TSTP Solution File: GRP077-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:56:00 EDT 2022
% Result : Unsatisfiable 3.14s 3.33s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of clauses : 72 ( 66 unt; 0 nHn; 10 RR)
% Number of literals : 84 ( 83 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP077-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP077-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C,
file('GRP077-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP077-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP077-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP077-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6])]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6,flip.3')] ).
cnf(14,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2.1.1.2.2,10.1.1')] ).
cnf(16,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2.1.1.2,10.1.1')] ).
cnf(21,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[16,11]),
[iquote('para_into,16.1.1.2.1,10.1.1')] ).
cnf(27,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[16,3]),14])]),
[iquote('para_from,16.1.1,3.1.1.2.1.1.2.2,demod,14,flip.1')] ).
cnf(32,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,3]),14]),
[iquote('para_from,21.1.1,3.1.1.2.1.1.2.2,demod,14')] ).
cnf(37,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,B))),A),identity)) = B,
inference(para_from,[status(thm),theory(equality)],[32,3]),
[iquote('para_from,31.1.1,3.1.1.2.1.1.2.1')] ).
cnf(40,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,B))),A),identity) = double_divide(B,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,3]),32])]),
[iquote('para_into,27.1.1.1,3.1.1,demod,32,flip.1')] ).
cnf(42,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),40]),
[iquote('back_demod,37,demod,40')] ).
cnf(43,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,32]),32,11,42]),
[iquote('para_into,13.1.1.2.1.1.2.1,31.1.1,demod,32,11,42')] ).
cnf(48,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,A))),double_divide(double_divide(A,B),identity)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[14,3]),
[iquote('para_into,13.1.1.2.1.1,3.1.1')] ).
cnf(50,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity),identity)),B),identity),identity) = double_divide(A,double_divide(double_divide(B,identity),identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,14])]),
[iquote('para_into,13.1.1.2.1,13.1.1,flip.1')] ).
cnf(53,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity),identity) = double_divide(A,double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,11])]),
[iquote('para_into,13.1.1.2.1,10.1.1,flip.1')] ).
cnf(54,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity),double_divide(B,C))),B),identity),identity) = double_divide(A,double_divide(C,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,3])]),
[iquote('para_into,13.1.1.2.1,3.1.1,flip.1')] ).
cnf(56,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])]),
[iquote('copy,43,flip.1')] ).
cnf(57,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),B),identity),identity) = double_divide(A,double_divide(double_divide(B,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[50]),53]),
[iquote('back_demod,50,demod,53')] ).
cnf(59,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(B,identity)),double_divide(double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)),B)),identity)) = identity,
inference(para_from,[status(thm),theory(equality)],[14,3]),
[iquote('para_from,13.1.1,3.1.1.2.1.1.2')] ).
cnf(61,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),C),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),identity)),B),identity),
inference(para_from,[status(thm),theory(equality)],[14,3]),
[iquote('para_from,13.1.1,3.1.1.2.1.1.2.2')] ).
cnf(62,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),double_divide(B,identity))),A),identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[61])]),
[iquote('copy,61,flip.1')] ).
cnf(64,plain,
double_divide(double_divide(double_divide(identity,A),identity),identity) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,14]),32,11])]),
[iquote('para_into,43.1.1,13.1.1,demod,32,11,flip.1')] ).
cnf(66,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,11]),32])]),
[iquote('para_into,43.1.1,10.1.1,demod,32,flip.1')] ).
cnf(67,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity),identity) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,3]),66])]),
[iquote('para_into,43.1.1,3.1.1,demod,66,flip.1')] ).
cnf(70,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[53]),64,66]),
[iquote('back_demod,52,demod,64,66')] ).
cnf(71,plain,
double_divide(double_divide(double_divide(double_divide(identity,double_divide(A,identity)),B),identity),identity) = double_divide(A,double_divide(double_divide(B,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),66]),
[iquote('back_demod,57,demod,66')] ).
cnf(73,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,A))),double_divide(double_divide(A,B),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),66]),
[iquote('back_demod,48,demod,66')] ).
cnf(76,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[42]),66]),
[iquote('back_demod,41,demod,66')] ).
cnf(78,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),66]),
[iquote('back_demod,39,demod,66')] ).
cnf(81,plain,
( identity != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),66]),
[iquote('back_demod,12,demod,66')] ).
cnf(82,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,B)),identity)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),76,70,76]),
[iquote('back_demod,59,demod,76,70,76')] ).
cnf(85,plain,
double_divide(double_divide(double_divide(A,B),identity),identity) = double_divide(A,double_divide(double_divide(B,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),76]),
[iquote('back_demod,71,demod,76')] ).
cnf(86,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(C,double_divide(double_divide(double_divide(identity,double_divide(double_divide(C,identity),double_divide(B,identity))),A),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),76]),
[iquote('back_demod,62,demod,76')] ).
cnf(87,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),C),identity)) = double_divide(double_divide(double_divide(C,identity),B),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[61]),76]),
[iquote('back_demod,61,demod,76')] ).
cnf(88,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,C))),double_divide(double_divide(B,identity),identity)) = double_divide(A,double_divide(C,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[54]),76,85]),
[iquote('back_demod,54,demod,76,85')] ).
cnf(90,plain,
double_divide(A,double_divide(double_divide(double_divide(A,identity),B),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),76]),
[iquote('back_demod,13,demod,76')] ).
cnf(93,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),78]),
[iquote('back_demod,67,demod,78')] ).
cnf(94,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,C))),B) = double_divide(A,double_divide(C,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[88]),93,93]),
[iquote('back_demod,88,demod,93,93')] ).
cnf(96,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),93]),
[iquote('back_demod,81,demod,93')] ).
cnf(101,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(para_from,[status(thm),theory(equality)],[56,11]),
[iquote('para_from,56.1.1,10.1.1.2')] ).
cnf(104,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[76,56]),
[iquote('para_into,75.1.1.2,56.1.1')] ).
cnf(105,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(A,B),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),104]),
[iquote('back_demod,73,demod,104')] ).
cnf(107,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[82,76]),76]),
[iquote('para_into,82.1.1.2.1.2,75.1.1,demod,76')] ).
cnf(112,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(para_into,[status(thm),theory(equality)],[93,56]),
[iquote('para_into,92.1.1.1,56.1.1')] ).
cnf(113,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(para_from,[status(thm),theory(equality)],[104,101]),
[iquote('para_from,103.1.1,101.1.1.2')] ).
cnf(155,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(double_divide(identity,B),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,113]),66,76,76])]),
[iquote('para_into,87.1.1.2.1.1.2.1,113.1.1,demod,66,76,76,flip.1')] ).
cnf(165,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),C),identity)) = double_divide(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,112]),155,104]),
[iquote('para_into,87.1.1.2.1.1.2.2,111.1.1,demod,155,104')] ).
cnf(167,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,107]),66,112,155]),
[iquote('para_into,87.1.1.2.1.1.2,107.1.1,demod,66,112,155')] ).
cnf(168,plain,
double_divide(A,double_divide(double_divide(B,C),identity)) = double_divide(double_divide(identity,double_divide(A,B)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,90]),76,93,155]),
[iquote('para_into,87.1.1.2.1.1.2,90.1.1,demod,76,93,155')] ).
cnf(175,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,112]),155,76,66,112]),
[iquote('para_into,87.1.1.2.1,111.1.1,demod,155,76,66,112')] ).
cnf(186,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(identity,a3),double_divide(c3,b3)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),155])]),
[iquote('back_demod,96,demod,155,flip.3')] ).
cnf(187,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),155,165]),
[iquote('back_demod,86,demod,155,165')] ).
cnf(210,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[175,175]),
[iquote('para_into,174.1.1.2,174.1.1')] ).
cnf(215,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[187,175])]),
[iquote('para_into,187.1.1,174.1.1,flip.1')] ).
cnf(242,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(double_divide(A,double_divide(identity,B)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[94,167]),104]),
[iquote('para_from,94.1.1,167.1.1.1,demod,104')] ).
cnf(244,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(para_from,[status(thm),theory(equality)],[94,93]),
[iquote('para_from,94.1.1,92.1.1.1')] ).
cnf(249,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[186]),244])]),
[iquote('back_demod,186,demod,244,flip.3')] ).
cnf(273,plain,
double_divide(double_divide(A,double_divide(identity,B)),identity) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[105,215]),175])]),
[iquote('para_into,105.1.1.2.1,215.1.1,demod,175,flip.1')] ).
cnf(278,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[105,94]),66,273]),
[iquote('para_into,105.1.1.2,94.1.1,demod,66,273')] ).
cnf(284,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[278])]),
[iquote('copy,278,flip.1')] ).
cnf(313,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,B),double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[155,210]),
[iquote('para_into,154.1.1.1.1,209.1.1')] ).
cnf(321,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(double_divide(identity,B),A),
inference(para_into,[status(thm),theory(equality)],[155,56]),
[iquote('para_into,154.1.1,56.1.1')] ).
cnf(564,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[168,56])]),
[iquote('para_into,168.1.1.2,56.1.1,flip.1')] ).
cnf(984,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(B,double_divide(identity,double_divide(double_divide(A,identity),C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[242,284]),564])]),
[iquote('para_into,242.1.1.1,284.1.1,demod,564,flip.1')] ).
cnf(1056,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(identity,C),double_divide(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[321,313]),984,210]),
[iquote('para_into,321.1.1.2.1,313.1.1,demod,984,210')] ).
cnf(1057,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,A)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1056])]),
[iquote('copy,1056,flip.1')] ).
cnf(4211,plain,
$false,
inference(hyper,[status(thm)],[1057,249,2,2]),
[iquote('hyper,1057,249,2,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:21:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.14/3.33 ----- Otter 3.3f, August 2004 -----
% 3.14/3.33 The process was started by sandbox2 on n022.cluster.edu,
% 3.14/3.33 Wed Jul 27 05:21:50 2022
% 3.14/3.33 The command was "./otter". The process ID is 24985.
% 3.14/3.33
% 3.14/3.33 set(prolog_style_variables).
% 3.14/3.33 set(auto).
% 3.14/3.33 dependent: set(auto1).
% 3.14/3.33 dependent: set(process_input).
% 3.14/3.33 dependent: clear(print_kept).
% 3.14/3.33 dependent: clear(print_new_demod).
% 3.14/3.33 dependent: clear(print_back_demod).
% 3.14/3.33 dependent: clear(print_back_sub).
% 3.14/3.33 dependent: set(control_memory).
% 3.14/3.33 dependent: assign(max_mem, 12000).
% 3.14/3.33 dependent: assign(pick_given_ratio, 4).
% 3.14/3.33 dependent: assign(stats_level, 1).
% 3.14/3.33 dependent: assign(max_seconds, 10800).
% 3.14/3.33 clear(print_given).
% 3.14/3.33
% 3.14/3.33 list(usable).
% 3.14/3.33 0 [] A=A.
% 3.14/3.33 0 [] double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity))=Z.
% 3.14/3.33 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 3.14/3.33 0 [] inverse(X)=double_divide(X,identity).
% 3.14/3.33 0 [] identity=double_divide(X,inverse(X)).
% 3.14/3.33 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 3.14/3.33 end_of_list.
% 3.14/3.33
% 3.14/3.33 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 3.14/3.33
% 3.14/3.33 This is a Horn set with equality. The strategy will be
% 3.14/3.33 Knuth-Bendix and hyper_res, with positive clauses in
% 3.14/3.33 sos and nonpositive clauses in usable.
% 3.14/3.33
% 3.14/3.33 dependent: set(knuth_bendix).
% 3.14/3.33 dependent: set(anl_eq).
% 3.14/3.33 dependent: set(para_from).
% 3.14/3.33 dependent: set(para_into).
% 3.14/3.33 dependent: clear(para_from_right).
% 3.14/3.33 dependent: clear(para_into_right).
% 3.14/3.33 dependent: set(para_from_vars).
% 3.14/3.33 dependent: set(eq_units_both_ways).
% 3.14/3.33 dependent: set(dynamic_demod_all).
% 3.14/3.33 dependent: set(dynamic_demod).
% 3.14/3.33 dependent: set(order_eq).
% 3.14/3.33 dependent: set(back_demod).
% 3.14/3.33 dependent: set(lrpo).
% 3.14/3.33 dependent: set(hyper_res).
% 3.14/3.33 dependent: clear(order_hyper).
% 3.14/3.33
% 3.14/3.33 ------------> process usable:
% 3.14/3.33 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 3.14/3.33
% 3.14/3.33 ------------> process sos:
% 3.14/3.33 ** KEPT (pick-wt=3): 2 [] A=A.
% 3.14/3.33 ** KEPT (pick-wt=17): 3 [] double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))=C.
% 3.14/3.33 ---> New Demodulator: 4 [new_demod,3] double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))=C.
% 3.14/3.33 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 3.14/3.33 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 3.14/3.33 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 3.14/3.33 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 3.14/3.33 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 3.14/3.33 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 3.14/3.33 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 3.14/3.33 >>>> Starting back demodulation with 4.
% 3.14/3.33 >>>> Starting back demodulation with 6.
% 3.14/3.33 >> back demodulating 1 with 6.
% 3.14/3.33 >>>> Starting back demodulation with 8.
% 3.14/3.33 >>>> Starting back demodulation with 11.
% 3.14/3.33
% 3.14/3.33 ======= end of input processing =======
% 3.14/3.33
% 3.14/3.33 =========== start of search ===========
% 3.14/3.33
% 3.14/3.33
% 3.14/3.33 Resetting weight limit to 17.
% 3.14/3.33
% 3.14/3.33
% 3.14/3.33 Resetting weight limit to 17.
% 3.14/3.33
% 3.14/3.33 sos_size=2476
% 3.14/3.33
% 3.14/3.33 -------- PROOF --------
% 3.14/3.33
% 3.14/3.33 -----> EMPTY CLAUSE at 1.35 sec ----> 4211 [hyper,1057,249,2,2] $F.
% 3.14/3.33
% 3.14/3.33 Length of proof is 65. Level of proof is 21.
% 3.14/3.33
% 3.14/3.33 ---------------- PROOF ----------------
% 3.14/3.33 % SZS status Unsatisfiable
% 3.14/3.33 % SZS output start Refutation
% See solution above
% 3.14/3.33 ------------ end of proof -------------
% 3.14/3.33
% 3.14/3.33
% 3.14/3.33 Search stopped by max_proofs option.
% 3.14/3.33
% 3.14/3.33
% 3.14/3.33 Search stopped by max_proofs option.
% 3.14/3.33
% 3.14/3.33 ============ end of search ============
% 3.14/3.33
% 3.14/3.33 -------------- statistics -------------
% 3.14/3.33 clauses given 322
% 3.14/3.33 clauses generated 156790
% 3.14/3.33 clauses kept 3633
% 3.14/3.33 clauses forward subsumed 110917
% 3.14/3.33 clauses back subsumed 156
% 3.14/3.33 Kbytes malloced 4882
% 3.14/3.33
% 3.14/3.33 ----------- times (seconds) -----------
% 3.14/3.33 user CPU time 1.35 (0 hr, 0 min, 1 sec)
% 3.14/3.33 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.14/3.33 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.14/3.33
% 3.14/3.33 That finishes the proof of the theorem.
% 3.14/3.33
% 3.14/3.33 Process 24985 finished Wed Jul 27 05:21:53 2022
% 3.14/3.33 Otter interrupted
% 3.14/3.33 PROOF FOUND
%------------------------------------------------------------------------------