TSTP Solution File: GRP685-10 by EQP---0.9e
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : GRP685-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n011.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 08:48:52 EDT 2022
% Result : Unsatisfiable 0.87s 1.26s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of clauses : 167 ( 167 unt; 0 nHn; 3 RR)
% Number of literals : 167 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 447 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(ld(A,mult(A,A)),A),
file('GRP685-10.p',unknown),
[] ).
cnf(2,plain,
equal(rd(mult(A,A),A),A),
file('GRP685-10.p',unknown),
[] ).
cnf(3,plain,
equal(mult(A,ld(A,B)),ld(A,mult(A,B))),
file('GRP685-10.p',unknown),
[] ).
cnf(4,plain,
equal(rd(mult(A,B),B),mult(rd(A,B),B)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(5,plain,
equal(mult(rd(A,A),A),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2]),4]),
[iquote('back_demod(2),demod([4])')] ).
cnf(6,plain,
equal(ld(ld(A,B),mult(ld(A,B),mult(C,D))),mult(ld(A,mult(A,C)),D)),
file('GRP685-10.p',unknown),
[] ).
cnf(7,plain,
equal(mult(ld(A,mult(A,B)),C),ld(ld(A,D),mult(ld(A,D),mult(B,C)))),
inference(flip,[status(thm),theory(equality)],[6]),
[iquote('flip(6)')] ).
cnf(8,plain,
equal(mult(rd(mult(A,B),rd(C,D)),rd(C,D)),mult(A,mult(rd(B,D),D))),
inference(demod,[status(thm),theory(equality)],[4,4]),
[iquote('demod([4,4])')] ).
cnf(9,plain,
equal(mult(rd(rd(A,A),B),B),ld(A,mult(A,ld(B,B)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[4]),1]),
[iquote('demod([4]),flip(1)')] ).
cnf(10,plain,
~ equal(mult(rd(x6,ld(x7,x8)),ld(x7,x8)),mult(rd(x6,x8),x8)),
inference(demod,[status(thm),theory(equality)],[4,4]),
[iquote('demod([4,4])')] ).
cnf(12,plain,
equal(rd(A,A),ld(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,4]),9,3,1]),
[iquote('para(5,4),demod([9,3,1])')] ).
cnf(13,plain,
equal(mult(rd(ld(A,A),B),B),ld(A,mult(A,ld(B,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[9]),12]),
[iquote('back_demod(9),demod([12])')] ).
cnf(14,plain,
equal(mult(ld(A,A),A),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[5]),12]),
[iquote('back_demod(5),demod([12])')] ).
cnf(15,plain,
equal(rd(ld(A,mult(A,B)),ld(A,B)),mult(rd(A,ld(A,B)),ld(A,B))),
inference(para,[status(thm),theory(equality)],[3,4]),
[iquote('para(3,4)')] ).
cnf(16,plain,
equal(mult(ld(A,mult(A,B)),C),ld(A,mult(A,mult(B,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,6]),1]),1]),
[iquote('para(1,6),demod([1]),flip(1)')] ).
cnf(17,plain,
equal(ld(ld(A,B),mult(ld(A,B),mult(C,D))),ld(A,mult(A,mult(C,D)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[7]),16]),1]),
[iquote('back_demod(7),demod([16]),flip(1)')] ).
cnf(19,plain,
equal(mult(rd(ld(A,mult(A,B)),rd(C,D)),rd(C,D)),mult(A,mult(rd(ld(A,B),D),D))),
inference(para,[status(thm),theory(equality)],[3,8]),
[iquote('para(3,8)')] ).
cnf(22,plain,
equal(mult(rd(mult(A,B),mult(rd(C,D),D)),mult(rd(C,D),D)),mult(A,mult(rd(B,D),D))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,8]),4]),
[iquote('para(4,8),demod([4])')] ).
cnf(23,plain,
equal(mult(mult(rd(A,rd(B,C)),rd(B,C)),rd(B,C)),mult(A,mult(rd(rd(B,C),C),C))),
inference(para,[status(thm),theory(equality)],[4,8]),
[iquote('para(4,8)')] ).
cnf(24,plain,
equal(mult(A,mult(rd(rd(B,C),C),C)),mult(mult(rd(A,rd(B,C)),rd(B,C)),rd(B,C))),
inference(flip,[status(thm),theory(equality)],[23]),
[iquote('flip(23)')] ).
cnf(26,plain,
equal(ld(A,mult(A,mult(A,B))),mult(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,16]),1]),
[iquote('para(1,16),flip(1)')] ).
cnf(33,plain,
equal(ld(A,mult(A,mult(B,ld(ld(A,mult(A,B)),C)))),ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C))))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,3]),16]),
[iquote('para(16,3),demod([16])')] ).
cnf(35,plain,
equal(mult(A,mult(rd(ld(A,ld(B,B)),C),C)),mult(rd(ld(A,A),B),mult(rd(B,C),C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[13,8]),19]),
[iquote('para(13,8),demod([19])')] ).
cnf(36,plain,
equal(mult(rd(ld(A,A),B),mult(rd(B,C),C)),mult(A,mult(rd(ld(A,ld(B,B)),C),C))),
inference(flip,[status(thm),theory(equality)],[35]),
[iquote('flip(35)')] ).
cnf(37,plain,
equal(rd(ld(A,mult(A,mult(B,C))),C),mult(rd(ld(A,mult(A,B)),C),C)),
inference(para,[status(thm),theory(equality)],[16,4]),
[iquote('para(16,4)')] ).
cnf(41,plain,
equal(mult(rd(A,rd(B,C)),rd(B,C)),mult(ld(A,A),mult(rd(A,C),C))),
inference(para,[status(thm),theory(equality)],[14,8]),
[iquote('para(14,8)')] ).
cnf(42,plain,
equal(mult(A,mult(rd(rd(B,C),C),C)),mult(mult(ld(A,A),mult(rd(A,C),C)),rd(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[24]),41]),
[iquote('back_demod(24),demod([41])')] ).
cnf(43,plain,
equal(mult(mult(ld(A,A),mult(rd(A,B),B)),rd(C,B)),mult(A,mult(rd(rd(C,B),B),B))),
inference(flip,[status(thm),theory(equality)],[42]),
[iquote('flip(42)')] ).
cnf(45,plain,
equal(mult(ld(ld(A,mult(A,B)),ld(A,mult(A,B))),mult(rd(ld(A,mult(A,B)),C),C)),mult(A,mult(rd(ld(A,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[19]),41]),
[iquote('back_demod(19),demod([41])')] ).
cnf(49,plain,
equal(mult(rd(A,ld(A,A)),ld(A,A)),rd(A,ld(A,A))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,15]),1]),
[iquote('para(1,15),flip(1)')] ).
cnf(55,plain,
equal(ld(ld(A,B),mult(ld(A,B),C)),ld(A,mult(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,17]),14]),
[iquote('para(14,17),demod([14])')] ).
cnf(56,plain,
equal(ld(A,ld(A,mult(A,B))),ld(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[55,1]),3]),
[iquote('para(55,1),demod([3])')] ).
cnf(61,plain,
equal(rd(ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C)))),ld(ld(A,mult(A,B)),C)),mult(rd(ld(A,mult(A,B)),ld(ld(A,mult(A,B)),C)),ld(ld(A,mult(A,B)),C))),
inference(para,[status(thm),theory(equality)],[16,15]),
[iquote('para(16,15)')] ).
cnf(62,plain,
equal(mult(ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C)))),D),ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,mult(C,D)))))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,16]),16]),
[iquote('para(16,16),demod([16])')] ).
cnf(64,plain,
equal(ld(ld(A,mult(A,B)),ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C))))),ld(ld(A,mult(A,B)),C)),
inference(para,[status(thm),theory(equality)],[16,56]),
[iquote('para(16,56)')] ).
cnf(68,plain,
equal(ld(A,mult(A,ld(ld(A,B),C))),ld(ld(A,B),ld(A,mult(A,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,55]),55]),1]),
[iquote('para(3,55),demod([55]),flip(1)')] ).
cnf(74,plain,
equal(ld(mult(A,B),mult(mult(A,B),C)),ld(A,mult(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[26,55]),26]),
[iquote('para(26,55),demod([26])')] ).
cnf(75,plain,
equal(mult(rd(mult(A,B),C),C),mult(A,mult(rd(B,C),C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,22]),14,12,14]),
[iquote('para(12,22),demod([14,12,14])')] ).
cnf(82,plain,
equal(mult(ld(A,A),mult(rd(A,B),B)),mult(rd(A,B),B)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,75]),1]),
[iquote('para(14,75),flip(1)')] ).
cnf(83,plain,
equal(mult(rd(ld(A,mult(A,B)),C),C),mult(A,mult(rd(ld(A,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[45]),82]),
[iquote('back_demod(45),demod([82])')] ).
cnf(84,plain,
equal(rd(ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C)))),ld(ld(A,mult(A,B)),C)),mult(A,mult(rd(ld(A,B),ld(ld(A,mult(A,B)),C)),ld(ld(A,mult(A,B)),C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[61]),83]),
[iquote('back_demod(61),demod([83])')] ).
cnf(85,plain,
equal(rd(ld(A,mult(A,mult(B,C))),C),mult(A,mult(rd(ld(A,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[37]),83]),
[iquote('back_demod(37),demod([83])')] ).
cnf(87,plain,
equal(mult(mult(rd(A,B),B),rd(C,B)),mult(A,mult(rd(rd(C,B),B),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[43]),82]),
[iquote('back_demod(43),demod([82])')] ).
cnf(88,plain,
equal(mult(A,mult(rd(rd(B,C),C),C)),mult(mult(rd(A,C),C),rd(B,C))),
inference(flip,[status(thm),theory(equality)],[87]),
[iquote('flip(87)')] ).
cnf(89,plain,
equal(mult(rd(A,rd(B,C)),rd(B,C)),mult(rd(A,C),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[41]),82]),
[iquote('back_demod(41),demod([82])')] ).
cnf(91,plain,
equal(mult(rd(A,ld(B,B)),ld(B,B)),mult(rd(A,B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,89]),12]),
[iquote('para(12,89),demod([12])')] ).
cnf(93,plain,
equal(rd(A,ld(A,A)),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[49]),91,12,14]),1]),
[iquote('back_demod(49),demod([91,12,14]),flip(1)')] ).
cnf(95,plain,
equal(mult(rd(rd(A,B),B),B),rd(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,89]),14]),1]),
[iquote('para(12,89),demod([14]),flip(1)')] ).
cnf(96,plain,
equal(mult(mult(rd(A,B),B),rd(C,B)),mult(A,rd(C,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[88]),95]),1]),
[iquote('back_demod(88),demod([95]),flip(1)')] ).
cnf(107,plain,
equal(mult(mult(rd(A,B),B),ld(B,B)),mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,96]),12]),
[iquote('para(12,96),demod([12])')] ).
cnf(108,plain,
equal(mult(mult(rd(A,B),B),B),mult(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[93,96]),91,93]),
[iquote('para(93,96),demod([91,93])')] ).
cnf(120,plain,
equal(mult(A,ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C))))),mult(A,mult(B,ld(ld(A,mult(A,B)),C)))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[33,3]),26]),
[iquote('para(33,3),demod([26])')] ).
cnf(121,plain,
equal(mult(A,mult(B,ld(ld(A,mult(A,B)),C))),mult(A,ld(ld(A,mult(A,B)),ld(A,mult(A,mult(B,C)))))),
inference(flip,[status(thm),theory(equality)],[120]),
[iquote('flip(120)')] ).
cnf(129,plain,
equal(ld(ld(A,B),ld(A,mult(A,C))),ld(ld(A,B),C)),
inference(para,[status(thm),theory(equality)],[55,56]),
[iquote('para(55,56)')] ).
cnf(133,plain,
equal(mult(A,mult(B,ld(ld(A,mult(A,B)),C))),mult(A,ld(ld(A,mult(A,B)),mult(B,C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[121]),129]),
[iquote('back_demod(121),demod([129])')] ).
cnf(138,plain,
equal(rd(ld(ld(A,mult(A,B)),mult(B,C)),ld(ld(A,mult(A,B)),C)),mult(A,mult(rd(ld(A,B),ld(ld(A,mult(A,B)),C)),ld(ld(A,mult(A,B)),C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[84]),129]),
[iquote('back_demod(84),demod([129])')] ).
cnf(140,plain,
equal(ld(A,mult(A,ld(ld(A,B),C))),ld(ld(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[68]),129]),
[iquote('back_demod(68),demod([129])')] ).
cnf(141,plain,
equal(ld(ld(A,mult(A,B)),ld(ld(A,mult(A,B)),mult(B,C))),ld(ld(A,mult(A,B)),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[64]),129]),
[iquote('back_demod(64),demod([129])')] ).
cnf(142,plain,
equal(mult(ld(ld(A,mult(A,B)),mult(B,C)),D),ld(ld(A,mult(A,B)),mult(B,mult(C,D)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[62]),129,129]),
[iquote('back_demod(62),demod([129,129])')] ).
cnf(153,plain,
equal(ld(ld(A,mult(A,B)),mult(B,C)),ld(A,mult(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,74]),3,16,129]),
[iquote('para(3,74),demod([3,16,129])')] ).
cnf(154,plain,
equal(ld(A,mult(A,B)),ld(ld(A,mult(A,C)),mult(C,B))),
inference(flip,[status(thm),theory(equality)],[153]),
[iquote('flip(153)')] ).
cnf(155,plain,
equal(ld(A,mult(A,ld(mult(A,B),C))),ld(mult(A,B),ld(A,mult(A,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[3,74]),74]),1]),
[iquote('para(3,74),demod([74]),flip(1)')] ).
cnf(170,plain,
equal(mult(A,mult(rd(ld(A,ld(mult(B,C),mult(B,C))),C),C)),ld(A,mult(A,ld(mult(B,C),mult(B,C))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,36]),108,13]),1]),
[iquote('para(4,36),demod([108,13]),flip(1)')] ).
cnf(176,plain,
equal(mult(A,mult(rd(ld(A,ld(ld(B,mult(B,C)),C)),ld(B,C)),ld(B,C))),ld(A,mult(A,ld(ld(B,mult(B,C)),C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[15,36]),108,3,13,129,129]),1]),
[iquote('para(15,36),demod([108,3,13,129,129]),flip(1)')] ).
cnf(177,plain,
equal(ld(mult(A,B),ld(A,mult(A,C))),ld(mult(A,B),C)),
inference(para,[status(thm),theory(equality)],[74,56]),
[iquote('para(74,56)')] ).
cnf(178,plain,
equal(ld(A,mult(A,ld(mult(A,B),C))),ld(mult(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[155]),177]),
[iquote('back_demod(155),demod([177])')] ).
cnf(183,plain,
equal(rd(mult(A,mult(rd(B,C),C)),C),rd(mult(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[75,4]),95]),
[iquote('para(75,4),demod([95])')] ).
cnf(187,plain,
equal(mult(rd(rd(A,B),C),C),mult(rd(rd(A,B),B),mult(rd(B,C),C))),
inference(para,[status(thm),theory(equality)],[95,75]),
[iquote('para(95,75)')] ).
cnf(189,plain,
equal(ld(A,mult(A,ld(mult(rd(A,B),B),mult(rd(A,B),B)))),ld(mult(rd(A,B),B),mult(rd(A,B),B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[82,4]),12,13]),1]),
[iquote('para(82,4),demod([12,13]),flip(1)')] ).
cnf(191,plain,
equal(mult(rd(rd(A,rd(B,C)),C),C),rd(mult(rd(A,C),C),rd(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[89,4]),89]),1]),
[iquote('para(89,4),demod([89]),flip(1)')] ).
cnf(201,plain,
equal(rd(mult(rd(A,B),B),rd(C,B)),rd(A,rd(C,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[89,95]),191]),
[iquote('para(89,95),demod([191])')] ).
cnf(202,plain,
equal(mult(rd(rd(A,rd(B,C)),C),C),rd(A,rd(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[191]),201]),
[iquote('back_demod(191),demod([201])')] ).
cnf(205,plain,
equal(mult(rd(rd(A,ld(B,B)),B),B),rd(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,202]),12]),
[iquote('para(12,202),demod([12])')] ).
cnf(206,plain,
equal(ld(rd(A,B),mult(rd(A,B),ld(B,B))),ld(rd(A,B),rd(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[12,202]),13,12]),
[iquote('para(12,202),demod([13,12])')] ).
cnf(225,plain,
equal(mult(ld(A,A),B),ld(A,mult(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[13,108]),16,14]),1]),
[iquote('para(13,108),demod([16,14]),flip(1)')] ).
cnf(239,plain,
equal(ld(A,mult(A,B)),ld(ld(A,A),B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[225,26]),225,3,26,129,225]),1]),
[iquote('para(225,26),demod([225,3,26,129,225]),flip(1)')] ).
cnf(252,plain,
equal(mult(ld(A,A),B),ld(ld(A,A),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[225]),239]),
[iquote('back_demod(225),demod([239])')] ).
cnf(259,plain,
equal(ld(ld(rd(A,B),rd(A,B)),ld(B,B)),ld(rd(A,B),rd(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[206]),239]),
[iquote('back_demod(206),demod([239])')] ).
cnf(267,plain,
equal(ld(ld(A,A),ld(mult(rd(A,B),B),mult(rd(A,B),B))),ld(mult(rd(A,B),B),mult(rd(A,B),B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[189]),239]),
[iquote('back_demod(189),demod([239])')] ).
cnf(271,plain,
equal(ld(ld(A,A),ld(mult(A,B),C)),ld(mult(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[178]),239]),
[iquote('back_demod(178),demod([239])')] ).
cnf(273,plain,
equal(mult(A,mult(rd(ld(A,ld(ld(ld(B,B),C),C)),ld(B,C)),ld(B,C))),ld(ld(A,A),ld(ld(ld(B,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[176]),239,239,239]),
[iquote('back_demod(176),demod([239,239,239])')] ).
cnf(277,plain,
equal(mult(A,mult(rd(ld(A,ld(mult(B,C),mult(B,C))),C),C)),ld(ld(A,A),ld(mult(B,C),mult(B,C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[170]),239]),
[iquote('back_demod(170),demod([239])')] ).
cnf(288,plain,
equal(ld(ld(ld(A,A),B),mult(B,C)),ld(ld(A,A),C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[154]),239,239]),1]),
[iquote('back_demod(154),demod([239,239]),flip(1)')] ).
cnf(294,plain,
equal(mult(ld(ld(A,A),B),C),ld(ld(A,A),mult(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[142]),239,288,239,288]),
[iquote('back_demod(142),demod([239,288,239,288])')] ).
cnf(295,plain,
equal(ld(ld(ld(A,A),B),ld(ld(A,A),C)),ld(ld(ld(A,A),B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[141]),239,239,288,239]),
[iquote('back_demod(141),demod([239,239,288,239])')] ).
cnf(296,plain,
equal(ld(ld(A,A),ld(ld(A,B),C)),ld(ld(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[140]),239]),
[iquote('back_demod(140),demod([239])')] ).
cnf(297,plain,
equal(rd(ld(ld(A,A),B),ld(ld(ld(A,A),C),B)),mult(A,mult(rd(ld(A,C),ld(ld(ld(A,A),C),B)),ld(ld(ld(A,A),C),B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[138]),239,288,239,239,239]),
[iquote('back_demod(138),demod([239,288,239,239,239])')] ).
cnf(298,plain,
equal(mult(A,mult(rd(ld(A,B),ld(ld(ld(A,A),B),C)),ld(ld(ld(A,A),B),C))),rd(ld(ld(A,A),C),ld(ld(ld(A,A),B),C))),
inference(flip,[status(thm),theory(equality)],[297]),
[iquote('flip(297)')] ).
cnf(302,plain,
equal(mult(A,mult(B,ld(ld(ld(A,A),B),C))),mult(A,ld(ld(A,A),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[133]),239,239,288]),
[iquote('back_demod(133),demod([239,239,288])')] ).
cnf(310,plain,
equal(rd(ld(ld(A,A),mult(B,C)),C),mult(A,mult(rd(ld(A,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[85]),239]),
[iquote('back_demod(85),demod([239])')] ).
cnf(311,plain,
equal(mult(rd(ld(ld(A,A),B),C),C),mult(A,mult(rd(ld(A,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[83]),239]),
[iquote('back_demod(83),demod([239])')] ).
cnf(312,plain,
equal(ld(ld(mult(A,B),mult(A,B)),C),ld(ld(A,A),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[74]),239,239]),
[iquote('back_demod(74),demod([239,239])')] ).
cnf(316,plain,
equal(ld(A,ld(ld(A,A),B)),ld(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[56]),239]),
[iquote('back_demod(56),demod([239])')] ).
cnf(319,plain,
equal(ld(ld(A,A),mult(A,B)),mult(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[26]),239]),
[iquote('back_demod(26),demod([239])')] ).
cnf(320,plain,
equal(rd(ld(ld(A,A),B),ld(A,B)),mult(rd(A,ld(A,B)),ld(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[15]),239]),
[iquote('back_demod(15),demod([239])')] ).
cnf(321,plain,
equal(mult(rd(ld(A,A),B),B),ld(ld(A,A),ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[13]),239]),
[iquote('back_demod(13),demod([239])')] ).
cnf(322,plain,
equal(mult(A,ld(A,B)),ld(ld(A,A),B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3]),239]),
[iquote('back_demod(3),demod([239])')] ).
cnf(335,plain,
equal(mult(rd(mult(A,B),C),mult(rd(C,D),D)),mult(A,mult(rd(B,C),mult(rd(C,D),D)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[75,75]),75,75]),1]),
[iquote('para(75,75),demod([75,75]),flip(1)')] ).
cnf(337,plain,
equal(ld(ld(A,A),ld(A,B)),ld(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[322,239]),316]),1]),
[iquote('para(322,239),demod([316]),flip(1)')] ).
cnf(340,plain,
equal(mult(A,ld(ld(A,A),B)),mult(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[239,322]),319]),
[iquote('para(239,322),demod([319])')] ).
cnf(341,plain,
equal(mult(A,mult(B,ld(ld(ld(A,A),B),C))),mult(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[302]),340]),
[iquote('back_demod(302),demod([340])')] ).
cnf(343,plain,
equal(mult(rd(A,B),mult(rd(B,C),C)),mult(rd(A,ld(B,B)),ld(ld(B,B),ld(C,C)))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[91,75]),75,321]),
[iquote('para(91,75),demod([75,321])')] ).
cnf(344,plain,
equal(mult(rd(A,ld(B,B)),ld(ld(B,B),ld(C,C))),mult(rd(A,B),mult(rd(B,C),C))),
inference(flip,[status(thm),theory(equality)],[343]),
[iquote('flip(343)')] ).
cnf(345,plain,
equal(mult(A,mult(rd(ld(A,ld(rd(B,C),rd(B,C))),C),C)),ld(ld(A,A),ld(C,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[95,36]),89,321]),1]),
[iquote('para(95,36),demod([89,321]),flip(1)')] ).
cnf(350,plain,
equal(mult(mult(A,mult(rd(B,C),C)),C),mult(mult(A,B),C)),
inference(para,[status(thm),theory(equality)],[75,108]),
[iquote('para(75,108)')] ).
cnf(358,plain,
equal(ld(mult(rd(A,B),B),mult(A,ld(B,B))),ld(rd(A,B),rd(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[107,239]),312,259]),
[iquote('para(107,239),demod([312,259])')] ).
cnf(369,plain,
equal(mult(A,mult(rd(ld(A,B),C),C)),ld(ld(A,A),mult(rd(B,C),C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[252,75]),311,252]),
[iquote('para(252,75),demod([311,252])')] ).
cnf(371,plain,
equal(ld(ld(A,A),ld(rd(B,C),rd(B,C))),ld(ld(A,A),ld(C,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[345]),369,321,259]),
[iquote('back_demod(345),demod([369,321,259])')] ).
cnf(375,plain,
equal(rd(ld(ld(A,A),mult(B,C)),C),ld(ld(A,A),mult(rd(B,C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[310]),369]),
[iquote('back_demod(310),demod([369])')] ).
cnf(376,plain,
equal(ld(ld(A,A),mult(rd(B,ld(ld(ld(A,A),B),C)),ld(ld(ld(A,A),B),C))),rd(ld(ld(A,A),C),ld(ld(ld(A,A),B),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[298]),369]),
[iquote('back_demod(298),demod([369])')] ).
cnf(377,plain,
equal(rd(ld(ld(A,A),B),ld(ld(ld(A,A),C),B)),ld(ld(A,A),mult(rd(C,ld(ld(ld(A,A),C),B)),ld(ld(ld(A,A),C),B)))),
inference(flip,[status(thm),theory(equality)],[376]),
[iquote('flip(376)')] ).
cnf(379,plain,
equal(ld(ld(A,A),ld(mult(B,C),mult(B,C))),ld(ld(A,A),ld(ld(B,B),ld(C,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[277]),369,321,312]),1]),
[iquote('back_demod(277),demod([369,321,312]),flip(1)')] ).
cnf(380,plain,
equal(ld(mult(rd(A,B),B),mult(rd(A,B),B)),ld(ld(A,A),ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[267]),379,259,371]),1]),
[iquote('back_demod(267),demod([379,259,371]),flip(1)')] ).
cnf(382,plain,
equal(ld(ld(A,A),mult(rd(ld(ld(ld(B,B),C),C),ld(B,C)),ld(B,C))),ld(ld(A,A),ld(ld(ld(B,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[273]),369]),
[iquote('back_demod(273),demod([369])')] ).
cnf(399,plain,
equal(rd(ld(ld(A,A),B),C),ld(ld(A,A),rd(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[252,183]),375,95,252]),1]),
[iquote('para(252,183),demod([375,95,252]),flip(1)')] ).
cnf(401,plain,
equal(ld(ld(A,A),rd(B,ld(ld(ld(A,A),C),B))),ld(ld(A,A),mult(rd(C,ld(ld(ld(A,A),C),B)),ld(ld(ld(A,A),C),B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[377]),399]),
[iquote('back_demod(377),demod([399])')] ).
cnf(402,plain,
equal(ld(ld(A,A),mult(rd(B,ld(ld(ld(A,A),B),C)),ld(ld(ld(A,A),B),C))),ld(ld(A,A),rd(C,ld(ld(ld(A,A),B),C)))),
inference(flip,[status(thm),theory(equality)],[401]),
[iquote('flip(401)')] ).
cnf(403,plain,
equal(ld(ld(A,A),rd(B,ld(A,B))),mult(rd(A,ld(A,B)),ld(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[320]),399]),
[iquote('back_demod(320),demod([399])')] ).
cnf(404,plain,
equal(mult(rd(A,ld(A,B)),ld(A,B)),ld(ld(A,A),rd(B,ld(A,B)))),
inference(flip,[status(thm),theory(equality)],[403]),
[iquote('flip(403)')] ).
cnf(417,plain,
equal(mult(mult(rd(A,B),B),ld(ld(B,B),ld(C,C))),mult(A,ld(ld(B,B),ld(C,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[107,75]),75,321,321]),1]),
[iquote('para(107,75),demod([75,321,321]),flip(1)')] ).
cnf(419,plain,
equal(mult(mult(rd(A,B),B),ld(rd(C,B),rd(C,B))),mult(A,ld(rd(C,B),rd(C,B)))),
inference(para,[status(thm),theory(equality)],[89,107]),
[iquote('para(89,107)')] ).
cnf(423,plain,
equal(ld(ld(A,A),ld(ld(ld(A,A),B),C)),ld(ld(ld(A,A),B),C)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[252,271]),337,252]),
[iquote('para(252,271),demod([337,252])')] ).
cnf(439,plain,
equal(ld(ld(ld(A,A),ld(B,B)),ld(ld(B,B),C)),ld(ld(A,A),C)),
inference(para,[status(thm),theory(equality)],[252,288]),
[iquote('para(252,288)')] ).
cnf(445,plain,
equal(ld(ld(ld(ld(A,A),B),B),C),ld(ld(A,A),C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[294,239]),295,288,295]),1]),
[iquote('para(294,239),demod([295,288,295]),flip(1)')] ).
cnf(451,plain,
equal(ld(ld(ld(A,A),ld(B,B)),C),ld(ld(A,A),C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[108,312]),108,312,380]),1]),
[iquote('para(108,312),demod([108,312,380]),flip(1)')] ).
cnf(452,plain,
equal(ld(ld(A,A),ld(ld(B,B),C)),ld(ld(A,A),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[439]),451]),
[iquote('back_demod(439),demod([451])')] ).
cnf(488,plain,
equal(ld(ld(ld(A,A),B),ld(ld(B,B),C)),ld(ld(A,A),ld(B,C))),
inference(para,[status(thm),theory(equality)],[322,288]),
[iquote('para(322,288)')] ).
cnf(493,plain,
equal(rd(mult(A,B),mult(C,ld(ld(ld(A,A),C),B))),mult(rd(A,mult(C,ld(ld(ld(A,A),C),B))),mult(C,ld(ld(ld(A,A),C),B)))),
inference(para,[status(thm),theory(equality)],[341,4]),
[iquote('para(341,4)')] ).
cnf(496,plain,
equal(mult(rd(A,B),B),mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[93,187]),93,93,321,340]),
[iquote('para(93,187),demod([93,93,321,340])')] ).
cnf(499,plain,
equal(rd(mult(A,B),mult(C,ld(ld(ld(A,A),C),B))),mult(A,ld(mult(C,ld(ld(ld(A,A),C),B)),mult(C,ld(ld(ld(A,A),C),B))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[493]),496]),
[iquote('back_demod(493),demod([496])')] ).
cnf(528,plain,
equal(mult(mult(A,ld(B,B)),ld(rd(C,B),rd(C,B))),mult(A,ld(rd(C,B),rd(C,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[419]),496]),
[iquote('back_demod(419),demod([496])')] ).
cnf(530,plain,
equal(mult(mult(A,ld(B,B)),ld(ld(B,B),ld(C,C))),mult(A,ld(ld(B,B),ld(C,C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[417]),496]),
[iquote('back_demod(417),demod([496])')] ).
cnf(536,plain,
equal(ld(ld(A,A),rd(B,ld(A,B))),mult(A,ld(ld(A,B),ld(A,B)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[404]),496]),1]),
[iquote('back_demod(404),demod([496]),flip(1)')] ).
cnf(537,plain,
equal(ld(ld(A,A),rd(B,ld(ld(ld(A,A),C),B))),ld(ld(A,A),mult(C,ld(ld(ld(ld(A,A),C),B),ld(ld(ld(A,A),C),B))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[402]),496]),1]),
[iquote('back_demod(402),demod([496]),flip(1)')] ).
cnf(541,plain,
equal(ld(ld(A,A),mult(ld(ld(ld(B,B),C),C),ld(ld(B,C),ld(B,C)))),ld(ld(A,A),ld(ld(ld(B,B),C),C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[382]),496]),
[iquote('back_demod(382),demod([496])')] ).
cnf(542,plain,
equal(ld(mult(A,ld(B,B)),mult(A,ld(B,B))),ld(ld(A,A),ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[380]),496,496]),
[iquote('back_demod(380),demod([496,496])')] ).
cnf(550,plain,
equal(ld(rd(A,B),rd(A,B)),ld(ld(A,A),ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[358]),496,542]),1]),
[iquote('back_demod(358),demod([496,542]),flip(1)')] ).
cnf(551,plain,
equal(mult(mult(A,ld(B,B)),ld(ld(C,C),ld(B,B))),mult(A,ld(ld(C,C),ld(B,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[528]),550,550]),
[iquote('back_demod(528),demod([550,550])')] ).
cnf(565,plain,
equal(mult(mult(A,mult(B,ld(C,C))),C),mult(mult(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[350]),496]),
[iquote('back_demod(350),demod([496])')] ).
cnf(570,plain,
equal(mult(rd(A,ld(B,B)),ld(ld(B,B),ld(C,C))),mult(rd(A,B),mult(B,ld(C,C)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[344]),496]),
[iquote('back_demod(344),demod([496])')] ).
cnf(572,plain,
equal(mult(rd(mult(A,B),C),mult(C,ld(D,D))),mult(A,mult(rd(B,C),mult(C,ld(D,D))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[335]),496,496]),
[iquote('back_demod(335),demod([496,496])')] ).
cnf(580,plain,
equal(rd(A,ld(B,B)),mult(A,ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[205]),496,496,337]),1]),
[iquote('back_demod(205),demod([496,496,337]),flip(1)')] ).
cnf(581,plain,
equal(mult(rd(A,B),mult(B,ld(C,C))),mult(A,ld(ld(B,B),ld(C,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[570]),580,530]),1]),
[iquote('back_demod(570),demod([580,530]),flip(1)')] ).
cnf(585,plain,
equal(mult(mult(A,B),ld(ld(C,C),ld(D,D))),mult(A,mult(B,ld(ld(C,C),ld(D,D))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[572]),581,581]),
[iquote('back_demod(572),demod([581,581])')] ).
cnf(586,plain,
equal(mult(A,ld(ld(B,B),ld(C,C))),mult(A,ld(C,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[551]),585,252,452,337]),1]),
[iquote('back_demod(551),demod([585,252,452,337]),flip(1)')] ).
cnf(603,plain,
equal(mult(mult(A,ld(B,B)),B),mult(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[108]),496]),
[iquote('back_demod(108),demod([496])')] ).
cnf(605,plain,
equal(mult(rd(A,B),ld(B,B)),rd(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[95]),496]),
[iquote('back_demod(95),demod([496])')] ).
cnf(607,plain,
~ equal(mult(x6,ld(ld(x7,x8),ld(x7,x8))),mult(x6,ld(x8,x8))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[10]),496,496]),
[iquote('back_demod(10),demod([496,496])')] ).
cnf(608,plain,
equal(rd(mult(A,B),B),mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[4]),496]),
[iquote('back_demod(4),demod([496])')] ).
cnf(610,plain,
equal(rd(mult(A,ld(B,B)),B),rd(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[496,608]),605]),
[iquote('para(496,608),demod([605])')] ).
cnf(627,plain,
equal(mult(ld(ld(ld(A,A),B),B),C),ld(ld(A,A),C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[445,319]),423,239,445,423,445]),1]),
[iquote('para(445,319),demod([423,239,445,423,445]),flip(1)')] ).
cnf(629,plain,
equal(ld(ld(A,A),ld(ld(ld(B,B),C),C)),ld(ld(A,A),ld(ld(B,C),ld(B,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[541]),627,296]),1]),
[iquote('back_demod(541),demod([627,296]),flip(1)')] ).
cnf(639,plain,
equal(ld(A,ld(ld(B,B),C)),ld(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[452,316]),316]),1]),
[iquote('para(452,316),demod([316]),flip(1)')] ).
cnf(646,plain,
equal(ld(ld(ld(A,A),B),C),ld(ld(A,A),ld(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[488]),639]),
[iquote('back_demod(488),demod([639])')] ).
cnf(647,plain,
equal(ld(ld(A,A),ld(ld(B,C),ld(B,C))),ld(ld(A,A),ld(C,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[629]),646,639]),1]),
[iquote('back_demod(629),demod([646,639]),flip(1)')] ).
cnf(651,plain,
equal(ld(ld(A,A),rd(B,ld(ld(A,A),ld(C,B)))),ld(ld(A,A),mult(C,ld(B,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[537]),646,646,646,639,646,647,586]),
[iquote('back_demod(537),demod([646,646,646,639,646,647,586])')] ).
cnf(655,plain,
equal(rd(mult(A,B),mult(C,ld(ld(A,A),ld(C,B)))),mult(A,ld(mult(C,ld(ld(A,A),ld(C,B))),mult(C,ld(ld(A,A),ld(C,B)))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[499]),646,646,646]),
[iquote('back_demod(499),demod([646,646,646])')] ).
cnf(660,plain,
equal(mult(A,ld(ld(B,B),C)),mult(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[639,340]),340]),1]),
[iquote('para(639,340),demod([340]),flip(1)')] ).
cnf(661,plain,
equal(rd(mult(A,B),ld(ld(C,C),B)),mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[655]),660,322,660,322,660,322,639,646,660]),
[iquote('back_demod(655),demod([660,322,660,322,660,322,639,646,660])')] ).
cnf(675,plain,
equal(mult(mult(A,ld(B,B)),C),mult(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[252,565]),660,603]),1]),
[iquote('para(252,565),demod([660,603]),flip(1)')] ).
cnf(680,plain,
equal(rd(mult(A,ld(B,B)),C),rd(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[675,610]),610]),1]),
[iquote('para(675,610),demod([610]),flip(1)')] ).
cnf(739,plain,
equal(rd(A,ld(ld(B,B),C)),rd(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[496,661]),680,605]),
[iquote('para(496,661),demod([680,605])')] ).
cnf(740,plain,
equal(ld(ld(A,A),rd(B,ld(C,B))),ld(ld(A,A),mult(C,ld(B,B)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[651]),739]),
[iquote('back_demod(651),demod([739])')] ).
cnf(742,plain,
equal(mult(A,ld(ld(A,B),ld(A,B))),mult(A,ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[536]),740,319]),1]),
[iquote('back_demod(536),demod([740,319]),flip(1)')] ).
cnf(785,plain,
equal(ld(ld(A,A),ld(B,B)),ld(ld(A,B),ld(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[742,239]),239,296]),
[iquote('para(742,239),demod([239,296])')] ).
cnf(817,plain,
equal(mult(A,ld(ld(B,C),ld(B,C))),mult(A,ld(C,C))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[785,739]),580,580]),
[iquote('para(785,739),demod([580,580])')] ).
cnf(818,plain,
$false,
inference(conflict,[status(thm)],[817,607]),
[iquote('conflict(817,607)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP685-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_eqp %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 07:28:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.87/1.26 ----- EQP 0.9e, May 2009 -----
% 0.87/1.26 The job began on n011.cluster.edu, Tue Jun 14 07:28:05 2022
% 0.87/1.26 The command was "./eqp09e".
% 0.87/1.26
% 0.87/1.26 set(prolog_style_variables).
% 0.87/1.26 set(lrpo).
% 0.87/1.26 set(basic_paramod).
% 0.87/1.26 set(functional_subsume).
% 0.87/1.26 set(ordered_paramod).
% 0.87/1.26 set(prime_paramod).
% 0.87/1.26 set(para_pairs).
% 0.87/1.26 assign(pick_given_ratio,4).
% 0.87/1.26 clear(print_kept).
% 0.87/1.26 clear(print_new_demod).
% 0.87/1.26 clear(print_back_demod).
% 0.87/1.26 clear(print_given).
% 0.87/1.26 assign(max_mem,64000).
% 0.87/1.26 end_of_commands.
% 0.87/1.26
% 0.87/1.26 Usable:
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Sos:
% 0.87/1.26 0 (wt=-1) [] ld(A,mult(A,A)) = A.
% 0.87/1.26 0 (wt=-1) [] rd(mult(A,A),A) = A.
% 0.87/1.26 0 (wt=-1) [] mult(A,ld(A,B)) = ld(A,mult(A,B)).
% 0.87/1.26 0 (wt=-1) [] mult(rd(A,B),B) = rd(mult(A,B),B).
% 0.87/1.26 0 (wt=-1) [] ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D).
% 0.87/1.26 0 (wt=-1) [] rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)).
% 0.87/1.26 0 (wt=-1) [] ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B).
% 0.87/1.26 0 (wt=-1) [] -(rd(mult(x6,ld(x7,x8)),ld(x7,x8)) = rd(mult(x6,x8),x8)).
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Demodulators:
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Passive:
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Starting to process input.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 1 (wt=7) [] ld(A,mult(A,A)) = A.
% 0.87/1.26 1 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 2 (wt=7) [] rd(mult(A,A),A) = A.
% 0.87/1.26 2 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 3 (wt=11) [] mult(A,ld(A,B)) = ld(A,mult(A,B)).
% 0.87/1.26 3 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 4 (wt=11) [flip(1)] rd(mult(A,B),B) = mult(rd(A,B),B).
% 0.87/1.26 4 is a new demodulator.
% 0.87/1.26 -> 4 back demodulating 2.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 5 (wt=7) [back_demod(2),demod([4])] mult(rd(A,A),A) = A.
% 0.87/1.26 5 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 6 (wt=19) [] ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D).
% 0.87/1.26
% 0.87/1.26 ** KEPT: 7 (wt=19) [flip(6)] mult(ld(A,mult(A,B)),C) = ld(ld(A,D),mult(ld(A,D),mult(B,C))).
% 0.87/1.26 clause forward subsumed: 0 (wt=19) [flip(7)] ld(ld(A,D),mult(ld(A,D),mult(B,C))) = mult(ld(A,mult(A,B)),C).
% 0.87/1.26
% 0.87/1.26 ** KEPT: 8 (wt=19) [demod([4,4])] mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)).
% 0.87/1.26 8 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 9 (wt=15) [demod([4]),flip(1)] mult(rd(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))).
% 0.87/1.26 9 is a new demodulator.
% 0.87/1.26
% 0.87/1.26 ** KEPT: 10 (wt=15) [demod([4,4])] -(mult(rd(x6,ld(x7,x8)),ld(x7,x8)) = mult(rd(x6,x8),x8)).
% 0.87/1.26 ---------------- PROOF FOUND ----------------
% 0.87/1.26 % SZS status Unsatisfiable
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 After processing input:
% 0.87/1.26
% 0.87/1.26 Usable:
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Sos:
% 0.87/1.26 1 (wt=7) [] ld(A,mult(A,A)) = A.
% 0.87/1.26 5 (wt=7) [back_demod(2),demod([4])] mult(rd(A,A),A) = A.
% 0.87/1.26 3 (wt=11) [] mult(A,ld(A,B)) = ld(A,mult(A,B)).
% 0.87/1.26 4 (wt=11) [flip(1)] rd(mult(A,B),B) = mult(rd(A,B),B).
% 0.87/1.26 9 (wt=15) [demod([4]),flip(1)] mult(rd(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))).
% 0.87/1.26 10 (wt=15) [demod([4,4])] -(mult(rd(x6,ld(x7,x8)),ld(x7,x8)) = mult(rd(x6,x8),x8)).
% 0.87/1.26 6 (wt=19) [] ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D).
% 0.87/1.26 7 (wt=19) [flip(6)] mult(ld(A,mult(A,B)),C) = ld(ld(A,D),mult(ld(A,D),mult(B,C))).
% 0.87/1.26 8 (wt=19) [demod([4,4])] mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)).
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Demodulators:
% 0.87/1.26 1 (wt=7) [] ld(A,mult(A,A)) = A.
% 0.87/1.26 3 (wt=11) [] mult(A,ld(A,B)) = ld(A,mult(A,B)).
% 0.87/1.26 4 (wt=11) [flip(1)] rd(mult(A,B),B) = mult(rd(A,B),B).
% 0.87/1.26 5 (wt=7) [back_demod(2),demod([4])] mult(rd(A,A),A) = A.
% 0.87/1.26 8 (wt=19) [demod([4,4])] mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)).
% 0.87/1.26 9 (wt=15) [demod([4]),flip(1)] mult(rd(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))).
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 Passive:
% 0.87/1.26 end_of_list.
% 0.87/1.26
% 0.87/1.26 UNIT CONFLICT from 817 and 607 at 0.08 seconds.
% 0.87/1.26
% 0.87/1.26 ---------------- PROOF ----------------
% 0.87/1.26 % SZS output start Refutation
% See solution above
% 0.87/1.27 ------------ end of proof -------------
% 0.87/1.27
% 0.87/1.27
% 0.87/1.27 ------------- memory usage ------------
% 0.87/1.27 Memory dynamically allocated (tp_alloc): 1464.
% 0.87/1.27 type (bytes each) gets frees in use avail bytes
% 0.87/1.27 sym_ent ( 96) 58 0 58 0 5.4 K
% 0.87/1.27 term ( 16) 130374 110491 19883 44 386.0 K
% 0.87/1.27 gen_ptr ( 8) 121722 38880 82842 166 648.5 K
% 0.87/1.27 context ( 808) 73267 73265 2 6 6.3 K
% 0.87/1.27 trail ( 12) 6032 6032 0 6 0.1 K
% 0.87/1.27 bt_node ( 68) 22734 22729 5 18 1.5 K
% 0.87/1.27 ac_position (285432) 0 0 0 0 0.0 K
% 0.87/1.27 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.87/1.27 ac_match_free_vars_pos (4020)
% 0.87/1.27 0 0 0 0 0.0 K
% 0.87/1.27 discrim ( 12) 19335 15939 3396 787 49.0 K
% 0.87/1.27 flat ( 40) 244864 244864 0 43 1.7 K
% 0.87/1.27 discrim_pos ( 12) 7138 7138 0 1 0.0 K
% 0.87/1.27 fpa_head ( 12) 5768 0 5768 0 67.6 K
% 0.87/1.27 fpa_tree ( 28) 2753 2753 0 25 0.7 K
% 0.87/1.27 fpa_pos ( 36) 1474 1474 0 1 0.0 K
% 0.87/1.27 literal ( 12) 3894 3077 817 1 9.6 K
% 0.87/1.27 clause ( 24) 3894 3077 817 1 19.2 K
% 0.87/1.27 list ( 12) 716 660 56 7 0.7 K
% 0.87/1.27 list_pos ( 20) 4436 3134 1302 0 25.4 K
% 0.87/1.27 pair_index ( 40) 2 0 2 0 0.1 K
% 0.87/1.27
% 0.87/1.27 -------------- statistics -------------
% 0.87/1.27 Clauses input 8
% 0.87/1.27 Usable input 0
% 0.87/1.27 Sos input 8
% 0.87/1.27 Demodulators input 0
% 0.87/1.27 Passive input 0
% 0.87/1.27
% 0.87/1.27 Processed BS (before search) 11
% 0.87/1.27 Forward subsumed BS 1
% 0.87/1.27 Kept BS 10
% 0.87/1.27 New demodulators BS 7
% 0.87/1.27 Back demodulated BS 1
% 0.87/1.27
% 0.87/1.27 Clauses or pairs given 2493
% 0.87/1.27 Clauses generated 2544
% 0.87/1.27 Forward subsumed 1737
% 0.87/1.27 Deleted by weight 0
% 0.87/1.27 Deleted by variable count 0
% 0.87/1.27 Kept 807
% 0.87/1.27 New demodulators 650
% 0.87/1.27 Back demodulated 637
% 0.87/1.27 Ordered paramod prunes 0
% 0.87/1.27 Basic paramod prunes 3261
% 0.87/1.27 Prime paramod prunes 150
% 0.87/1.27 Semantic prunes 0
% 0.87/1.27
% 0.87/1.27 Rewrite attmepts 42795
% 0.87/1.27 Rewrites 6774
% 0.87/1.27
% 0.87/1.27 FPA overloads 0
% 0.87/1.27 FPA underloads 0
% 0.87/1.27
% 0.87/1.27 Usable size 0
% 0.87/1.27 Sos size 178
% 0.87/1.27 Demodulators size 130
% 0.87/1.27 Passive size 0
% 0.87/1.27 Disabled size 638
% 0.87/1.27
% 0.87/1.27 Proofs found 1
% 0.87/1.27
% 0.87/1.27 ----------- times (seconds) ----------- Tue Jun 14 07:28:05 2022
% 0.87/1.27
% 0.87/1.27 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 0.87/1.27 system CPU time 0.07 (0 hr, 0 min, 0 sec)
% 0.87/1.27 wall-clock time 0 (0 hr, 0 min, 0 sec)
% 0.87/1.27 input time 0.00
% 0.87/1.27 paramodulation time 0.01
% 0.87/1.27 demodulation time 0.01
% 0.87/1.27 orient time 0.01
% 0.87/1.27 weigh time 0.01
% 0.87/1.27 forward subsume time 0.00
% 0.87/1.27 back demod find time 0.00
% 0.87/1.27 conflict time 0.00
% 0.87/1.27 LRPO time 0.01
% 0.87/1.27 store clause time 0.01
% 0.87/1.27 disable clause time 0.01
% 0.87/1.27 prime paramod time 0.00
% 0.87/1.27 semantics time 0.00
% 0.87/1.27
% 0.87/1.27 EQP interrupted
%------------------------------------------------------------------------------