TSTP Solution File: GRP129-2.004 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 8.19s 8.40s
% Output : Refutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of clauses : 101 ( 30 unt; 66 nHn; 101 RR)
% Number of literals : 241 ( 0 equ; 25 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('GRP129-2.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_3),
file('GRP129-2.004.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_1,e_4),
file('GRP129-2.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_1),
file('GRP129-2.004.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_3),
file('GRP129-2.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_2,e_4),
file('GRP129-2.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_1),
file('GRP129-2.004.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_3,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(10,axiom,
~ e_qualish(e_3,e_4),
file('GRP129-2.004.p',unknown),
[] ).
cnf(11,axiom,
~ e_qualish(e_4,e_1),
file('GRP129-2.004.p',unknown),
[] ).
cnf(12,axiom,
~ e_qualish(e_4,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(14,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('GRP129-2.004.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP129-2.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP129-2.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP129-2.004.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
file('GRP129-2.004.p',unknown),
[] ).
cnf(19,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)],[14]),
[iquote('factor,14.1.2')] ).
cnf(23,axiom,
next(e_1,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(24,axiom,
next(e_2,e_3),
file('GRP129-2.004.p',unknown),
[] ).
cnf(29,axiom,
greater(e_3,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(30,axiom,
greater(e_4,e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(31,axiom,
greater(e_4,e_3),
file('GRP129-2.004.p',unknown),
[] ).
cnf(32,axiom,
group_element(e_1),
file('GRP129-2.004.p',unknown),
[] ).
cnf(33,axiom,
group_element(e_2),
file('GRP129-2.004.p',unknown),
[] ).
cnf(34,axiom,
group_element(e_3),
file('GRP129-2.004.p',unknown),
[] ).
cnf(35,axiom,
group_element(e_4),
file('GRP129-2.004.p',unknown),
[] ).
cnf(36,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)],[32,19]),
[iquote('hyper,32,19')] ).
cnf(37,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(hyper,[status(thm)],[33,19]),
[iquote('hyper,33,19')] ).
cnf(38,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)],[33,14,32]),
[iquote('hyper,33,14,32')] ).
cnf(39,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)],[33,14,32]),
[iquote('hyper,33,14,32')] ).
cnf(42,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[34,14,32]),
[iquote('hyper,34,14,32')] ).
cnf(44,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)],[34,14,32]),
[iquote('hyper,34,14,32')] ).
cnf(51,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)],[35,14,32]),
[iquote('hyper,35,14,32')] ).
cnf(57,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_4) ),
inference(hyper,[status(thm)],[36,1,23,29]),
[iquote('hyper,36,1,23,29')] ).
cnf(66,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[57,1,23,30]),
[iquote('hyper,57,1,23,30')] ).
cnf(130,plain,
( 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)],[39,1,24,31]),
[iquote('hyper,39,1,24,31')] ).
cnf(137,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[130,17,66]),2]),
[iquote('hyper,130,17,66,unit_del,2')] ).
cnf(206,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)],[137,18,130])])]),
[iquote('hyper,137,18,130,factor_simp,factor_simp')] ).
cnf(262,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[206,18,38])]),
[iquote('hyper,206,18,38,factor_simp')] ).
cnf(278,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)],[206,18,137])])])]),
[iquote('hyper,206,18,137,factor_simp,factor_simp,factor_simp')] ).
cnf(282,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[278,17,66]),2]),
[iquote('hyper,278,17,66,unit_del,2')] ).
cnf(294,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[278,16,37]),5]),
[iquote('hyper,278,16,37,unit_del,5')] ).
cnf(358,plain,
( product(e_3,e_1,e_1)
| 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)],[44,17,278]),6]),
[iquote('hyper,44,17,278,unit_del,6')] ).
cnf(359,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,17,66]),3]),
[iquote('hyper,44,17,66,unit_del,3')] ).
cnf(659,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,17,282]),4]),
[iquote('hyper,51,17,282,unit_del,4')] ).
cnf(676,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,17,66]),4]),
[iquote('hyper,51,17,66,unit_del,4')] ).
cnf(3462,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[294,18,278])]),
[iquote('hyper,294,18,278,factor_simp')] ).
cnf(3744,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[358,17,282]),3])]),
[iquote('hyper,358,17,282,unit_del,3,factor_simp')] ).
cnf(3781,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[359,17,282]),6])]),
[iquote('hyper,359,17,282,unit_del,6,factor_simp')] ).
cnf(3784,plain,
( product(e_3,e_1,e_4)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3781,18,66])]),
[iquote('hyper,3781,18,66,factor_simp')] ).
cnf(3804,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,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)],[262,17,38]),2])])])]),
[iquote('hyper,262,17,38,unit_del,2,factor_simp,factor_simp,factor_simp')] ).
cnf(3827,plain,
( product(e_3,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3784,16,66]),3])]),
[iquote('hyper,3784,16,66,unit_del,3,factor_simp')] ).
cnf(3845,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3827,17,44]),8])]),
[iquote('hyper,3827,17,44,unit_del,8,factor_simp')] ).
cnf(4034,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[659,17,278]),7])]),
[iquote('hyper,659,17,278,unit_del,7,factor_simp')] ).
cnf(4051,plain,
( product(e_4,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4034,17,3744]),10])]),
[iquote('hyper,4034,17,3744,unit_del,10,factor_simp')] ).
cnf(4082,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4051,17,3845]),9])]),
[iquote('hyper,4051,17,3845,unit_del,9,factor_simp')] ).
cnf(4143,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[676,17,282]),7])]),
[iquote('hyper,676,17,282,unit_del,7,factor_simp')] ).
cnf(4160,plain,
( product(e_4,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4143,17,3827]),10])]),
[iquote('hyper,4143,17,3827,unit_del,10,factor_simp')] ).
cnf(4171,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_4,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4160,18,66])]),
[iquote('hyper,4160,18,66,factor_simp')] ).
cnf(4199,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4171,16,66]),4])]),
[iquote('hyper,4171,16,66,unit_del,4,factor_simp')] ).
cnf(4202,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)],[4199,17,51]),11]),
[iquote('hyper,4199,17,51,unit_del,11')] ).
cnf(4217,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4199,16,42]),8]),
[iquote('hyper,4199,16,42,unit_del,8')] ).
cnf(4218,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)],[4199,16,38]),5]),
[iquote('hyper,4199,16,38,unit_del,5')] ).
cnf(4248,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4202,17,4082]),10])]),
[iquote('hyper,4202,17,4082,unit_del,10,factor_simp')] ).
cnf(4343,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4248,17,4051]),7])])]),
[iquote('hyper,4248,17,4051,unit_del,7,factor_simp,factor_simp')] ).
cnf(4468,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3804,16,4199]),2]),
[iquote('hyper,3804,16,4199,unit_del,2')] ).
cnf(4486,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4468,18,278])]),
[iquote('hyper,4468,18,278,factor_simp')] ).
cnf(4521,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4486,15,3462]),6])])]),
[iquote('hyper,4486,15,3462,unit_del,6,factor_simp,factor_simp')] ).
cnf(4536,plain,
( product(e_2,e_1,e_3)
| 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)],[4486,17,4468]),2])])]),
[iquote('hyper,4486,17,4468,unit_del,2,factor_simp,factor_simp')] ).
cnf(4555,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4536,18,278])]),
[iquote('hyper,4536,18,278,factor_simp')] ).
cnf(4584,plain,
product(e_2,e_1,e_3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4555,17,4536]),2])]),
[iquote('hyper,4555,17,4536,unit_del,2,factor_simp')] ).
cnf(4589,plain,
( product(e_3,e_2,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[4584,18,4217]),
[iquote('hyper,4584,18,4217')] ).
cnf(4591,plain,
( product(e_3,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[4584,18,4217]),
[iquote('hyper,4584,18,4217')] ).
cnf(4592,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4584,17,4202]),12]),
[iquote('hyper,4584,17,4202,unit_del,12')] ).
cnf(4593,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4584,17,3845]),9]),
[iquote('hyper,4584,17,3845,unit_del,9')] ).
cnf(4656,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4521,17,4218]),2])]),
[iquote('hyper,4521,17,4218,unit_del,2,factor_simp')] ).
cnf(4661,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4589,16,4593]),2]),
[iquote('hyper,4589,16,4593,unit_del,2')] ).
cnf(4662,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_4,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4589,16,4343]),2]),
[iquote('hyper,4589,16,4343,unit_del,2')] ).
cnf(4678,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4591,18,4217])])]),
[iquote('hyper,4591,18,4217,factor_simp,factor_simp')] ).
cnf(4733,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4656,18,4218])])]),
[iquote('hyper,4656,18,4218,factor_simp,factor_simp')] ).
cnf(4840,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4678,15,4584]),9]),
[iquote('hyper,4678,15,4584,unit_del,9')] ).
cnf(4841,plain,
( product(e_1,e_3,e_4)
| product(e_3,e_2,e_3) ),
inference(hyper,[status(thm)],[4840,18,4584]),
[iquote('hyper,4840,18,4584')] ).
cnf(4857,plain,
( product(e_1,e_3,e_3)
| product(e_4,e_1,e_4) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4840,15,4662]),7])]),
[iquote('hyper,4840,15,4662,unit_del,7,factor_simp')] ).
cnf(4858,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4840,15,4661]),7])]),
[iquote('hyper,4840,15,4661,unit_del,7,factor_simp')] ).
cnf(4860,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(hyper,[status(thm)],[4841,18,4584]),
[iquote('hyper,4841,18,4584')] ).
cnf(4889,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_2,e_3) ),
inference(hyper,[status(thm)],[4857,18,4584]),
[iquote('hyper,4857,18,4584')] ).
cnf(4901,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_3) ),
inference(hyper,[status(thm)],[4858,18,4584]),
[iquote('hyper,4858,18,4584')] ).
cnf(4980,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4733,16,4656]),5])])]),
[iquote('hyper,4733,16,4656,unit_del,5,factor_simp,factor_simp')] ).
cnf(4990,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4980,17,4901]),8]),
[iquote('hyper,4980,17,4901,unit_del,8')] ).
cnf(4991,plain,
( product(e_1,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4980,17,4889]),8]),
[iquote('hyper,4980,17,4889,unit_del,8')] ).
cnf(5018,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4990,18,4980])]),
[iquote('hyper,4990,18,4980,factor_simp')] ).
cnf(5021,plain,
( product(e_4,e_1,e_4)
| product(e_2,e_4,e_4) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4991,18,4592])]),
[iquote('hyper,4991,18,4592,factor_simp')] ).
cnf(5101,plain,
product(e_1,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5018,16,4584]),3]),
[iquote('hyper,5018,16,4584,unit_del,3')] ).
cnf(5110,plain,
product(e_3,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5101,17,4860]),8]),
[iquote('hyper,5101,17,4860,unit_del,8')] ).
cnf(5125,plain,
product(e_4,e_1,e_4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[5021,18,5101])]),
[iquote('hyper,5021,18,5101,factor_simp')] ).
cnf(5126,plain,
product(e_3,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5125,17,4593]),10]),
[iquote('hyper,5125,17,4593,unit_del,10')] ).
cnf(5128,plain,
product(e_2,e_3,e_4),
inference(hyper,[status(thm)],[5126,18,5101]),
[iquote('hyper,5126,18,5101')] ).
cnf(5129,plain,
product(e_3,e_3,e_4),
inference(hyper,[status(thm)],[5128,18,5110]),
[iquote('hyper,5128,18,5110')] ).
cnf(5131,plain,
e_qualish(e_2,e_3),
inference(hyper,[status(thm)],[5129,17,5128]),
[iquote('hyper,5129,17,5128')] ).
cnf(5132,plain,
$false,
inference(binary,[status(thm)],[5131,6]),
[iquote('binary,5131.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 05:41:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 7.94/8.14 ----- Otter 3.3f, August 2004 -----
% 7.94/8.14 The process was started by sandbox on n027.cluster.edu,
% 7.94/8.14 Wed Jul 27 05:41:51 2022
% 7.94/8.14 The command was "./otter". The process ID is 13907.
% 7.94/8.14
% 7.94/8.14 set(prolog_style_variables).
% 7.94/8.14 set(auto).
% 7.94/8.14 dependent: set(auto1).
% 7.94/8.14 dependent: set(process_input).
% 7.94/8.14 dependent: clear(print_kept).
% 7.94/8.14 dependent: clear(print_new_demod).
% 7.94/8.14 dependent: clear(print_back_demod).
% 7.94/8.14 dependent: clear(print_back_sub).
% 7.94/8.14 dependent: set(control_memory).
% 7.94/8.14 dependent: assign(max_mem, 12000).
% 7.94/8.14 dependent: assign(pick_given_ratio, 4).
% 7.94/8.14 dependent: assign(stats_level, 1).
% 7.94/8.14 dependent: assign(max_seconds, 10800).
% 7.94/8.14 clear(print_given).
% 7.94/8.14
% 7.94/8.14 list(usable).
% 7.94/8.14 0 [] next(e_1,e_2).
% 7.94/8.14 0 [] next(e_2,e_3).
% 7.94/8.14 0 [] next(e_3,e_4).
% 7.94/8.14 0 [] greater(e_2,e_1).
% 7.94/8.14 0 [] greater(e_3,e_1).
% 7.94/8.14 0 [] greater(e_4,e_1).
% 7.94/8.14 0 [] greater(e_3,e_2).
% 7.94/8.14 0 [] greater(e_4,e_2).
% 7.94/8.14 0 [] greater(e_4,e_3).
% 7.94/8.14 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 7.94/8.14 0 [] group_element(e_1).
% 7.94/8.14 0 [] group_element(e_2).
% 7.94/8.14 0 [] group_element(e_3).
% 7.94/8.14 0 [] group_element(e_4).
% 7.94/8.14 0 [] -e_qualish(e_1,e_2).
% 7.94/8.14 0 [] -e_qualish(e_1,e_3).
% 7.94/8.14 0 [] -e_qualish(e_1,e_4).
% 7.94/8.14 0 [] -e_qualish(e_2,e_1).
% 7.94/8.14 0 [] -e_qualish(e_2,e_3).
% 7.94/8.14 0 [] -e_qualish(e_2,e_4).
% 7.94/8.14 0 [] -e_qualish(e_3,e_1).
% 7.94/8.14 0 [] -e_qualish(e_3,e_2).
% 7.94/8.14 0 [] -e_qualish(e_3,e_4).
% 7.94/8.14 0 [] -e_qualish(e_4,e_1).
% 7.94/8.14 0 [] -e_qualish(e_4,e_2).
% 7.94/8.14 0 [] -e_qualish(e_4,e_3).
% 7.94/8.14 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).
% 7.94/8.14 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 7.94/8.14 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 7.94/8.14 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 7.94/8.14 0 [] -product(Y,X,Z1)| -product(X,Z1,Z2)|product(Z1,Y,Z2).
% 7.94/8.14 end_of_list.
% 7.94/8.14
% 7.94/8.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 7.94/8.14
% 7.94/8.14 This is a non-Horn set without equality. The strategy will
% 7.94/8.14 be ordered hyper_res, unit deletion, and factoring, with
% 7.94/8.14 satellites in sos and with nuclei in usable.
% 7.94/8.14
% 7.94/8.14 dependent: set(hyper_res).
% 7.94/8.14 dependent: set(factor).
% 7.94/8.14 dependent: set(unit_deletion).
% 7.94/8.14
% 7.94/8.14 ------------> process usable:
% 7.94/8.14 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 7.94/8.14 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 7.94/8.14 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_4).
% 7.94/8.14 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 7.94/8.14 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_4).
% 7.94/8.14 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_4).
% 7.94/8.14 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 13 [] -e_qualish(e_4,e_3).
% 7.94/8.14 ** KEPT (pick-wt=20): 14 [] -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).
% 7.94/8.14 ** KEPT (pick-wt=11): 15 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 7.94/8.14 ** KEPT (pick-wt=11): 16 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 7.94/8.14 ** KEPT (pick-wt=11): 17 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 7.94/8.14 ** KEPT (pick-wt=12): 18 [] -product(A,B,C)| -product(B,C,D)|product(C,A,D).
% 7.94/8.14
% 7.94/8.14 ------------> process sos:
% 7.94/8.14 ** KEPT (pick-wt=3): 23 [] next(e_1,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 24 [] next(e_2,e_3).
% 7.94/8.14 ** KEPT (pick-wt=3): 25 [] next(e_3,e_4).
% 7.94/8.14 ** KEPT (pick-wt=3): 26 [] greater(e_2,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 27 [] greater(e_3,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 28 [] greater(e_4,e_1).
% 7.94/8.14 ** KEPT (pick-wt=3): 29 [] greater(e_3,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 30 [] greater(e_4,e_2).
% 7.94/8.14 ** KEPT (pick-wt=3): 31 [] greater(e_4,e_3).
% 7.94/8.14 ** KEPT (pick-wt=2): 32 [] group_element(e_1).
% 7.94/8.14 ** KEPT (pick-wt=2): 33 [] group_element(e_2).
% 7.94/8.14 ** KEPT (pick-wt=2): 34 [] group_element(e_3).
% 7.94/8.14 ** KEPT (pick-wt=2): 35 [] group_element(e_4).
% 7.94/8.14
% 7.94/8.14 ======= end of input processing =======
% 7.94/8.14
% 7.94/8.14 =========== start of search ===========
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 23.
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 23.
% 7.94/8.14
% 7.94/8.14 sos_size=2532
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 20.
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 20.
% 7.94/8.14
% 7.94/8.14 sos_size=2402
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 19.
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 19.
% 7.94/8.14
% 7.94/8.14 sos_size=1206
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 16.
% 7.94/8.14
% 7.94/8.14
% 7.94/8.14 Resetting weight limit to 16.
% 7.94/8.14
% 7.94/8.14 sos_size=979
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 Resetting weight limit to 12.
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 Resetting weight limit to 12.
% 8.19/8.40
% 8.19/8.40 sos_size=575
% 8.19/8.40
% 8.19/8.40 -------- PROOF --------
% 8.19/8.40
% 8.19/8.40 ----> UNIT CONFLICT at 6.51 sec ----> 5132 [binary,5131.1,6.1] $F.
% 8.19/8.40
% 8.19/8.40 Length of proof is 74. Level of proof is 32.
% 8.19/8.40
% 8.19/8.40 ---------------- PROOF ----------------
% 8.19/8.40 % SZS status Unsatisfiable
% 8.19/8.40 % SZS output start Refutation
% See solution above
% 8.19/8.40 ------------ end of proof -------------
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 Search stopped by max_proofs option.
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 Search stopped by max_proofs option.
% 8.19/8.40
% 8.19/8.40 ============ end of search ============
% 8.19/8.40
% 8.19/8.40 -------------- statistics -------------
% 8.19/8.40 clauses given 530
% 8.19/8.40 clauses generated 122045
% 8.19/8.40 clauses kept 5131
% 8.19/8.40 clauses forward subsumed 33486
% 8.19/8.40 clauses back subsumed 4940
% 8.19/8.40 Kbytes malloced 4882
% 8.19/8.40
% 8.19/8.40 ----------- times (seconds) -----------
% 8.19/8.40 user CPU time 6.51 (0 hr, 0 min, 6 sec)
% 8.19/8.40 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 8.19/8.40 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 8.19/8.40
% 8.19/8.40 That finishes the proof of the theorem.
% 8.19/8.40
% 8.19/8.40 Process 13907 finished Wed Jul 27 05:41:59 2022
% 8.19/8.40 Otter interrupted
% 8.19/8.40 PROOF FOUND
%------------------------------------------------------------------------------