TSTP Solution File: ALG113+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.40s 0.60s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 77
% Syntax : Number of clauses : 176 ( 110 unt; 56 nHn; 176 RR)
% Number of literals : 359 ( 0 equ; 90 neg)
% Maximal clause size : 20 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e11,e10),
file('ALG113+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e12,e10),
file('ALG113+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e13,e10),
file('ALG113+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e12,e11),
file('ALG113+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e13,e11),
file('ALG113+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e13,e12),
file('ALG113+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e21,e20),
file('ALG113+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e22,e20),
file('ALG113+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e23,e20),
file('ALG113+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e22,e21),
file('ALG113+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e23,e21),
file('ALG113+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(e22,e23),
file('ALG113+1.p',unknown),
[] ).
cnf(51,axiom,
equal(h12(e12),e23),
file('ALG113+1.p',unknown),
[] ).
cnf(52,axiom,
equal(h12(e13),e22),
file('ALG113+1.p',unknown),
[] ).
cnf(53,axiom,
equal(op1(e10,e10),e10),
file('ALG113+1.p',unknown),
[] ).
cnf(54,axiom,
equal(op1(e11,e11),e11),
file('ALG113+1.p',unknown),
[] ).
cnf(55,axiom,
equal(op1(e12,e12),e12),
file('ALG113+1.p',unknown),
[] ).
cnf(56,axiom,
equal(op1(e13,e13),e13),
file('ALG113+1.p',unknown),
[] ).
cnf(57,axiom,
equal(op2(e20,e20),e20),
file('ALG113+1.p',unknown),
[] ).
cnf(58,axiom,
equal(op2(e21,e21),e21),
file('ALG113+1.p',unknown),
[] ).
cnf(59,axiom,
equal(op2(e22,e22),e22),
file('ALG113+1.p',unknown),
[] ).
cnf(60,axiom,
equal(op2(e23,e23),e23),
file('ALG113+1.p',unknown),
[] ).
cnf(61,axiom,
equal(op1(e12,e13),e10),
file('ALG113+1.p',unknown),
[] ).
cnf(62,axiom,
equal(op2(e22,e23),e20),
file('ALG113+1.p',unknown),
[] ).
cnf(196,axiom,
( ~ equal(h12(e11),e20)
| skC33 ),
file('ALG113+1.p',unknown),
[] ).
cnf(199,axiom,
( ~ equal(h12(e10),e21)
| skC34 ),
file('ALG113+1.p',unknown),
[] ).
cnf(206,axiom,
( ~ equal(h12(e13),e22)
| skC35 ),
file('ALG113+1.p',unknown),
[] ).
cnf(207,axiom,
equal(op2(e20,e21),h1(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(208,axiom,
equal(op2(e20,e22),h2(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(209,axiom,
equal(op2(e20,e23),h3(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(210,axiom,
equal(op2(e21,e20),h4(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(211,axiom,
equal(op2(e21,e22),h5(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(212,axiom,
equal(op2(e21,e23),h6(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(213,axiom,
equal(op2(e22,e20),h7(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(214,axiom,
equal(op2(e22,e21),h8(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(216,axiom,
equal(op2(e23,e20),h10(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(217,axiom,
equal(op2(e23,e21),h11(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(218,axiom,
equal(op2(e23,e22),h12(e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(219,axiom,
equal(op1(op1(e12,e13),e13),e11),
file('ALG113+1.p',unknown),
[] ).
cnf(220,axiom,
equal(op2(op2(e22,e23),e23),e21),
file('ALG113+1.p',unknown),
[] ).
cnf(223,axiom,
~ equal(op1(e13,e10),op1(e10,e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(230,axiom,
~ equal(op1(e12,e11),op1(e11,e11)),
file('ALG113+1.p',unknown),
[] ).
cnf(238,axiom,
~ equal(op1(e13,e12),op1(e12,e12)),
file('ALG113+1.p',unknown),
[] ).
cnf(246,axiom,
~ equal(op1(e10,e12),op1(e10,e10)),
file('ALG113+1.p',unknown),
[] ).
cnf(250,axiom,
~ equal(op1(e10,e13),op1(e10,e12)),
file('ALG113+1.p',unknown),
[] ).
cnf(254,axiom,
~ equal(op1(e11,e12),op1(e11,e11)),
file('ALG113+1.p',unknown),
[] ).
cnf(268,axiom,
~ equal(op1(e13,e13),op1(e13,e12)),
file('ALG113+1.p',unknown),
[] ).
cnf(271,axiom,
~ equal(op2(e23,e20),op2(e20,e20)),
file('ALG113+1.p',unknown),
[] ).
cnf(278,axiom,
~ equal(op2(e22,e21),op2(e21,e21)),
file('ALG113+1.p',unknown),
[] ).
cnf(286,axiom,
~ equal(op2(e22,e22),op2(e23,e22)),
file('ALG113+1.p',unknown),
[] ).
cnf(294,axiom,
~ equal(op2(e20,e22),op2(e20,e20)),
file('ALG113+1.p',unknown),
[] ).
cnf(298,axiom,
~ equal(op2(e20,e22),op2(e20,e23)),
file('ALG113+1.p',unknown),
[] ).
cnf(302,axiom,
~ equal(op2(e21,e22),op2(e21,e21)),
file('ALG113+1.p',unknown),
[] ).
cnf(316,axiom,
~ equal(op2(e23,e22),op2(e23,e23)),
file('ALG113+1.p',unknown),
[] ).
cnf(319,axiom,
equal(op2(op2(e20,e23),e23),h3(e11)),
file('ALG113+1.p',unknown),
[] ).
cnf(328,axiom,
equal(op2(op2(e23,e22),e22),h12(e11)),
file('ALG113+1.p',unknown),
[] ).
cnf(331,axiom,
( equal(op2(e20,e23),e22)
| equal(op2(e21,e23),e22)
| equal(op2(e22,e23),e22)
| equal(op2(e23,e23),e22) ),
file('ALG113+1.p',unknown),
[] ).
cnf(332,axiom,
( equal(op2(e23,e20),e22)
| equal(op2(e23,e21),e22)
| equal(op2(e23,e22),e22)
| equal(op2(e23,e23),e22) ),
file('ALG113+1.p',unknown),
[] ).
cnf(336,axiom,
( equal(op2(e23,e20),e20)
| equal(op2(e23,e21),e20)
| equal(op2(e23,e22),e20)
| equal(op2(e23,e23),e20) ),
file('ALG113+1.p',unknown),
[] ).
cnf(337,axiom,
( equal(op2(e20,e22),e23)
| equal(op2(e21,e22),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e23,e22),e23) ),
file('ALG113+1.p',unknown),
[] ).
cnf(338,axiom,
( equal(op2(e22,e20),e23)
| equal(op2(e22,e21),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e22,e23),e23) ),
file('ALG113+1.p',unknown),
[] ).
cnf(341,axiom,
( equal(op2(e20,e22),e21)
| equal(op2(e21,e22),e21)
| equal(op2(e22,e22),e21)
| equal(op2(e23,e22),e21) ),
file('ALG113+1.p',unknown),
[] ).
cnf(342,axiom,
( equal(op2(e22,e20),e21)
| equal(op2(e22,e21),e21)
| equal(op2(e22,e22),e21)
| equal(op2(e22,e23),e21) ),
file('ALG113+1.p',unknown),
[] ).
cnf(343,axiom,
( equal(op2(e20,e22),e20)
| equal(op2(e21,e22),e20)
| equal(op2(e22,e22),e20)
| equal(op2(e23,e22),e20) ),
file('ALG113+1.p',unknown),
[] ).
cnf(346,axiom,
( equal(op2(e21,e20),e23)
| equal(op2(e21,e21),e23)
| equal(op2(e21,e22),e23)
| equal(op2(e21,e23),e23) ),
file('ALG113+1.p',unknown),
[] ).
cnf(347,axiom,
( equal(op2(e20,e21),e22)
| equal(op2(e21,e21),e22)
| equal(op2(e22,e21),e22)
| equal(op2(e23,e21),e22) ),
file('ALG113+1.p',unknown),
[] ).
cnf(379,axiom,
( equal(op1(e10,e13),e12)
| equal(op1(e11,e13),e12)
| equal(op1(e12,e13),e12)
| equal(op1(e13,e13),e12) ),
file('ALG113+1.p',unknown),
[] ).
cnf(380,axiom,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(op1(e13,e13),e12) ),
file('ALG113+1.p',unknown),
[] ).
cnf(384,axiom,
( equal(op1(e13,e10),e10)
| equal(op1(e13,e11),e10)
| equal(op1(e13,e12),e10)
| equal(op1(e13,e13),e10) ),
file('ALG113+1.p',unknown),
[] ).
cnf(385,axiom,
( equal(op1(e10,e12),e13)
| equal(op1(e11,e12),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e13,e12),e13) ),
file('ALG113+1.p',unknown),
[] ).
cnf(386,axiom,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e12,e13),e13) ),
file('ALG113+1.p',unknown),
[] ).
cnf(389,axiom,
( equal(op1(e10,e12),e11)
| equal(op1(e11,e12),e11)
| equal(op1(e12,e12),e11)
| equal(op1(e13,e12),e11) ),
file('ALG113+1.p',unknown),
[] ).
cnf(390,axiom,
( equal(op1(e12,e10),e11)
| equal(op1(e12,e11),e11)
| equal(op1(e12,e12),e11)
| equal(op1(e12,e13),e11) ),
file('ALG113+1.p',unknown),
[] ).
cnf(391,axiom,
( equal(op1(e10,e12),e10)
| equal(op1(e11,e12),e10)
| equal(op1(e12,e12),e10)
| equal(op1(e13,e12),e10) ),
file('ALG113+1.p',unknown),
[] ).
cnf(394,axiom,
( equal(op1(e11,e10),e13)
| equal(op1(e11,e11),e13)
| equal(op1(e11,e12),e13)
| equal(op1(e11,e13),e13) ),
file('ALG113+1.p',unknown),
[] ).
cnf(395,axiom,
( equal(op1(e10,e11),e12)
| equal(op1(e11,e11),e12)
| equal(op1(e12,e11),e12)
| equal(op1(e13,e11),e12) ),
file('ALG113+1.p',unknown),
[] ).
cnf(426,axiom,
( ~ equal(h12(e12),e23)
| ~ equal(op2(h12(e10),h12(e10)),h12(op1(e10,e10)))
| ~ equal(op2(h12(e10),h12(e11)),h12(op1(e10,e11)))
| ~ equal(op2(h12(e10),h12(e12)),h12(op1(e10,e12)))
| ~ equal(op2(h12(e10),h12(e13)),h12(op1(e10,e13)))
| ~ equal(op2(h12(e11),h12(e10)),h12(op1(e11,e10)))
| ~ equal(op2(h12(e11),h12(e11)),h12(op1(e11,e11)))
| ~ equal(op2(h12(e11),h12(e12)),h12(op1(e11,e12)))
| ~ equal(op2(h12(e11),h12(e13)),h12(op1(e11,e13)))
| ~ equal(op2(h12(e12),h12(e10)),h12(op1(e12,e10)))
| ~ equal(op2(h12(e12),h12(e11)),h12(op1(e12,e11)))
| ~ equal(op2(h12(e12),h12(e12)),h12(op1(e12,e12)))
| ~ equal(op2(h12(e12),h12(e13)),h12(op1(e12,e13)))
| ~ equal(op2(h12(e13),h12(e10)),h12(op1(e13,e10)))
| ~ equal(op2(h12(e13),h12(e11)),h12(op1(e13,e11)))
| ~ equal(op2(h12(e13),h12(e12)),h12(op1(e13,e12)))
| ~ equal(op2(h12(e13),h12(e13)),h12(op1(e13,e13)))
| ~ skC33
| ~ skC34
| ~ skC35 ),
file('ALG113+1.p',unknown),
[] ).
cnf(474,plain,
( ~ equal(e22,e22)
| skC35 ),
inference(rew,[status(thm),theory(equality)],[52,206]),
[iquote('0:Rew:52.0,206.0')] ).
cnf(475,plain,
skC35,
inference(obv,[status(thm),theory(equality)],[474]),
[iquote('0:Obv:474.0')] ).
cnf(558,plain,
equal(h3(e10),e21),
inference(rew,[status(thm),theory(equality)],[209,220,62]),
[iquote('0:Rew:209.0,220.0,62.0,220.0')] ).
cnf(559,plain,
equal(op2(e20,e23),e21),
inference(rew,[status(thm),theory(equality)],[558,209]),
[iquote('0:Rew:558.0,209.0')] ).
cnf(563,plain,
equal(op1(e10,e13),e11),
inference(rew,[status(thm),theory(equality)],[61,219]),
[iquote('0:Rew:61.0,219.0')] ).
cnf(564,plain,
equal(op2(h12(e10),e22),h12(e11)),
inference(rew,[status(thm),theory(equality)],[218,328]),
[iquote('0:Rew:218.0,328.0')] ).
cnf(575,plain,
equal(h6(e10),h3(e11)),
inference(rew,[status(thm),theory(equality)],[212,319,559]),
[iquote('0:Rew:212.0,319.0,559.0,319.0')] ).
cnf(576,plain,
equal(op2(e21,e23),h3(e11)),
inference(rew,[status(thm),theory(equality)],[575,212]),
[iquote('0:Rew:575.0,212.0')] ).
cnf(582,plain,
~ equal(h12(e10),e23),
inference(rew,[status(thm),theory(equality)],[218,316,60]),
[iquote('0:Rew:218.0,316.0,60.0,316.0')] ).
cnf(596,plain,
~ equal(h5(e10),e21),
inference(rew,[status(thm),theory(equality)],[211,302,58]),
[iquote('0:Rew:211.0,302.0,58.0,302.0')] ).
cnf(600,plain,
~ equal(h2(e10),e21),
inference(rew,[status(thm),theory(equality)],[208,298,559]),
[iquote('0:Rew:208.0,298.0,559.0,298.0')] ).
cnf(604,plain,
~ equal(h2(e10),e20),
inference(rew,[status(thm),theory(equality)],[208,294,57]),
[iquote('0:Rew:208.0,294.0,57.0,294.0')] ).
cnf(612,plain,
~ equal(h12(e10),e22),
inference(rew,[status(thm),theory(equality)],[59,286,218]),
[iquote('0:Rew:59.0,286.0,218.0,286.0')] ).
cnf(620,plain,
~ equal(h8(e10),e21),
inference(rew,[status(thm),theory(equality)],[214,278,58]),
[iquote('0:Rew:214.0,278.0,58.0,278.0')] ).
cnf(627,plain,
~ equal(h10(e10),e20),
inference(rew,[status(thm),theory(equality)],[216,271,57]),
[iquote('0:Rew:216.0,271.0,57.0,271.0')] ).
cnf(630,plain,
~ equal(op1(e13,e12),e13),
inference(rew,[status(thm),theory(equality)],[56,268]),
[iquote('0:Rew:56.0,268.0')] ).
cnf(639,plain,
~ equal(op1(e11,e12),e11),
inference(rew,[status(thm),theory(equality)],[54,254]),
[iquote('0:Rew:54.0,254.0')] ).
cnf(641,plain,
~ equal(op1(e10,e12),e11),
inference(rew,[status(thm),theory(equality)],[563,250]),
[iquote('0:Rew:563.0,250.0')] ).
cnf(644,plain,
~ equal(op1(e10,e12),e10),
inference(rew,[status(thm),theory(equality)],[53,246]),
[iquote('0:Rew:53.0,246.0')] ).
cnf(652,plain,
~ equal(op1(e13,e12),e12),
inference(rew,[status(thm),theory(equality)],[55,238]),
[iquote('0:Rew:55.0,238.0')] ).
cnf(656,plain,
~ equal(op1(e12,e11),e11),
inference(rew,[status(thm),theory(equality)],[54,230]),
[iquote('0:Rew:54.0,230.0')] ).
cnf(658,plain,
~ equal(op1(e13,e10),e10),
inference(rew,[status(thm),theory(equality)],[53,223]),
[iquote('0:Rew:53.0,223.0')] ).
cnf(661,plain,
( equal(e22,e21)
| equal(h3(e11),e22)
| equal(e22,e20)
| equal(e22,e23) ),
inference(rew,[status(thm),theory(equality)],[60,331,62,576,559]),
[iquote('0:Rew:60.0,331.3,62.0,331.2,576.0,331.1,559.0,331.0')] ).
cnf(662,plain,
equal(h3(e11),e22),
inference(mrr,[status(thm)],[661,10,8,12]),
[iquote('0:MRR:661.0,661.2,661.3,10.0,8.0,12.0')] ).
cnf(666,plain,
equal(op2(e21,e23),e22),
inference(rew,[status(thm),theory(equality)],[662,576]),
[iquote('0:Rew:662.0,576.0')] ).
cnf(678,plain,
( equal(h10(e10),e22)
| equal(h11(e10),e22)
| equal(h12(e10),e22)
| equal(e22,e23) ),
inference(rew,[status(thm),theory(equality)],[60,332,218,217,216]),
[iquote('0:Rew:60.0,332.3,218.0,332.2,217.0,332.1,216.0,332.0')] ).
cnf(679,plain,
( equal(h10(e10),e22)
| equal(h11(e10),e22) ),
inference(mrr,[status(thm)],[678,612,12]),
[iquote('0:MRR:678.2,678.3,612.0,12.0')] ).
cnf(682,plain,
( equal(h10(e10),e20)
| equal(h11(e10),e20)
| equal(h12(e10),e20)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[60,336,218,217,216]),
[iquote('0:Rew:60.0,336.3,218.0,336.2,217.0,336.1,216.0,336.0')] ).
cnf(683,plain,
( equal(h11(e10),e20)
| equal(h12(e10),e20) ),
inference(mrr,[status(thm)],[682,627,9]),
[iquote('0:MRR:682.0,682.3,627.0,9.0')] ).
cnf(684,plain,
( equal(h2(e10),e23)
| equal(h5(e10),e23)
| equal(e22,e23)
| equal(h12(e10),e23) ),
inference(rew,[status(thm),theory(equality)],[218,337,59,211,208]),
[iquote('0:Rew:218.0,337.3,59.0,337.2,211.0,337.1,208.0,337.0')] ).
cnf(685,plain,
( equal(h2(e10),e23)
| equal(h5(e10),e23) ),
inference(mrr,[status(thm)],[684,12,582]),
[iquote('0:MRR:684.2,684.3,12.0,582.0')] ).
cnf(686,plain,
( equal(h7(e10),e23)
| equal(h8(e10),e23)
| equal(e22,e23)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[62,338,59,214,213]),
[iquote('0:Rew:62.0,338.3,59.0,338.2,214.0,338.1,213.0,338.0')] ).
cnf(687,plain,
( equal(h7(e10),e23)
| equal(h8(e10),e23) ),
inference(mrr,[status(thm)],[686,12,9]),
[iquote('0:MRR:686.2,686.3,12.0,9.0')] ).
cnf(688,plain,
( equal(h2(e10),e21)
| equal(h5(e10),e21)
| equal(e22,e21)
| equal(h12(e10),e21) ),
inference(rew,[status(thm),theory(equality)],[218,341,59,211,208]),
[iquote('0:Rew:218.0,341.3,59.0,341.2,211.0,341.1,208.0,341.0')] ).
cnf(689,plain,
equal(h12(e10),e21),
inference(mrr,[status(thm)],[688,600,596,10]),
[iquote('0:MRR:688.0,688.1,688.2,600.0,596.0,10.0')] ).
cnf(690,plain,
equal(op2(e23,e22),e21),
inference(rew,[status(thm),theory(equality)],[689,218]),
[iquote('0:Rew:689.0,218.0')] ).
cnf(691,plain,
( ~ equal(e21,e21)
| skC34 ),
inference(rew,[status(thm),theory(equality)],[689,199]),
[iquote('0:Rew:689.0,199.0')] ).
cnf(692,plain,
( equal(h11(e10),e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[689,683]),
[iquote('0:Rew:689.0,683.1')] ).
cnf(694,plain,
equal(op2(e21,e22),h12(e11)),
inference(rew,[status(thm),theory(equality)],[689,564]),
[iquote('0:Rew:689.0,564.0')] ).
cnf(701,plain,
skC34,
inference(obv,[status(thm),theory(equality)],[691]),
[iquote('0:Obv:691.0')] ).
cnf(702,plain,
equal(h12(e11),h5(e10)),
inference(rew,[status(thm),theory(equality)],[211,694]),
[iquote('0:Rew:211.0,694.0')] ).
cnf(703,plain,
( ~ equal(h5(e10),e20)
| skC33 ),
inference(rew,[status(thm),theory(equality)],[702,196]),
[iquote('0:Rew:702.0,196.0')] ).
cnf(704,plain,
equal(h11(e10),e20),
inference(mrr,[status(thm)],[692,7]),
[iquote('0:MRR:692.1,7.0')] ).
cnf(705,plain,
equal(op2(e23,e21),e20),
inference(rew,[status(thm),theory(equality)],[704,217]),
[iquote('0:Rew:704.0,217.0')] ).
cnf(706,plain,
( equal(h10(e10),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[704,679]),
[iquote('0:Rew:704.0,679.1')] ).
cnf(718,plain,
equal(h10(e10),e22),
inference(mrr,[status(thm)],[706,8]),
[iquote('0:MRR:706.1,8.0')] ).
cnf(719,plain,
equal(op2(e23,e20),e22),
inference(rew,[status(thm),theory(equality)],[718,216]),
[iquote('0:Rew:718.0,216.0')] ).
cnf(730,plain,
( equal(h7(e10),e21)
| equal(h8(e10),e21)
| equal(e22,e21)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[62,342,59,214,213]),
[iquote('0:Rew:62.0,342.3,59.0,342.2,214.0,342.1,213.0,342.0')] ).
cnf(731,plain,
equal(h7(e10),e21),
inference(mrr,[status(thm)],[730,620,10,7]),
[iquote('0:MRR:730.1,730.2,730.3,620.0,10.0,7.0')] ).
cnf(732,plain,
equal(op2(e22,e20),e21),
inference(rew,[status(thm),theory(equality)],[731,213]),
[iquote('0:Rew:731.0,213.0')] ).
cnf(740,plain,
( equal(e23,e21)
| equal(h8(e10),e23) ),
inference(rew,[status(thm),theory(equality)],[731,687]),
[iquote('0:Rew:731.0,687.0')] ).
cnf(745,plain,
equal(h8(e10),e23),
inference(mrr,[status(thm)],[740,11]),
[iquote('0:MRR:740.0,11.0')] ).
cnf(746,plain,
equal(op2(e22,e21),e23),
inference(rew,[status(thm),theory(equality)],[745,214]),
[iquote('0:Rew:745.0,214.0')] ).
cnf(755,plain,
( equal(h2(e10),e20)
| equal(h5(e10),e20)
| equal(e22,e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[690,343,59,211,208]),
[iquote('0:Rew:690.0,343.3,59.0,343.2,211.0,343.1,208.0,343.0')] ).
cnf(756,plain,
equal(h5(e10),e20),
inference(mrr,[status(thm)],[755,604,8,7]),
[iquote('0:MRR:755.0,755.2,755.3,604.0,8.0,7.0')] ).
cnf(757,plain,
equal(op2(e21,e22),e20),
inference(rew,[status(thm),theory(equality)],[756,211]),
[iquote('0:Rew:756.0,211.0')] ).
cnf(758,plain,
( ~ equal(e20,e20)
| skC33 ),
inference(rew,[status(thm),theory(equality)],[756,703]),
[iquote('0:Rew:756.0,703.0')] ).
cnf(765,plain,
( equal(h2(e10),e23)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[756,685]),
[iquote('0:Rew:756.0,685.1')] ).
cnf(766,plain,
equal(h12(e11),e20),
inference(rew,[status(thm),theory(equality)],[756,702]),
[iquote('0:Rew:756.0,702.0')] ).
cnf(767,plain,
skC33,
inference(obv,[status(thm),theory(equality)],[758]),
[iquote('0:Obv:758.0')] ).
cnf(770,plain,
equal(h2(e10),e23),
inference(mrr,[status(thm)],[765,9]),
[iquote('0:MRR:765.1,9.0')] ).
cnf(771,plain,
equal(op2(e20,e22),e23),
inference(rew,[status(thm),theory(equality)],[770,208]),
[iquote('0:Rew:770.0,208.0')] ).
cnf(781,plain,
( equal(h4(e10),e23)
| equal(e23,e21)
| equal(e23,e20)
| equal(e22,e23) ),
inference(rew,[status(thm),theory(equality)],[666,346,757,58,210]),
[iquote('0:Rew:666.0,346.3,757.0,346.2,58.0,346.1,210.0,346.0')] ).
cnf(782,plain,
equal(h4(e10),e23),
inference(mrr,[status(thm)],[781,11,9,12]),
[iquote('0:MRR:781.1,781.2,781.3,11.0,9.0,12.0')] ).
cnf(783,plain,
equal(op2(e21,e20),e23),
inference(rew,[status(thm),theory(equality)],[782,210]),
[iquote('0:Rew:782.0,210.0')] ).
cnf(792,plain,
( equal(h1(e10),e22)
| equal(e22,e21)
| equal(e22,e23)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[705,347,746,58,207]),
[iquote('0:Rew:705.0,347.3,746.0,347.2,58.0,347.1,207.0,347.0')] ).
cnf(793,plain,
equal(h1(e10),e22),
inference(mrr,[status(thm)],[792,10,12,8]),
[iquote('0:MRR:792.1,792.2,792.3,10.0,12.0,8.0')] ).
cnf(794,plain,
equal(op2(e20,e21),e22),
inference(rew,[status(thm),theory(equality)],[793,207]),
[iquote('0:Rew:793.0,207.0')] ).
cnf(805,plain,
( equal(e12,e11)
| equal(op1(e11,e13),e12)
| equal(e12,e10)
| equal(e13,e12) ),
inference(rew,[status(thm),theory(equality)],[56,379,61,563]),
[iquote('0:Rew:56.0,379.3,61.0,379.2,563.0,379.0')] ).
cnf(806,plain,
equal(op1(e11,e13),e12),
inference(mrr,[status(thm)],[805,4,2,6]),
[iquote('0:MRR:805.0,805.2,805.3,4.0,2.0,6.0')] ).
cnf(812,plain,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(e13,e12) ),
inference(rew,[status(thm),theory(equality)],[56,380]),
[iquote('0:Rew:56.0,380.3')] ).
cnf(813,plain,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12) ),
inference(mrr,[status(thm)],[812,652,6]),
[iquote('0:MRR:812.2,812.3,652.0,6.0')] ).
cnf(816,plain,
( equal(op1(e13,e10),e10)
| equal(op1(e13,e11),e10)
| equal(op1(e13,e12),e10)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[56,384]),
[iquote('0:Rew:56.0,384.3')] ).
cnf(817,plain,
( equal(op1(e13,e11),e10)
| equal(op1(e13,e12),e10) ),
inference(mrr,[status(thm)],[816,658,3]),
[iquote('0:MRR:816.0,816.3,658.0,3.0')] ).
cnf(818,plain,
( equal(op1(e10,e12),e13)
| equal(op1(e11,e12),e13)
| equal(e13,e12)
| equal(op1(e13,e12),e13) ),
inference(rew,[status(thm),theory(equality)],[55,385]),
[iquote('0:Rew:55.0,385.2')] ).
cnf(819,plain,
( equal(op1(e10,e12),e13)
| equal(op1(e11,e12),e13) ),
inference(mrr,[status(thm)],[818,6,630]),
[iquote('0:MRR:818.2,818.3,6.0,630.0')] ).
cnf(820,plain,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(e13,e12)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[61,386,55]),
[iquote('0:Rew:61.0,386.3,55.0,386.2')] ).
cnf(821,plain,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13) ),
inference(mrr,[status(thm)],[820,6,3]),
[iquote('0:MRR:820.2,820.3,6.0,3.0')] ).
cnf(822,plain,
( equal(op1(e10,e12),e11)
| equal(op1(e11,e12),e11)
| equal(e12,e11)
| equal(op1(e13,e12),e11) ),
inference(rew,[status(thm),theory(equality)],[55,389]),
[iquote('0:Rew:55.0,389.2')] ).
cnf(823,plain,
equal(op1(e13,e12),e11),
inference(mrr,[status(thm)],[822,641,639,4]),
[iquote('0:MRR:822.0,822.1,822.2,641.0,639.0,4.0')] ).
cnf(830,plain,
( equal(op1(e13,e11),e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[823,817]),
[iquote('0:Rew:823.0,817.1')] ).
cnf(831,plain,
equal(op1(e13,e11),e10),
inference(mrr,[status(thm)],[830,1]),
[iquote('0:MRR:830.1,1.0')] ).
cnf(837,plain,
( equal(op1(e13,e10),e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[831,813]),
[iquote('0:Rew:831.0,813.1')] ).
cnf(838,plain,
equal(op1(e13,e10),e12),
inference(mrr,[status(thm)],[837,2]),
[iquote('0:MRR:837.1,2.0')] ).
cnf(844,plain,
( equal(op1(e12,e10),e11)
| equal(op1(e12,e11),e11)
| equal(e12,e11)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[61,390,55]),
[iquote('0:Rew:61.0,390.3,55.0,390.2')] ).
cnf(845,plain,
equal(op1(e12,e10),e11),
inference(mrr,[status(thm)],[844,656,4,1]),
[iquote('0:MRR:844.1,844.2,844.3,656.0,4.0,1.0')] ).
cnf(850,plain,
( equal(e13,e11)
| equal(op1(e12,e11),e13) ),
inference(rew,[status(thm),theory(equality)],[845,821]),
[iquote('0:Rew:845.0,821.0')] ).
cnf(851,plain,
equal(op1(e12,e11),e13),
inference(mrr,[status(thm)],[850,5]),
[iquote('0:MRR:850.0,5.0')] ).
cnf(856,plain,
( equal(op1(e10,e12),e10)
| equal(op1(e11,e12),e10)
| equal(e12,e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[823,391,55]),
[iquote('0:Rew:823.0,391.3,55.0,391.2')] ).
cnf(857,plain,
equal(op1(e11,e12),e10),
inference(mrr,[status(thm)],[856,644,2,1]),
[iquote('0:MRR:856.0,856.2,856.3,644.0,2.0,1.0')] ).
cnf(862,plain,
( equal(op1(e10,e12),e13)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[857,819]),
[iquote('0:Rew:857.0,819.1')] ).
cnf(863,plain,
equal(op1(e10,e12),e13),
inference(mrr,[status(thm)],[862,3]),
[iquote('0:MRR:862.1,3.0')] ).
cnf(868,plain,
( equal(op1(e11,e10),e13)
| equal(e13,e11)
| equal(e13,e10)
| equal(e13,e12) ),
inference(rew,[status(thm),theory(equality)],[806,394,857,54]),
[iquote('0:Rew:806.0,394.3,857.0,394.2,54.0,394.1')] ).
cnf(869,plain,
equal(op1(e11,e10),e13),
inference(mrr,[status(thm)],[868,5,3,6]),
[iquote('0:MRR:868.1,868.2,868.3,5.0,3.0,6.0')] ).
cnf(873,plain,
( equal(op1(e10,e11),e12)
| equal(e12,e11)
| equal(e13,e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[831,395,851,54]),
[iquote('0:Rew:831.0,395.3,851.0,395.2,54.0,395.1')] ).
cnf(874,plain,
equal(op1(e10,e11),e12),
inference(mrr,[status(thm)],[873,4,6,2]),
[iquote('0:MRR:873.1,873.2,873.3,4.0,6.0,2.0')] ).
cnf(880,plain,
( ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e22,e22)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e20,e20)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ skC33
| ~ skC34
| ~ skC35 ),
inference(rew,[status(thm),theory(equality)],[59,426,52,56,62,51,766,823,732,689,831,746,838,690,61,60,55,719,851,705,845,771,806,559,857,57,54,794,869,757,563,666,863,783,874,58,53]),
[iquote('0:Rew:59.0,426.16,52.0,426.16,56.0,426.16,62.0,426.15,52.0,426.15,51.0,426.15,766.0,426.15,823.0,426.15,732.0,426.14,52.0,426.14,766.0,426.14,689.0,426.14,831.0,426.14,746.0,426.13,52.0,426.13,689.0,426.13,51.0,426.13,838.0,426.13,690.0,426.12,51.0,426.12,52.0,426.12,689.0,426.12,61.0,426.12,60.0,426.11,51.0,426.11,55.0,426.11,719.0,426.10,51.0,426.10,766.0,426.10,52.0,426.10,851.0,426.10,705.0,426.9,51.0,426.9,689.0,426.9,766.0,426.9,845.0,426.9,771.0,426.8,766.0,426.8,52.0,426.8,51.0,426.8,806.0,426.8,559.0,426.7,766.0,426.7,51.0,426.7,689.0,426.7,857.0,426.7,57.0,426.6,766.0,426.6,54.0,426.6,794.0,426.5,766.0,426.5,689.0,426.5,52.0,426.5,869.0,426.5,757.0,426.4,689.0,426.4,52.0,426.4,766.0,426.4,563.0,426.4,666.0,426.3,689.0,426.3,51.0,426.3,52.0,426.3,863.0,426.3,783.0,426.2,689.0,426.2,766.0,426.2,51.0,426.2,874.0,426.2,58.0,426.1,689.0,426.1,53.0,426.1,51.0,426.0')] ).
cnf(881,plain,
( ~ skC33
| ~ skC34
| ~ skC35 ),
inference(obv,[status(thm),theory(equality)],[880]),
[iquote('0:Obv:880.16')] ).
cnf(882,plain,
$false,
inference(mrr,[status(thm)],[881,767,701,475]),
[iquote('0:MRR:881.0,881.1,881.2,767.0,701.0,475.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 05:29:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/0.60
% 0.40/0.60 SPASS V 3.9
% 0.40/0.60 SPASS beiseite: Proof found.
% 0.40/0.60 % SZS status Theorem
% 0.40/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.60 SPASS derived 148 clauses, backtracked 0 clauses, performed 0 splits and kept 309 clauses.
% 0.40/0.60 SPASS allocated 87521 KBytes.
% 0.40/0.60 SPASS spent 0:00:00.26 on the problem.
% 0.40/0.60 0:00:00.04 for the input.
% 0.40/0.60 0:00:00.14 for the FLOTTER CNF translation.
% 0.40/0.60 0:00:00.00 for inferences.
% 0.40/0.60 0:00:00.00 for the backtracking.
% 0.40/0.60 0:00:00.02 for the reduction.
% 0.40/0.60
% 0.40/0.60
% 0.40/0.60 Here is a proof with depth 0, length 176 :
% 0.40/0.60 % SZS output start Refutation
% See solution above
% 0.40/0.61 Formulae used in the proof : ax7 ax8 ax25 ax10 ax11 ax12 ax13 co1 ax14 ax15 ax16 ax17 ax18 ax19 ax20 ax21 ax23 ax24 ax5 ax6 ax4 ax2
% 0.40/0.61
%------------------------------------------------------------------------------