TSTP Solution File: GRP201-1 by EQP---0.9e
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : GRP201-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %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 : 600s
% DateTime : Sat Jul 16 08:45:55 EDT 2022
% Result : Unsatisfiable 2.48s 2.85s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of clauses : 197 ( 197 unt; 0 nHn; 8 RR)
% Number of literals : 197 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 418 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(multiply(identity,A),A),
file('GRP201-1.p',unknown),
[] ).
cnf(2,plain,
equal(multiply(A,identity),A),
file('GRP201-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(A,left_division(A,B)),B),
file('GRP201-1.p',unknown),
[] ).
cnf(4,plain,
equal(left_division(A,multiply(A,B)),B),
file('GRP201-1.p',unknown),
[] ).
cnf(5,plain,
equal(multiply(right_division(A,B),B),A),
file('GRP201-1.p',unknown),
[] ).
cnf(6,plain,
equal(right_division(multiply(A,B),B),A),
file('GRP201-1.p',unknown),
[] ).
cnf(9,plain,
equal(multiply(multiply(multiply(A,B),C),B),multiply(A,multiply(B,multiply(C,B)))),
file('GRP201-1.p',unknown),
[] ).
cnf(10,plain,
~ equal(multiply(multiply(multiply(a,b),a),c),multiply(a,multiply(b,multiply(a,c)))),
file('GRP201-1.p',unknown),
[] ).
cnf(12,plain,
equal(left_division(identity,A),A),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,1]),1]),
[iquote('para(3,1),flip(1)')] ).
cnf(14,plain,
equal(left_division(A,A),identity),
inference(para,[status(thm),theory(equality)],[2,4]),
[iquote('para(2,4)')] ).
cnf(16,plain,
equal(left_division(right_division(A,B),A),B),
inference(para,[status(thm),theory(equality)],[5,4]),
[iquote('para(5,4)')] ).
cnf(17,plain,
equal(right_division(A,A),identity),
inference(para,[status(thm),theory(equality)],[1,6]),
[iquote('para(1,6)')] ).
cnf(18,plain,
equal(right_division(A,left_division(B,A)),B),
inference(para,[status(thm),theory(equality)],[3,6]),
[iquote('para(3,6)')] ).
cnf(22,plain,
equal(multiply(multiply(A,B),A),multiply(A,multiply(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,9]),1]),
[iquote('para(1,9),demod([1])')] ).
cnf(23,plain,
~ equal(multiply(multiply(a,multiply(b,a)),c),multiply(a,multiply(b,multiply(a,c)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[10]),22]),
[iquote('back_demod(10),demod([22])')] ).
cnf(24,plain,
equal(multiply(multiply(A,B),B),multiply(A,multiply(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,9]),1]),
[iquote('para(2,9),demod([1])')] ).
cnf(25,plain,
equal(multiply(multiply(A,B),left_division(C,A)),multiply(C,multiply(left_division(C,A),multiply(B,left_division(C,A))))),
inference(para,[status(thm),theory(equality)],[3,9]),
[iquote('para(3,9)')] ).
cnf(26,plain,
equal(multiply(A,multiply(left_division(A,B),multiply(C,left_division(A,B)))),multiply(multiply(B,C),left_division(A,B))),
inference(flip,[status(thm),theory(equality)],[25]),
[iquote('flip(25)')] ).
cnf(28,plain,
equal(left_division(multiply(multiply(A,B),C),multiply(A,multiply(B,multiply(C,B)))),B),
inference(para,[status(thm),theory(equality)],[9,4]),
[iquote('para(9,4)')] ).
cnf(29,plain,
equal(multiply(multiply(A,B),C),multiply(right_division(A,C),multiply(C,multiply(B,C)))),
inference(para,[status(thm),theory(equality)],[5,9]),
[iquote('para(5,9)')] ).
cnf(30,plain,
equal(multiply(right_division(A,B),multiply(B,multiply(C,B))),multiply(multiply(A,C),B)),
inference(flip,[status(thm),theory(equality)],[29]),
[iquote('flip(29)')] ).
cnf(34,plain,
equal(multiply(A,multiply(left_division(A,B),A)),multiply(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,22]),1]),
[iquote('para(3,22),flip(1)')] ).
cnf(35,plain,
equal(left_division(multiply(A,B),multiply(A,multiply(B,A))),A),
inference(para,[status(thm),theory(equality)],[22,4]),
[iquote('para(22,4)')] ).
cnf(37,plain,
equal(right_division(multiply(A,multiply(B,A)),A),multiply(A,B)),
inference(para,[status(thm),theory(equality)],[22,6]),
[iquote('para(22,6)')] ).
cnf(44,plain,
equal(right_division(multiply(A,multiply(B,B)),B),multiply(A,B)),
inference(para,[status(thm),theory(equality)],[24,6]),
[iquote('para(24,6)')] ).
cnf(45,plain,
equal(multiply(left_division(A,B),A),left_division(A,multiply(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[34,4]),1]),
[iquote('para(34,4),flip(1)')] ).
cnf(47,plain,
equal(left_division(multiply(A,right_division(B,A)),multiply(A,B)),A),
inference(para,[status(thm),theory(equality)],[5,35]),
[iquote('para(5,35)')] ).
cnf(50,plain,
equal(right_division(multiply(A,B),A),multiply(A,right_division(B,A))),
inference(para,[status(thm),theory(equality)],[5,37]),
[iquote('para(5,37)')] ).
cnf(51,plain,
equal(multiply(A,right_division(identity,A)),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,50]),17]),1]),
[iquote('para(2,50),demod([17]),flip(1)')] ).
cnf(55,plain,
equal(right_division(identity,A),left_division(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[51,4]),1]),
[iquote('para(51,4),flip(1)')] ).
cnf(63,plain,
equal(left_division(left_division(A,identity),identity),A),
inference(para,[status(thm),theory(equality)],[55,18]),
[iquote('para(55,18)')] ).
cnf(71,plain,
equal(multiply(A,multiply(left_division(A,B),multiply(left_division(A,B),left_division(A,B)))),multiply(B,multiply(left_division(A,B),left_division(A,B)))),
inference(para,[status(thm),theory(equality)],[25,24]),
[iquote('para(25,24)')] ).
cnf(74,plain,
equal(multiply(right_division(A,multiply(B,B)),B),right_division(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,44]),1]),
[iquote('para(5,44),flip(1)')] ).
cnf(77,plain,
equal(left_division(left_division(A,B),left_division(A,multiply(B,A))),A),
inference(para,[status(thm),theory(equality)],[45,4]),
[iquote('para(45,4)')] ).
cnf(81,plain,
equal(multiply(multiply(A,right_division(B,left_division(C,A))),left_division(C,A)),multiply(C,multiply(left_division(C,A),B))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,26]),1]),
[iquote('para(5,26),flip(1)')] ).
cnf(82,plain,
equal(right_division(left_division(A,multiply(B,A)),A),left_division(A,B)),
inference(para,[status(thm),theory(equality)],[45,6]),
[iquote('para(45,6)')] ).
cnf(96,plain,
equal(left_division(right_division(A,multiply(B,B)),right_division(A,B)),B),
inference(para,[status(thm),theory(equality)],[74,4]),
[iquote('para(74,4)')] ).
cnf(103,plain,
equal(right_division(right_division(A,B),B),right_division(A,multiply(B,B))),
inference(para,[status(thm),theory(equality)],[74,6]),
[iquote('para(74,6)')] ).
cnf(105,plain,
equal(right_division(A,multiply(A,A)),left_division(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[17,103]),55]),1]),
[iquote('para(17,103),demod([55]),flip(1)')] ).
cnf(107,plain,
equal(multiply(left_division(A,identity),multiply(A,A)),A),
inference(para,[status(thm),theory(equality)],[105,5]),
[iquote('para(105,5)')] ).
cnf(112,plain,
equal(multiply(A,A),left_division(left_division(A,identity),A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[107,4]),1]),
[iquote('para(107,4),flip(1)')] ).
cnf(113,plain,
equal(right_division(right_division(A,B),B),right_division(A,left_division(left_division(B,identity),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[103]),112]),
[iquote('back_demod(103),demod([112])')] ).
cnf(115,plain,
equal(left_division(right_division(A,left_division(left_division(B,identity),B)),right_division(A,B)),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[96]),112]),
[iquote('back_demod(96),demod([112])')] ).
cnf(116,plain,
equal(multiply(right_division(A,left_division(left_division(B,identity),B)),B),right_division(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[74]),112]),
[iquote('back_demod(74),demod([112])')] ).
cnf(119,plain,
equal(multiply(A,multiply(left_division(A,B),left_division(left_division(left_division(A,B),identity),left_division(A,B)))),multiply(B,left_division(left_division(left_division(A,B),identity),left_division(A,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[71]),112,112]),
[iquote('back_demod(71),demod([112,112])')] ).
cnf(135,plain,
equal(multiply(left_division(A,identity),multiply(A,multiply(B,A))),multiply(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,29]),55]),1]),
[iquote('para(1,29),demod([55]),flip(1)')] ).
cnf(136,plain,
equal(multiply(right_division(A,B),left_division(left_division(B,identity),B)),multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,29]),1,112]),1]),
[iquote('para(2,29),demod([1,112]),flip(1)')] ).
cnf(139,plain,
equal(multiply(right_division(A,B),multiply(B,multiply(left_division(A,C),B))),multiply(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,29]),1]),
[iquote('para(3,29),flip(1)')] ).
cnf(140,plain,
equal(left_division(left_division(A,right_division(B,A)),left_division(A,B)),A),
inference(para,[status(thm),theory(equality)],[5,77]),
[iquote('para(5,77)')] ).
cnf(145,plain,
equal(right_division(left_division(A,B),A),left_division(A,right_division(B,A))),
inference(para,[status(thm),theory(equality)],[5,82]),
[iquote('para(5,82)')] ).
cnf(152,plain,
~ equal(multiply(right_division(a,c),multiply(c,multiply(multiply(b,a),c))),multiply(a,multiply(b,multiply(a,c)))),
inference(para,[status(thm),theory(equality)],[29,23]),
[iquote('para(29,23)')] ).
cnf(168,plain,
equal(multiply(right_division(A,left_division(B,C)),multiply(left_division(B,C),C)),multiply(multiply(A,B),left_division(B,C))),
inference(para,[status(thm),theory(equality)],[3,30]),
[iquote('para(3,30)')] ).
cnf(187,plain,
equal(multiply(left_division(left_division(A,identity),A),A),multiply(A,left_division(left_division(A,identity),A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[112,22]),112]),
[iquote('para(112,22),demod([112])')] ).
cnf(201,plain,
equal(right_division(multiply(A,B),left_division(left_division(B,identity),B)),right_division(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[6,113]),1]),
[iquote('para(6,113),flip(1)')] ).
cnf(208,plain,
equal(left_division(left_division(left_division(A,identity),A),identity),left_division(A,left_division(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[55,113]),145,55,55]),1]),
[iquote('para(55,113),demod([145,55,55]),flip(1)')] ).
cnf(216,plain,
equal(left_division(right_division(A,left_division(left_division(left_division(B,A),identity),left_division(B,A))),B),left_division(B,A)),
inference(para,[status(thm),theory(equality)],[18,115]),
[iquote('para(18,115)')] ).
cnf(217,plain,
equal(left_division(left_division(A,left_division(A,identity)),left_division(A,identity)),A),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[55,115]),55,208]),
[iquote('para(55,115),demod([55,208])')] ).
cnf(219,plain,
equal(multiply(right_division(A,left_division(B,left_division(B,identity))),left_division(B,identity)),right_division(A,left_division(B,identity))),
inference(para,[status(thm),theory(equality)],[63,116]),
[iquote('para(63,116)')] ).
cnf(244,plain,
equal(multiply(left_division(left_division(A,B),identity),multiply(left_division(A,B),B)),B),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,135]),3]),
[iquote('para(3,135),demod([3])')] ).
cnf(251,plain,
equal(multiply(A,multiply(B,A)),left_division(left_division(A,identity),multiply(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[135,4]),1]),
[iquote('para(135,4),flip(1)')] ).
cnf(328,plain,
~ equal(multiply(right_division(a,c),left_division(left_division(c,identity),multiply(multiply(b,a),c))),multiply(a,multiply(b,multiply(a,c)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[152]),251]),
[iquote('back_demod(152),demod([251])')] ).
cnf(334,plain,
equal(multiply(right_division(A,B),left_division(left_division(B,identity),multiply(left_division(A,C),B))),multiply(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[139]),251]),
[iquote('back_demod(139),demod([251])')] ).
cnf(378,plain,
equal(multiply(right_division(A,B),left_division(left_division(B,identity),multiply(C,B))),multiply(multiply(A,C),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[30]),251]),
[iquote('back_demod(30),demod([251])')] ).
cnf(379,plain,
equal(multiply(multiply(A,B),C),multiply(right_division(A,C),left_division(left_division(C,identity),multiply(B,C)))),
inference(flip,[status(thm),theory(equality)],[378]),
[iquote('flip(378)')] ).
cnf(380,plain,
equal(left_division(multiply(multiply(A,B),C),multiply(A,left_division(left_division(B,identity),multiply(C,B)))),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[28]),251]),
[iquote('back_demod(28),demod([251])')] ).
cnf(389,plain,
equal(left_division(right_division(A,B),multiply(A,B)),left_division(left_division(B,identity),B)),
inference(para,[status(thm),theory(equality)],[136,4]),
[iquote('para(136,4)')] ).
cnf(396,plain,
equal(multiply(left_division(A,B),B),left_division(left_division(left_division(A,B),identity),B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[244,4]),1]),
[iquote('para(244,4),flip(1)')] ).
cnf(402,plain,
equal(multiply(A,left_division(left_division(A,identity),A)),left_division(left_division(A,left_division(A,identity)),A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[187]),396,208]),1]),
[iquote('back_demod(187),demod([396,208]),flip(1)')] ).
cnf(406,plain,
equal(multiply(A,left_division(left_division(left_division(A,B),left_division(left_division(A,B),identity)),left_division(A,B))),multiply(B,left_division(left_division(left_division(A,B),identity),left_division(A,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[119]),402]),
[iquote('back_demod(119),demod([402])')] ).
cnf(407,plain,
equal(multiply(A,left_division(left_division(left_division(B,A),identity),left_division(B,A))),multiply(B,left_division(left_division(left_division(B,A),left_division(left_division(B,A),identity)),left_division(B,A)))),
inference(flip,[status(thm),theory(equality)],[406]),
[iquote('flip(406)')] ).
cnf(408,plain,
equal(multiply(right_division(A,left_division(B,C)),left_division(left_division(left_division(B,C),identity),C)),multiply(multiply(A,B),left_division(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[168]),396]),
[iquote('back_demod(168),demod([396])')] ).
cnf(416,plain,
equal(multiply(A,multiply(left_division(A,identity),B)),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,81]),5]),1]),
[iquote('para(1,81),demod([5]),flip(1)')] ).
cnf(417,plain,
equal(multiply(A,B),left_division(left_division(A,identity),B)),
inference(para,[status(thm),theory(equality)],[3,416]),
[iquote('para(3,416)')] ).
cnf(418,plain,
equal(left_division(left_division(A,identity),left_division(A,B)),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[416]),417,63,417]),
[iquote('back_demod(416),demod([417,63,417])')] ).
cnf(427,plain,
equal(left_division(left_division(right_division(A,left_division(B,C)),identity),left_division(left_division(left_division(B,C),identity),C)),left_division(left_division(left_division(left_division(A,identity),B),identity),left_division(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[408]),417,417,417]),
[iquote('back_demod(408),demod([417,417,417])')] ).
cnf(428,plain,
equal(left_division(left_division(A,identity),left_division(left_division(left_division(A,B),left_division(left_division(A,B),identity)),left_division(A,B))),left_division(left_division(B,identity),left_division(left_division(left_division(A,B),identity),left_division(A,B)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[407]),417,417]),1]),
[iquote('back_demod(407),demod([417,417]),flip(1)')] ).
cnf(431,plain,
equal(left_division(left_division(A,left_division(A,identity)),A),left_division(left_division(A,identity),left_division(left_division(A,identity),A))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[402]),417]),1]),
[iquote('back_demod(402),demod([417]),flip(1)')] ).
cnf(434,plain,
equal(left_division(left_division(A,identity),left_division(left_division(left_division(A,B),identity),left_division(left_division(left_division(A,B),identity),left_division(A,B)))),left_division(left_division(B,identity),left_division(left_division(left_division(A,B),identity),left_division(A,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[428]),431]),
[iquote('back_demod(428),demod([431])')] ).
cnf(442,plain,
equal(left_division(right_division(A,B),left_division(left_division(A,identity),B)),left_division(left_division(B,identity),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[389]),417]),
[iquote('back_demod(389),demod([417])')] ).
cnf(448,plain,
equal(left_division(left_division(left_division(left_division(left_division(A,identity),B),identity),C),left_division(left_division(A,identity),left_division(left_division(B,identity),left_division(left_division(C,identity),B)))),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[380]),417,417,417,417]),
[iquote('back_demod(380),demod([417,417,417,417])')] ).
cnf(449,plain,
equal(left_division(left_division(left_division(left_division(A,identity),B),identity),C),left_division(left_division(right_division(A,C),identity),left_division(left_division(C,identity),left_division(left_division(B,identity),C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[379]),417,417,417,417]),
[iquote('back_demod(379),demod([417,417,417,417])')] ).
cnf(496,plain,
equal(left_division(left_division(right_division(A,B),identity),left_division(left_division(B,identity),left_division(left_division(left_division(A,C),identity),B))),left_division(left_division(C,identity),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[334]),417,417,417]),
[iquote('back_demod(334),demod([417,417,417])')] ).
cnf(502,plain,
~ equal(left_division(left_division(right_division(a,c),identity),left_division(left_division(c,identity),left_division(left_division(left_division(left_division(b,identity),a),identity),c))),left_division(left_division(a,identity),left_division(left_division(b,identity),left_division(left_division(a,identity),c)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[328]),417,417,417,417,417,417]),
[iquote('back_demod(328),demod([417,417,417,417,417,417])')] ).
cnf(582,plain,
equal(left_division(left_division(right_division(A,left_division(B,left_division(B,identity))),identity),left_division(B,identity)),right_division(A,left_division(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[219]),417]),
[iquote('back_demod(219),demod([417])')] ).
cnf(583,plain,
equal(right_division(left_division(left_division(A,identity),B),left_division(left_division(B,identity),B)),right_division(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[201]),417]),
[iquote('back_demod(201),demod([417])')] ).
cnf(587,plain,
equal(left_division(left_division(right_division(A,B),identity),left_division(left_division(B,identity),B)),left_division(left_division(A,identity),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[136]),417,417]),
[iquote('back_demod(136),demod([417,417])')] ).
cnf(598,plain,
equal(left_division(left_division(A,B),left_division(A,left_division(left_division(B,identity),A))),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[77]),417]),
[iquote('back_demod(77),demod([417])')] ).
cnf(599,plain,
equal(right_division(left_division(left_division(A,identity),B),A),left_division(left_division(A,identity),right_division(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[50]),417,417]),
[iquote('back_demod(50),demod([417,417])')] ).
cnf(600,plain,
equal(left_division(left_division(left_division(A,identity),right_division(B,A)),left_division(left_division(A,identity),B)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[47]),417,417]),
[iquote('back_demod(47),demod([417,417])')] ).
cnf(601,plain,
equal(left_division(left_division(left_division(A,B),identity),A),left_division(A,left_division(left_division(B,identity),A))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[45]),417,417]),
[iquote('back_demod(45),demod([417,417])')] ).
cnf(602,plain,
equal(right_division(left_division(left_division(A,identity),B),B),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[6]),417]),
[iquote('back_demod(6),demod([417])')] ).
cnf(603,plain,
equal(left_division(left_division(right_division(A,B),identity),B),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[5]),417]),
[iquote('back_demod(5),demod([417])')] ).
cnf(604,plain,
equal(left_division(A,left_division(left_division(A,identity),B)),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[4]),417]),
[iquote('back_demod(4),demod([417])')] ).
cnf(607,plain,
equal(right_division(left_division(A,B),B),left_division(A,identity)),
inference(para,[status(thm),theory(equality)],[63,602]),
[iquote('para(63,602)')] ).
cnf(608,plain,
equal(right_division(A,B),left_division(right_division(B,A),identity)),
inference(para,[status(thm),theory(equality)],[16,607]),
[iquote('para(16,607)')] ).
cnf(609,plain,
equal(left_division(right_division(A,B),identity),right_division(B,A)),
inference(flip,[status(thm),theory(equality)],[608]),
[iquote('flip(608)')] ).
cnf(618,plain,
equal(left_division(right_division(A,B),left_division(right_division(B,A),C)),C),
inference(para,[status(thm),theory(equality)],[609,418]),
[iquote('para(609,418)')] ).
cnf(636,plain,
equal(left_division(left_division(right_division(A,B),right_division(B,A)),left_division(right_division(A,B),identity)),right_division(A,B)),
inference(para,[status(thm),theory(equality)],[609,217]),
[iquote('para(609,217)')] ).
cnf(637,plain,
equal(left_division(left_division(A,left_division(B,identity)),left_division(A,left_division(B,A))),A),
inference(para,[status(thm),theory(equality)],[63,598]),
[iquote('para(63,598)')] ).
cnf(640,plain,
equal(left_division(left_division(A,left_division(right_division(A,B),identity)),left_division(A,B)),A),
inference(para,[status(thm),theory(equality)],[16,637]),
[iquote('para(16,637)')] ).
cnf(655,plain,
equal(right_division(left_division(A,identity),B),right_division(left_division(A,B),left_division(left_division(B,identity),B))),
inference(para,[status(thm),theory(equality)],[607,113]),
[iquote('para(607,113)')] ).
cnf(656,plain,
equal(right_division(left_division(A,B),left_division(left_division(B,identity),B)),right_division(left_division(A,identity),B)),
inference(flip,[status(thm),theory(equality)],[655]),
[iquote('flip(655)')] ).
cnf(658,plain,
equal(right_division(A,right_division(B,A)),left_division(right_division(B,left_division(left_division(A,identity),A)),identity)),
inference(para,[status(thm),theory(equality)],[115,607]),
[iquote('para(115,607)')] ).
cnf(659,plain,
equal(left_division(right_division(A,left_division(left_division(B,identity),B)),identity),right_division(B,right_division(A,B))),
inference(flip,[status(thm),theory(equality)],[658]),
[iquote('flip(658)')] ).
cnf(662,plain,
equal(right_division(left_division(right_division(A,B),identity),A),right_division(B,left_division(left_division(A,identity),A))),
inference(para,[status(thm),theory(equality)],[608,113]),
[iquote('para(608,113)')] ).
cnf(663,plain,
equal(left_division(right_division(A,right_division(B,A)),identity),right_division(B,left_division(left_division(A,identity),A))),
inference(para,[status(thm),theory(equality)],[608,113]),
[iquote('para(608,113)')] ).
cnf(664,plain,
equal(right_division(A,left_division(left_division(B,identity),B)),left_division(right_division(B,right_division(A,B)),identity)),
inference(flip,[status(thm),theory(equality)],[663]),
[iquote('flip(663)')] ).
cnf(679,plain,
equal(left_division(left_division(left_division(A,identity),left_division(right_division(left_division(A,identity),left_division(A,B)),identity)),B),left_division(A,identity)),
inference(para,[status(thm),theory(equality)],[418,640]),
[iquote('para(418,640)')] ).
cnf(681,plain,
equal(left_division(left_division(A,left_division(right_division(A,left_division(left_division(A,identity),B)),identity)),B),A),
inference(para,[status(thm),theory(equality)],[604,640]),
[iquote('para(604,640)')] ).
cnf(704,plain,
equal(left_division(left_division(A,right_division(B,left_division(A,identity))),left_division(A,B)),left_division(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[63,600]),63]),
[iquote('para(63,600),demod([63])')] ).
cnf(707,plain,
equal(right_division(left_division(A,left_division(B,identity)),left_division(B,left_division(B,identity))),right_division(left_division(A,identity),left_division(B,identity))),
inference(para,[status(thm),theory(equality)],[63,656]),
[iquote('para(63,656)')] ).
cnf(710,plain,
equal(right_division(A,left_division(B,left_division(B,identity))),left_division(right_division(left_division(B,identity),right_division(A,left_division(B,identity))),identity)),
inference(para,[status(thm),theory(equality)],[63,664]),
[iquote('para(63,664)')] ).
cnf(711,plain,
equal(left_division(right_division(left_division(A,identity),right_division(B,left_division(A,identity))),identity),right_division(B,left_division(A,left_division(A,identity)))),
inference(flip,[status(thm),theory(equality)],[710]),
[iquote('flip(710)')] ).
cnf(725,plain,
equal(left_division(right_division(left_division(left_division(A,identity),A),B),A),right_division(B,A)),
inference(para,[status(thm),theory(equality)],[115,618]),
[iquote('para(115,618)')] ).
cnf(729,plain,
equal(right_division(left_division(A,left_division(left_division(B,identity),B)),B),left_division(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[18,725]),1]),
[iquote('para(18,725),flip(1)')] ).
cnf(731,plain,
equal(left_division(left_division(right_division(left_division(left_division(A,identity),A),B),identity),right_division(B,A)),A),
inference(para,[status(thm),theory(equality)],[725,418]),
[iquote('para(725,418)')] ).
cnf(739,plain,
equal(left_division(left_division(left_division(A,B),identity),B),left_division(A,left_division(left_division(B,identity),B))),
inference(para,[status(thm),theory(equality)],[729,603]),
[iquote('para(729,603)')] ).
cnf(745,plain,
equal(left_division(left_division(right_division(A,left_division(B,C)),identity),left_division(B,left_division(left_division(C,identity),C))),left_division(left_division(left_division(left_division(A,identity),B),identity),left_division(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[427]),739]),
[iquote('back_demod(427),demod([739])')] ).
cnf(795,plain,
equal(right_division(left_division(right_division(A,B),C),left_division(left_division(C,identity),C)),right_division(right_division(B,A),C)),
inference(para,[status(thm),theory(equality)],[609,583]),
[iquote('para(609,583)')] ).
cnf(796,plain,
equal(right_division(right_division(A,B),C),right_division(left_division(right_division(B,A),C),left_division(left_division(C,identity),C))),
inference(flip,[status(thm),theory(equality)],[795]),
[iquote('flip(795)')] ).
cnf(807,plain,
equal(right_division(left_division(A,B),left_division(left_division(B,identity),B)),left_division(right_division(B,left_division(A,identity)),identity)),
inference(para,[status(thm),theory(equality)],[655,608]),
[iquote('para(655,608)')] ).
cnf(809,plain,
equal(right_division(right_division(A,B),C),left_division(right_division(C,left_division(right_division(B,A),identity)),identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[796]),807]),
[iquote('back_demod(796),demod([807])')] ).
cnf(810,plain,
equal(left_division(right_division(A,left_division(right_division(B,C),identity)),identity),right_division(right_division(C,B),A)),
inference(flip,[status(thm),theory(equality)],[809]),
[iquote('flip(809)')] ).
cnf(818,plain,
equal(left_division(left_division(left_division(left_division(A,identity),left_division(B,identity)),identity),left_division(left_division(B,identity),B)),left_division(left_division(A,identity),B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[115,434]),115,115,745,115,115,587]),
[iquote('para(115,434),demod([115,115,745,115,115,587])')] ).
cnf(832,plain,
equal(right_division(A,left_division(left_division(B,identity),B)),left_division(right_division(B,left_division(right_division(B,A),identity)),identity)),
inference(para,[status(thm),theory(equality)],[662,608]),
[iquote('para(662,608)')] ).
cnf(833,plain,
equal(left_division(right_division(A,left_division(right_division(A,B),identity)),identity),right_division(B,left_division(left_division(A,identity),A))),
inference(flip,[status(thm),theory(equality)],[832]),
[iquote('flip(832)')] ).
cnf(849,plain,
equal(left_division(left_division(A,left_division(right_division(A,left_division(left_division(A,identity),B)),identity)),identity),right_division(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[681,607]),1]),
[iquote('para(681,607),flip(1)')] ).
cnf(856,plain,
equal(left_division(left_division(right_division(A,B),right_division(left_division(left_division(A,identity),B),right_division(A,B))),left_division(left_division(B,identity),B)),right_division(A,B)),
inference(para,[status(thm),theory(equality)],[442,140]),
[iquote('para(442,140)')] ).
cnf(858,plain,
equal(right_division(left_division(left_division(A,identity),A),right_division(B,A)),left_division(right_division(B,A),right_division(left_division(left_division(B,identity),A),right_division(B,A)))),
inference(para,[status(thm),theory(equality)],[442,145]),
[iquote('para(442,145)')] ).
cnf(859,plain,
equal(left_division(right_division(A,B),right_division(left_division(left_division(A,identity),B),right_division(A,B))),right_division(left_division(left_division(B,identity),B),right_division(A,B))),
inference(flip,[status(thm),theory(equality)],[858]),
[iquote('flip(858)')] ).
cnf(863,plain,
equal(right_division(left_division(A,identity),left_division(A,B)),left_division(left_division(A,right_division(B,left_division(A,identity))),identity)),
inference(para,[status(thm),theory(equality)],[704,607]),
[iquote('para(704,607)')] ).
cnf(864,plain,
equal(left_division(left_division(A,right_division(B,left_division(A,identity))),identity),right_division(left_division(A,identity),left_division(A,B))),
inference(flip,[status(thm),theory(equality)],[863]),
[iquote('flip(863)')] ).
cnf(870,plain,
equal(right_division(A,right_division(B,A)),right_division(left_division(left_division(A,identity),A),B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[731,607]),63]),
[iquote('para(731,607),demod([63])')] ).
cnf(871,plain,
equal(right_division(left_division(left_division(A,identity),A),B),right_division(A,right_division(B,A))),
inference(flip,[status(thm),theory(equality)],[870]),
[iquote('flip(870)')] ).
cnf(882,plain,
equal(left_division(left_division(A,B),left_division(A,left_division(left_division(B,identity),B))),B),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[739,418]),63]),
[iquote('para(739,418),demod([63])')] ).
cnf(896,plain,
equal(left_division(right_division(right_division(A,B),C),left_division(right_division(C,left_division(right_division(B,A),identity)),D)),D),
inference(para,[status(thm),theory(equality)],[810,418]),
[iquote('para(810,418)')] ).
cnf(898,plain,
equal(left_division(right_division(right_division(A,B),C),identity),right_division(C,left_division(right_division(B,A),identity))),
inference(para,[status(thm),theory(equality)],[14,896]),
[iquote('para(14,896)')] ).
cnf(899,plain,
equal(right_division(A,left_division(right_division(B,C),identity)),left_division(right_division(right_division(C,B),A),identity)),
inference(flip,[status(thm),theory(equality)],[898]),
[iquote('flip(898)')] ).
cnf(989,plain,
equal(right_division(A,left_division(B,left_division(B,identity))),left_division(right_division(left_division(B,identity),left_division(right_division(left_division(B,identity),A),identity)),identity)),
inference(para,[status(thm),theory(equality)],[63,832]),
[iquote('para(63,832)')] ).
cnf(990,plain,
equal(left_division(right_division(left_division(A,identity),left_division(right_division(left_division(A,identity),B),identity)),identity),right_division(B,left_division(A,left_division(A,identity)))),
inference(flip,[status(thm),theory(equality)],[989]),
[iquote('flip(989)')] ).
cnf(992,plain,
equal(left_division(left_division(left_division(left_division(A,B),identity),C),left_division(A,left_division(left_division(B,identity),left_division(left_division(C,identity),B)))),B),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[63,448]),63]),
[iquote('para(63,448),demod([63])')] ).
cnf(996,plain,
equal(left_division(left_division(right_division(A,B),identity),left_division(left_division(B,identity),left_division(A,B))),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,449]),14,12,63]),1]),
[iquote('para(14,449),demod([14,12,63]),flip(1)')] ).
cnf(1000,plain,
equal(left_division(right_division(A,B),B),left_division(left_division(B,identity),left_division(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[996,418]),63]),
[iquote('para(996,418),demod([63])')] ).
cnf(1004,plain,
equal(left_division(right_division(A,B),identity),left_division(left_division(B,identity),left_division(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1000,607]),599,607]),1]),
[iquote('para(1000,607),demod([599,607]),flip(1)')] ).
cnf(1009,plain,
equal(right_division(A,left_division(B,left_division(B,identity))),left_division(left_division(A,identity),left_division(left_division(B,identity),B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[990]),1004,63,1004,63,739]),1]),
[iquote('back_demod(990),demod([1004,63,1004,63,739]),flip(1)')] ).
cnf(1025,plain,
equal(left_division(left_division(A,left_division(B,identity)),A),left_division(left_division(B,identity),left_division(left_division(A,identity),A))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[711]),1004,1004,63,63,1009]),
[iquote('back_demod(711),demod([1004,1004,63,63,1009])')] ).
cnf(1026,plain,
equal(right_division(left_division(A,identity),left_division(B,identity)),left_division(left_division(left_division(A,left_division(B,identity)),identity),left_division(left_division(B,identity),B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[707]),1009]),1]),
[iquote('back_demod(707),demod([1009]),flip(1)')] ).
cnf(1027,plain,
equal(right_division(A,left_division(B,identity)),left_division(left_division(left_division(left_division(A,identity),left_division(left_division(B,identity),B)),identity),left_division(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[582]),1009]),1]),
[iquote('back_demod(582),demod([1009]),flip(1)')] ).
cnf(1028,plain,
equal(left_division(left_division(left_division(A,left_division(left_division(B,identity),B)),identity),left_division(B,identity)),left_division(left_division(left_division(A,left_division(B,identity)),identity),left_division(left_division(B,identity),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1026]),1027,63]),
[iquote('back_demod(1026),demod([1027,63])')] ).
cnf(1029,plain,
equal(right_division(A,left_division(B,identity)),left_division(left_division(A,identity),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1027]),1028,818]),
[iquote('back_demod(1027),demod([1028,818])')] ).
cnf(1045,plain,
equal(right_division(A,left_division(left_division(B,identity),left_division(C,identity))),left_division(left_division(A,identity),left_division(left_division(C,identity),left_division(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[899]),1004,1004,1004]),
[iquote('back_demod(899),demod([1004,1004,1004])')] ).
cnf(1055,plain,
equal(right_division(left_division(A,identity),left_division(A,B)),left_division(left_division(A,left_division(left_division(B,identity),A)),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[864]),1029]),1]),
[iquote('back_demod(864),demod([1029]),flip(1)')] ).
cnf(1056,plain,
equal(left_division(left_division(left_division(A,identity),B),A),left_division(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[679]),1055,63,418]),
[iquote('back_demod(679),demod([1055,63,418])')] ).
cnf(1061,plain,
equal(right_division(A,left_division(left_division(B,identity),B)),left_division(left_division(left_division(B,identity),left_division(left_division(B,identity),left_division(A,identity))),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[833]),1004,1045]),1]),
[iquote('back_demod(833),demod([1004,1045]),flip(1)')] ).
cnf(1085,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(A,identity),left_division(B,identity))),identity),left_division(left_division(B,identity),left_division(A,left_division(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[664]),1061,1004,1004,1025,63]),
[iquote('back_demod(664),demod([1061,1004,1004,1025,63])')] ).
cnf(1096,plain,
equal(right_division(A,left_division(left_division(B,identity),B)),left_division(left_division(A,identity),left_division(B,left_division(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1061]),1085]),
[iquote('back_demod(1061),demod([1085])')] ).
cnf(1099,plain,
equal(right_division(A,right_division(B,A)),left_division(left_division(left_division(B,identity),left_division(A,left_division(A,identity))),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[659]),1096]),1]),
[iquote('back_demod(659),demod([1096]),flip(1)')] ).
cnf(1103,plain,
equal(right_division(left_division(left_division(A,identity),A),B),left_division(left_division(left_division(B,identity),left_division(A,left_division(A,identity))),identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[871]),1099]),
[iquote('back_demod(871),demod([1099])')] ).
cnf(1104,plain,
equal(left_division(right_division(A,B),right_division(left_division(left_division(A,identity),B),right_division(A,B))),left_division(left_division(left_division(left_division(B,identity),left_division(A,identity)),left_division(B,left_division(B,identity))),identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[859]),1103,1004]),
[iquote('back_demod(859),demod([1103,1004])')] ).
cnf(1105,plain,
equal(right_division(A,B),left_division(left_division(left_division(left_division(left_division(B,identity),left_division(A,identity)),left_division(B,left_division(B,identity))),identity),left_division(left_division(B,identity),B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[856]),1104]),1]),
[iquote('back_demod(856),demod([1104]),flip(1)')] ).
cnf(1121,plain,
equal(left_division(left_division(left_division(left_division(A,left_division(left_division(B,identity),A)),left_division(left_division(A,B),left_division(left_division(A,B),identity))),identity),left_division(left_division(left_division(A,B),identity),left_division(A,B))),left_division(left_division(A,left_division(left_division(B,identity),A)),identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1055]),1105,63,601]),
[iquote('back_demod(1055),demod([1105,63,601])')] ).
cnf(1179,plain,
equal(left_division(left_division(left_division(left_division(left_division(A,identity),left_division(B,identity)),left_division(A,left_division(A,identity))),identity),left_division(left_division(A,identity),A)),left_division(left_division(left_division(A,identity),left_division(B,identity)),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[849]),1105,601,1121,63,604,1105]),1]),
[iquote('back_demod(849),demod([1105,601,1121,63,604,1105]),flip(1)')] ).
cnf(1205,plain,
equal(right_division(A,B),left_division(left_division(left_division(B,identity),left_division(A,identity)),identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1105]),1179]),
[iquote('back_demod(1105),demod([1179])')] ).
cnf(1263,plain,
equal(left_division(left_division(left_division(A,identity),left_division(B,identity)),identity),left_division(left_division(B,identity),left_division(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[636]),1205,1205,1205,63,1056,63,1205]),1]),
[iquote('back_demod(636),demod([1205,1205,1205,63,1056,63,1205]),flip(1)')] ).
cnf(1286,plain,
equal(right_division(A,B),left_division(left_division(A,identity),left_division(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1205]),1263]),
[iquote('back_demod(1205),demod([1263])')] ).
cnf(1364,plain,
~ equal(left_division(left_division(left_division(c,identity),left_division(a,identity)),left_division(left_division(c,identity),left_division(left_division(left_division(left_division(b,identity),a),identity),c))),left_division(left_division(a,identity),left_division(left_division(b,identity),left_division(left_division(a,identity),c)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[502]),1286,1263]),
[iquote('back_demod(502),demod([1286,1263])')] ).
cnf(1372,plain,
equal(left_division(left_division(left_division(A,identity),left_division(B,identity)),left_division(left_division(A,identity),left_division(left_division(left_division(B,C),identity),A))),left_division(left_division(C,identity),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[496]),1286,1263]),
[iquote('back_demod(496),demod([1286,1263])')] ).
cnf(1377,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,A),left_division(left_division(B,A),identity))),B),left_division(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[216]),1286,208]),
[iquote('back_demod(216),demod([1286,208])')] ).
cnf(1402,plain,
equal(left_division(left_division(A,identity),B),left_division(left_division(B,identity),left_division(left_division(A,B),B))),
inference(para,[status(thm),theory(equality)],[607,1000]),
[iquote('para(607,1000)')] ).
cnf(1404,plain,
equal(left_division(left_division(A,B),left_division(A,identity)),left_division(B,identity)),
inference(para,[status(thm),theory(equality)],[63,1056]),
[iquote('para(63,1056)')] ).
cnf(1411,plain,
equal(left_division(left_division(A,B),identity),left_division(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[418,1056]),1]),
[iquote('para(418,1056),flip(1)')] ).
cnf(1435,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,A),left_division(A,B))),B),left_division(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1377]),1411]),
[iquote('back_demod(1377),demod([1411])')] ).
cnf(1439,plain,
equal(left_division(left_division(left_division(A,identity),left_division(B,identity)),left_division(left_division(A,identity),left_division(left_division(C,B),A))),left_division(left_division(C,identity),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1372]),1411]),
[iquote('back_demod(1372),demod([1411])')] ).
cnf(1446,plain,
~ equal(left_division(left_division(left_division(c,identity),left_division(a,identity)),left_division(left_division(c,identity),left_division(left_division(a,left_division(b,identity)),c))),left_division(left_division(a,identity),left_division(left_division(b,identity),left_division(left_division(a,identity),c)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1364]),1411]),
[iquote('back_demod(1364),demod([1411])')] ).
cnf(1573,plain,
equal(left_division(left_division(left_division(A,B),C),left_division(B,left_division(left_division(A,identity),left_division(left_division(C,identity),A)))),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[992]),1411]),
[iquote('back_demod(992),demod([1411])')] ).
cnf(1700,plain,
equal(left_division(left_division(A,B),left_division(left_division(B,A),C)),C),
inference(para,[status(thm),theory(equality)],[1411,418]),
[iquote('para(1411,418)')] ).
cnf(1732,plain,
equal(left_division(left_division(left_division(A,identity),A),B),left_division(A,left_division(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[882,1404]),1411,1411]),1]),
[iquote('para(882,1404),demod([1411,1411]),flip(1)')] ).
cnf(1760,plain,
equal(left_division(left_division(left_division(A,B),left_division(B,A)),C),left_division(left_division(B,A),left_division(left_division(B,A),C))),
inference(para,[status(thm),theory(equality)],[1411,1732]),
[iquote('para(1411,1732)')] ).
cnf(2000,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,A),A)),left_division(left_division(A,left_division(B,identity)),C)),C),
inference(para,[status(thm),theory(equality)],[1402,1700]),
[iquote('para(1402,1700)')] ).
cnf(4046,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,identity),A)),C),left_division(A,left_division(B,left_division(A,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1573,1404]),1411,1411]),1]),
[iquote('para(1573,1404),demod([1411,1411]),flip(1)')] ).
cnf(4513,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,C),A)),D),left_division(A,left_division(left_division(C,B),left_division(A,D)))),
inference(para,[status(thm),theory(equality)],[1411,4046]),
[iquote('para(1411,4046)')] ).
cnf(4613,plain,
equal(left_division(A,left_division(left_division(A,B),left_division(A,left_division(left_division(A,left_division(B,identity)),C)))),C),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2000]),4513]),
[iquote('back_demod(2000),demod([4513])')] ).
cnf(4627,plain,
equal(left_division(left_division(left_division(A,identity),left_division(B,identity)),left_division(left_division(A,identity),left_division(left_division(B,C),A))),left_division(left_division(left_division(C,B),left_division(B,identity)),A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1435,1439]),1411,1760,1404]),
[iquote('para(1435,1439),demod([1411,1760,1404])')] ).
cnf(4628,plain,
equal(left_division(left_division(left_division(A,B),left_division(B,identity)),C),left_division(left_division(left_division(C,identity),left_division(B,identity)),left_division(left_division(C,identity),left_division(left_division(B,A),C)))),
inference(flip,[status(thm),theory(equality)],[4627]),
[iquote('flip(4627)')] ).
cnf(4632,plain,
equal(left_division(left_division(A,B),left_division(A,left_division(left_division(A,left_division(B,identity)),C))),left_division(left_division(A,identity),C)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4613,418]),1]),
[iquote('para(4613,418),flip(1)')] ).
cnf(5060,plain,
equal(left_division(left_division(A,B),left_division(left_division(B,identity),C)),left_division(B,left_division(left_division(B,left_division(A,identity)),C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4632,418]),1411]),
[iquote('para(4632,418),demod([1411])')] ).
cnf(5472,plain,
equal(left_division(left_division(A,B),C),left_division(B,left_division(left_division(B,left_division(A,identity)),left_division(B,C)))),
inference(para,[status(thm),theory(equality)],[418,5060]),
[iquote('para(418,5060)')] ).
cnf(5520,plain,
equal(left_division(left_division(A,left_division(left_division(A,left_division(B,identity)),left_division(A,C))),left_division(left_division(C,left_division(B,A)),D)),D),
inference(para,[status(thm),theory(equality)],[5472,1700]),
[iquote('para(5472,1700)')] ).
cnf(5543,plain,
equal(left_division(left_division(left_division(A,left_division(B,identity)),left_division(A,C)),A),left_division(C,left_division(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,5520]),1411]),
[iquote('para(14,5520),demod([1411])')] ).
cnf(5546,plain,
equal(left_division(left_division(left_division(A,B),left_division(A,left_division(C,identity))),left_division(B,left_division(C,A))),A),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5543,418]),1411]),
[iquote('para(5543,418),demod([1411])')] ).
cnf(5565,plain,
equal(left_division(left_division(left_division(A,B),left_division(A,left_division(C,D))),left_division(B,left_division(left_division(D,C),A))),A),
inference(para,[status(thm),theory(equality)],[1411,5546]),
[iquote('para(1411,5546)')] ).
cnf(5566,plain,
equal(left_division(left_division(left_division(A,B),left_division(A,C)),left_division(B,left_division(left_division(C,identity),A))),A),
inference(para,[status(thm),theory(equality)],[12,5565]),
[iquote('para(12,5565)')] ).
cnf(5660,plain,
equal(left_division(A,left_division(left_division(A,B),left_division(A,C))),left_division(left_division(left_division(B,identity),A),C)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5566,1404]),1411,1411]),
[iquote('para(5566,1404),demod([1411,1411])')] ).
cnf(5679,plain,
equal(left_division(left_division(left_division(A,B),left_division(B,identity)),C),left_division(left_division(B,identity),left_division(A,left_division(left_division(B,identity),C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[418,5660]),1411]),1]),
[iquote('para(418,5660),demod([1411]),flip(1)')] ).
cnf(5702,plain,
equal(left_division(left_division(A,identity),left_division(B,left_division(left_division(A,identity),C))),left_division(left_division(left_division(C,identity),left_division(A,identity)),left_division(left_division(C,identity),left_division(left_division(A,B),C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[4628]),5679]),
[iquote('back_demod(4628),demod([5679])')] ).
cnf(5703,plain,
equal(left_division(left_division(left_division(A,identity),left_division(B,identity)),left_division(left_division(A,identity),left_division(left_division(B,C),A))),left_division(left_division(B,identity),left_division(C,left_division(left_division(B,identity),A)))),
inference(flip,[status(thm),theory(equality)],[5702]),
[iquote('flip(5702)')] ).
cnf(5704,plain,
$false,
inference(conflict,[status(thm)],[5703,1446]),
[iquote('conflict(5703,1446)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP201-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14 % Command : tptp2X_and_run_eqp %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 06:35:21 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.48/2.85 ----- EQP 0.9e, May 2009 -----
% 2.48/2.85 The job began on n023.cluster.edu, Mon Jun 13 06:35:22 2022
% 2.48/2.85 The command was "./eqp09e".
% 2.48/2.85
% 2.48/2.85 set(prolog_style_variables).
% 2.48/2.85 set(lrpo).
% 2.48/2.85 set(basic_paramod).
% 2.48/2.85 set(functional_subsume).
% 2.48/2.85 set(ordered_paramod).
% 2.48/2.85 set(prime_paramod).
% 2.48/2.85 set(para_pairs).
% 2.48/2.85 assign(pick_given_ratio,4).
% 2.48/2.85 clear(print_kept).
% 2.48/2.85 clear(print_new_demod).
% 2.48/2.85 clear(print_back_demod).
% 2.48/2.85 clear(print_given).
% 2.48/2.85 assign(max_mem,64000).
% 2.48/2.85 end_of_commands.
% 2.48/2.85
% 2.48/2.85 Usable:
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Sos:
% 2.48/2.85 0 (wt=-1) [] multiply(identity,A) = A.
% 2.48/2.85 0 (wt=-1) [] multiply(A,identity) = A.
% 2.48/2.85 0 (wt=-1) [] multiply(A,left_division(A,B)) = B.
% 2.48/2.85 0 (wt=-1) [] left_division(A,multiply(A,B)) = B.
% 2.48/2.85 0 (wt=-1) [] multiply(right_division(A,B),B) = A.
% 2.48/2.85 0 (wt=-1) [] right_division(multiply(A,B),B) = A.
% 2.48/2.85 0 (wt=-1) [] multiply(A,right_inverse(A)) = identity.
% 2.48/2.85 0 (wt=-1) [] multiply(left_inverse(A),A) = identity.
% 2.48/2.85 0 (wt=-1) [] multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))).
% 2.48/2.85 0 (wt=-1) [] -(multiply(multiply(multiply(a,b),a),c) = multiply(a,multiply(b,multiply(a,c)))).
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Demodulators:
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Passive:
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Starting to process input.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 1 (wt=5) [] multiply(identity,A) = A.
% 2.48/2.85 1 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 2 (wt=5) [] multiply(A,identity) = A.
% 2.48/2.85 2 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 2.48/2.85 3 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 2.48/2.85 4 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 2.48/2.85 5 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 2.48/2.85 6 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 2.48/2.85 7 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 2.48/2.85 8 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 9 (wt=15) [] multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))).
% 2.48/2.85 9 is a new demodulator.
% 2.48/2.85
% 2.48/2.85 ** KEPT: 10 (wt=15) [] -(multiply(multiply(multiply(a,b),a),c) = multiply(a,multiply(b,multiply(a,c)))).
% 2.48/2.85 ---------------- PROOF FOUND ----------------
% 2.48/2.85 % SZS status Unsatisfiable
% 2.48/2.85
% 2.48/2.85
% 2.48/2.85 After processing input:
% 2.48/2.85
% 2.48/2.85 Usable:
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Sos:
% 2.48/2.85 1 (wt=5) [] multiply(identity,A) = A.
% 2.48/2.85 2 (wt=5) [] multiply(A,identity) = A.
% 2.48/2.85 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 2.48/2.85 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 2.48/2.85 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 2.48/2.85 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 2.48/2.85 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 2.48/2.85 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 2.48/2.85 9 (wt=15) [] multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))).
% 2.48/2.85 10 (wt=15) [] -(multiply(multiply(multiply(a,b),a),c) = multiply(a,multiply(b,multiply(a,c)))).
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Demodulators:
% 2.48/2.85 1 (wt=5) [] multiply(identity,A) = A.
% 2.48/2.85 2 (wt=5) [] multiply(A,identity) = A.
% 2.48/2.85 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 2.48/2.85 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 2.48/2.85 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 2.48/2.85 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 2.48/2.85 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 2.48/2.85 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 2.48/2.85 9 (wt=15) [] multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))).
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 Passive:
% 2.48/2.85 end_of_list.
% 2.48/2.85
% 2.48/2.85 UNIT CONFLICT from 5703 and 1446 at 1.47 seconds.
% 2.48/2.85
% 2.48/2.85 ---------------- PROOF ----------------
% 2.48/2.85 % SZS output start Refutation
% See solution above
% 2.48/2.85 ------------ end of proof -------------
% 2.48/2.85
% 2.48/2.85
% 2.48/2.85 ------------- memory usage ------------
% 2.48/2.85 Memory dynamically allocated (tp_alloc): 18554.
% 2.48/2.85 type (bytes each) gets frees in use avail bytes
% 2.48/2.85 sym_ent ( 96) 60 0 60 0 5.6 K
% 2.48/2.85 term ( 16) 1062324 807227 255097 109 4962.2 K
% 2.48/2.85 gen_ptr ( 8) 1683338 280007 1403331 196 10965.1 K
% 2.48/2.85 context ( 808) 683722 683720 2 7 7.1 K
% 2.48/2.85 trail ( 12) 575154 575154 0 5 0.1 K
% 2.48/2.85 bt_node ( 68) 176385 176382 3 36 2.6 K
% 2.48/2.85 ac_position (285432) 0 0 0 0 0.0 K
% 2.48/2.85 ac_match_pos (14044) 0 0 0 0 0.0 K
% 2.48/2.85 ac_match_free_vars_pos (4020)
% 2.48/2.85 0 0 0 0 0.0 K
% 2.48/2.85 discrim ( 12) 237026 121150 115876 136 1359.5 K
% 2.48/2.85 flat ( 40) 2869209 2869209 0 243 9.5 K
% 2.48/2.85 discrim_pos ( 12) 63168 63168 0 1 0.0 K
% 2.48/2.85 fpa_head ( 12) 7809 0 7809 0 91.5 K
% 2.48/2.85 fpa_tree ( 28) 47870 47870 0 115 3.1 K
% 2.48/2.85 fpa_pos ( 36) 9401 9401 0 1 0.0 K
% 2.48/2.85 literal ( 12) 24597 18894 5703 1 66.8 K
% 2.48/2.85 clause ( 24) 24597 18894 5703 1 133.7 K
% 2.48/2.85 list ( 12) 3757 3700 57 18 0.9 K
% 2.48/2.85 list_pos ( 20) 27356 14245 13111 7 256.2 K
% 2.48/2.85 pair_index ( 40) 2 0 2 0 0.1 K
% 2.48/2.85
% 2.48/2.85 -------------- statistics -------------
% 2.48/2.85 Clauses input 10
% 2.48/2.85 Usable input 0
% 2.48/2.85 Sos input 10
% 2.48/2.85 Demodulators input 0
% 2.48/2.85 Passive input 0
% 2.48/2.85
% 2.48/2.85 Processed BS (before search) 10
% 2.48/2.85 Forward subsumed BS 0
% 2.48/2.85 Kept BS 10
% 2.48/2.85 New demodulators BS 9
% 2.48/2.85 Back demodulated BS 0
% 2.48/2.85
% 2.48/2.85 Clauses or pairs given 10397
% 2.48/2.85 Clauses generated 16376
% 2.48/2.85 Forward subsumed 10683
% 2.48/2.85 Deleted by weight 0
% 2.48/2.85 Deleted by variable count 0
% 2.48/2.85 Kept 5693
% 2.48/2.85 New demodulators 3689
% 2.48/2.85 Back demodulated 2898
% 2.48/2.85 Ordered paramod prunes 0
% 2.48/2.85 Basic paramod prunes 35503
% 2.48/2.85 Prime paramod prunes 3205
% 2.48/2.85 Semantic prunes 0
% 2.48/2.85
% 2.48/2.85 Rewrite attmepts 484250
% 2.48/2.85 Rewrites 57748
% 2.48/2.85
% 2.48/2.85 FPA overloads 0
% 2.48/2.85 FPA underloads 0
% 2.48/2.85
% 2.48/2.85 Usable size 0
% 2.48/2.85 Sos size 2804
% 2.48/2.85 Demodulators size 1754
% 2.48/2.85 Passive size 0
% 2.48/2.85 Disabled size 2898
% 2.48/2.85
% 2.48/2.85 Proofs found 1
% 2.48/2.85
% 2.48/2.85 ----------- times (seconds) ----------- Mon Jun 13 06:35:23 2022
% 2.48/2.85
% 2.48/2.85 user CPU time 1.47 (0 hr, 0 min, 1 sec)
% 2.48/2.85 system CPU time 0.26 (0 hr, 0 min, 0 sec)
% 2.48/2.85 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.48/2.85 input time 0.00
% 2.48/2.85 paramodulation time 0.09
% 2.48/2.85 demodulation time 0.17
% 2.48/2.85 orient time 0.04
% 2.48/2.85 weigh time 0.01
% 2.48/2.85 forward subsume time 0.03
% 2.48/2.85 back demod find time 0.70
% 2.48/2.85 conflict time 0.01
% 2.48/2.85 LRPO time 0.02
% 2.48/2.85 store clause time 0.26
% 2.48/2.85 disable clause time 0.06
% 2.48/2.85 prime paramod time 0.04
% 2.48/2.85 semantics time 0.00
% 2.48/2.85
% 2.48/2.85 EQP interrupted
%------------------------------------------------------------------------------