TSTP Solution File: GRP205-1 by EQP---0.9e
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n003.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 08:45:56 EDT 2022
% Result : Unsatisfiable 18.27s 18.64s
% Output : Refutation 18.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of clauses : 99 ( 99 unt; 0 nHn; 4 RR)
% Number of literals : 99 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 201 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(multiply(identity,A),A),
file('GRP205-1.p',unknown),
[] ).
cnf(2,plain,
equal(multiply(A,identity),A),
file('GRP205-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(A,left_division(A,B)),B),
file('GRP205-1.p',unknown),
[] ).
cnf(4,plain,
equal(left_division(A,multiply(A,B)),B),
file('GRP205-1.p',unknown),
[] ).
cnf(5,plain,
equal(multiply(right_division(A,B),B),A),
file('GRP205-1.p',unknown),
[] ).
cnf(6,plain,
equal(right_division(multiply(A,B),B),A),
file('GRP205-1.p',unknown),
[] ).
cnf(9,plain,
equal(multiply(multiply(multiply(A,B),A),C),multiply(A,multiply(B,multiply(A,C)))),
file('GRP205-1.p',unknown),
[] ).
cnf(10,plain,
~ equal(multiply(x,multiply(multiply(y,z),x)),multiply(multiply(x,y),multiply(z,x))),
file('GRP205-1.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(15,plain,
equal(right_division(A,identity),A),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,2]),1]),
[iquote('para(5,2),flip(1)')] ).
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(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[9,2]),2]),1]),
[iquote('para(9,2),demod([2]),flip(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)],[9]),22]),
[iquote('back_demod(9),demod([22])')] ).
cnf(24,plain,
equal(multiply(multiply(A,A),B),multiply(A,multiply(A,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(left_division(multiply(A,B),multiply(A,multiply(B,A))),A),
inference(para,[status(thm),theory(equality)],[22,4]),
[iquote('para(22,4)')] ).
cnf(26,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(27,plain,
equal(multiply(A,multiply(A,left_division(multiply(A,A),B))),B),
inference(para,[status(thm),theory(equality)],[24,3]),
[iquote('para(24,3)')] ).
cnf(30,plain,
equal(multiply(multiply(left_division(A,B),B),C),multiply(left_division(A,B),multiply(A,multiply(left_division(A,B),C)))),
inference(para,[status(thm),theory(equality)],[3,23]),
[iquote('para(3,23)')] ).
cnf(31,plain,
equal(left_division(multiply(A,multiply(B,A)),multiply(A,multiply(B,multiply(A,C)))),C),
inference(para,[status(thm),theory(equality)],[23,4]),
[iquote('para(23,4)')] ).
cnf(32,plain,
equal(right_division(multiply(A,multiply(A,B)),B),multiply(A,A)),
inference(para,[status(thm),theory(equality)],[24,6]),
[iquote('para(24,6)')] ).
cnf(34,plain,
equal(right_division(multiply(A,multiply(B,multiply(A,C))),C),multiply(A,multiply(B,A))),
inference(para,[status(thm),theory(equality)],[23,6]),
[iquote('para(23,6)')] ).
cnf(39,plain,
equal(right_division(multiply(A,B),A),multiply(A,right_division(B,A))),
inference(para,[status(thm),theory(equality)],[5,26]),
[iquote('para(5,26)')] ).
cnf(40,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)],[2,39]),17]),1]),
[iquote('para(2,39),demod([17]),flip(1)')] ).
cnf(44,plain,
equal(right_division(identity,A),left_division(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[40,4]),1]),
[iquote('para(40,4),flip(1)')] ).
cnf(51,plain,
equal(multiply(left_division(A,identity),A),identity),
inference(para,[status(thm),theory(equality)],[44,5]),
[iquote('para(44,5)')] ).
cnf(54,plain,
equal(left_division(left_division(A,identity),identity),A),
inference(para,[status(thm),theory(equality)],[44,18]),
[iquote('para(44,18)')] ).
cnf(55,plain,
equal(multiply(A,left_division(multiply(A,A),B)),left_division(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[27,4]),1]),
[iquote('para(27,4),flip(1)')] ).
cnf(62,plain,
equal(right_division(multiply(A,B),left_division(A,B)),multiply(A,A)),
inference(para,[status(thm),theory(equality)],[3,32]),
[iquote('para(3,32)')] ).
cnf(63,plain,
equal(right_division(A,left_division(A,identity)),multiply(A,A)),
inference(para,[status(thm),theory(equality)],[2,62]),
[iquote('para(2,62)')] ).
cnf(66,plain,
equal(left_division(multiply(A,multiply(left_division(B,C),C)),multiply(A,multiply(left_division(B,C),multiply(B,multiply(left_division(B,C),A))))),A),
inference(para,[status(thm),theory(equality)],[30,25]),
[iquote('para(30,25)')] ).
cnf(70,plain,
equal(left_division(multiply(A,multiply(B,A)),multiply(A,multiply(B,C))),left_division(A,C)),
inference(para,[status(thm),theory(equality)],[3,31]),
[iquote('para(3,31)')] ).
cnf(73,plain,
equal(multiply(A,right_division(left_division(A,B),A)),right_division(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,39]),1]),
[iquote('para(3,39),flip(1)')] ).
cnf(78,plain,
equal(left_division(multiply(A,A),B),left_division(A,left_division(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[55,4]),1]),
[iquote('para(55,4),flip(1)')] ).
cnf(85,plain,
equal(multiply(left_division(A,identity),multiply(A,A)),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[51,39]),18,63]),1]),
[iquote('para(51,39),demod([18,63]),flip(1)')] ).
cnf(87,plain,
equal(right_division(multiply(A,B),C),multiply(A,multiply(right_division(B,multiply(A,C)),A))),
inference(para,[status(thm),theory(equality)],[5,34]),
[iquote('para(5,34)')] ).
cnf(89,plain,
equal(multiply(A,multiply(right_division(B,multiply(A,B)),A)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[6]),87]),
[iquote('back_demod(6),demod([87])')] ).
cnf(90,plain,
equal(multiply(A,A),left_division(left_division(A,identity),A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[85,4]),1]),
[iquote('para(85,4),flip(1)')] ).
cnf(95,plain,
equal(left_division(left_division(left_division(A,identity),A),B),left_division(A,left_division(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[78]),90]),
[iquote('back_demod(78),demod([90])')] ).
cnf(99,plain,
equal(multiply(left_division(left_division(A,identity),A),B),multiply(A,multiply(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[24]),90]),
[iquote('back_demod(24),demod([90])')] ).
cnf(101,plain,
equal(right_division(left_division(A,B),A),left_division(A,right_division(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[73,4]),1]),
[iquote('para(73,4),flip(1)')] ).
cnf(102,plain,
equal(multiply(A,multiply(right_division(left_division(A,B),B),A)),A),
inference(para,[status(thm),theory(equality)],[3,89]),
[iquote('para(3,89)')] ).
cnf(105,plain,
equal(multiply(right_division(A,multiply(B,A)),B),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[89,4]),14]),1]),
[iquote('para(89,4),demod([14]),flip(1)')] ).
cnf(107,plain,
equal(left_division(right_division(A,multiply(B,A)),identity),B),
inference(para,[status(thm),theory(equality)],[105,4]),
[iquote('para(105,4)')] ).
cnf(112,plain,
equal(multiply(A,right_division(B,multiply(A,B))),identity),
inference(para,[status(thm),theory(equality)],[107,51]),
[iquote('para(107,51)')] ).
cnf(114,plain,
equal(right_division(A,multiply(B,A)),left_division(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[112,4]),1]),
[iquote('para(112,4),flip(1)')] ).
cnf(115,plain,
equal(multiply(left_division(A,identity),multiply(A,B)),B),
inference(para,[status(thm),theory(equality)],[114,5]),
[iquote('para(114,5)')] ).
cnf(116,plain,
equal(multiply(A,B),left_division(left_division(A,identity),B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[115,4]),1]),
[iquote('para(115,4),flip(1)')] ).
cnf(117,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)],[115]),116,116,54]),
[iquote('back_demod(115),demod([116,116,54])')] ).
cnf(126,plain,
equal(left_division(left_division(A,identity),left_division(left_division(right_division(left_division(A,B),B),identity),A)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[102]),116,116]),
[iquote('back_demod(102),demod([116,116])')] ).
cnf(127,plain,
equal(left_division(left_division(A,left_division(A,identity)),B),left_division(left_division(A,identity),left_division(left_division(A,identity),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[99]),116,95,116,116]),
[iquote('back_demod(99),demod([116,95,116,116])')] ).
cnf(131,plain,
equal(right_division(left_division(left_division(A,identity),B),C),left_division(left_division(A,identity),left_division(left_division(right_division(B,left_division(left_division(A,identity),C)),identity),A))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[87]),116,116,116,116]),
[iquote('back_demod(87),demod([116,116,116,116])')] ).
cnf(136,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,identity),A)),left_division(left_division(A,identity),left_division(left_division(B,identity),C))),left_division(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[70]),116,116,116,116]),
[iquote('back_demod(70),demod([116,116,116,116])')] ).
cnf(138,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(left_division(B,C),identity),C)),left_division(left_division(A,identity),left_division(left_division(left_division(B,C),identity),left_division(left_division(B,identity),left_division(left_division(left_division(B,C),identity),A))))),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[66]),116,116,116,116,116,116]),
[iquote('back_demod(66),demod([116,116,116,116,116,116])')] ).
cnf(158,plain,
~ equal(left_division(left_division(x,identity),left_division(left_division(left_division(left_division(y,identity),z),identity),x)),left_division(left_division(left_division(left_division(x,identity),y),identity),left_division(left_division(z,identity),x))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[10]),116,116,116,116,116,116]),
[iquote('back_demod(10),demod([116,116,116,116,116,116])')] ).
cnf(159,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]),116]),
[iquote('back_demod(5),demod([116])')] ).
cnf(160,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)],[3]),116]),
[iquote('back_demod(3),demod([116])')] ).
cnf(161,plain,
equal(left_division(left_division(left_division(A,right_division(B,A)),identity),A),left_division(A,B)),
inference(para,[status(thm),theory(equality)],[101,159]),
[iquote('para(101,159)')] ).
cnf(164,plain,
equal(left_division(left_division(A,right_division(B,A)),left_division(A,B)),A),
inference(para,[status(thm),theory(equality)],[161,117]),
[iquote('para(161,117)')] ).
cnf(165,plain,
equal(left_division(left_division(right_division(A,B),identity),left_division(left_division(right_division(B,A),identity),right_division(A,B))),right_division(A,B)),
inference(para,[status(thm),theory(equality)],[16,126]),
[iquote('para(16,126)')] ).
cnf(175,plain,
equal(left_division(left_division(right_division(left_division(A,B),B),identity),A),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[126,117]),14]),1]),
[iquote('para(126,117),demod([14]),flip(1)')] ).
cnf(177,plain,
equal(left_division(right_division(left_division(A,B),B),identity),A),
inference(para,[status(thm),theory(equality)],[175,117]),
[iquote('para(175,117)')] ).
cnf(179,plain,
equal(left_division(A,left_division(right_division(left_division(A,B),B),C)),C),
inference(para,[status(thm),theory(equality)],[177,160]),
[iquote('para(177,160)')] ).
cnf(180,plain,
equal(right_division(left_division(A,B),B),left_division(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,179]),1]),
[iquote('para(14,179),flip(1)')] ).
cnf(185,plain,
equal(left_division(left_division(left_division(A,left_division(B,identity)),identity),A),left_division(A,left_division(B,A))),
inference(para,[status(thm),theory(equality)],[180,161]),
[iquote('para(180,161)')] ).
cnf(187,plain,
equal(left_division(left_division(left_division(A,B),identity),A),left_division(A,left_division(left_division(B,identity),A))),
inference(para,[status(thm),theory(equality)],[54,185]),
[iquote('para(54,185)')] ).
cnf(195,plain,
equal(left_division(left_division(A,B),left_division(A,left_division(left_division(B,identity),A))),A),
inference(para,[status(thm),theory(equality)],[187,117]),
[iquote('para(187,117)')] ).
cnf(213,plain,
equal(left_division(left_division(A,right_division(B,A)),left_division(left_division(left_division(A,B),identity),left_division(A,right_division(B,A)))),right_division(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[164,187]),160]),1]),
[iquote('para(164,187),demod([160]),flip(1)')] ).
cnf(256,plain,
equal(left_division(left_division(right_division(A,B),identity),right_division(B,A)),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[165,117]),14]),1]),
[iquote('para(165,117),demod([14]),flip(1)')] ).
cnf(259,plain,
equal(left_division(right_division(A,B),identity),right_division(B,A)),
inference(para,[status(thm),theory(equality)],[256,117]),
[iquote('para(256,117)')] ).
cnf(260,plain,
equal(right_division(A,B),left_division(right_division(B,A),identity)),
inference(flip,[status(thm),theory(equality)],[259]),
[iquote('flip(259)')] ).
cnf(283,plain,
equal(left_division(left_division(A,identity),left_division(left_division(right_division(left_division(A,identity),left_division(left_division(A,identity),B)),identity),A)),left_division(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,131]),44]),1]),
[iquote('para(14,131),demod([44]),flip(1)')] ).
cnf(289,plain,
equal(right_division(left_division(A,B),C),left_division(A,left_division(left_division(right_division(B,left_division(A,C)),identity),left_division(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[54,131]),54,54]),
[iquote('para(54,131),demod([54,54])')] ).
cnf(300,plain,
equal(left_division(left_division(left_division(A,left_division(B,identity)),identity),B),left_division(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[283]),289,117,44,54,187,160]),
[iquote('back_demod(283),demod([289,117,44,54,187,160])')] ).
cnf(310,plain,
equal(left_division(A,right_division(B,A)),left_division(A,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)],[101]),289,14,15]),1]),
[iquote('back_demod(101),demod([289,14,15]),flip(1)')] ).
cnf(320,plain,
equal(right_division(A,B),left_division(left_division(B,left_division(left_division(A,identity),left_division(B,identity))),left_division(left_division(left_division(B,A),identity),left_division(B,left_division(left_division(A,identity),left_division(B,identity)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[213]),310,310]),1]),
[iquote('back_demod(213),demod([310,310]),flip(1)')] ).
cnf(336,plain,
equal(left_division(A,left_division(left_division(left_division(left_division(left_division(A,B),left_division(left_division(C,identity),left_division(left_division(A,B),identity))),left_division(left_division(left_division(left_division(A,B),C),identity),left_division(left_division(A,B),left_division(left_division(C,identity),left_division(left_division(A,B),identity))))),identity),left_division(A,identity))),left_division(left_division(B,left_division(left_division(left_division(A,C),identity),left_division(B,identity))),left_division(left_division(left_division(B,left_division(A,C)),identity),left_division(B,left_division(left_division(left_division(A,C),identity),left_division(B,identity)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[289]),320,320]),1]),
[iquote('back_demod(289),demod([320,320]),flip(1)')] ).
cnf(350,plain,
equal(left_division(left_division(left_division(A,left_division(left_division(B,identity),left_division(A,identity))),left_division(left_division(left_division(A,B),identity),left_division(A,left_division(left_division(B,identity),left_division(A,identity))))),identity),left_division(left_division(B,left_division(left_division(A,identity),left_division(B,identity))),left_division(left_division(left_division(B,A),identity),left_division(B,left_division(left_division(A,identity),left_division(B,identity)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[260]),320,320]),1]),
[iquote('back_demod(260),demod([320,320]),flip(1)')] ).
cnf(356,plain,
equal(left_division(A,left_division(left_division(left_division(B,left_division(left_division(left_division(A,C),identity),left_division(B,identity))),left_division(left_division(left_division(B,left_division(A,C)),identity),left_division(B,left_division(left_division(left_division(A,C),identity),left_division(B,identity))))),left_division(A,identity))),left_division(left_division(C,left_division(left_division(left_division(A,B),identity),left_division(C,identity))),left_division(left_division(left_division(C,left_division(A,B)),identity),left_division(C,left_division(left_division(left_division(A,B),identity),left_division(C,identity)))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[336]),350]),
[iquote('back_demod(336),demod([350])')] ).
cnf(357,plain,
equal(left_division(left_division(A,left_division(left_division(left_division(B,C),identity),left_division(A,identity))),left_division(left_division(left_division(A,left_division(B,C)),identity),left_division(A,left_division(left_division(left_division(B,C),identity),left_division(A,identity))))),left_division(B,left_division(left_division(left_division(C,left_division(left_division(left_division(B,A),identity),left_division(C,identity))),left_division(left_division(left_division(C,left_division(B,A)),identity),left_division(C,left_division(left_division(left_division(B,A),identity),left_division(C,identity))))),left_division(B,identity)))),
inference(flip,[status(thm),theory(equality)],[356]),
[iquote('flip(356)')] ).
cnf(400,plain,
equal(left_division(left_division(A,left_division(left_division(B,identity),left_division(A,identity))),left_division(left_division(left_division(A,B),identity),left_division(A,left_division(left_division(B,identity),left_division(A,identity))))),left_division(left_division(B,identity),left_division(left_division(left_division(B,identity),A),B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[54,131]),320,320,14,12,54,14,12,127,160,160,54]),
[iquote('para(54,131),demod([320,320,14,12,54,14,12,127,160,160,54])')] ).
cnf(436,plain,
equal(left_division(left_division(left_division(A,B),identity),left_division(left_division(left_division(left_division(A,B),identity),C),left_division(A,B))),left_division(A,left_division(left_division(left_division(left_division(A,C),identity),left_division(left_division(left_division(left_division(A,C),identity),B),left_division(A,C))),left_division(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[357]),400,400]),
[iquote('back_demod(357),demod([400,400])')] ).
cnf(437,plain,
equal(left_division(A,left_division(left_division(left_division(left_division(A,B),identity),left_division(left_division(left_division(left_division(A,B),identity),C),left_division(A,B))),left_division(A,identity))),left_division(left_division(left_division(A,C),identity),left_division(left_division(left_division(left_division(A,C),identity),B),left_division(A,C)))),
inference(flip,[status(thm),theory(equality)],[436]),
[iquote('flip(436)')] ).
cnf(451,plain,
equal(left_division(left_division(left_division(A,B),identity),left_division(B,identity)),left_division(A,identity)),
inference(para,[status(thm),theory(equality)],[54,300]),
[iquote('para(54,300)')] ).
cnf(452,plain,
equal(left_division(left_division(left_division(A,identity),left_division(left_division(B,identity),A)),A),left_division(A,left_division(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,136]),54]),
[iquote('para(14,136),demod([54])')] ).
cnf(462,plain,
equal(left_division(left_division(A,B),left_division(A,identity)),left_division(B,identity)),
inference(para,[status(thm),theory(equality)],[451,117]),
[iquote('para(451,117)')] ).
cnf(500,plain,
equal(left_division(left_division(left_division(A,identity),B),A),left_division(B,identity)),
inference(para,[status(thm),theory(equality)],[54,462]),
[iquote('para(54,462)')] ).
cnf(506,plain,
equal(left_division(left_division(left_division(A,identity),B),identity),left_division(B,left_division(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[452]),500]),
[iquote('back_demod(452),demod([500])')] ).
cnf(542,plain,
~ equal(left_division(left_division(x,identity),left_division(left_division(z,left_division(y,identity)),x)),left_division(left_division(y,left_division(x,identity)),left_division(left_division(z,identity),x))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[158]),506,506]),
[iquote('back_demod(158),demod([506,506])')] ).
cnf(572,plain,
equal(left_division(A,left_division(left_division(left_division(left_division(A,B),identity),left_division(C,identity)),left_division(A,identity))),left_division(left_division(left_division(A,C),identity),left_division(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[437]),500,500]),
[iquote('back_demod(437),demod([500,500])')] ).
cnf(573,plain,
equal(left_division(left_division(left_division(A,B),identity),left_division(C,identity)),left_division(A,left_division(left_division(left_division(left_division(A,C),identity),left_division(B,identity)),left_division(A,identity)))),
inference(flip,[status(thm),theory(equality)],[572]),
[iquote('flip(572)')] ).
cnf(594,plain,
equal(left_division(left_division(A,B),identity),left_division(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,138]),54,117,54,54,187,195]),1]),
[iquote('para(14,138),demod([54,117,54,54,187,195]),flip(1)')] ).
cnf(603,plain,
equal(left_division(left_division(A,B),left_division(C,identity)),left_division(B,left_division(left_division(left_division(C,B),left_division(A,identity)),left_division(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[573]),594,594]),
[iquote('back_demod(573),demod([594,594])')] ).
cnf(604,plain,
equal(left_division(A,left_division(left_division(left_division(B,A),left_division(C,identity)),left_division(A,identity))),left_division(left_division(C,A),left_division(B,identity))),
inference(flip,[status(thm),theory(equality)],[603]),
[iquote('flip(603)')] ).
cnf(4209,plain,
equal(left_division(left_division(A,B),left_division(left_division(B,left_division(C,identity)),left_division(B,A))),left_division(left_division(C,left_division(A,B)),A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[160,604]),594,594,12]),
[iquote('para(160,604),demod([594,594,12])')] ).
cnf(7024,plain,
equal(left_division(left_division(A,identity),left_division(left_division(B,left_division(C,identity)),A)),left_division(left_division(C,left_division(A,identity)),left_division(left_division(B,identity),A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[117,4209]),500,500]),
[iquote('para(117,4209),demod([500,500])')] ).
cnf(7025,plain,
$false,
inference(conflict,[status(thm)],[7024,542]),
[iquote('conflict(7024,542)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% 0.05/0.15 % Command : tptp2X_and_run_eqp %s
% 0.14/0.37 % Computer : n003.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Tue Jun 14 03:39:55 EDT 2022
% 0.14/0.37 % CPUTime :
% 18.27/18.64 ----- EQP 0.9e, May 2009 -----
% 18.27/18.64 The job began on n003.cluster.edu, Tue Jun 14 03:39:55 2022
% 18.27/18.64 The command was "./eqp09e".
% 18.27/18.64
% 18.27/18.64 set(prolog_style_variables).
% 18.27/18.64 set(lrpo).
% 18.27/18.64 set(basic_paramod).
% 18.27/18.64 set(functional_subsume).
% 18.27/18.64 set(ordered_paramod).
% 18.27/18.64 set(prime_paramod).
% 18.27/18.64 set(para_pairs).
% 18.27/18.64 assign(pick_given_ratio,4).
% 18.27/18.64 clear(print_kept).
% 18.27/18.64 clear(print_new_demod).
% 18.27/18.64 clear(print_back_demod).
% 18.27/18.64 clear(print_given).
% 18.27/18.64 assign(max_mem,64000).
% 18.27/18.64 end_of_commands.
% 18.27/18.64
% 18.27/18.64 Usable:
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Sos:
% 18.27/18.64 0 (wt=-1) [] multiply(identity,A) = A.
% 18.27/18.64 0 (wt=-1) [] multiply(A,identity) = A.
% 18.27/18.64 0 (wt=-1) [] multiply(A,left_division(A,B)) = B.
% 18.27/18.64 0 (wt=-1) [] left_division(A,multiply(A,B)) = B.
% 18.27/18.64 0 (wt=-1) [] multiply(right_division(A,B),B) = A.
% 18.27/18.64 0 (wt=-1) [] right_division(multiply(A,B),B) = A.
% 18.27/18.64 0 (wt=-1) [] multiply(A,right_inverse(A)) = identity.
% 18.27/18.64 0 (wt=-1) [] multiply(left_inverse(A),A) = identity.
% 18.27/18.64 0 (wt=-1) [] multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))).
% 18.27/18.64 0 (wt=-1) [] -(multiply(x,multiply(multiply(y,z),x)) = multiply(multiply(x,y),multiply(z,x))).
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Demodulators:
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Passive:
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Starting to process input.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 1 (wt=5) [] multiply(identity,A) = A.
% 18.27/18.64 1 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 2 (wt=5) [] multiply(A,identity) = A.
% 18.27/18.64 2 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 18.27/18.64 3 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 18.27/18.64 4 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 18.27/18.64 5 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 18.27/18.64 6 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 18.27/18.64 7 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 18.27/18.64 8 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 9 (wt=15) [] multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))).
% 18.27/18.64 9 is a new demodulator.
% 18.27/18.64
% 18.27/18.64 ** KEPT: 10 (wt=15) [] -(multiply(x,multiply(multiply(y,z),x)) = multiply(multiply(x,y),multiply(z,x))).
% 18.27/18.64 ---------------- PROOF FOUND ----------------
% 18.27/18.64 % SZS status Unsatisfiable
% 18.27/18.64
% 18.27/18.64
% 18.27/18.64 After processing input:
% 18.27/18.64
% 18.27/18.64 Usable:
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Sos:
% 18.27/18.64 1 (wt=5) [] multiply(identity,A) = A.
% 18.27/18.64 2 (wt=5) [] multiply(A,identity) = A.
% 18.27/18.64 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 18.27/18.64 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 18.27/18.64 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 18.27/18.64 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 18.27/18.64 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 18.27/18.64 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 18.27/18.64 9 (wt=15) [] multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))).
% 18.27/18.64 10 (wt=15) [] -(multiply(x,multiply(multiply(y,z),x)) = multiply(multiply(x,y),multiply(z,x))).
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Demodulators:
% 18.27/18.64 1 (wt=5) [] multiply(identity,A) = A.
% 18.27/18.64 2 (wt=5) [] multiply(A,identity) = A.
% 18.27/18.64 3 (wt=7) [] multiply(A,left_division(A,B)) = B.
% 18.27/18.64 4 (wt=7) [] left_division(A,multiply(A,B)) = B.
% 18.27/18.64 5 (wt=7) [] multiply(right_division(A,B),B) = A.
% 18.27/18.64 6 (wt=7) [] right_division(multiply(A,B),B) = A.
% 18.27/18.64 7 (wt=6) [] multiply(A,right_inverse(A)) = identity.
% 18.27/18.64 8 (wt=6) [] multiply(left_inverse(A),A) = identity.
% 18.27/18.64 9 (wt=15) [] multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))).
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 Passive:
% 18.27/18.64 end_of_list.
% 18.27/18.64
% 18.27/18.64 UNIT CONFLICT from 7024 and 542 at 17.15 seconds.
% 18.27/18.64
% 18.27/18.64 ---------------- PROOF ----------------
% 18.27/18.64 % SZS output start Refutation
% See solution above
% 18.27/18.64 ------------ end of proof -------------
% 18.27/18.64
% 18.27/18.64
% 18.27/18.64 ------------- memory usage ------------
% 18.27/18.64 Memory dynamically allocated (tp_alloc): 57617.
% 18.27/18.64 type (bytes each) gets frees in use avail bytes
% 18.27/18.64 sym_ent ( 96) 60 0 60 0 5.6 K
% 18.27/18.64 term ( 16) 5563243 4893165 670078 76 13061.5 K
% 18.27/18.64 gen_ptr ( 8) 5522864 810826 4712038 98 36813.6 K
% 18.27/18.64 context ( 808) 2214388 2214386 2 10 9.5 K
% 18.27/18.64 trail ( 12) 2570374 2570374 0 6 0.1 K
% 18.27/18.64 bt_node ( 68) 349761 349758 3 112 7.6 K
% 18.27/18.64 ac_position (285432) 0 0 0 0 0.0 K
% 18.27/18.64 ac_match_pos (14044) 0 0 0 0 0.0 K
% 18.27/18.64 ac_match_free_vars_pos (4020)
% 18.27/18.64 0 0 0 0 0.0 K
% 18.27/18.64 discrim ( 12) 905705 454245 451460 0 5290.5 K
% 18.27/18.64 flat ( 40) 13594485 13594485 0 1239 48.4 K
% 18.27/18.64 discrim_pos ( 12) 215006 215006 0 1 0.0 K
% 18.27/18.64 fpa_head ( 12) 4412 0 4412 0 51.7 K
% 18.27/18.64 fpa_tree ( 28) 123450 123450 0 141 3.9 K
% 18.27/18.64 fpa_pos ( 36) 13041 13041 0 1 0.0 K
% 18.27/18.64 literal ( 12) 31048 24024 7024 1 82.3 K
% 18.27/18.64 clause ( 24) 31048 24024 7024 1 164.6 K
% 18.27/18.64 list ( 12) 6076 6020 56 6 0.7 K
% 18.27/18.64 list_pos ( 20) 32589 13469 19120 0 373.4 K
% 18.27/18.64 pair_index ( 40) 2 0 2 0 0.1 K
% 18.27/18.64
% 18.27/18.64 -------------- statistics -------------
% 18.27/18.64 Clauses input 10
% 18.27/18.64 Usable input 0
% 18.27/18.64 Sos input 10
% 18.27/18.64 Demodulators input 0
% 18.27/18.64 Passive input 0
% 18.27/18.64
% 18.27/18.64 Processed BS (before search) 10
% 18.27/18.64 Forward subsumed BS 0
% 18.27/18.64 Kept BS 10
% 18.27/18.64 New demodulators BS 9
% 18.27/18.64 Back demodulated BS 0
% 18.27/18.64
% 18.27/18.64 Clauses or pairs given 12446
% 18.27/18.64 Clauses generated 22259
% 18.27/18.64 Forward subsumed 15245
% 18.27/18.64 Deleted by weight 0
% 18.27/18.64 Deleted by variable count 0
% 18.27/18.64 Kept 7014
% 18.27/18.64 New demodulators 6008
% 18.27/18.64 Back demodulated 2724
% 18.27/18.64 Ordered paramod prunes 0
% 18.27/18.64 Basic paramod prunes 43299
% 18.27/18.64 Prime paramod prunes 4929
% 18.27/18.64 Semantic prunes 0
% 18.27/18.64
% 18.27/18.64 Rewrite attmepts 1842981
% 18.27/18.64 Rewrites 208737
% 18.27/18.64
% 18.27/18.64 FPA overloads 0
% 18.27/18.64 FPA underloads 0
% 18.27/18.64
% 18.27/18.64 Usable size 0
% 18.27/18.64 Sos size 4299
% 18.27/18.64 Demodulators size 3499
% 18.27/18.64 Passive size 0
% 18.27/18.64 Disabled size 2724
% 18.27/18.64
% 18.27/18.64 Proofs found 1
% 18.27/18.64
% 18.27/18.64 ----------- times (seconds) ----------- Tue Jun 14 03:40:13 2022
% 18.27/18.64
% 18.27/18.64 user CPU time 17.15 (0 hr, 0 min, 17 sec)
% 18.27/18.64 system CPU time 0.33 (0 hr, 0 min, 0 sec)
% 18.27/18.64 wall-clock time 18 (0 hr, 0 min, 18 sec)
% 18.27/18.64 input time 0.00
% 18.27/18.64 paramodulation time 0.21
% 18.27/18.64 demodulation time 0.96
% 18.27/18.64 orient time 0.05
% 18.27/18.64 weigh time 0.01
% 18.27/18.64 forward subsume time 0.09
% 18.27/18.64 back demod find time 14.51
% 18.27/18.64 conflict time 0.01
% 18.27/18.64 LRPO time 0.03
% 18.27/18.64 store clause time 0.98
% 18.27/18.64 disable clause time 0.17
% 18.27/18.64 prime paramod time 0.07
% 18.27/18.64 semantics time 0.00
% 18.27/18.64
% 18.27/18.64 EQP interrupted
%------------------------------------------------------------------------------