TSTP Solution File: GRP129-3.004 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP129-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 : 300s
% DateTime : Wed Jul 27 12:56:28 EDT 2022
% Result : Unsatisfiable 9.65s 9.85s
% Output : Refutation 9.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 38
% Syntax : Number of clauses : 117 ( 35 unt; 74 nHn; 117 RR)
% Number of literals : 303 ( 0 equ; 45 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ group_element(A)
| cycle(A,e_0)
| cycle(A,e_1)
| cycle(A,e_2)
| cycle(A,e_3) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(3,axiom,
( ~ cycle(A,B)
| ~ cycle(C,D)
| ~ next(A,C)
| ~ greater(B,e_0)
| ~ next(D,E)
| e_qualish(B,E) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(4,axiom,
( ~ cycle(A,B)
| ~ cycle(C,e_0)
| ~ cycle(D,E)
| ~ next(C,D)
| ~ greater(C,A)
| ~ greater(B,E) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(5,axiom,
( ~ cycle(A,e_0)
| ~ product(A,e_1,B)
| ~ greater(B,A) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(6,axiom,
( ~ cycle(A,B)
| ~ product(A,e_1,C)
| ~ greater(B,e_0)
| ~ next(A,D)
| e_qualish(C,D) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_1,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_1,e_3),
file('GRP129-3.004.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_1,e_4),
file('GRP129-3.004.p',unknown),
[] ).
cnf(10,axiom,
~ e_qualish(e_2,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(11,axiom,
~ e_qualish(e_2,e_3),
file('GRP129-3.004.p',unknown),
[] ).
cnf(12,axiom,
~ e_qualish(e_2,e_4),
file('GRP129-3.004.p',unknown),
[] ).
cnf(13,axiom,
~ e_qualish(e_3,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(14,axiom,
~ e_qualish(e_3,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(15,axiom,
~ e_qualish(e_3,e_4),
file('GRP129-3.004.p',unknown),
[] ).
cnf(16,axiom,
~ e_qualish(e_4,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(17,axiom,
~ e_qualish(e_4,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(18,axiom,
~ e_qualish(e_4,e_3),
file('GRP129-3.004.p',unknown),
[] ).
cnf(19,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3)
| product(A,B,e_4) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(22,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
file('GRP129-3.004.p',unknown),
[] ).
cnf(30,plain,
( ~ cycle(A,B)
| ~ cycle(B,e_0)
| ~ cycle(C,A)
| ~ next(B,C)
| ~ greater(B,A) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.5.6')] ).
cnf(31,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2)
| product(A,A,e_3)
| product(A,A,e_4) ),
inference(factor,[status(thm)],[19]),
[iquote('factor,19.1.2')] ).
cnf(40,axiom,
next(e_0,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(41,axiom,
next(e_1,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(42,axiom,
next(e_2,e_3),
file('GRP129-3.004.p',unknown),
[] ).
cnf(43,axiom,
next(e_3,e_4),
file('GRP129-3.004.p',unknown),
[] ).
cnf(44,axiom,
greater(e_1,e_0),
file('GRP129-3.004.p',unknown),
[] ).
cnf(45,axiom,
greater(e_2,e_0),
file('GRP129-3.004.p',unknown),
[] ).
cnf(46,axiom,
greater(e_3,e_0),
file('GRP129-3.004.p',unknown),
[] ).
cnf(48,axiom,
greater(e_2,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(49,axiom,
greater(e_3,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(50,axiom,
greater(e_4,e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(51,axiom,
greater(e_3,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(52,axiom,
greater(e_4,e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(54,axiom,
cycle(e_4,e_0),
file('GRP129-3.004.p',unknown),
[] ).
cnf(55,axiom,
group_element(e_1),
file('GRP129-3.004.p',unknown),
[] ).
cnf(56,axiom,
group_element(e_2),
file('GRP129-3.004.p',unknown),
[] ).
cnf(57,axiom,
group_element(e_3),
file('GRP129-3.004.p',unknown),
[] ).
cnf(58,axiom,
group_element(e_4),
file('GRP129-3.004.p',unknown),
[] ).
cnf(59,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(hyper,[status(thm)],[55,31]),
[iquote('hyper,55,31')] ).
cnf(60,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| cycle(e_1,e_3) ),
inference(hyper,[status(thm)],[55,2]),
[iquote('hyper,55,2')] ).
cnf(62,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[56,19,55]),
[iquote('hyper,56,19,55')] ).
cnf(63,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(hyper,[status(thm)],[56,19,55]),
[iquote('hyper,56,19,55')] ).
cnf(64,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_1)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(hyper,[status(thm)],[56,2]),
[iquote('hyper,56,2')] ).
cnf(66,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(hyper,[status(thm)],[57,19,56]),
[iquote('hyper,57,19,56')] ).
cnf(69,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(hyper,[status(thm)],[57,19,55]),
[iquote('hyper,57,19,55')] ).
cnf(70,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_3) ),
inference(hyper,[status(thm)],[57,2]),
[iquote('hyper,57,2')] ).
cnf(73,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(hyper,[status(thm)],[58,19,56]),
[iquote('hyper,58,19,56')] ).
cnf(74,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(hyper,[status(thm)],[58,19,55]),
[iquote('hyper,58,19,55')] ).
cnf(77,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(hyper,[status(thm)],[58,19,55]),
[iquote('hyper,58,19,55')] ).
cnf(126,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_1)
| cycle(e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[70,3,54,43,45,40]),10]),
[iquote('hyper,70,3,54,43,45,40,unit_del,10')] ).
cnf(146,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[126,3,54,43,46,40]),13]),
[iquote('hyper,126,3,54,43,46,40,unit_del,13')] ).
cnf(155,plain,
( cycle(e_3,e_1)
| cycle(e_2,e_0)
| cycle(e_2,e_1)
| cycle(e_2,e_2) ),
inference(hyper,[status(thm)],[146,4,64,54,43,51,46]),
[iquote('hyper,146,4,64,54,43,51,46')] ).
cnf(158,plain,
( cycle(e_3,e_1)
| cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_2) ),
inference(hyper,[status(thm)],[146,4,60,54,43,49,46]),
[iquote('hyper,146,4,60,54,43,49,46')] ).
cnf(236,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_1)
| cycle(e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[155,3,64,42,46,41]),14])])])]),
[iquote('hyper,155,3,64,42,46,41,unit_del,14,factor_simp,factor_simp,factor_simp')] ).
cnf(243,plain,
( cycle(e_3,e_1)
| cycle(e_2,e_0)
| cycle(e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[155,4,146,54,43,51,44])]),
[iquote('hyper,155,4,146,54,43,51,44,factor_simp')] ).
cnf(268,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[243,3,236,42,44,41]),7])])]),
[iquote('hyper,243,3,236,42,44,41,unit_del,7,factor_simp,factor_simp')] ).
cnf(275,plain,
( cycle(e_3,e_1)
| cycle(e_2,e_0) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[243,4,146,54,43,51,45])]),
[iquote('hyper,243,4,146,54,43,51,45,factor_simp')] ).
cnf(277,plain,
( cycle(e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[268,5,63,52]),
[iquote('hyper,268,5,63,52')] ).
cnf(280,plain,
( cycle(e_2,e_2)
| cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[268,3,60,41,46,40]),13]),
[iquote('hyper,268,3,60,41,46,40,unit_del,13')] ).
cnf(306,plain,
( cycle(e_3,e_1)
| cycle(e_1,e_0)
| cycle(e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[158,4,275,146,42,48,44])])]),
[iquote('hyper,158,4,275,146,42,48,44,factor_simp,factor_simp')] ).
cnf(354,plain,
( cycle(e_3,e_1)
| cycle(e_1,e_0) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[306,4,275,146,42,48,45])])]),
[iquote('hyper,306,4,275,146,42,48,45,factor_simp,factor_simp')] ).
cnf(369,plain,
( cycle(e_2,e_2)
| cycle(e_1,e_0)
| cycle(e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[280,30,268,354,42,48])])]),
[iquote('hyper,280,30,268,354,42,48,factor_simp,factor_simp')] ).
cnf(412,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[369,3,60,41,45,42]),11])])]),
[iquote('hyper,369,3,60,41,45,42,unit_del,11,factor_simp,factor_simp')] ).
cnf(419,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[412,5,59,50]),
[iquote('hyper,412,5,59,50')] ).
cnf(498,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| cycle(e_1,e_0) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[69,6,354,44,43]),9]),
[iquote('hyper,69,6,354,44,43,unit_del,9')] ).
cnf(950,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[277,6,63,45,42]),18])])])]),
[iquote('hyper,277,6,63,45,42,unit_del,18,factor_simp,factor_simp,factor_simp')] ).
cnf(3589,plain,
( cycle(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[419,6,59,44,41]),17])])])]),
[iquote('hyper,419,6,59,44,41,unit_del,17,factor_simp,factor_simp,factor_simp')] ).
cnf(3601,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3589,6,59,46,41]),17])])])]),
[iquote('hyper,3589,6,59,46,41,unit_del,17,factor_simp,factor_simp,factor_simp')] ).
cnf(3645,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| cycle(e_1,e_0)
| cycle(e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3601,6,412,46,41]),14]),
[iquote('hyper,3601,6,412,46,41,unit_del,14')] ).
cnf(3682,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| cycle(e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3645,5,3601,49])])]),
[iquote('hyper,3645,5,3601,49,factor_simp,factor_simp')] ).
cnf(3684,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3682,6,3601,44,41]),14])])]),
[iquote('hyper,3682,6,3601,44,41,unit_del,14,factor_simp,factor_simp')] ).
cnf(3689,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3684,22,950]),10]),
[iquote('hyper,3684,22,950,unit_del,10')] ).
cnf(3691,plain,
( product(e_1,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3684,22,69]),13]),
[iquote('hyper,3684,22,69,unit_del,13')] ).
cnf(3711,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3684,22,77]),16]),
[iquote('hyper,3684,22,77,unit_del,16')] ).
cnf(3738,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3689,23,950])])]),
[iquote('hyper,3689,23,950,factor_simp,factor_simp')] ).
cnf(3828,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3738,23,3689])])])]),
[iquote('hyper,3738,23,3689,factor_simp,factor_simp,factor_simp')] ).
cnf(3834,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3828,22,3684]),7]),
[iquote('hyper,3828,22,3684,unit_del,7')] ).
cnf(3854,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3828,21,73]),16]),
[iquote('hyper,3828,21,73,unit_del,16')] ).
cnf(3855,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3828,21,66]),13]),
[iquote('hyper,3828,21,66,unit_del,13')] ).
cnf(3911,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3691,5,498,48])])])]),
[iquote('hyper,3691,5,498,48,factor_simp,factor_simp,factor_simp')] ).
cnf(3931,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3911,22,3828]),11]),
[iquote('hyper,3911,22,3828,unit_del,11')] ).
cnf(3940,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| cycle(e_2,e_0) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3911,6,275,44,43]),12]),
[iquote('hyper,3911,6,275,44,43,unit_del,12')] ).
cnf(3993,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3931,5,3940,51])])]),
[iquote('hyper,3931,5,3940,51,factor_simp,factor_simp')] ).
cnf(4004,plain,
( product(e_3,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3993,22,3834]),11]),
[iquote('hyper,3993,22,3834,unit_del,11')] ).
cnf(4005,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3993,22,3828]),11]),
[iquote('hyper,3993,22,3828,unit_del,11')] ).
cnf(4140,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3711,22,3834]),12])]),
[iquote('hyper,3711,22,3834,unit_del,12,factor_simp')] ).
cnf(4158,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4140,22,4004]),15])]),
[iquote('hyper,4140,22,4004,unit_del,15,factor_simp')] ).
cnf(4174,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_4,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4158,23,3684])]),
[iquote('hyper,4158,23,3684,factor_simp')] ).
cnf(4179,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4174,21,74]),16])]),
[iquote('hyper,4174,21,74,unit_del,16,factor_simp')] ).
cnf(4197,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4174,21,3684]),9])]),
[iquote('hyper,4174,21,3684,unit_del,9,factor_simp')] ).
cnf(4200,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4197,22,77]),16]),
[iquote('hyper,4197,22,77,unit_del,16')] ).
cnf(4219,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4197,21,62]),10]),
[iquote('hyper,4197,21,62,unit_del,10')] ).
cnf(4229,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_4,e_3,e_2)
| product(e_2,e_1,e_2) ),
inference(hyper,[status(thm)],[4179,23,4005]),
[iquote('hyper,4179,23,4005')] ).
cnf(4257,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4200,22,3828]),12]),
[iquote('hyper,4200,22,3828,unit_del,12')] ).
cnf(4385,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4257,22,4005]),15])]),
[iquote('hyper,4257,22,4005,unit_del,15,factor_simp')] ).
cnf(4519,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4229,21,4385]),8])]),
[iquote('hyper,4229,21,4385,unit_del,8,factor_simp')] ).
cnf(4522,plain,
( product(e_1,e_4,e_4)
| product(e_2,e_1,e_2)
| product(e_4,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4519,23,4005])]),
[iquote('hyper,4519,23,4005,factor_simp')] ).
cnf(4543,plain,
( product(e_1,e_4,e_4)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4522,23,4519])])]),
[iquote('hyper,4522,23,4519,factor_simp,factor_simp')] ).
cnf(4567,plain,
( product(e_1,e_4,e_4)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4543,22,3828]),11])]),
[iquote('hyper,4543,22,3828,unit_del,11,factor_simp')] ).
cnf(4569,plain,
( product(e_2,e_1,e_2)
| product(e_4,e_3,e_4) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4567,23,4005])]),
[iquote('hyper,4567,23,4005,factor_simp')] ).
cnf(4570,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4567,22,3854]),10])]),
[iquote('hyper,4567,22,3854,unit_del,10,factor_simp')] ).
cnf(4572,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4567,21,4219]),12]),
[iquote('hyper,4567,21,4219,unit_del,12')] ).
cnf(4597,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4569,22,3855]),12])]),
[iquote('hyper,4569,22,3855,unit_del,12,factor_simp')] ).
cnf(4607,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_1,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4570,23,4385])]),
[iquote('hyper,4570,23,4385,factor_simp')] ).
cnf(4612,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4572,23,4219])])]),
[iquote('hyper,4572,23,4219,factor_simp,factor_simp')] ).
cnf(4663,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4607,23,4385])])]),
[iquote('hyper,4607,23,4385,factor_simp,factor_simp')] ).
cnf(4673,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4663,21,4597]),15])]),
[iquote('hyper,4663,21,4597,unit_del,15,factor_simp')] ).
cnf(4687,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_2,e_4) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4673,23,4005])]),
[iquote('hyper,4673,23,4005,factor_simp')] ).
cnf(4701,plain,
product(e_2,e_1,e_2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4687,21,4567]),17])]),
[iquote('hyper,4687,21,4567,unit_del,17,factor_simp')] ).
cnf(4743,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4612,22,4219]),7])])]),
[iquote('hyper,4612,22,4219,unit_del,7,factor_simp,factor_simp')] ).
cnf(4744,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[4743,23,4701]),
[iquote('hyper,4743,23,4701')] ).
cnf(4765,plain,
product(e_1,e_2,e_3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4744,22,4743]),7])]),
[iquote('hyper,4744,22,4743,unit_del,7,factor_simp')] ).
cnf(4767,plain,
product(e_2,e_2,e_3),
inference(hyper,[status(thm)],[4765,23,4701]),
[iquote('hyper,4765,23,4701')] ).
cnf(4773,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[4767,22,4765]),
[iquote('hyper,4767,22,4765')] ).
cnf(4774,plain,
$false,
inference(binary,[status(thm)],[4773,7]),
[iquote('binary,4773.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP129-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:41:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.55/2.12 ----- Otter 3.3f, August 2004 -----
% 1.55/2.12 The process was started by sandbox on n026.cluster.edu,
% 1.55/2.12 Wed Jul 27 05:41:54 2022
% 1.55/2.12 The command was "./otter". The process ID is 27989.
% 1.55/2.12
% 1.55/2.12 set(prolog_style_variables).
% 1.55/2.12 set(auto).
% 1.55/2.12 dependent: set(auto1).
% 1.55/2.12 dependent: set(process_input).
% 1.55/2.12 dependent: clear(print_kept).
% 1.55/2.12 dependent: clear(print_new_demod).
% 1.55/2.12 dependent: clear(print_back_demod).
% 1.55/2.12 dependent: clear(print_back_sub).
% 1.55/2.12 dependent: set(control_memory).
% 1.55/2.12 dependent: assign(max_mem, 12000).
% 1.55/2.12 dependent: assign(pick_given_ratio, 4).
% 1.55/2.12 dependent: assign(stats_level, 1).
% 1.55/2.12 dependent: assign(max_seconds, 10800).
% 1.55/2.12 clear(print_given).
% 1.55/2.12
% 1.55/2.12 list(usable).
% 1.55/2.12 0 [] next(e_0,e_1).
% 1.55/2.12 0 [] next(e_1,e_2).
% 1.55/2.12 0 [] next(e_2,e_3).
% 1.55/2.12 0 [] next(e_3,e_4).
% 1.55/2.12 0 [] greater(e_1,e_0).
% 1.55/2.12 0 [] greater(e_2,e_0).
% 1.55/2.12 0 [] greater(e_3,e_0).
% 1.55/2.12 0 [] greater(e_4,e_0).
% 1.55/2.12 0 [] greater(e_2,e_1).
% 1.55/2.12 0 [] greater(e_3,e_1).
% 1.55/2.12 0 [] greater(e_4,e_1).
% 1.55/2.12 0 [] greater(e_3,e_2).
% 1.55/2.12 0 [] greater(e_4,e_2).
% 1.55/2.12 0 [] greater(e_4,e_3).
% 1.55/2.12 0 [] -cycle(X,Y)| -cycle(X,Z)|e_qualish(Y,Z).
% 1.55/2.12 0 [] -group_element(X)|cycle(X,e_0)|cycle(X,e_1)|cycle(X,e_2)|cycle(X,e_3).
% 1.55/2.12 0 [] cycle(e_4,e_0).
% 1.55/2.12 0 [] -cycle(X,Y)| -cycle(W,Z)| -next(X,W)| -greater(Y,e_0)| -next(Z,Z1)|e_qualish(Y,Z1).
% 1.55/2.12 0 [] -cycle(X,Z1)| -cycle(Y,e_0)| -cycle(W,Z2)| -next(Y,W)| -greater(Y,X)| -greater(Z1,Z2).
% 1.55/2.12 0 [] -cycle(X,e_0)| -product(X,e_1,Y)| -greater(Y,X).
% 1.55/2.12 0 [] -cycle(X,Y)| -product(X,e_1,Z)| -greater(Y,e_0)| -next(X,X1)|e_qualish(Z,X1).
% 1.55/2.12 0 [] group_element(e_1).
% 1.55/2.12 0 [] group_element(e_2).
% 1.55/2.12 0 [] group_element(e_3).
% 1.55/2.12 0 [] group_element(e_4).
% 1.55/2.12 0 [] -e_qualish(e_1,e_2).
% 1.55/2.12 0 [] -e_qualish(e_1,e_3).
% 1.55/2.12 0 [] -e_qualish(e_1,e_4).
% 1.55/2.12 0 [] -e_qualish(e_2,e_1).
% 1.55/2.12 0 [] -e_qualish(e_2,e_3).
% 1.55/2.12 0 [] -e_qualish(e_2,e_4).
% 1.55/2.12 0 [] -e_qualish(e_3,e_1).
% 1.55/2.12 0 [] -e_qualish(e_3,e_2).
% 1.55/2.12 0 [] -e_qualish(e_3,e_4).
% 1.55/2.12 0 [] -e_qualish(e_4,e_1).
% 1.55/2.12 0 [] -e_qualish(e_4,e_2).
% 1.55/2.12 0 [] -e_qualish(e_4,e_3).
% 1.55/2.12 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3)|product(X,Y,e_4).
% 1.55/2.12 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.55/2.12 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.55/2.12 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.55/2.12 0 [] -product(Y,X,Z1)| -product(X,Z1,Z2)|product(Z1,Y,Z2).
% 1.55/2.12 end_of_list.
% 1.55/2.12
% 1.55/2.12 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.55/2.12
% 1.55/2.12 This is a non-Horn set without equality. The strategy will
% 1.55/2.12 be ordered hyper_res, unit deletion, and factoring, with
% 1.55/2.12 satellites in sos and with nuclei in usable.
% 1.55/2.12
% 1.55/2.12 dependent: set(hyper_res).
% 1.55/2.12 dependent: set(factor).
% 1.55/2.12 dependent: set(unit_deletion).
% 1.55/2.12
% 1.55/2.12 ------------> process usable:
% 1.55/2.12 ** KEPT (pick-wt=9): 1 [] -cycle(A,B)| -cycle(A,C)|e_qualish(B,C).
% 1.55/2.12 ** KEPT (pick-wt=14): 2 [] -group_element(A)|cycle(A,e_0)|cycle(A,e_1)|cycle(A,e_2)|cycle(A,e_3).
% 1.55/2.12 ** KEPT (pick-wt=18): 3 [] -cycle(A,B)| -cycle(C,D)| -next(A,C)| -greater(B,e_0)| -next(D,E)|e_qualish(B,E).
% 1.55/2.12 ** KEPT (pick-wt=18): 4 [] -cycle(A,B)| -cycle(C,e_0)| -cycle(D,E)| -next(C,D)| -greater(C,A)| -greater(B,E).
% 1.55/2.12 ** KEPT (pick-wt=10): 5 [] -cycle(A,e_0)| -product(A,e_1,B)| -greater(B,A).
% 1.55/2.12 ** KEPT (pick-wt=16): 6 [] -cycle(A,B)| -product(A,e_1,C)| -greater(B,e_0)| -next(A,D)|e_qualish(C,D).
% 1.55/2.12 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_1,e_2).
% 1.55/2.12 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_1,e_3).
% 1.55/2.12 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_1,e_4).
% 1.55/2.12 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_2,e_1).
% 1.55/2.12 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_2,e_3).
% 1.55/2.12 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_2,e_4).
% 1.55/2.12 ** KEPT (pick-wt=3): 13 [] -e_qualish(e_3,e_1).
% 1.55/2.12 ** KEPT (pick-wt=3): 14 [] -e_qualish(e_3,e_2).
% 1.55/2.12 ** KEPT (pick-wt=3): 15 [] -e_qualish(e_3,e_4).
% 1.55/2.12 ** KEPT (pick-wt=3): 16 [] -e_qualish(e_4,e_1).
% 1.55/2.12 ** KEPT (pick-wt=3): 17 [] -e_qualish(e_4,e_2).
% 1.55/2.12 ** KEPT (pick-wt=3): 18 [] -e_qualish(e_4,e_3).
% 1.55/2.12 ** KEPT (pick-wt=20): 19 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)|product(A,B,e_4).
% 1.55/2.12 ** KEPT (pick-wt=11): 20 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.55/2.12 ** KEPT (pick-wt=11): 21 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.55/2.12 ** KEPT (pick-wt=11): 22 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.55/2.12 ** KEPT (pick-wt=12): 23 [] -product(A,B,C)| -product(B,C,D)|product(C,A,D).
% 9.65/9.85
% 9.65/9.85 ------------> process sos:
% 9.65/9.85 ** KEPT (pick-wt=3): 40 [] next(e_0,e_1).
% 9.65/9.85 ** KEPT (pick-wt=3): 41 [] next(e_1,e_2).
% 9.65/9.85 ** KEPT (pick-wt=3): 42 [] next(e_2,e_3).
% 9.65/9.85 ** KEPT (pick-wt=3): 43 [] next(e_3,e_4).
% 9.65/9.85 ** KEPT (pick-wt=3): 44 [] greater(e_1,e_0).
% 9.65/9.85 ** KEPT (pick-wt=3): 45 [] greater(e_2,e_0).
% 9.65/9.85 ** KEPT (pick-wt=3): 46 [] greater(e_3,e_0).
% 9.65/9.85 ** KEPT (pick-wt=3): 47 [] greater(e_4,e_0).
% 9.65/9.85 ** KEPT (pick-wt=3): 48 [] greater(e_2,e_1).
% 9.65/9.85 ** KEPT (pick-wt=3): 49 [] greater(e_3,e_1).
% 9.65/9.85 ** KEPT (pick-wt=3): 50 [] greater(e_4,e_1).
% 9.65/9.85 ** KEPT (pick-wt=3): 51 [] greater(e_3,e_2).
% 9.65/9.85 ** KEPT (pick-wt=3): 52 [] greater(e_4,e_2).
% 9.65/9.85 ** KEPT (pick-wt=3): 53 [] greater(e_4,e_3).
% 9.65/9.85 ** KEPT (pick-wt=3): 54 [] cycle(e_4,e_0).
% 9.65/9.85 ** KEPT (pick-wt=2): 55 [] group_element(e_1).
% 9.65/9.85 ** KEPT (pick-wt=2): 56 [] group_element(e_2).
% 9.65/9.85 ** KEPT (pick-wt=2): 57 [] group_element(e_3).
% 9.65/9.85 ** KEPT (pick-wt=2): 58 [] group_element(e_4).
% 9.65/9.85
% 9.65/9.85 ======= end of input processing =======
% 9.65/9.85
% 9.65/9.85 =========== start of search ===========
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 23.
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 23.
% 9.65/9.85
% 9.65/9.85 sos_size=2526
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 20.
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 20.
% 9.65/9.85
% 9.65/9.85 sos_size=1819
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 16.
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Resetting weight limit to 16.
% 9.65/9.85
% 9.65/9.85 sos_size=1318
% 9.65/9.85
% 9.65/9.85 -------- PROOF --------
% 9.65/9.85
% 9.65/9.85 ----> UNIT CONFLICT at 7.73 sec ----> 4774 [binary,4773.1,7.1] $F.
% 9.65/9.85
% 9.65/9.85 Length of proof is 78. Level of proof is 42.
% 9.65/9.85
% 9.65/9.85 ---------------- PROOF ----------------
% 9.65/9.85 % SZS status Unsatisfiable
% 9.65/9.85 % SZS output start Refutation
% See solution above
% 9.65/9.85 ------------ end of proof -------------
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Search stopped by max_proofs option.
% 9.65/9.85
% 9.65/9.85
% 9.65/9.85 Search stopped by max_proofs option.
% 9.65/9.85
% 9.65/9.85 ============ end of search ============
% 9.65/9.85
% 9.65/9.85 -------------- statistics -------------
% 9.65/9.85 clauses given 673
% 9.65/9.85 clauses generated 230962
% 9.65/9.85 clauses kept 4773
% 9.65/9.85 clauses forward subsumed 32477
% 9.65/9.85 clauses back subsumed 4024
% 9.65/9.85 Kbytes malloced 4882
% 9.65/9.85
% 9.65/9.85 ----------- times (seconds) -----------
% 9.65/9.85 user CPU time 7.73 (0 hr, 0 min, 7 sec)
% 9.65/9.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 9.65/9.85 wall-clock time 9 (0 hr, 0 min, 9 sec)
% 9.65/9.85
% 9.65/9.85 That finishes the proof of the theorem.
% 9.65/9.85
% 9.65/9.85 Process 27989 finished Wed Jul 27 05:42:03 2022
% 9.65/9.85 Otter interrupted
% 9.65/9.85 PROOF FOUND
%------------------------------------------------------------------------------