TSTP Solution File: GRP102-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP102-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:56:03 EDT 2022
% Result : Unsatisfiable 2.24s 2.46s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of clauses : 97 ( 88 unt; 0 nHn; 13 RR)
% Number of literals : 124 ( 123 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 : 191 ( 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('GRP102-1.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('GRP102-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
file('GRP102-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP102-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP102-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP102-1.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(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1.1,11.1.1')] ).
cnf(18,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(21,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),C),double_divide(A,identity)) = double_divide(double_divide(B,C),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4])]),
[iquote('para_into,4.1.1.1.2,4.1.1,flip.1')] ).
cnf(26,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[14,12]),
[iquote('para_into,14.1.1.1.2,11.1.1')] ).
cnf(34,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(para_into,[status(thm),theory(equality)],[26,12]),
[iquote('para_into,26.1.1.1.1.1,11.1.1')] ).
cnf(38,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B,
inference(para_from,[status(thm),theory(equality)],[26,4]),
[iquote('para_from,26.1.1,4.1.1.1.2.1.1')] ).
cnf(41,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[34,4]),12]),
[iquote('para_from,34.1.1,4.1.1.1.2.1,demod,12')] ).
cnf(45,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[41,14]),41,41]),
[iquote('para_from,40.1.1,14.1.1.1.2,demod,41,41')] ).
cnf(48,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),45,45]),
[iquote('back_demod,38,demod,45,45')] ).
cnf(59,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),45]),
[iquote('back_demod,26,demod,45')] ).
cnf(63,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),C),double_divide(A,identity)) = double_divide(double_divide(B,C),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),45]),
[iquote('back_demod,21,demod,45')] ).
cnf(67,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),45]),
[iquote('back_demod,18,demod,45')] ).
cnf(72,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]),45]),
[iquote('back_demod,13,demod,45')] ).
cnf(73,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),identity) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),45]),
[iquote('back_demod,4,demod,45')] ).
cnf(75,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),59]),
[iquote('back_demod,48,demod,59')] ).
cnf(81,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[75,12]),
[iquote('para_into,75.1.1.1.2.1,11.1.1')] ).
cnf(83,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[75,75]),
[iquote('para_into,75.1.1.1.2,75.1.1')] ).
cnf(85,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B),
inference(para_from,[status(thm),theory(equality)],[75,59]),
[iquote('para_from,75.1.1,58.1.1.1.1')] ).
cnf(86,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity,
inference(para_from,[status(thm),theory(equality)],[75,12]),
[iquote('para_from,75.1.1,11.1.1.2')] ).
cnf(88,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[85])]),
[iquote('copy,85,flip.1')] ).
cnf(96,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(para_from,[status(thm),theory(equality)],[81,59]),
[iquote('para_from,81.1.1,58.1.1.1.1')] ).
cnf(102,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),96]),
[iquote('back_demod,58,demod,96')] ).
cnf(109,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)],[83,45]),45])]),
[iquote('para_into,83.1.1.1,44.1.1,demod,45,flip.1')] ).
cnf(112,plain,
double_divide(double_divide(A,double_divide(double_divide(B,C),B)),A) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[83,75])]),
[iquote('para_into,83.1.1,75.1.1,flip.1')] ).
cnf(139,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,109])]),
[iquote('para_into,88.1.1.1,109.1.1,flip.1')] ).
cnf(142,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,88]),139,139]),
[iquote('para_into,88.1.1.1,88.1.1,demod,139,139')] ).
cnf(144,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,86]),102,139]),
[iquote('para_into,88.1.1.1,86.1.1,demod,102,139')] ).
cnf(156,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),139,144,139,102]),
[iquote('back_demod,95,demod,139,144,139,102')] ).
cnf(157,plain,
( identity != identity
| double_divide(identity,double_divide(a2,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)],[72]),139]),
[iquote('back_demod,72,demod,139')] ).
cnf(160,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(identity,double_divide(B,identity)),double_divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[142])]),
[iquote('copy,142,flip.1')] ).
cnf(164,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[112]),144,144,144,139,102]),
[iquote('back_demod,112,demod,144,144,144,139,102')] ).
cnf(165,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),144,164]),
[iquote('back_demod,86,demod,144,164')] ).
cnf(172,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[160])]),164,164]),
[iquote('copy,160,flip.1,demod,164,164')] ).
cnf(175,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)],[157]),172]),
[iquote('back_demod,157,demod,172')] ).
cnf(181,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[144]),172]),
[iquote('back_demod,143,demod,172')] ).
cnf(182,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),172]),
[iquote('back_demod,67,demod,172')] ).
cnf(195,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[165,63]),102]),
[iquote('para_from,165.1.1,63.1.1.1.1,demod,102')] ).
cnf(196,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)],[195])]),
[iquote('copy,195,flip.1')] ).
cnf(199,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(para_into,[status(thm),theory(equality)],[172,12]),
[iquote('para_into,171.1.1.2,11.1.1')] ).
cnf(205,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)) = double_divide(double_divide(double_divide(B,identity),C),identity),
inference(para_from,[status(thm),theory(equality)],[172,63]),
[iquote('para_from,171.1.1,63.1.1.1.1.2')] ).
cnf(206,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(double_divide(double_divide(C,A),B),double_divide(C,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[205])]),
[iquote('copy,205,flip.1')] ).
cnf(210,plain,
double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,C),A),identity)) = double_divide(double_divide(C,B),identity),
inference(para_from,[status(thm),theory(equality)],[181,63]),
[iquote('para_from,180.1.1,63.1.1.1.1')] ).
cnf(214,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(C,B),double_divide(double_divide(double_divide(identity,A),C),identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[210])]),
[iquote('copy,210,flip.1')] ).
cnf(267,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[182,182]),199,181]),
[iquote('para_into,182.1.1.1,182.1.1,demod,199,181')] ).
cnf(275,plain,
double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[182,156])]),
[iquote('para_into,182.1.1,156.1.1,flip.1')] ).
cnf(312,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(A,double_divide(identity,C)))) = double_divide(identity,double_divide(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[214]),275,275])]),
[iquote('back_demod,214,demod,275,275,flip.1')] ).
cnf(321,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)) = double_divide(identity,double_divide(C,double_divide(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[206]),275])]),
[iquote('back_demod,206,demod,275,flip.1')] ).
cnf(326,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)],[196]),275])]),
[iquote('back_demod,196,demod,275,flip.1')] ).
cnf(336,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)],[182]),275,275]),
[iquote('back_demod,182,demod,275,275')] ).
cnf(341,plain,
( identity != identity
| a2 != a2
| double_divide(identity,double_divide(double_divide(identity,double_divide(a3,b3)),c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3))))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[175]),275,275,275,275,275,275])])]),
[iquote('back_demod,175,demod,275,275,275,275,275,275,flip.3,flip.4')] ).
cnf(344,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),321,275]),
[iquote('back_demod,73,demod,321,275')] ).
cnf(353,plain,
double_divide(A,double_divide(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[267,181])]),
[iquote('para_into,267.1.1,180.1.1,flip.1')] ).
cnf(354,plain,
double_divide(double_divide(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[267,172])]),
[iquote('para_into,267.1.1,171.1.1,flip.1')] ).
cnf(356,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(B,A))) = identity,
inference(para_from,[status(thm),theory(equality)],[275,353]),
[iquote('para_from,274.1.1,352.1.1.2')] ).
cnf(406,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(double_divide(identity,A),B)),
inference(para_into,[status(thm),theory(equality)],[326,353]),
[iquote('para_into,326.1.1.1,352.1.1')] ).
cnf(416,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[326,181]),
[iquote('para_into,326.1.1.2,180.1.1')] ).
cnf(418,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[406])]),416,353]),
[iquote('copy,406,flip.1,demod,416,353')] ).
cnf(429,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[406]),416,353]),
[iquote('back_demod,406,demod,416,353')] ).
cnf(434,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[344]),416,353]),
[iquote('back_demod,344,demod,416,353')] ).
cnf(436,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3))))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[341]),416,353]),
[iquote('back_demod,341,demod,416,353')] ).
cnf(446,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,double_divide(identity,A))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[418,356]),416,353]),
[iquote('para_from,418.1.1,356.1.1.1,demod,416,353')] ).
cnf(448,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_from,[status(thm),theory(equality)],[418,336]),416,353]),
[iquote('para_from,418.1.1,336.1.1.2,demod,416,353')] ).
cnf(450,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[418,275]),275,416,353]),
[iquote('para_from,418.1.1,274.1.1.1,demod,275,416,353')] ).
cnf(469,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[429,336]),450]),
[iquote('para_from,429.1.1,336.1.1.2,demod,450')] ).
cnf(475,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,C))),double_divide(identity,double_divide(C,B))) = A,
inference(para_into,[status(thm),theory(equality)],[434,275]),
[iquote('para_into,434.1.1.1.2,274.1.1')] ).
cnf(538,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[416,172]),
[iquote('para_from,415.1.1,171.1.1.2')] ).
cnf(714,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,C))),
inference(para_from,[status(thm),theory(equality)],[469,416]),
[iquote('para_from,469.1.1,415.1.1.1')] ).
cnf(723,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,C))) = double_divide(double_divide(B,double_divide(identity,A)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[714])]),
[iquote('copy,714,flip.1')] ).
cnf(824,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,C)) = double_divide(identity,double_divide(A,double_divide(B,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,538]),416,353,416,353])]),
[iquote('para_into,312.1.1.1,538.1.1,demod,416,353,416,353,flip.1')] ).
cnf(829,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,B)),C)) = double_divide(identity,double_divide(B,double_divide(A,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,469]),353,824])]),
[iquote('para_into,312.1.1.1,469.1.1,demod,353,824,flip.1')] ).
cnf(831,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),C)) = double_divide(identity,double_divide(B,double_divide(A,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,448]),353,824])]),
[iquote('para_into,312.1.1.1,448.1.1,demod,353,824,flip.1')] ).
cnf(832,plain,
double_divide(A,double_divide(B,C)) = double_divide(identity,double_divide(B,double_divide(A,double_divide(identity,C)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,446]),831,353,353,829]),
[iquote('para_into,312.1.1.1,446.1.1,demod,831,353,353,829')] ).
cnf(841,plain,
double_divide(identity,double_divide(double_divide(A,B),C)) = double_divide(B,double_divide(identity,double_divide(A,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,353])]),
[iquote('para_into,312.1.1.1,352.1.1,flip.1')] ).
cnf(872,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)],[723]),824,353])]),
[iquote('back_demod,723,demod,824,353,flip.1')] ).
cnf(894,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[475]),872,353]),
[iquote('back_demod,475,demod,872,353')] ).
cnf(999,plain,
double_divide(double_divide(A,B),C) = double_divide(C,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[894,354]),
[iquote('para_into,894.1.1.2,354.1.1')] ).
cnf(1000,plain,
double_divide(double_divide(A,B),double_divide(double_divide(B,A),C)) = C,
inference(para_into,[status(thm),theory(equality)],[894,267]),
[iquote('para_into,894.1.1.2,267.1.1')] ).
cnf(1002,plain,
double_divide(double_divide(A,B),C) = double_divide(double_divide(B,A),C),
inference(para_into,[status(thm),theory(equality)],[894,181]),
[iquote('para_into,894.1.1.2,180.1.1')] ).
cnf(1005,plain,
double_divide(A,double_divide(B,C)) = double_divide(double_divide(C,B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[999])]),
[iquote('copy,999,flip.1')] ).
cnf(1006,plain,
double_divide(A,double_divide(B,C)) = double_divide(A,double_divide(C,B)),
inference(para_from,[status(thm),theory(equality)],[894,181]),
[iquote('para_from,894.1.1,180.1.1.1')] ).
cnf(1042,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(C,D))) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(A,double_divide(C,D))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[321,1000]),275,275]),
[iquote('para_into,320.1.1.1.1,1000.1.1,demod,275,275')] ).
cnf(1047,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(A,C)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[321,353]),275]),
[iquote('para_into,320.1.1.1.1,352.1.1,demod,275')] ).
cnf(1089,plain,
double_divide(double_divide(double_divide(A,B),C),D) = double_divide(double_divide(double_divide(B,A),C),D),
inference(para_from,[status(thm),theory(equality)],[1005,1002]),
[iquote('para_from,1005.1.1,1002.1.1.1')] ).
cnf(1106,plain,
( identity != identity
| a2 != a2
| double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(b3,double_divide(identity,double_divide(a3,c3))))
| 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(para_into,[status(thm),theory(equality)],[436,267]),1047])]),
[iquote('para_into,436.3.1.2,267.1.1,demod,1047,flip.3')] ).
cnf(1203,plain,
double_divide(double_divide(double_divide(A,B),C),D) = double_divide(B,double_divide(C,double_divide(A,D))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[832,1002]),416,841,353,1042,1042,353,353])]),
[iquote('para_from,832.1.1,1002.1.1.1,demod,416,841,353,1042,1042,353,353,flip.1')] ).
cnf(1221,plain,
double_divide(A,double_divide(B,double_divide(C,D))) = double_divide(C,double_divide(B,double_divide(A,D))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1089]),1203,1203]),
[iquote('back_demod,1089,demod,1203,1203')] ).
cnf(1868,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(C,double_divide(D,double_divide(A,double_divide(B,E)))),
inference(para_into,[status(thm),theory(equality)],[1221,1221]),
[iquote('para_into,1221.1.1.2,1221.1.1')] ).
cnf(4010,plain,
$false,
inference(hyper,[status(thm)],[1868,1106,3,3,1006]),
[iquote('hyper,1868,1106,3,3,1006')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP102-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.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 05:26:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.24/2.46 ----- Otter 3.3f, August 2004 -----
% 2.24/2.46 The process was started by sandbox2 on n020.cluster.edu,
% 2.24/2.46 Wed Jul 27 05:26:08 2022
% 2.24/2.46 The command was "./otter". The process ID is 23401.
% 2.24/2.46
% 2.24/2.46 set(prolog_style_variables).
% 2.24/2.46 set(auto).
% 2.24/2.46 dependent: set(auto1).
% 2.24/2.46 dependent: set(process_input).
% 2.24/2.46 dependent: clear(print_kept).
% 2.24/2.46 dependent: clear(print_new_demod).
% 2.24/2.46 dependent: clear(print_back_demod).
% 2.24/2.46 dependent: clear(print_back_sub).
% 2.24/2.46 dependent: set(control_memory).
% 2.24/2.46 dependent: assign(max_mem, 12000).
% 2.24/2.46 dependent: assign(pick_given_ratio, 4).
% 2.24/2.46 dependent: assign(stats_level, 1).
% 2.24/2.46 dependent: assign(max_seconds, 10800).
% 2.24/2.46 clear(print_given).
% 2.24/2.46
% 2.24/2.46 list(usable).
% 2.24/2.46 0 [] A=A.
% 2.24/2.46 0 [] double_divide(double_divide(X,double_divide(double_divide(double_divide(Y,X),Z),double_divide(Y,identity))),double_divide(identity,identity))=Z.
% 2.24/2.46 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 2.24/2.46 0 [] inverse(X)=double_divide(X,identity).
% 2.24/2.46 0 [] identity=double_divide(X,inverse(X)).
% 2.24/2.46 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).
% 2.24/2.46 end_of_list.
% 2.24/2.46
% 2.24/2.46 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.24/2.46
% 2.24/2.46 This is a Horn set with equality. The strategy will be
% 2.24/2.46 Knuth-Bendix and hyper_res, with positive clauses in
% 2.24/2.46 sos and nonpositive clauses in usable.
% 2.24/2.46
% 2.24/2.46 dependent: set(knuth_bendix).
% 2.24/2.46 dependent: set(anl_eq).
% 2.24/2.46 dependent: set(para_from).
% 2.24/2.46 dependent: set(para_into).
% 2.24/2.46 dependent: clear(para_from_right).
% 2.24/2.46 dependent: clear(para_into_right).
% 2.24/2.46 dependent: set(para_from_vars).
% 2.24/2.46 dependent: set(eq_units_both_ways).
% 2.24/2.46 dependent: set(dynamic_demod_all).
% 2.24/2.46 dependent: set(dynamic_demod).
% 2.24/2.46 dependent: set(order_eq).
% 2.24/2.46 dependent: set(back_demod).
% 2.24/2.46 dependent: set(lrpo).
% 2.24/2.46 dependent: set(hyper_res).
% 2.24/2.46 dependent: clear(order_hyper).
% 2.24/2.46
% 2.24/2.46 ------------> process usable:
% 2.24/2.46 ** 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).
% 2.24/2.46
% 2.24/2.46 ------------> process sos:
% 2.24/2.46 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.24/2.46 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 2.24/2.46 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 2.24/2.46 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.24/2.46 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.24/2.46 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 2.24/2.46 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 2.24/2.46 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.24/2.46 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 2.24/2.46 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.24/2.46 >>>> Starting back demodulation with 5.
% 2.24/2.46 >>>> Starting back demodulation with 7.
% 2.24/2.46 >> back demodulating 2 with 7.
% 2.24/2.46 >>>> Starting back demodulation with 9.
% 2.24/2.46 >>>> Starting back demodulation with 12.
% 2.24/2.46
% 2.24/2.46 ======= end of input processing =======
% 2.24/2.46
% 2.24/2.46 =========== start of search ===========
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Resetting weight limit to 19.
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Resetting weight limit to 19.
% 2.24/2.46
% 2.24/2.46 sos_size=2026
% 2.24/2.46
% 2.24/2.46 -------- PROOF --------
% 2.24/2.46
% 2.24/2.46 -----> EMPTY CLAUSE at 0.44 sec ----> 4010 [hyper,1868,1106,3,3,1006] $F.
% 2.24/2.46
% 2.24/2.46 Length of proof is 90. Level of proof is 30.
% 2.24/2.46
% 2.24/2.46 ---------------- PROOF ----------------
% 2.24/2.46 % SZS status Unsatisfiable
% 2.24/2.46 % SZS output start Refutation
% See solution above
% 2.24/2.46 ------------ end of proof -------------
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Search stopped by max_proofs option.
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Search stopped by max_proofs option.
% 2.24/2.46
% 2.24/2.46 ============ end of search ============
% 2.24/2.46
% 2.24/2.46 -------------- statistics -------------
% 2.24/2.46 clauses given 204
% 2.24/2.46 clauses generated 37789
% 2.24/2.46 clauses kept 3348
% 2.24/2.46 clauses forward subsumed 30743
% 2.24/2.46 clauses back subsumed 441
% 2.24/2.46 Kbytes malloced 4882
% 2.24/2.46
% 2.24/2.46 ----------- times (seconds) -----------
% 2.24/2.46 user CPU time 0.44 (0 hr, 0 min, 0 sec)
% 2.24/2.46 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.24/2.46 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.24/2.46
% 2.24/2.46 That finishes the proof of the theorem.
% 2.24/2.46
% 2.24/2.46 Process 23401 finished Wed Jul 27 05:26:10 2022
% 2.24/2.46 Otter interrupted
% 2.24/2.46 PROOF FOUND
%------------------------------------------------------------------------------