),op1(e11,e12)),
file('ALG115+1.p',unknown),
[] ).
cnf(544,axiom,
~ equal(op1(e13,e12),op1(e12,e12)),
file('ALG115+1.p',unknown),
[] ).
cnf(553,axiom,
~ equal(op1(e10,e13),op1(e10,e10)),
file('ALG115+1.p',unknown),
[] ).
cnf(560,axiom,
~ equal(op1(e11,e12),op1(e11,e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(561,axiom,
~ equal(op1(e11,e13),op1(e11,e11)),
file('ALG115+1.p',unknown),
[] ).
cnf(577,axiom,
~ equal(op2(e23,e20),op2(e20,e20)),
file('ALG115+1.p',unknown),
[] ).
cnf(584,axiom,
~ equal(op2(e22,e21),op2(e21,e21)),
file('ALG115+1.p',unknown),
[] ).
cnf(585,axiom,
~ equal(op2(e23,e21),op2(e21,e21)),
file('ALG115+1.p',unknown),
[] ).
cnf(590,axiom,
~ equal(op2(e22,e22),op2(e21,e22)),
file('ALG115+1.p',unknown),
[] ).
cnf(591,axiom,
~ equal(op2(e23,e22),op2(e21,e22)),
file('ALG115+1.p',unknown),
[] ).
cnf(592,axiom,
~ equal(op2(e23,e22),op2(e22,e22)),
file('ALG115+1.p',unknown),
[] ).
cnf(601,axiom,
~ equal(op2(e20,e23),op2(e20,e20)),
file('ALG115+1.p',unknown),
[] ).
cnf(608,axiom,
~ equal(op2(e21,e22),op2(e21,e21)),
file('ALG115+1.p',unknown),
[] ).
cnf(609,axiom,
~ equal(op2(e21,e23),op2(e21,e21)),
file('ALG115+1.p',unknown),
[] ).
cnf(624,axiom,
equal(op2(op2(e21,e21),e21),h2(e12)),
file('ALG115+1.p',unknown),
[] ).
cnf(626,axiom,
equal(op2(op2(e23,e23),e23),h4(e12)),
file('ALG115+1.p',unknown),
[] ).
cnf(659,axiom,
equal(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e10),
file('ALG115+1.p',unknown),
[] ).
cnf(660,axiom,
equal(op2(op2(e23,e23),op2(op2(e23,e23),e23)),e20),
file('ALG115+1.p',unknown),
[] ).
cnf(662,axiom,
equal(op2(op2(e21,e21),op2(op2(e21,e21),e21)),h2(e10)),
file('ALG115+1.p',unknown),
[] ).
cnf(664,axiom,
equal(op2(op2(e23,e23),op2(op2(e23,e23),e23)),h4(e10)),
file('ALG115+1.p',unknown),
[] ).
cnf(665,axiom,
( equal(op2(e20,e20),e23)
| equal(op2(e21,e21),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e23,e23),e23) ),
file('ALG115+1.p',unknown),
[] ).
cnf(666,axiom,
( equal(op2(e20,e20),e22)
| equal(op2(e21,e21),e22)
| equal(op2(e22,e22),e22)
| equal(op2(e23,e23),e22) ),
file('ALG115+1.p',unknown),
[] ).
cnf(668,axiom,
( equal(op2(e20,e20),e20)
| equal(op2(e21,e21),e20)
| equal(op2(e22,e22),e20)
| equal(op2(e23,e23),e20) ),
file('ALG115+1.p',unknown),
[] ).
cnf(669,axiom,
( equal(op1(e10,e10),e13)
| equal(op1(e11,e11),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e13,e13),e13) ),
file('ALG115+1.p',unknown),
[] ).
cnf(670,axiom,
( equal(op1(e10,e10),e12)
| equal(op1(e11,e11),e12)
| equal(op1(e12,e12),e12)
| equal(op1(e13,e13),e12) ),
file('ALG115+1.p',unknown),
[] ).
cnf(672,axiom,
( equal(op1(e10,e10),e10)
| equal(op1(e11,e11),e10)
| equal(op1(e12,e12),e10)
| equal(op1(e13,e13),e10) ),
file('ALG115+1.p',unknown),
[] ).
cnf(673,axiom,
( equal(op2(e20,e23),e23)
| equal(op2(e21,e23),e23)
| equal(op2(e22,e23),e23)
| equal(op2(e23,e23),e23) ),
file('ALG115+1.p',unknown),
[] ).
cnf(674,axiom,
( equal(op2(e23,e20),e23)
| equal(op2(e23,e21),e23)
| equal(op2(e23,e22),e23)
| equal(op2(e23,e23),e23) ),
file('ALG115+1.p',unknown),
[] ).
cnf(676,axiom,
( equal(op2(e23,e20),e22)
| equal(op2(e23,e21),e22)
| equal(op2(e23,e22),e22)
| equal(op2(e23,e23),e22) ),
file('ALG115+1.p',unknown),
[] ).
cnf(679,axiom,
( equal(op2(e20,e23),e20)
| equal(op2(e21,e23),e20)
| equal(op2(e22,e23),e20)
| equal(op2(e23,e23),e20) ),
file('ALG115+1.p',unknown),
[] ).
cnf(680,axiom,
( equal(op2(e23,e20),e20)
| equal(op2(e23,e21),e20)
| equal(op2(e23,e22),e20)
| equal(op2(e23,e23),e20) ),
file('ALG115+1.p',unknown),
[] ).
cnf(682,axiom,
( equal(op2(e22,e20),e23)
| equal(op2(e22,e21),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e22,e23),e23) ),
file('ALG115+1.p',unknown),
[] ).
cnf(685,axiom,
( equal(op2(e20,e22),e21)
| equal(op2(e21,e22),e21)
| equal(op2(e22,e22),e21)
| equal(op2(e23,e22),e21) ),
file('ALG115+1.p',unknown),
[] ).
cnf(686,axiom,
( equal(op2(e22,e20),e21)
| equal(op2(e22,e21),e21)
| equal(op2(e22,e22),e21)
| equal(op2(e22,e23),e21) ),
file('ALG115+1.p',unknown),
[] ).
cnf(691,axiom,
( equal(op2(e20,e21),e22)
| equal(op2(e21,e21),e22)
| equal(op2(e22,e21),e22)
| equal(op2(e23,e21),e22) ),
file('ALG115+1.p',unknown),
[] ).
cnf(694,axiom,
( equal(op2(e21,e20),e21)
| equal(op2(e21,e21),e21)
| equal(op2(e21,e22),e21)
| equal(op2(e21,e23),e21) ),
file('ALG115+1.p',unknown),
[] ).
cnf(721,axiom,
( equal(op1(e10,e13),e13)
| equal(op1(e11,e13),e13)
| equal(op1(e12,e13),e13)
| equal(op1(e13,e13),e13) ),
file('ALG115+1.p',unknown),
[] ).
cnf(722,axiom,
( equal(op1(e13,e10),e13)
| equal(op1(e13,e11),e13)
| equal(op1(e13,e12),e13)
| equal(op1(e13,e13),e13) ),
file('ALG115+1.p',unknown),
[] ).
cnf(724,axiom,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(op1(e13,e13),e12) ),
file('ALG115+1.p',unknown),
[] ).
cnf(727,axiom,
( equal(op1(e10,e13),e10)
| equal(op1(e11,e13),e10)
| equal(op1(e12,e13),e10)
| equal(op1(e13,e13),e10) ),
file('ALG115+1.p',unknown),
[] ).
cnf(728,axiom,
( equal(op1(e13,e10),e10)
| equal(op1(e13,e11),e10)
| equal(op1(e13,e12),e10)
| equal(op1(e13,e13),e10) ),
file('ALG115+1.p',unknown),
[] ).
cnf(730,axiom,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e12,e13),e13) ),
file('ALG115+1.p',unknown),
[] ).
cnf(733,axiom,
( equal(op1(e10,e12),e11)
| equal(op1(e11,e12),e11)
| equal(op1(e12,e12),e11)
| equal(op1(e13,e12),e11) ),
file('ALG115+1.p',unknown),
[] ).
cnf(734,axiom,
( equal(op1(e12,e10),e11)
| equal(op1(e12,e11),e11)
| equal(op1(e12,e12),e11)
| equal(op1(e12,e13),e11) ),
file('ALG115+1.p',unknown),
[] ).
cnf(739,axiom,
( equal(op1(e10,e11),e12)
| equal(op1(e11,e11),e12)
| equal(op1(e12,e11),e12)
| equal(op1(e13,e11),e12) ),
file('ALG115+1.p',unknown),
[] ).
cnf(742,axiom,
( equal(op1(e11,e10),e11)
| equal(op1(e11,e11),e11)
| equal(op1(e11,e12),e11)
| equal(op1(e11,e13),e11) ),
file('ALG115+1.p',unknown),
[] ).
cnf(771,axiom,
( ~ equal(h4(e13),e23)
| ~ equal(op2(h4(e10),h4(e10)),h4(op1(e10,e10)))
| ~ equal(op2(h4(e10),h4(e11)),h4(op1(e10,e11)))
| ~ equal(op2(h4(e10),h4(e12)),h4(op1(e10,e12)))
| ~ equal(op2(h4(e10),h4(e13)),h4(op1(e10,e13)))
| ~ equal(op2(h4(e11),h4(e10)),h4(op1(e11,e10)))
| ~ equal(op2(h4(e11),h4(e11)),h4(op1(e11,e11)))
| ~ equal(op2(h4(e11),h4(e12)),h4(op1(e11,e12)))
| ~ equal(op2(h4(e11),h4(e13)),h4(op1(e11,e13)))
| ~ equal(op2(h4(e12),h4(e10)),h4(op1(e12,e10)))
| ~ equal(op2(h4(e12),h4(e11)),h4(op1(e12,e11)))
| ~ equal(op2(h4(e12),h4(e12)),h4(op1(e12,e12)))
| ~ equal(op2(h4(e12),h4(e13)),h4(op1(e12,e13)))
| ~ equal(op2(h4(e13),h4(e10)),h4(op1(e13,e10)))
| ~ equal(op2(h4(e13),h4(e11)),h4(op1(e13,e11)))
| ~ equal(op2(h4(e13),h4(e12)),h4(op1(e13,e12)))
| ~ equal(op2(h4(e13),h4(e13)),h4(op1(e13,e13)))
| ~ skC141
| ~ skC142
| ~ skC143 ),
file('ALG115+1.p',unknown),
[] ).
cnf(787,plain,
equal(h4(e11),e21),
inference(rew,[status(thm),theory(equality)],[34,86]),
[iquote('0:Rew:34.0,86.0')] ).
cnf(791,plain,
( ~ equal(e21,e21)
| skC142 ),
inference(rew,[status(thm),theory(equality)],[787,76]),
[iquote('0:Rew:787.0,76.0')] ).
cnf(792,plain,
skC142,
inference(obv,[status(thm),theory(equality)],[791]),
[iquote('0:Obv:791.0')] ).
cnf(807,plain,
equal(op2(e21,e23),e22),
inference(rew,[status(thm),theory(equality)],[34,526]),
[iquote('0:Rew:34.0,526.0')] ).
cnf(808,plain,
equal(op1(e11,e13),e12),
inference(rew,[status(thm),theory(equality)],[33,525]),
[iquote('0:Rew:33.0,525.0')] ).
cnf(941,plain,
equal(h4(e12),e22),
inference(rew,[status(thm),theory(equality)],[807,626,34]),
[iquote('0:Rew:807.0,626.0,34.0,626.0')] ).
cnf(942,plain,
( ~ equal(e22,e22)
| skC143 ),
inference(rew,[status(thm),theory(equality)],[941,81]),
[iquote('0:Rew:941.0,81.0')] ).
cnf(944,plain,
skC143,
inference(obv,[status(thm),theory(equality)],[942]),
[iquote('0:Obv:942.0')] ).
cnf(946,plain,
equal(op2(h2(e11),e21),h2(e12)),
inference(rew,[status(thm),theory(equality)],[84,624]),
[iquote('0:Rew:84.0,624.0')] ).
cnf(960,plain,
~ equal(h2(e11),e22),
inference(rew,[status(thm),theory(equality)],[807,609,84]),
[iquote('0:Rew:807.0,609.0,84.0,609.0')] ).
cnf(961,plain,
~ equal(op2(e21,e22),h2(e11)),
inference(rew,[status(thm),theory(equality)],[84,608]),
[iquote('0:Rew:84.0,608.0')] ).
cnf(964,plain,
~ equal(op2(e20,e23),h1(e11)),
inference(rew,[status(thm),theory(equality)],[83,601]),
[iquote('0:Rew:83.0,601.0')] ).
cnf(976,plain,
~ equal(op2(e23,e22),h3(e11)),
inference(rew,[status(thm),theory(equality)],[85,592]),
[iquote('0:Rew:85.0,592.0')] ).
cnf(977,plain,
~ equal(op2(e21,e22),h3(e11)),
inference(rew,[status(thm),theory(equality)],[85,590]),
[iquote('0:Rew:85.0,590.0')] ).
cnf(979,plain,
~ equal(op2(e23,e21),h2(e11)),
inference(rew,[status(thm),theory(equality)],[84,585]),
[iquote('0:Rew:84.0,585.0')] ).
cnf(980,plain,
~ equal(op2(e22,e21),h2(e11)),
inference(rew,[status(thm),theory(equality)],[84,584]),
[iquote('0:Rew:84.0,584.0')] ).
cnf(982,plain,
~ equal(op2(e23,e20),h1(e11)),
inference(rew,[status(thm),theory(equality)],[83,577]),
[iquote('0:Rew:83.0,577.0')] ).
cnf(994,plain,
~ equal(op1(e11,e11),e12),
inference(rew,[status(thm),theory(equality)],[808,561]),
[iquote('0:Rew:808.0,561.0')] ).
cnf(1010,plain,
equal(op2(e21,e22),e20),
inference(rew,[status(thm),theory(equality)],[807,660,34]),
[iquote('0:Rew:807.0,660.0,34.0,660.0')] ).
cnf(1016,plain,
~ equal(h2(e11),e20),
inference(rew,[status(thm),theory(equality)],[1010,961]),
[iquote('0:Rew:1010.0,961.0')] ).
cnf(1018,plain,
~ equal(op2(e23,e22),e20),
inference(rew,[status(thm),theory(equality)],[1010,591]),
[iquote('0:Rew:1010.0,591.0')] ).
cnf(1019,plain,
~ equal(h3(e11),e20),
inference(rew,[status(thm),theory(equality)],[1010,977]),
[iquote('0:Rew:1010.0,977.0')] ).
cnf(1035,plain,
equal(op1(e11,e12),e10),
inference(rew,[status(thm),theory(equality)],[808,659,33]),
[iquote('0:Rew:808.0,659.0,33.0,659.0')] ).
cnf(1041,plain,
~ equal(op1(e11,e11),e10),
inference(rew,[status(thm),theory(equality)],[1035,560]),
[iquote('0:Rew:1035.0,560.0')] ).
cnf(1043,plain,
~ equal(op1(e13,e12),e10),
inference(rew,[status(thm),theory(equality)],[1035,543]),
[iquote('0:Rew:1035.0,543.0')] ).
cnf(1044,plain,
~ equal(op1(e12,e12),e10),
inference(rew,[status(thm),theory(equality)],[1035,542]),
[iquote('0:Rew:1035.0,542.0')] ).
cnf(1062,plain,
equal(h4(e10),e20),
inference(rew,[status(thm),theory(equality)],[1010,664,807,34]),
[iquote('0:Rew:1010.0,664.0,807.0,664.0,34.0,664.0')] ).
cnf(1063,plain,
( ~ equal(e20,e20)
| skC141 ),
inference(rew,[status(thm),theory(equality)],[1062,71]),
[iquote('0:Rew:1062.0,71.0')] ).
cnf(1064,plain,
skC141,
inference(obv,[status(thm),theory(equality)],[1063]),
[iquote('0:Obv:1063.0')] ).
cnf(1066,plain,
equal(op2(h2(e11),h2(e12)),h2(e10)),
inference(rew,[status(thm),theory(equality)],[946,662,84]),
[iquote('0:Rew:946.0,662.0,84.0,662.0')] ).
cnf(1068,plain,
( equal(h1(e11),e23)
| equal(h2(e11),e23)
| equal(h3(e11),e23)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[34,665,85,84,83]),
[iquote('0:Rew:34.0,665.3,85.0,665.2,84.0,665.1,83.0,665.0')] ).
cnf(1069,plain,
( equal(h1(e11),e23)
| equal(h2(e11),e23)
| equal(h3(e11),e23) ),
inference(mrr,[status(thm)],[1068,11]),
[iquote('0:MRR:1068.3,11.0')] ).
cnf(1070,plain,
( equal(h1(e11),e22)
| equal(h2(e11),e22)
| equal(h3(e11),e22)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[34,666,85,84,83]),
[iquote('0:Rew:34.0,666.3,85.0,666.2,84.0,666.1,83.0,666.0')] ).
cnf(1071,plain,
( equal(h1(e11),e22)
| equal(h3(e11),e22) ),
inference(mrr,[status(thm)],[1070,960,10]),
[iquote('0:MRR:1070.1,1070.3,960.0,10.0')] ).
cnf(1072,plain,
( equal(h1(e11),e20)
| equal(h2(e11),e20)
| equal(h3(e11),e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[34,668,85,84,83]),
[iquote('0:Rew:34.0,668.3,85.0,668.2,84.0,668.1,83.0,668.0')] ).
cnf(1073,plain,
equal(h1(e11),e20),
inference(mrr,[status(thm)],[1072,1016,1019,7]),
[iquote('0:MRR:1072.1,1072.2,1072.3,1016.0,1019.0,7.0')] ).
cnf(1074,plain,
equal(op2(e20,e20),e20),
inference(rew,[status(thm),theory(equality)],[1073,83]),
[iquote('0:Rew:1073.0,83.0')] ).
cnf(1075,plain,
( equal(e22,e20)
| equal(h3(e11),e22) ),
inference(rew,[status(thm),theory(equality)],[1073,1071]),
[iquote('0:Rew:1073.0,1071.0')] ).
cnf(1079,plain,
~ equal(op2(e20,e23),e20),
inference(rew,[status(thm),theory(equality)],[1073,964]),
[iquote('0:Rew:1073.0,964.0')] ).
cnf(1082,plain,
~ equal(op2(e23,e20),e20),
inference(rew,[status(thm),theory(equality)],[1073,982]),
[iquote('0:Rew:1073.0,982.0')] ).
cnf(1087,plain,
( equal(e23,e20)
| equal(h2(e11),e23)
| equal(h3(e11),e23) ),
inference(rew,[status(thm),theory(equality)],[1073,1069]),
[iquote('0:Rew:1073.0,1069.0')] ).
cnf(1095,plain,
equal(h3(e11),e22),
inference(mrr,[status(thm)],[1075,8]),
[iquote('0:MRR:1075.0,8.0')] ).
cnf(1096,plain,
equal(op2(e22,e22),e22),
inference(rew,[status(thm),theory(equality)],[1095,85]),
[iquote('0:Rew:1095.0,85.0')] ).
cnf(1102,plain,
~ equal(op2(e23,e22),e22),
inference(rew,[status(thm),theory(equality)],[1095,976]),
[iquote('0:Rew:1095.0,976.0')] ).
cnf(1131,plain,
( equal(e23,e20)
| equal(h2(e11),e23)
| equal(e23,e22) ),
inference(rew,[status(thm),theory(equality)],[1095,1087]),
[iquote('0:Rew:1095.0,1087.2')] ).
cnf(1132,plain,
equal(h2(e11),e23),
inference(mrr,[status(thm)],[1131,9,12]),
[iquote('0:MRR:1131.0,1131.2,9.0,12.0')] ).
cnf(1133,plain,
equal(op2(e21,e21),e23),
inference(rew,[status(thm),theory(equality)],[1132,84]),
[iquote('0:Rew:1132.0,84.0')] ).
cnf(1136,plain,
equal(op2(e23,e21),h2(e12)),
inference(rew,[status(thm),theory(equality)],[1132,946]),
[iquote('0:Rew:1132.0,946.0')] ).
cnf(1139,plain,
~ equal(op2(e23,e21),e23),
inference(rew,[status(thm),theory(equality)],[1132,979]),
[iquote('0:Rew:1132.0,979.0')] ).
cnf(1140,plain,
~ equal(op2(e22,e21),e23),
inference(rew,[status(thm),theory(equality)],[1132,980]),
[iquote('0:Rew:1132.0,980.0')] ).
cnf(1144,plain,
equal(op2(e23,h2(e12)),h2(e10)),
inference(rew,[status(thm),theory(equality)],[1132,1066]),
[iquote('0:Rew:1132.0,1066.0')] ).
cnf(1154,plain,
~ equal(h2(e12),e23),
inference(rew,[status(thm),theory(equality)],[1136,1139]),
[iquote('0:Rew:1136.0,1139.0')] ).
cnf(1157,plain,
( equal(op1(e10,e10),e13)
| equal(op1(e11,e11),e13)
| equal(op1(e12,e12),e13)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[33,669]),
[iquote('0:Rew:33.0,669.3')] ).
cnf(1158,plain,
( equal(op1(e10,e10),e13)
| equal(op1(e11,e11),e13)
| equal(op1(e12,e12),e13) ),
inference(mrr,[status(thm)],[1157,5]),
[iquote('0:MRR:1157.3,5.0')] ).
cnf(1159,plain,
( equal(op1(e10,e10),e12)
| equal(op1(e11,e11),e12)
| equal(op1(e12,e12),e12)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[33,670]),
[iquote('0:Rew:33.0,670.3')] ).
cnf(1160,plain,
( equal(op1(e10,e10),e12)
| equal(op1(e12,e12),e12) ),
inference(mrr,[status(thm)],[1159,994,4]),
[iquote('0:MRR:1159.1,1159.3,994.0,4.0')] ).
cnf(1161,plain,
( equal(op1(e10,e10),e10)
| equal(op1(e11,e11),e10)
| equal(op1(e12,e12),e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[33,672]),
[iquote('0:Rew:33.0,672.3')] ).
cnf(1162,plain,
equal(op1(e10,e10),e10),
inference(mrr,[status(thm)],[1161,1041,1044,1]),
[iquote('0:MRR:1161.1,1161.2,1161.3,1041.0,1044.0,1.0')] ).
cnf(1163,plain,
~ equal(op1(e10,e13),e10),
inference(rew,[status(thm),theory(equality)],[1162,553]),
[iquote('0:Rew:1162.0,553.0')] ).
cnf(1166,plain,
~ equal(op1(e13,e10),e10),
inference(rew,[status(thm),theory(equality)],[1162,529]),
[iquote('0:Rew:1162.0,529.0')] ).
cnf(1170,plain,
( equal(e13,e10)
| equal(op1(e11,e11),e13)
| equal(op1(e12,e12),e13) ),
inference(rew,[status(thm),theory(equality)],[1162,1158]),
[iquote('0:Rew:1162.0,1158.0')] ).
cnf(1171,plain,
( equal(e12,e10)
| equal(op1(e12,e12),e12) ),
inference(rew,[status(thm),theory(equality)],[1162,1160]),
[iquote('0:Rew:1162.0,1160.0')] ).
cnf(1182,plain,
equal(op1(e12,e12),e12),
inference(mrr,[status(thm)],[1171,2]),
[iquote('0:MRR:1171.0,2.0')] ).
cnf(1186,plain,
~ equal(op1(e13,e12),e12),
inference(rew,[status(thm),theory(equality)],[1182,544]),
[iquote('0:Rew:1182.0,544.0')] ).
cnf(1199,plain,
( equal(e13,e10)
| equal(op1(e11,e11),e13)
| equal(e13,e12) ),
inference(rew,[status(thm),theory(equality)],[1182,1170]),
[iquote('0:Rew:1182.0,1170.2')] ).
cnf(1200,plain,
equal(op1(e11,e11),e13),
inference(mrr,[status(thm)],[1199,3,6]),
[iquote('0:MRR:1199.0,1199.2,3.0,6.0')] ).
cnf(1205,plain,
~ equal(op1(e13,e11),e13),
inference(rew,[status(thm),theory(equality)],[1200,537]),
[iquote('0:Rew:1200.0,537.0')] ).
cnf(1206,plain,
~ equal(op1(e12,e11),e13),
inference(rew,[status(thm),theory(equality)],[1200,536]),
[iquote('0:Rew:1200.0,536.0')] ).
cnf(1213,plain,
( equal(op2(e20,e23),e23)
| equal(e23,e22)
| equal(op2(e22,e23),e23)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[34,673,807]),
[iquote('0:Rew:34.0,673.3,807.0,673.1')] ).
cnf(1214,plain,
( equal(op2(e20,e23),e23)
| equal(op2(e22,e23),e23) ),
inference(mrr,[status(thm)],[1213,12,11]),
[iquote('0:MRR:1213.1,1213.3,12.0,11.0')] ).
cnf(1215,plain,
( equal(op2(e23,e20),e23)
| equal(h2(e12),e23)
| equal(op2(e23,e22),e23)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[34,674,1136]),
[iquote('0:Rew:34.0,674.3,1136.0,674.1')] ).
cnf(1216,plain,
( equal(op2(e23,e20),e23)
| equal(op2(e23,e22),e23) ),
inference(mrr,[status(thm)],[1215,1154,11]),
[iquote('0:MRR:1215.1,1215.3,1154.0,11.0')] ).
cnf(1217,plain,
( equal(op2(e23,e20),e22)
| equal(h2(e12),e22)
| equal(op2(e23,e22),e22)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[34,676,1136]),
[iquote('0:Rew:34.0,676.3,1136.0,676.1')] ).
cnf(1218,plain,
( equal(op2(e23,e20),e22)
| equal(h2(e12),e22) ),
inference(mrr,[status(thm)],[1217,1102,10]),
[iquote('0:MRR:1217.2,1217.3,1102.0,10.0')] ).
cnf(1219,plain,
( equal(op2(e20,e23),e20)
| equal(e22,e20)
| equal(op2(e22,e23),e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[34,679,807]),
[iquote('0:Rew:34.0,679.3,807.0,679.1')] ).
cnf(1220,plain,
equal(op2(e22,e23),e20),
inference(mrr,[status(thm)],[1219,1079,8,7]),
[iquote('0:MRR:1219.0,1219.1,1219.3,1079.0,8.0,7.0')] ).
cnf(1221,plain,
( equal(op2(e20,e23),e23)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[1220,1214]),
[iquote('0:Rew:1220.0,1214.1')] ).
cnf(1229,plain,
equal(op2(e20,e23),e23),
inference(mrr,[status(thm)],[1221,9]),
[iquote('0:MRR:1221.1,9.0')] ).
cnf(1235,plain,
( equal(op2(e23,e20),e20)
| equal(h2(e12),e20)
| equal(op2(e23,e22),e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[34,680,1136]),
[iquote('0:Rew:34.0,680.3,1136.0,680.1')] ).
cnf(1236,plain,
equal(h2(e12),e20),
inference(mrr,[status(thm)],[1235,1082,1018,7]),
[iquote('0:MRR:1235.0,1235.2,1235.3,1082.0,1018.0,7.0')] ).
cnf(1237,plain,
( equal(op2(e23,e20),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[1236,1218]),
[iquote('0:Rew:1236.0,1218.1')] ).
cnf(1240,plain,
equal(op2(e23,e21),e20),
inference(rew,[status(thm),theory(equality)],[1236,1136]),
[iquote('0:Rew:1236.0,1136.0')] ).
cnf(1243,plain,
equal(op2(e23,e20),h2(e10)),
inference(rew,[status(thm),theory(equality)],[1236,1144]),
[iquote('0:Rew:1236.0,1144.0')] ).
cnf(1249,plain,
( equal(h2(e10),e23)
| equal(op2(e23,e22),e23) ),
inference(rew,[status(thm),theory(equality)],[1243,1216]),
[iquote('0:Rew:1243.0,1216.0')] ).
cnf(1258,plain,
( equal(h2(e10),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[1243,1237]),
[iquote('0:Rew:1243.0,1237.0')] ).
cnf(1259,plain,
equal(h2(e10),e22),
inference(mrr,[status(thm)],[1258,8]),
[iquote('0:MRR:1258.1,8.0')] ).
cnf(1261,plain,
equal(op2(e23,e20),e22),
inference(rew,[status(thm),theory(equality)],[1259,1243]),
[iquote('0:Rew:1259.0,1243.0')] ).
cnf(1271,plain,
( equal(e23,e22)
| equal(op2(e23,e22),e23) ),
inference(rew,[status(thm),theory(equality)],[1259,1249]),
[iquote('0:Rew:1259.0,1249.0')] ).
cnf(1272,plain,
equal(op2(e23,e22),e23),
inference(mrr,[status(thm)],[1271,12]),
[iquote('0:MRR:1271.0,12.0')] ).
cnf(1279,plain,
( equal(op2(e22,e20),e23)
| equal(op2(e22,e21),e23)
| equal(e23,e22)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[1220,682,1096]),
[iquote('0:Rew:1220.0,682.3,1096.0,682.2')] ).
cnf(1280,plain,
equal(op2(e22,e20),e23),
inference(mrr,[status(thm)],[1279,1140,12,9]),
[iquote('0:MRR:1279.1,1279.2,1279.3,1140.0,12.0,9.0')] ).
cnf(1285,plain,
( equal(op2(e20,e22),e21)
| equal(e21,e20)
| equal(e22,e21)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[1272,685,1096,1010]),
[iquote('0:Rew:1272.0,685.3,1096.0,685.2,1010.0,685.1')] ).
cnf(1286,plain,
equal(op2(e20,e22),e21),
inference(mrr,[status(thm)],[1285,7,10,11]),
[iquote('0:MRR:1285.1,1285.2,1285.3,7.0,10.0,11.0')] ).
cnf(1292,plain,
( equal(e23,e21)
| equal(op2(e22,e21),e21)
| equal(e22,e21)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[1220,686,1096,1280]),
[iquote('0:Rew:1220.0,686.3,1096.0,686.2,1280.0,686.0')] ).
cnf(1293,plain,
equal(op2(e22,e21),e21),
inference(mrr,[status(thm)],[1292,11,10,7]),
[iquote('0:MRR:1292.0,1292.2,1292.3,11.0,10.0,7.0')] ).
cnf(1298,plain,
( equal(op2(e20,e21),e22)
| equal(e23,e22)
| equal(e22,e21)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[1240,691,1293,1133]),
[iquote('0:Rew:1240.0,691.3,1293.0,691.2,1133.0,691.1')] ).
cnf(1299,plain,
equal(op2(e20,e21),e22),
inference(mrr,[status(thm)],[1298,12,10,8]),
[iquote('0:MRR:1298.1,1298.2,1298.3,12.0,10.0,8.0')] ).
cnf(1303,plain,
( equal(op2(e21,e20),e21)
| equal(e23,e21)
| equal(e21,e20)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[807,694,1010,1133]),
[iquote('0:Rew:807.0,694.3,1010.0,694.2,1133.0,694.1')] ).
cnf(1304,plain,
equal(op2(e21,e20),e21),
inference(mrr,[status(thm)],[1303,11,7,10]),
[iquote('0:MRR:1303.1,1303.2,1303.3,11.0,7.0,10.0')] ).
cnf(1310,plain,
( equal(op1(e10,e13),e13)
| equal(e13,e12)
| equal(op1(e12,e13),e13)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[33,721,808]),
[iquote('0:Rew:33.0,721.3,808.0,721.1')] ).
cnf(1311,plain,
( equal(op1(e10,e13),e13)
| equal(op1(e12,e13),e13) ),
inference(mrr,[status(thm)],[1310,6,5]),
[iquote('0:MRR:1310.1,1310.3,6.0,5.0')] ).
cnf(1312,plain,
( equal(op1(e13,e10),e13)
| equal(op1(e13,e11),e13)
| equal(op1(e13,e12),e13)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[33,722]),
[iquote('0:Rew:33.0,722.3')] ).
cnf(1313,plain,
( equal(op1(e13,e10),e13)
| equal(op1(e13,e12),e13) ),
inference(mrr,[status(thm)],[1312,1205,5]),
[iquote('0:MRR:1312.1,1312.3,1205.0,5.0')] ).
cnf(1314,plain,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[33,724]),
[iquote('0:Rew:33.0,724.3')] ).
cnf(1315,plain,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12) ),
inference(mrr,[status(thm)],[1314,1186,4]),
[iquote('0:MRR:1314.2,1314.3,1186.0,4.0')] ).
cnf(1316,plain,
( equal(op1(e10,e13),e10)
| equal(e12,e10)
| equal(op1(e12,e13),e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[33,727,808]),
[iquote('0:Rew:33.0,727.3,808.0,727.1')] ).
cnf(1317,plain,
equal(op1(e12,e13),e10),
inference(mrr,[status(thm)],[1316,1163,2,1]),
[iquote('0:MRR:1316.0,1316.1,1316.3,1163.0,2.0,1.0')] ).
cnf(1318,plain,
( equal(op1(e10,e13),e13)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[1317,1311]),
[iquote('0:Rew:1317.0,1311.1')] ).
cnf(1326,plain,
equal(op1(e10,e13),e13),
inference(mrr,[status(thm)],[1318,3]),
[iquote('0:MRR:1318.1,3.0')] ).
cnf(1332,plain,
( equal(op1(e13,e10),e10)
| equal(op1(e13,e11),e10)
| equal(op1(e13,e12),e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[33,728]),
[iquote('0:Rew:33.0,728.3')] ).
cnf(1333,plain,
equal(op1(e13,e11),e10),
inference(mrr,[status(thm)],[1332,1166,1043,1]),
[iquote('0:MRR:1332.0,1332.2,1332.3,1166.0,1043.0,1.0')] ).
cnf(1341,plain,
( equal(op1(e13,e10),e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[1333,1315]),
[iquote('0:Rew:1333.0,1315.1')] ).
cnf(1342,plain,
equal(op1(e13,e10),e12),
inference(mrr,[status(thm)],[1341,2]),
[iquote('0:MRR:1341.1,2.0')] ).
cnf(1343,plain,
( equal(e13,e12)
| equal(op1(e13,e12),e13) ),
inference(rew,[status(thm),theory(equality)],[1342,1313]),
[iquote('0:Rew:1342.0,1313.0')] ).
cnf(1352,plain,
equal(op1(e13,e12),e13),
inference(mrr,[status(thm)],[1343,6]),
[iquote('0:MRR:1343.0,6.0')] ).
cnf(1359,plain,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(e13,e12)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[1317,730,1182]),
[iquote('0:Rew:1317.0,730.3,1182.0,730.2')] ).
cnf(1360,plain,
equal(op1(e12,e10),e13),
inference(mrr,[status(thm)],[1359,1206,6,3]),
[iquote('0:MRR:1359.1,1359.2,1359.3,1206.0,6.0,3.0')] ).
cnf(1365,plain,
( equal(op1(e10,e12),e11)
| equal(e11,e10)
| equal(e12,e11)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[1352,733,1182,1035]),
[iquote('0:Rew:1352.0,733.3,1182.0,733.2,1035.0,733.1')] ).
cnf(1366,plain,
equal(op1(e10,e12),e11),
inference(mrr,[status(thm)],[1365,1,4,5]),
[iquote('0:MRR:1365.1,1365.2,1365.3,1.0,4.0,5.0')] ).
cnf(1372,plain,
( equal(e13,e11)
| equal(op1(e12,e11),e11)
| equal(e12,e11)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[1317,734,1182,1360]),
[iquote('0:Rew:1317.0,734.3,1182.0,734.2,1360.0,734.0')] ).
cnf(1373,plain,
equal(op1(e12,e11),e11),
inference(mrr,[status(thm)],[1372,5,4,1]),
[iquote('0:MRR:1372.0,1372.2,1372.3,5.0,4.0,1.0')] ).
cnf(1378,plain,
( equal(op1(e10,e11),e12)
| equal(e13,e12)
| equal(e12,e11)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[1333,739,1373,1200]),
[iquote('0:Rew:1333.0,739.3,1373.0,739.2,1200.0,739.1')] ).
cnf(1379,plain,
equal(op1(e10,e11),e12),
inference(mrr,[status(thm)],[1378,6,4,2]),
[iquote('0:MRR:1378.1,1378.2,1378.3,6.0,4.0,2.0')] ).
cnf(1383,plain,
( equal(op1(e11,e10),e11)
| equal(e13,e11)
| equal(e11,e10)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[808,742,1035,1200]),
[iquote('0:Rew:808.0,742.3,1035.0,742.2,1200.0,742.1')] ).
cnf(1384,plain,
equal(op1(e11,e10),e11),
inference(mrr,[status(thm)],[1383,5,1,4]),
[iquote('0:MRR:1383.1,1383.2,1383.3,5.0,1.0,4.0')] ).
cnf(1394,plain,
( ~ equal(e23,e23)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e22,e22)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e20,e20)
| ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ skC141
| ~ skC142
| ~ skC143 ),
inference(rew,[status(thm),theory(equality)],[34,771,32,787,33,1272,941,1352,1240,1062,1333,1261,1342,1220,1317,1096,1182,1293,1373,1280,1360,807,808,1010,1035,1133,1200,1304,1384,1229,1326,1286,1366,1299,1379,1074,1162]),
[iquote('0:Rew:34.0,771.16,32.0,771.16,787.0,771.16,33.0,771.16,1272.0,771.15,941.0,771.15,32.0,771.15,1352.0,771.15,1240.0,771.14,32.0,771.14,787.0,771.14,1062.0,771.14,1333.0,771.14,1261.0,771.13,32.0,771.13,1062.0,771.13,941.0,771.13,1342.0,771.13,1220.0,771.12,941.0,771.12,32.0,771.12,1062.0,771.12,1317.0,771.12,1096.0,771.11,941.0,771.11,1182.0,771.11,1293.0,771.10,941.0,771.10,787.0,771.10,1373.0,771.10,1280.0,771.9,941.0,771.9,1062.0,771.9,32.0,771.9,1360.0,771.9,807.0,771.8,787.0,771.8,32.0,771.8,941.0,771.8,808.0,771.8,1010.0,771.7,787.0,771.7,941.0,771.7,1062.0,771.7,1035.0,771.7,1133.0,771.6,787.0,771.6,32.0,771.6,1200.0,771.6,1304.0,771.5,1062.0,771.5,787.0,771.5,1384.0,771.5,1229.0,771.4,1062.0,771.4,32.0,771.4,1326.0,771.4,1286.0,771.3,1062.0,771.3,941.0,771.3,787.0,771.3,1366.0,771.3,1299.0,771.2,1062.0,771.2,787.0,771.2,941.0,771.2,1379.0,771.2,1074.0,771.1,1062.0,771.1,1162.0,771.1,32.0,771.0')] ).
cnf(1395,plain,
( ~ skC141
| ~ skC142
| ~ skC143 ),
inference(obv,[status(thm),theory(equality)],[1394]),
[iquote('0:Obv:1394.16')] ).
cnf(1396,plain,
$false,
inference(mrr,[status(thm)],[1395,1064,792,944]),
[iquote('0:MRR:1395.0,1395.1,1395.2,1064.0,792.0,944.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 06:52:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.70
% 0.49/0.70 SPASS V 3.9
% 0.49/0.70 SPASS beiseite: Proof found.
% 0.49/0.70 % SZS status Theorem
% 0.49/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.70 SPASS derived 278 clauses, backtracked 0 clauses, performed 0 splits and kept 753 clauses.
% 0.49/0.70 SPASS allocated 87085 KBytes.
% 0.49/0.70 SPASS spent 0:00:00.36 on the problem.
% 0.49/0.70 0:00:00.04 for the input.
% 0.49/0.70 0:00:00.17 for the FLOTTER CNF translation.
% 0.49/0.70 0:00:00.00 for inferences.
% 0.49/0.70 0:00:00.00 for the backtracking.
% 0.49/0.70 0:00:00.11 for the reduction.
% 0.49/0.70
% 0.49/0.70
% 0.49/0.70 Here is a proof with depth 0, length 203 :
% 0.49/0.70 % SZS output start Refutation
% See solution above
% 0.49/0.71 Formulae used in the proof : ax7 ax8 ax17 ax12 ax13 co1 ax14 ax15 ax16 ax5 ax6 ax11 ax10 ax4 ax2
% 0.49/0.71
%------------------------------------------------------------------------------