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
%------------------------------------------------------------------------------