TSTP Solution File: REL013+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:11:49 EDT 2022

% Result   : Theorem 2.04s 2.20s
% Output   : Refutation 2.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   15
% Syntax   : Number of clauses     :  102 ( 100 unt;   0 nHn;  19 RR)
%            Number of literals    :  104 ( 103 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  120 (  14 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( composition(dollar_c1,zero) != zero
    | composition(zero,dollar_c1) != zero ),
    file('REL013+1.p',unknown),
    [] ).

cnf(2,axiom,
    A = A,
    file('REL013+1.p',unknown),
    [] ).

cnf(3,axiom,
    join(A,B) = join(B,A),
    file('REL013+1.p',unknown),
    [] ).

cnf(4,axiom,
    join(A,join(B,C)) = join(join(A,B),C),
    file('REL013+1.p',unknown),
    [] ).

cnf(6,plain,
    join(join(A,B),C) = join(A,join(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
    [iquote('copy,4,flip.1')] ).

cnf(7,axiom,
    A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
    file('REL013+1.p',unknown),
    [] ).

cnf(8,plain,
    join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(10,axiom,
    meet(A,B) = complement(join(complement(A),complement(B))),
    file('REL013+1.p',unknown),
    [] ).

cnf(12,plain,
    complement(join(complement(A),complement(B))) = meet(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
    [iquote('copy,10,flip.1')] ).

cnf(13,axiom,
    composition(A,composition(B,C)) = composition(composition(A,B),C),
    file('REL013+1.p',unknown),
    [] ).

cnf(14,plain,
    composition(composition(A,B),C) = composition(A,composition(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
    [iquote('copy,13,flip.1')] ).

cnf(16,axiom,
    composition(A,one) = A,
    file('REL013+1.p',unknown),
    [] ).

cnf(18,axiom,
    composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
    file('REL013+1.p',unknown),
    [] ).

cnf(19,plain,
    join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
    [iquote('copy,18,flip.1')] ).

cnf(22,axiom,
    converse(converse(A)) = A,
    file('REL013+1.p',unknown),
    [] ).

cnf(23,axiom,
    converse(join(A,B)) = join(converse(A),converse(B)),
    file('REL013+1.p',unknown),
    [] ).

cnf(25,axiom,
    converse(composition(A,B)) = composition(converse(B),converse(A)),
    file('REL013+1.p',unknown),
    [] ).

cnf(27,axiom,
    join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
    file('REL013+1.p',unknown),
    [] ).

cnf(29,axiom,
    top = join(A,complement(A)),
    file('REL013+1.p',unknown),
    [] ).

cnf(30,plain,
    join(A,complement(A)) = top,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[29])]),
    [iquote('copy,29,flip.1')] ).

cnf(32,axiom,
    zero = meet(A,complement(A)),
    file('REL013+1.p',unknown),
    [] ).

cnf(34,plain,
    meet(A,complement(A)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
    [iquote('copy,32,flip.1')] ).

cnf(35,plain,
    join(meet(A,B),complement(join(complement(A),B))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),12]),
    [iquote('back_demod,8,demod,12')] ).

cnf(37,plain,
    join(complement(A),A) = top,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,30])]),
    [iquote('para_into,3.1.1,30.1.1,flip.1')] ).

cnf(40,plain,
    complement(join(meet(A,B),complement(C))) = meet(join(complement(A),complement(B)),C),
    inference(para_into,[status(thm),theory(equality)],[12,12]),
    [iquote('para_into,11.1.1.1.1,11.1.1')] ).

cnf(43,plain,
    complement(top) = meet(complement(A),A),
    inference(para_into,[status(thm),theory(equality)],[12,37]),
    [iquote('para_into,11.1.1.1,37.1.1')] ).

cnf(45,plain,
    complement(top) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,30]),34]),
    [iquote('para_into,11.1.1.1,30.1.1,demod,34')] ).

cnf(46,plain,
    meet(A,B) = meet(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,3]),12]),
    [iquote('para_into,11.1.1.1,3.1.1,demod,12')] ).

cnf(47,plain,
    meet(complement(A),A) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])]),45]),
    [iquote('copy,43,flip.1,demod,45')] ).

cnf(51,plain,
    meet(join(complement(A),complement(B)),meet(A,B)) = zero,
    inference(para_from,[status(thm),theory(equality)],[12,34]),
    [iquote('para_from,11.1.1,33.1.1.2')] ).

cnf(53,plain,
    join(complement(A),join(complement(B),meet(A,B))) = top,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[12,30]),6]),
    [iquote('para_from,11.1.1,30.1.1.2,demod,6')] ).

cnf(56,plain,
    complement(join(complement(A),zero)) = meet(A,top),
    inference(para_from,[status(thm),theory(equality)],[45,12]),
    [iquote('para_from,44.1.1,11.1.1.1.2')] ).

cnf(57,plain,
    join(zero,top) = top,
    inference(para_from,[status(thm),theory(equality)],[45,37]),
    [iquote('para_from,44.1.1,37.1.1.1')] ).

cnf(61,plain,
    join(top,zero) = top,
    inference(para_from,[status(thm),theory(equality)],[45,30]),
    [iquote('para_from,44.1.1,30.1.1.2')] ).

cnf(63,plain,
    complement(join(zero,complement(A))) = meet(top,A),
    inference(para_from,[status(thm),theory(equality)],[45,12]),
    [iquote('para_from,44.1.1,11.1.1.1.1')] ).

cnf(65,plain,
    join(zero,join(top,A)) = join(top,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,57])]),
    [iquote('para_into,5.1.1.1,57.1.1,flip.1')] ).

cnf(71,plain,
    join(A,join(B,C)) = join(B,join(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,3]),6]),
    [iquote('para_into,5.1.1.1,3.1.1,demod,6')] ).

cnf(76,plain,
    join(top,join(zero,A)) = join(top,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,6])]),
    [iquote('para_from,61.1.1,5.1.1.1,flip.1')] ).

cnf(82,plain,
    composition(A,composition(one,B)) = composition(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,16])]),
    [iquote('para_into,14.1.1.1,16.1.1,flip.1')] ).

cnf(86,plain,
    complement(join(zero,zero)) = meet(top,top),
    inference(para_into,[status(thm),theory(equality)],[56,45]),
    [iquote('para_into,55.1.1.1.1,44.1.1')] ).

cnf(98,plain,
    meet(meet(top,top),join(zero,zero)) = zero,
    inference(para_from,[status(thm),theory(equality)],[86,47]),
    [iquote('para_from,86.1.1,47.1.1.1')] ).

cnf(124,plain,
    join(composition(A,B),composition(C,composition(D,B))) = composition(join(A,composition(C,D)),B),
    inference(para_into,[status(thm),theory(equality)],[19,14]),
    [iquote('para_into,19.1.1.2,14.1.1')] ).

cnf(129,plain,
    join(zero,join(A,top)) = join(top,A),
    inference(para_into,[status(thm),theory(equality)],[65,3]),
    [iquote('para_into,65.1.1.2,3.1.1')] ).

cnf(165,plain,
    composition(converse(one),converse(A)) = converse(A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,16])]),
    [iquote('para_into,25.1.1.1,16.1.1,flip.1')] ).

cnf(172,plain,
    composition(converse(one),A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[165,22]),22]),
    [iquote('para_into,165.1.1.2,21.1.1,demod,22')] ).

cnf(174,plain,
    composition(one,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[172,82]),172])]),
    [iquote('para_into,171.1.1,82.1.1,demod,172,flip.1')] ).

cnf(175,plain,
    converse(one) = one,
    inference(para_into,[status(thm),theory(equality)],[172,16]),
    [iquote('para_into,171.1.1,16.1.1')] ).

cnf(182,plain,
    join(complement(A),complement(A)) = complement(A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,175]),174,174]),
    [iquote('para_into,27.1.1.1.1,175.1.1,demod,174,174')] ).

cnf(197,plain,
    join(composition(converse(A),complement(composition(A,top))),zero) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,45]),45]),
    [iquote('para_into,27.1.1.2,44.1.1,demod,45')] ).

cnf(214,plain,
    join(zero,zero) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[182,45]),45,45]),
    [iquote('para_into,181.1.1.1,44.1.1,demod,45,45')] ).

cnf(216,plain,
    join(meet(A,B),meet(A,B)) = meet(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[182,12]),12,12]),
    [iquote('para_into,181.1.1.1,11.1.1,demod,12,12')] ).

cnf(225,plain,
    meet(meet(top,top),zero) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[98]),214]),
    [iquote('back_demod,98,demod,214')] ).

cnf(227,plain,
    complement(zero) = meet(top,top),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),214]),
    [iquote('back_demod,86,demod,214')] ).

cnf(242,plain,
    complement(complement(A)) = meet(A,A),
    inference(para_from,[status(thm),theory(equality)],[182,12]),
    [iquote('para_from,181.1.1,11.1.1.1')] ).

cnf(262,plain,
    join(zero,meet(A,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,34]),182,242]),
    [iquote('para_into,35.1.1.1,33.1.1,demod,182,242')] ).

cnf(274,plain,
    join(meet(A,A),zero) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,37]),45]),
    [iquote('para_into,35.1.1.2.1,37.1.1,demod,45')] ).

cnf(275,plain,
    join(meet(A,meet(A,A)),zero) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,30]),242,45]),
    [iquote('para_into,35.1.1.2.1,30.1.1,demod,242,45')] ).

cnf(289,plain,
    join(zero,meet(meet(top,top),top)) = meet(top,top),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[225,35]),56]),
    [iquote('para_from,225.1.1,35.1.1.1,demod,56')] ).

cnf(298,plain,
    complement(meet(A,B)) = meet(join(complement(A),complement(B)),join(complement(A),complement(B))),
    inference(para_into,[status(thm),theory(equality)],[242,12]),
    [iquote('para_into,241.1.1.1,11.1.1')] ).

cnf(301,plain,
    meet(top,complement(A)) = complement(A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[242,63]),262])]),
    [iquote('para_from,241.1.1,63.1.1.1.2,demod,262,flip.1')] ).

cnf(303,plain,
    meet(complement(A),top) = complement(A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[242,56]),274])]),
    [iquote('para_from,241.1.1,55.1.1.1.1,demod,274,flip.1')] ).

cnf(305,plain,
    meet(meet(A,A),complement(A)) = zero,
    inference(para_from,[status(thm),theory(equality)],[242,47]),
    [iquote('para_from,241.1.1,47.1.1.1')] ).

cnf(311,plain,
    join(complement(A),meet(A,A)) = top,
    inference(para_from,[status(thm),theory(equality)],[242,30]),
    [iquote('para_from,241.1.1,30.1.1.2')] ).

cnf(316,plain,
    join(top,meet(A,A)) = join(top,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[262,76])]),
    [iquote('para_from,261.1.1,76.1.1.2,flip.1')] ).

cnf(321,plain,
    join(converse(meet(A,A)),converse(zero)) = converse(A),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[274,23])]),
    [iquote('para_from,273.1.1,23.1.1.1,flip.1')] ).

cnf(363,plain,
    meet(top,meet(A,B)) = meet(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[301,12]),12]),
    [iquote('para_into,301.1.1.2,11.1.1,demod,12')] ).

cnf(367,plain,
    meet(meet(A,A),top) = meet(A,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[303,242]),242]),
    [iquote('para_into,303.1.1.1,241.1.1,demod,242')] ).

cnf(377,plain,
    meet(top,top) = top,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[289]),367,262])]),
    [iquote('back_demod,289,demod,367,262,flip.1')] ).

cnf(382,plain,
    complement(zero) = top,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[227]),377]),
    [iquote('back_demod,227,demod,377')] ).

cnf(386,plain,
    join(complement(A),complement(join(meet(A,A),top))) = complement(A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[303,35]),242]),
    [iquote('para_from,303.1.1,35.1.1.1,demod,242')] ).

cnf(389,plain,
    complement(join(meet(A,B),top)) = meet(join(complement(A),complement(B)),zero),
    inference(para_from,[status(thm),theory(equality)],[382,40]),
    [iquote('para_from,382.1.1,39.1.1.1.2')] ).

cnf(398,plain,
    join(complement(A),meet(complement(A),zero)) = complement(A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[386]),389,182]),
    [iquote('back_demod,386,demod,389,182')] ).

cnf(439,plain,
    join(zero,meet(meet(A,A),A)) = meet(A,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[305,35]),298,182,182,40,242,242,216]),
    [iquote('para_from,305.1.1,35.1.1.1,demod,298,182,182,40,242,242,216')] ).

cnf(555,plain,
    meet(join(complement(A),top),meet(A,zero)) = zero,
    inference(para_into,[status(thm),theory(equality)],[51,382]),
    [iquote('para_into,51.1.1.1.2,382.1.1')] ).

cnf(619,plain,
    join(top,join(complement(A),meet(zero,A))) = top,
    inference(para_into,[status(thm),theory(equality)],[53,382]),
    [iquote('para_into,53.1.1.1,382.1.1')] ).

cnf(648,plain,
    join(complement(A),top) = top,
    inference(para_into,[status(thm),theory(equality)],[53,311]),
    [iquote('para_into,53.1.1.2,311.1.1')] ).

cnf(654,plain,
    meet(A,zero) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[555]),648,363]),
    [iquote('back_demod,555,demod,648,363')] ).

cnf(656,plain,
    join(complement(A),zero) = complement(A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[398]),654]),
    [iquote('back_demod,398,demod,654')] ).

cnf(698,plain,
    meet(zero,A) = zero,
    inference(para_into,[status(thm),theory(equality)],[654,46]),
    [iquote('para_into,653.1.1,46.1.1')] ).

cnf(699,plain,
    join(top,complement(A)) = top,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[619]),698,656]),
    [iquote('back_demod,619,demod,698,656')] ).

cnf(722,plain,
    join(top,A) = top,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[699,242]),316]),
    [iquote('para_into,699.1.1.2,241.1.1,demod,316')] ).

cnf(738,plain,
    join(zero,join(A,top)) = top,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[129]),722]),
    [iquote('back_demod,129,demod,722')] ).

cnf(772,plain,
    join(A,top) = top,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[71,57]),738]),
    [iquote('para_into,71.1.1.2,57.1.1,demod,738')] ).

cnf(781,plain,
    join(A,join(B,complement(A))) = top,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[71,30]),772])]),
    [iquote('para_into,71.1.1.2,30.1.1,demod,772,flip.1')] ).

cnf(806,plain,
    join(converse(top),converse(A)) = converse(top),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[722,23])]),
    [iquote('para_from,721.1.1,23.1.1.1,flip.1')] ).

cnf(811,plain,
    meet(A,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[656,242]),274,242])]),
    [iquote('para_into,655.1.1.1,241.1.1,demod,274,242,flip.1')] ).

cnf(843,plain,
    join(zero,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[439]),811,811,811]),
    [iquote('back_demod,439,demod,811,811,811')] ).

cnf(846,plain,
    join(converse(A),converse(zero)) = converse(A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[321]),811]),
    [iquote('back_demod,321,demod,811')] ).

cnf(857,plain,
    join(A,zero) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[275]),811,811]),
    [iquote('back_demod,275,demod,811,811')] ).

cnf(884,plain,
    composition(converse(A),complement(composition(A,top))) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[197]),857]),
    [iquote('back_demod,197,demod,857')] ).

cnf(989,plain,
    join(converse(top),A) = converse(top),
    inference(para_into,[status(thm),theory(equality)],[806,22]),
    [iquote('para_into,806.1.1.2,21.1.1')] ).

cnf(993,plain,
    converse(top) = top,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[989,781])]),
    [iquote('para_into,989.1.1,781.1.1,flip.1')] ).

cnf(1025,plain,
    join(A,converse(zero)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[846,22]),22]),
    [iquote('para_into,846.1.1.1,21.1.1,demod,22')] ).

cnf(1028,plain,
    converse(zero) = zero,
    inference(para_into,[status(thm),theory(equality)],[1025,843]),
    [iquote('para_into,1025.1.1,842.1.1')] ).

cnf(1118,plain,
    composition(top,complement(composition(top,top))) = zero,
    inference(para_into,[status(thm),theory(equality)],[884,993]),
    [iquote('para_into,884.1.1.1,993.1.1')] ).

cnf(1144,plain,
    composition(A,complement(composition(top,top))) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1118,19]),857,772,1118]),
    [iquote('para_from,1117.1.1,19.1.1.2,demod,857,772,1118')] ).

cnf(1146,plain,
    composition(A,zero) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1118,124]),1144,843,722,1144]),
    [iquote('para_from,1117.1.1,124.1.1.1,demod,1144,843,722,1144')] ).

cnf(1147,plain,
    ( zero != zero
    | composition(zero,dollar_c1) != zero ),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),1146]),
    [iquote('back_demod,1,demod,1146')] ).

cnf(1148,plain,
    composition(zero,converse(A)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1146,25]),1028,1028])]),
    [iquote('para_from,1145.1.1,25.1.1.1,demod,1028,1028,flip.1')] ).

cnf(1159,plain,
    composition(zero,A) = zero,
    inference(para_into,[status(thm),theory(equality)],[1148,22]),
    [iquote('para_into,1148.1.1.2,21.1.1')] ).

cnf(1160,plain,
    zero != zero,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1147]),1159]),
    [iquote('back_demod,1147,demod,1159')] ).

cnf(1161,plain,
    $false,
    inference(binary,[status(thm)],[1160,2]),
    [iquote('binary,1160.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.14/0.34  % Computer : n006.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  : 300
% 0.14/0.34  % DateTime : Wed Jul 27 10:05:32 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 1.60/2.16  ----- Otter 3.3f, August 2004 -----
% 1.60/2.16  The process was started by sandbox on n006.cluster.edu,
% 1.60/2.16  Wed Jul 27 10:05:32 2022
% 1.60/2.16  The command was "./otter".  The process ID is 32633.
% 1.60/2.16  
% 1.60/2.16  set(prolog_style_variables).
% 1.60/2.16  set(auto).
% 1.60/2.16     dependent: set(auto1).
% 1.60/2.16     dependent: set(process_input).
% 1.60/2.16     dependent: clear(print_kept).
% 1.60/2.16     dependent: clear(print_new_demod).
% 1.60/2.16     dependent: clear(print_back_demod).
% 1.60/2.16     dependent: clear(print_back_sub).
% 1.60/2.16     dependent: set(control_memory).
% 1.60/2.16     dependent: assign(max_mem, 12000).
% 1.60/2.16     dependent: assign(pick_given_ratio, 4).
% 1.60/2.16     dependent: assign(stats_level, 1).
% 1.60/2.16     dependent: assign(max_seconds, 10800).
% 1.60/2.16  clear(print_given).
% 1.60/2.16  
% 1.60/2.16  formula_list(usable).
% 1.60/2.16  all A (A=A).
% 1.60/2.16  all X0 X1 (join(X0,X1)=join(X1,X0)).
% 1.60/2.16  all X0 X1 X2 (join(X0,join(X1,X2))=join(join(X0,X1),X2)).
% 1.60/2.16  all X0 X1 (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))).
% 1.60/2.16  all X0 X1 (meet(X0,X1)=complement(join(complement(X0),complement(X1)))).
% 1.60/2.16  all X0 X1 X2 (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2)).
% 1.60/2.16  all X0 (composition(X0,one)=X0).
% 1.60/2.16  all X0 X1 X2 (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2))).
% 1.60/2.16  all X0 (converse(converse(X0))=X0).
% 1.60/2.16  all X0 X1 (converse(join(X0,X1))=join(converse(X0),converse(X1))).
% 1.60/2.16  all X0 X1 (converse(composition(X0,X1))=composition(converse(X1),converse(X0))).
% 1.60/2.16  all X0 X1 (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1)).
% 1.60/2.16  all X0 (top=join(X0,complement(X0))).
% 1.60/2.16  all X0 (zero=meet(X0,complement(X0))).
% 1.60/2.16  -(all X0 (composition(X0,zero)=zero&composition(zero,X0)=zero)).
% 1.60/2.16  end_of_list.
% 1.60/2.16  
% 1.60/2.16  -------> usable clausifies to:
% 1.60/2.16  
% 1.60/2.16  list(usable).
% 1.60/2.16  0 [] A=A.
% 1.60/2.16  0 [] join(X0,X1)=join(X1,X0).
% 1.60/2.16  0 [] join(X0,join(X1,X2))=join(join(X0,X1),X2).
% 1.60/2.16  0 [] X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))).
% 1.60/2.16  0 [] meet(X0,X1)=complement(join(complement(X0),complement(X1))).
% 1.60/2.16  0 [] composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2).
% 1.60/2.16  0 [] composition(X0,one)=X0.
% 1.60/2.16  0 [] composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)).
% 1.60/2.16  0 [] converse(converse(X0))=X0.
% 1.60/2.16  0 [] converse(join(X0,X1))=join(converse(X0),converse(X1)).
% 1.60/2.16  0 [] converse(composition(X0,X1))=composition(converse(X1),converse(X0)).
% 1.60/2.16  0 [] join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1).
% 1.60/2.16  0 [] top=join(X0,complement(X0)).
% 1.60/2.16  0 [] zero=meet(X0,complement(X0)).
% 1.60/2.16  0 [] composition($c1,zero)!=zero|composition(zero,$c1)!=zero.
% 1.60/2.16  end_of_list.
% 1.60/2.16  
% 1.60/2.16  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.60/2.16  
% 1.60/2.16  This is a Horn set with equality.  The strategy will be
% 1.60/2.16  Knuth-Bendix and hyper_res, with positive clauses in
% 1.60/2.16  sos and nonpositive clauses in usable.
% 1.60/2.16  
% 1.60/2.16     dependent: set(knuth_bendix).
% 1.60/2.16     dependent: set(anl_eq).
% 1.60/2.16     dependent: set(para_from).
% 1.60/2.16     dependent: set(para_into).
% 1.60/2.16     dependent: clear(para_from_right).
% 1.60/2.16     dependent: clear(para_into_right).
% 1.60/2.16     dependent: set(para_from_vars).
% 1.60/2.16     dependent: set(eq_units_both_ways).
% 1.60/2.16     dependent: set(dynamic_demod_all).
% 1.60/2.16     dependent: set(dynamic_demod).
% 1.60/2.16     dependent: set(order_eq).
% 1.60/2.16     dependent: set(back_demod).
% 1.60/2.16     dependent: set(lrpo).
% 1.60/2.16     dependent: set(hyper_res).
% 1.60/2.16     dependent: clear(order_hyper).
% 1.60/2.16  
% 1.60/2.16  ------------> process usable:
% 1.60/2.16  ** KEPT (pick-wt=10): 1 [] composition($c1,zero)!=zero|composition(zero,$c1)!=zero.
% 1.60/2.16  
% 1.60/2.16  ------------> process sos:
% 1.60/2.16  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.60/2.16  ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 1.60/2.16  ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 1.60/2.16  ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 1.60/2.16  ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.60/2.16  ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.60/2.16  ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.60/2.16  ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.60/2.16  ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 2.04/2.20  ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 2.04/2.20  ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 2.04/2.20  ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 2.04/2.20  ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 2.04/2.20  ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 2.04/2.20  ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 2.04/2.20  ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 2.04/2.20  ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 2.04/2.20  ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 2.04/2.20  ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 2.04/2.20  ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 2.04/2.20  ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 2.04/2.20  ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 2.04/2.20  ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 2.04/2.20  ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 2.04/2.20  ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 2.04/2.20  ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 2.04/2.20    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.04/2.20    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 2.04/2.20  >>>> Starting back demodulation with 6.
% 2.04/2.20  >>>> Starting back demodulation with 9.
% 2.04/2.20  >>>> Starting back demodulation with 12.
% 2.04/2.20      >> back demodulating 8 with 12.
% 2.04/2.20  >>>> Starting back demodulation with 15.
% 2.04/2.20  >>>> Starting back demodulation with 17.
% 2.04/2.20  >>>> Starting back demodulation with 20.
% 2.04/2.20  >>>> Starting back demodulation with 22.
% 2.04/2.20  >>>> Starting back demodulation with 24.
% 2.04/2.20  >>>> Starting back demodulation with 26.
% 2.04/2.20  >>>> Starting back demodulation with 28.
% 2.04/2.20  >>>> Starting back demodulation with 31.
% 2.04/2.20  >>>> Starting back demodulation with 34.
% 2.04/2.20  >>>> Starting back demodulation with 36.
% 2.04/2.20  
% 2.04/2.20  ======= end of input processing =======
% 2.04/2.20  
% 2.04/2.20  =========== start of search ===========
% 2.04/2.20  
% 2.04/2.20  
% 2.04/2.20  Resetting weight limit to 10.
% 2.04/2.20  
% 2.04/2.20  
% 2.04/2.20  Resetting weight limit to 10.
% 2.04/2.20  
% 2.04/2.20  sos_size=185
% 2.04/2.20  
% 2.04/2.20  -------- PROOF -------- 
% 2.04/2.20  
% 2.04/2.20  ----> UNIT CONFLICT at   0.03 sec ----> 1161 [binary,1160.1,2.1] $F.
% 2.04/2.20  
% 2.04/2.20  Length of proof is 86.  Level of proof is 24.
% 2.04/2.20  
% 2.04/2.20  ---------------- PROOF ----------------
% 2.04/2.20  % SZS status Theorem
% 2.04/2.20  % SZS output start Refutation
% See solution above
% 2.04/2.20  ------------ end of proof -------------
% 2.04/2.20  
% 2.04/2.20  
% 2.04/2.20  Search stopped by max_proofs option.
% 2.04/2.20  
% 2.04/2.20  
% 2.04/2.20  Search stopped by max_proofs option.
% 2.04/2.20  
% 2.04/2.20  ============ end of search ============
% 2.04/2.20  
% 2.04/2.20  -------------- statistics -------------
% 2.04/2.20  clauses given                109
% 2.04/2.20  clauses generated           1686
% 2.04/2.20  clauses kept                 605
% 2.04/2.20  clauses forward subsumed    1482
% 2.04/2.20  clauses back subsumed          1
% 2.04/2.20  Kbytes malloced             4882
% 2.04/2.20  
% 2.04/2.20  ----------- times (seconds) -----------
% 2.04/2.20  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 2.04/2.20  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.04/2.20  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 2.04/2.20  
% 2.04/2.20  That finishes the proof of the theorem.
% 2.04/2.20  
% 2.04/2.20  Process 32633 finished Wed Jul 27 10:05:33 2022
% 2.04/2.20  Otter interrupted
% 2.04/2.20  PROOF FOUND
%------------------------------------------------------------------------------