TSTP Solution File: GRP101-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:56:03 EDT 2022
% Result : Unsatisfiable 3.16s 3.38s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of clauses : 115 ( 106 unt; 0 nHn; 11 RR)
% Number of literals : 142 ( 141 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 234 ( 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))
| multiply(a4,b4) != multiply(b4,a4) ),
file('GRP101-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.4')] ).
cnf(3,axiom,
A = A,
file('GRP101-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('GRP101-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP101-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP101-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP101-1.p',unknown),
[] ).
cnf(12,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)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,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)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),9,7,12,7,7,7,7,7,7,7])])]),
[iquote('back_demod,2,demod,9,7,12,7,7,7,7,7,7,7,flip.3,flip.4')] ).
cnf(14,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1.2,11.1.1')] ).
cnf(18,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(20,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1,4.1.1')] ).
cnf(21,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity,
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1.1.2')] ).
cnf(27,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1.1.2.1')] ).
cnf(30,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),27]),
[iquote('back_demod,21,demod,27')] ).
cnf(33,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)],[14,25]),25])]),
[iquote('para_into,14.1.1.1.2,24.1.1,demod,25,flip.1')] ).
cnf(35,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,12]),33]),
[iquote('para_into,14.1.1.1.2,11.1.1,demod,33')] ).
cnf(38,plain,
double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),33,33]),
[iquote('back_demod,26,demod,33,33')] ).
cnf(40,plain,
double_divide(double_divide(double_divide(A,identity),A),identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),33]),
[iquote('back_demod,24,demod,33')] ).
cnf(42,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),33]),
[iquote('back_demod,18,demod,33')] ).
cnf(46,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)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),33]),
[iquote('back_demod,13,demod,33')] ).
cnf(49,plain,
double_divide(double_divide(double_divide(A,double_divide(B,C)),double_divide(B,identity)),double_divide(double_divide(D,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(D,identity))),
inference(para_into,[status(thm),theory(equality)],[30,30]),
[iquote('para_into,30.1.1.2.1.2,30.1.1')] ).
cnf(55,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(para_from,[status(thm),theory(equality)],[33,30]),
[iquote('para_from,32.1.1,30.1.1.2.2')] ).
cnf(63,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,40]),33,33,33])]),
[iquote('para_into,34.1.1.1.1.1,40.1.1,demod,33,33,33,flip.1')] ).
cnf(65,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),A) = identity,
inference(para_from,[status(thm),theory(equality)],[35,12]),
[iquote('para_from,34.1.1,11.1.1.2')] ).
cnf(67,plain,
double_divide(A,double_divide(double_divide(B,double_divide(double_divide(double_divide(double_divide(C,identity),identity),identity),A)),C)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(para_from,[status(thm),theory(equality)],[35,30]),
[iquote('para_from,34.1.1,30.1.1.2.2')] ).
cnf(70,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[35,30]),35]),
[iquote('para_from,34.1.1,30.1.1.2.1.2,demod,35')] ).
cnf(71,plain,
double_divide(A,double_divide(double_divide(double_divide(A,identity),identity),identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[63,35]),
[iquote('para_into,63.1.1.1,34.1.1')] ).
cnf(73,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),identity)))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,30]),70])]),
[iquote('para_from,63.1.1,30.1.1.2.1,demod,70,flip.1')] ).
cnf(80,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,35]),35]),
[iquote('para_into,38.1.1.1.2,34.1.1,demod,35')] ).
cnf(82,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[42]),80]),
[iquote('back_demod,42,demod,80')] ).
cnf(83,plain,
double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),82]),
[iquote('back_demod,73,demod,82')] ).
cnf(84,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[83])]),
[iquote('copy,83,flip.1')] ).
cnf(87,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[65,30]),35]),
[iquote('para_from,65.1.1,30.1.1.2.1.2,demod,35')] ).
cnf(90,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[71,30]),87,87,82])]),
[iquote('para_from,71.1.1,30.1.1.2.1,demod,87,87,82,flip.1')] ).
cnf(94,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[87]),90]),
[iquote('back_demod,86,demod,90')] ).
cnf(96,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[82]),90]),
[iquote('back_demod,81,demod,90')] ).
cnf(101,plain,
double_divide(A,double_divide(double_divide(B,double_divide(double_divide(double_divide(double_divide(C,identity),identity),identity),A)),C)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),96]),
[iquote('back_demod,67,demod,96')] ).
cnf(103,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[55]),96]),
[iquote('back_demod,55,demod,96')] ).
cnf(107,plain,
double_divide(double_divide(double_divide(A,double_divide(B,C)),double_divide(B,identity)),double_divide(double_divide(D,double_divide(A,identity)),double_divide(C,identity))) = double_divide(D,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),96,96]),
[iquote('back_demod,49,demod,96,96')] ).
cnf(109,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),96]),
[iquote('back_demod,30,demod,96')] ).
cnf(111,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[90]),96]),
[iquote('back_demod,89,demod,96')] ).
cnf(112,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),96]),
[iquote('back_demod,79,demod,96')] ).
cnf(116,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[111,35]),94])]),
[iquote('para_into,111.1.1,34.1.1,demod,94,flip.1')] ).
cnf(117,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[84]),116]),
[iquote('back_demod,84,demod,116')] ).
cnf(125,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(para_from,[status(thm),theory(equality)],[112,35]),
[iquote('para_from,112.1.1,34.1.1.1.1.1')] ).
cnf(128,plain,
double_divide(A,double_divide(double_divide(B,double_divide(double_divide(identity,C),A)),C)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[101]),125]),
[iquote('back_demod,101,demod,125')] ).
cnf(133,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[117,116])]),
[iquote('para_into,117.1.1,115.1.1,flip.1')] ).
cnf(134,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)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[46]),133]),
[iquote('back_demod,46,demod,133')] ).
cnf(138,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[94,112]),96]),
[iquote('para_into,93.1.1.2.1,112.1.1,demod,96')] ).
cnf(145,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[138,138]),
[iquote('para_into,137.1.1.2,137.1.1')] ).
cnf(148,plain,
double_divide(A,double_divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[138,117]),
[iquote('para_into,137.1.1.2,117.1.1')] ).
cnf(150,plain,
double_divide(double_divide(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[138,117]),
[iquote('para_into,137.1.1,117.1.1')] ).
cnf(151,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[103,138]),
[iquote('para_into,103.1.1.2.1.2,137.1.1')] ).
cnf(153,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,identity)),identity)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[103,117]),
[iquote('para_into,103.1.1.2.1.2,117.1.1')] ).
cnf(156,plain,
double_divide(double_divide(double_divide(identity,A),B),identity) = double_divide(A,double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[103,145])]),
[iquote('para_into,103.1.1.2.1,145.1.1,flip.1')] ).
cnf(157,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[103,117]),
[iquote('para_into,103.1.1.2,117.1.1')] ).
cnf(178,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[153,150])]),
[iquote('para_into,153.1.1.2.1,149.1.1,flip.1')] ).
cnf(180,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(A,double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[153,145])]),
[iquote('para_into,153.1.1.2.1,145.1.1,flip.1')] ).
cnf(181,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity)))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[153,117]),
[iquote('para_into,153.1.1.2,117.1.1')] ).
cnf(183,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,b3),double_divide(a3,identity)) != double_divide(double_divide(b3,a3),double_divide(c3,identity))
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[134]),180,178]),
[iquote('back_demod,134,demod,180,178')] ).
cnf(206,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,double_divide(double_divide(A,double_divide(C,D)),identity))),D)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[107,107]),178,138,178,150]),
[iquote('para_into,107.1.1.1.1,107.1.1,demod,178,138,178,150')] ).
cnf(216,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,A),double_divide(B,identity))) = double_divide(C,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[107,145]),150]),
[iquote('para_into,107.1.1.1,145.1.1,demod,150')] ).
cnf(248,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,A),double_divide(B,identity)),
inference(para_into,[status(thm),theory(equality)],[156,148]),
[iquote('para_into,155.1.1.1.1,147.1.1')] ).
cnf(250,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(A,B),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[248])]),
[iquote('copy,248,flip.1')] ).
cnf(252,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(identity,B),A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[156,150]),178]),
[iquote('para_from,155.1.1,149.1.1.1,demod,178')] ).
cnf(259,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_from,[status(thm),theory(equality)],[156,151]),33,178,156]),
[iquote('para_from,155.1.1,151.1.1.2.1,demod,33,178,156')] ).
cnf(261,plain,
double_divide(double_divide(identity,A),B) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[252])]),
[iquote('copy,252,flip.1')] ).
cnf(269,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(A,identity),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[252,145])]),
[iquote('para_into,252.1.1,145.1.1,flip.1')] ).
cnf(271,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(para_into,[status(thm),theory(equality)],[252,117]),
[iquote('para_into,252.1.1,117.1.1')] ).
cnf(273,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[271])]),
[iquote('copy,271,flip.1')] ).
cnf(274,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(para_from,[status(thm),theory(equality)],[252,150]),
[iquote('para_from,252.1.1,149.1.1.1')] ).
cnf(281,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(para_into,[status(thm),theory(equality)],[261,117]),
[iquote('para_into,261.1.1,117.1.1')] ).
cnf(309,plain,
double_divide(double_divide(A,double_divide(B,C)),identity) = double_divide(C,double_divide(A,double_divide(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[109,150])]),
[iquote('para_into,109.1.1.2.1,149.1.1,flip.1')] ).
cnf(331,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,double_divide(D,double_divide(A,double_divide(C,identity))))),D)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[206]),309]),
[iquote('back_demod,206,demod,309')] ).
cnf(338,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(B,identity)) = double_divide(C,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[109,148])]),
[iquote('para_from,109.1.1,147.1.1.2,flip.1')] ).
cnf(354,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(para_into,[status(thm),theory(equality)],[269,151]),
[iquote('para_into,269.1.1.2,151.1.1')] ).
cnf(357,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,B),double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[354])]),
[iquote('copy,354,flip.1')] ).
cnf(380,plain,
double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[128,274]),148])]),
[iquote('para_into,128.1.1.2.1,274.1.1,demod,148,flip.1')] ).
cnf(401,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[357]),380])]),
[iquote('back_demod,357,demod,380,flip.1')] ).
cnf(410,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[250]),401,380]),
[iquote('back_demod,250,demod,401,380')] ).
cnf(419,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,b3),double_divide(a3,identity)) != double_divide(double_divide(b3,a3),double_divide(c3,identity))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[183]),380,380])]),
[iquote('back_demod,183,demod,380,380,flip.4')] ).
cnf(465,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(para_from,[status(thm),theory(equality)],[157,148]),
[iquote('para_from,157.1.1,147.1.1.2')] ).
cnf(467,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(para_from,[status(thm),theory(equality)],[157,145]),
[iquote('para_from,157.1.1,145.1.1.1')] ).
cnf(480,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[273]),467]),
[iquote('back_demod,273,demod,467')] ).
cnf(510,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[410,281]),480,148]),
[iquote('para_into,410.1.1.2,281.1.1,demod,480,148')] ).
cnf(719,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(A,identity)),double_divide(identity,C))),
inference(para_into,[status(thm),theory(equality)],[480,259]),
[iquote('para_into,479.1.1.1,259.1.1')] ).
cnf(722,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,C))) = double_divide(double_divide(B,double_divide(A,identity)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[719])]),
[iquote('copy,719,flip.1')] ).
cnf(726,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(A,identity)),double_divide(identity,C))),
inference(para_from,[status(thm),theory(equality)],[510,480]),
[iquote('para_from,510.1.1,479.1.1.1')] ).
cnf(732,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,C))) = double_divide(double_divide(B,double_divide(identity,A)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[726])]),
[iquote('copy,726,flip.1')] ).
cnf(900,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,identity))) = double_divide(identity,double_divide(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[216,150]),380]),
[iquote('para_into,216.1.1.2.1,149.1.1,demod,380')] ).
cnf(1168,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,C)))),double_divide(C,identity)) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[338,465]),467,138]),
[iquote('para_into,338.1.1.1.2,465.1.1,demod,467,138')] ).
cnf(1173,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),C)) = double_divide(double_divide(B,double_divide(A,identity)),double_divide(C,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[338,259]),33,380]),
[iquote('para_into,338.1.1.1.2,259.1.1,demod,33,380')] ).
cnf(1174,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(identity,double_divide(double_divide(B,double_divide(C,identity)),A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[338,181]),480,138]),
[iquote('para_into,338.1.1.1.2,181.1.1,demod,480,138')] ).
cnf(1192,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(identity,double_divide(double_divide(B,double_divide(A,identity)),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1173])]),
[iquote('copy,1173,flip.1')] ).
cnf(1303,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),C)) = double_divide(A,double_divide(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[331,138]),380])]),
[iquote('para_into,331.1.1.2.1,137.1.1,demod,380,flip.1')] ).
cnf(1318,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,identity)) = double_divide(B,double_divide(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1192]),1303]),
[iquote('back_demod,1192,demod,1303')] ).
cnf(1321,plain,
double_divide(A,double_divide(B,C)) = double_divide(A,double_divide(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1174]),1318,1303]),
[iquote('back_demod,1174,demod,1318,1303')] ).
cnf(1347,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(B,double_divide(A,double_divide(identity,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[732]),1303])]),
[iquote('back_demod,732,demod,1303,flip.1')] ).
cnf(1350,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(B,double_divide(A,double_divide(identity,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[722]),1303])]),
[iquote('back_demod,722,demod,1303,flip.1')] ).
cnf(1351,plain,
double_divide(A,double_divide(B,double_divide(identity,C))) = double_divide(identity,double_divide(B,double_divide(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[719]),1350,1350,148]),
[iquote('back_demod,719,demod,1350,1350,148')] ).
cnf(1391,plain,
double_divide(A,double_divide(B,double_divide(identity,double_divide(C,A)))) = double_divide(identity,double_divide(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1168]),1347,138,1347]),
[iquote('back_demod,1168,demod,1347,138,1347')] ).
cnf(1539,plain,
double_divide(identity,double_divide(A,B)) = double_divide(C,double_divide(A,double_divide(identity,double_divide(B,C)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1391])]),
[iquote('copy,1391,flip.1')] ).
cnf(1560,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,C)))) = double_divide(A,double_divide(C,double_divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[1321,480]),
[iquote('para_into,1321.1.1.2,479.1.1')] ).
cnf(1566,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,A)) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1321,145])]),
[iquote('para_into,1321.1.1,145.1.1,flip.1')] ).
cnf(1570,plain,
double_divide(A,double_divide(B,double_divide(identity,C))) = double_divide(A,double_divide(identity,double_divide(C,double_divide(identity,B)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1560])]),
[iquote('copy,1560,flip.1')] ).
cnf(2155,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,b3),double_divide(a3,identity)) != double_divide(double_divide(b3,a3),double_divide(c3,identity))
| double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(para_into,[status(thm),theory(equality)],[419,117]),
[iquote('para_into,419.4.1.2,117.1.1')] ).
cnf(2166,plain,
double_divide(double_divide(A,B),C) = double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,C))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[900,1566]),480]),
[iquote('para_into,900.1.1.2,1566.1.1,demod,480')] ).
cnf(2176,plain,
( identity != identity
| a2 != a2
| double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(identity,double_divide(b3,double_divide(identity,double_divide(a3,c3))))
| double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2155]),2166,138,2166,138]),
[iquote('back_demod,2155,demod,2166,138,2166,138')] ).
cnf(2926,plain,
double_divide(A,double_divide(B,C)) = double_divide(D,double_divide(B,double_divide(A,double_divide(C,D)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1539,1351]),148,2166,2166,148,148,148,148]),
[iquote('para_into,1539.1.1.2,1351.1.1,demod,148,2166,2166,148,148,148,148')] ).
cnf(2943,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,A)))) = double_divide(C,double_divide(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2926])]),
[iquote('copy,2926,flip.1')] ).
cnf(3859,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(A,D)))) = double_divide(C,double_divide(B,D)),
inference(para_into,[status(thm),theory(equality)],[2943,117]),
[iquote('para_into,2943.1.1.2.2.2,117.1.1')] ).
cnf(4680,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(A,double_divide(D,double_divide(C,double_divide(E,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1570,3859]),2166,148,2166,2166,148,148,148,148,148]),
[iquote('para_into,1570.1.1.2.2,3859.1.1,demod,2166,148,2166,2166,148,148,148,148,148')] ).
cnf(4686,plain,
$false,
inference(hyper,[status(thm)],[2176,3,3,4680,3]),
[iquote('hyper,2176,3,3,4680,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n023.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 05:39:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.16/3.38 ----- Otter 3.3f, August 2004 -----
% 3.16/3.38 The process was started by sandbox2 on n023.cluster.edu,
% 3.16/3.38 Wed Jul 27 05:39:03 2022
% 3.16/3.38 The command was "./otter". The process ID is 23316.
% 3.16/3.38
% 3.16/3.38 set(prolog_style_variables).
% 3.16/3.38 set(auto).
% 3.16/3.38 dependent: set(auto1).
% 3.16/3.38 dependent: set(process_input).
% 3.16/3.38 dependent: clear(print_kept).
% 3.16/3.38 dependent: clear(print_new_demod).
% 3.16/3.38 dependent: clear(print_back_demod).
% 3.16/3.38 dependent: clear(print_back_sub).
% 3.16/3.38 dependent: set(control_memory).
% 3.16/3.38 dependent: assign(max_mem, 12000).
% 3.16/3.38 dependent: assign(pick_given_ratio, 4).
% 3.16/3.38 dependent: assign(stats_level, 1).
% 3.16/3.38 dependent: assign(max_seconds, 10800).
% 3.16/3.38 clear(print_given).
% 3.16/3.38
% 3.16/3.38 list(usable).
% 3.16/3.38 0 [] A=A.
% 3.16/3.38 0 [] double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))),double_divide(identity,identity))=Y.
% 3.16/3.38 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 3.16/3.38 0 [] inverse(X)=double_divide(X,identity).
% 3.16/3.38 0 [] identity=double_divide(X,inverse(X)).
% 3.16/3.38 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(a4,b4)!=multiply(b4,a4).
% 3.16/3.38 end_of_list.
% 3.16/3.38
% 3.16/3.38 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 3.16/3.38
% 3.16/3.38 This is a Horn set with equality. The strategy will be
% 3.16/3.38 Knuth-Bendix and hyper_res, with positive clauses in
% 3.16/3.38 sos and nonpositive clauses in usable.
% 3.16/3.38
% 3.16/3.38 dependent: set(knuth_bendix).
% 3.16/3.38 dependent: set(anl_eq).
% 3.16/3.38 dependent: set(para_from).
% 3.16/3.38 dependent: set(para_into).
% 3.16/3.38 dependent: clear(para_from_right).
% 3.16/3.38 dependent: clear(para_into_right).
% 3.16/3.38 dependent: set(para_from_vars).
% 3.16/3.38 dependent: set(eq_units_both_ways).
% 3.16/3.38 dependent: set(dynamic_demod_all).
% 3.16/3.38 dependent: set(dynamic_demod).
% 3.16/3.38 dependent: set(order_eq).
% 3.16/3.38 dependent: set(back_demod).
% 3.16/3.38 dependent: set(lrpo).
% 3.16/3.38 dependent: set(hyper_res).
% 3.16/3.38 dependent: clear(order_hyper).
% 3.16/3.38
% 3.16/3.38 ------------> process usable:
% 3.16/3.38 ** KEPT (pick-wt=29): 2 [copy,1,flip.4] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(b4,a4)!=multiply(a4,b4).
% 3.16/3.38
% 3.16/3.38 ------------> process sos:
% 3.16/3.38 ** KEPT (pick-wt=3): 3 [] A=A.
% 3.16/3.38 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 3.16/3.38 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 3.16/3.38 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 3.16/3.38 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 3.16/3.38 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 3.16/3.38 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 3.16/3.38 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 3.16/3.38 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 3.16/3.38 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 3.16/3.38 >>>> Starting back demodulation with 5.
% 3.16/3.38 >>>> Starting back demodulation with 7.
% 3.16/3.38 >> back demodulating 2 with 7.
% 3.16/3.38 >>>> Starting back demodulation with 9.
% 3.16/3.38 >>>> Starting back demodulation with 12.
% 3.16/3.38
% 3.16/3.38 ======= end of input processing =======
% 3.16/3.38
% 3.16/3.38 =========== start of search ===========
% 3.16/3.38
% 3.16/3.38
% 3.16/3.38 Resetting weight limit to 19.
% 3.16/3.38
% 3.16/3.38
% 3.16/3.38 Resetting weight limit to 19.
% 3.16/3.38
% 3.16/3.38 sos_size=1558
% 3.16/3.38
% 3.16/3.38 -------- PROOF --------
% 3.16/3.38
% 3.16/3.38 -----> EMPTY CLAUSE at 1.33 sec ----> 4686 [hyper,2176,3,3,4680,3] $F.
% 3.16/3.38
% 3.16/3.38 Length of proof is 108. Level of proof is 30.
% 3.16/3.38
% 3.16/3.38 ---------------- PROOF ----------------
% 3.16/3.38 % SZS status Unsatisfiable
% 3.16/3.38 % SZS output start Refutation
% See solution above
% 3.16/3.38 ------------ end of proof -------------
% 3.16/3.38
% 3.16/3.38
% 3.16/3.38 Search stopped by max_proofs option.
% 3.16/3.38
% 3.16/3.38
% 3.16/3.38 Search stopped by max_proofs option.
% 3.16/3.38
% 3.16/3.38 ============ end of search ============
% 3.16/3.38
% 3.16/3.38 -------------- statistics -------------
% 3.16/3.38 clauses given 326
% 3.16/3.38 clauses generated 139963
% 3.16/3.38 clauses kept 3655
% 3.16/3.38 clauses forward subsumed 77181
% 3.16/3.38 clauses back subsumed 638
% 3.16/3.38 Kbytes malloced 4882
% 3.16/3.38
% 3.16/3.38 ----------- times (seconds) -----------
% 3.16/3.38 user CPU time 1.33 (0 hr, 0 min, 1 sec)
% 3.16/3.38 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.16/3.38 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.16/3.38
% 3.16/3.38 That finishes the proof of the theorem.
% 3.16/3.38
% 3.16/3.38 Process 23316 finished Wed Jul 27 05:39:06 2022
% 3.16/3.38 Otter interrupted
% 3.16/3.38 PROOF FOUND
%------------------------------------------------------------------------------