TSTP Solution File: REL018+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:11:51 EDT 2022
% Result : Theorem 1.82s 2.00s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 23 RR)
% Number of literals : 97 ( 96 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 105 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
composition(complement(dollar_c1),top) != complement(dollar_c1),
file('REL018+1.p',unknown),
[] ).
cnf(3,axiom,
join(A,B) = join(B,A),
file('REL018+1.p',unknown),
[] ).
cnf(4,axiom,
join(A,join(B,C)) = join(join(A,B),C),
file('REL018+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('REL018+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('REL018+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(16,axiom,
composition(A,one) = A,
file('REL018+1.p',unknown),
[] ).
cnf(18,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('REL018+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('REL018+1.p',unknown),
[] ).
cnf(23,axiom,
converse(join(A,B)) = join(converse(A),converse(B)),
file('REL018+1.p',unknown),
[] ).
cnf(26,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)),
file('REL018+1.p',unknown),
[] ).
cnf(27,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('REL018+1.p',unknown),
[] ).
cnf(29,axiom,
top = join(A,complement(A)),
file('REL018+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('REL018+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,axiom,
composition(dollar_c1,top) = dollar_c1,
file('REL018+1.p',unknown),
[] ).
cnf(37,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(39,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(42,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(45,plain,
complement(top) = meet(complement(A),A),
inference(para_into,[status(thm),theory(equality)],[12,39]),
[iquote('para_into,11.1.1.1,39.1.1')] ).
cnf(47,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(48,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(49,plain,
meet(complement(A),A) = zero,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[45])]),47]),
[iquote('copy,45,flip.1,demod,47')] ).
cnf(53,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(55,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(58,plain,
complement(join(complement(A),zero)) = meet(A,top),
inference(para_from,[status(thm),theory(equality)],[47,12]),
[iquote('para_from,46.1.1,11.1.1.1.2')] ).
cnf(59,plain,
join(zero,top) = top,
inference(para_from,[status(thm),theory(equality)],[47,39]),
[iquote('para_from,46.1.1,39.1.1.1')] ).
cnf(63,plain,
join(top,zero) = top,
inference(para_from,[status(thm),theory(equality)],[47,30]),
[iquote('para_from,46.1.1,30.1.1.2')] ).
cnf(65,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(para_from,[status(thm),theory(equality)],[47,12]),
[iquote('para_from,46.1.1,11.1.1.1.1')] ).
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(zero,join(top,A)) = join(top,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[59,6])]),
[iquote('para_from,59.1.1,5.1.1.1,flip.1')] ).
cnf(78,plain,
join(top,join(zero,A)) = join(top,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,6])]),
[iquote('para_from,63.1.1,5.1.1.1,flip.1')] ).
cnf(90,plain,
complement(join(zero,zero)) = meet(top,top),
inference(para_into,[status(thm),theory(equality)],[58,47]),
[iquote('para_into,57.1.1.1.1,46.1.1')] ).
cnf(102,plain,
meet(meet(top,top),join(zero,zero)) = zero,
inference(para_from,[status(thm),theory(equality)],[90,49]),
[iquote('para_from,90.1.1,49.1.1.1')] ).
cnf(137,plain,
join(zero,join(A,top)) = join(top,A),
inference(para_into,[status(thm),theory(equality)],[76,3]),
[iquote('para_into,76.1.1.2,3.1.1')] ).
cnf(175,plain,
composition(converse(one),converse(A)) = converse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,16])]),
[iquote('para_into,25.1.1.1,16.1.1,flip.1')] ).
cnf(187,plain,
composition(converse(one),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[175,22]),22]),
[iquote('para_into,175.1.1.2,21.1.1,demod,22')] ).
cnf(190,plain,
converse(one) = one,
inference(para_into,[status(thm),theory(equality)],[187,16]),
[iquote('para_into,187.1.1,16.1.1')] ).
cnf(192,plain,
composition(one,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),190]),
[iquote('back_demod,187,demod,190')] ).
cnf(194,plain,
join(complement(A),complement(A)) = complement(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,190]),192,192]),
[iquote('para_into,27.1.1.1.1,189.1.1,demod,192,192')] ).
cnf(205,plain,
join(composition(converse(dollar_c1),complement(dollar_c1)),zero) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,35]),47,47]),
[iquote('para_into,27.1.1.1.2.1,35.1.1,demod,47,47')] ).
cnf(221,plain,
join(composition(converse(complement(composition(A,B))),A),converse(complement(B))) = converse(complement(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[27,23]),26,22])]),
[iquote('para_from,27.1.1,23.1.1.1,demod,26,22,flip.1')] ).
cnf(226,plain,
join(composition(A,B),B) = composition(join(A,one),B),
inference(para_from,[status(thm),theory(equality)],[192,19]),
[iquote('para_from,191.1.1,19.1.1.2')] ).
cnf(240,plain,
join(zero,zero) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[194,47]),47,47]),
[iquote('para_into,193.1.1.1,46.1.1,demod,47,47')] ).
cnf(242,plain,
join(meet(A,B),meet(A,B)) = meet(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[194,12]),12,12]),
[iquote('para_into,193.1.1.1,11.1.1,demod,12,12')] ).
cnf(251,plain,
meet(meet(top,top),zero) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[102]),240]),
[iquote('back_demod,102,demod,240')] ).
cnf(253,plain,
complement(zero) = meet(top,top),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[90]),240]),
[iquote('back_demod,90,demod,240')] ).
cnf(268,plain,
complement(complement(A)) = meet(A,A),
inference(para_from,[status(thm),theory(equality)],[194,12]),
[iquote('para_from,193.1.1,11.1.1.1')] ).
cnf(286,plain,
join(zero,meet(A,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,34]),194,268]),
[iquote('para_into,37.1.1.1,33.1.1,demod,194,268')] ).
cnf(298,plain,
join(meet(A,A),zero) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,39]),47]),
[iquote('para_into,37.1.1.2.1,39.1.1,demod,47')] ).
cnf(299,plain,
join(meet(A,meet(A,A)),zero) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,30]),268,47]),
[iquote('para_into,37.1.1.2.1,30.1.1,demod,268,47')] ).
cnf(315,plain,
join(zero,meet(meet(top,top),top)) = meet(top,top),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[251,37]),58]),
[iquote('para_from,251.1.1,37.1.1.1,demod,58')] ).
cnf(324,plain,
complement(meet(A,B)) = meet(join(complement(A),complement(B)),join(complement(A),complement(B))),
inference(para_into,[status(thm),theory(equality)],[268,12]),
[iquote('para_into,267.1.1.1,11.1.1')] ).
cnf(327,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)],[268,65]),286])]),
[iquote('para_from,267.1.1,65.1.1.1.2,demod,286,flip.1')] ).
cnf(329,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)],[268,58]),298])]),
[iquote('para_from,267.1.1,57.1.1.1.1,demod,298,flip.1')] ).
cnf(331,plain,
meet(meet(A,A),complement(A)) = zero,
inference(para_from,[status(thm),theory(equality)],[268,49]),
[iquote('para_from,267.1.1,49.1.1.1')] ).
cnf(337,plain,
join(complement(A),meet(A,A)) = top,
inference(para_from,[status(thm),theory(equality)],[268,30]),
[iquote('para_from,267.1.1,30.1.1.2')] ).
cnf(342,plain,
join(top,meet(A,A)) = join(top,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[286,78])]),
[iquote('para_from,285.1.1,78.1.1.2,flip.1')] ).
cnf(376,plain,
join(converse(meet(A,A)),converse(zero)) = converse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[298,23])]),
[iquote('para_from,297.1.1,23.1.1.1,flip.1')] ).
cnf(389,plain,
meet(top,meet(A,B)) = meet(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[327,12]),12]),
[iquote('para_into,327.1.1.2,11.1.1,demod,12')] ).
cnf(393,plain,
meet(meet(A,A),top) = meet(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[329,268]),268]),
[iquote('para_into,329.1.1.1,267.1.1,demod,268')] ).
cnf(403,plain,
meet(top,top) = top,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[315]),393,286])]),
[iquote('back_demod,315,demod,393,286,flip.1')] ).
cnf(409,plain,
complement(zero) = top,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[253]),403]),
[iquote('back_demod,253,demod,403')] ).
cnf(412,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)],[329,37]),268]),
[iquote('para_from,329.1.1,37.1.1.1,demod,268')] ).
cnf(415,plain,
complement(join(meet(A,B),top)) = meet(join(complement(A),complement(B)),zero),
inference(para_from,[status(thm),theory(equality)],[409,42]),
[iquote('para_from,408.1.1,41.1.1.1.2')] ).
cnf(424,plain,
join(complement(A),meet(complement(A),zero)) = complement(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[412]),415,194]),
[iquote('back_demod,412,demod,415,194')] ).
cnf(495,plain,
join(zero,meet(meet(A,A),A)) = meet(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[331,37]),324,194,194,42,268,268,242]),
[iquote('para_from,331.1.1,37.1.1.1,demod,324,194,194,42,268,268,242')] ).
cnf(559,plain,
meet(join(complement(A),top),meet(A,zero)) = zero,
inference(para_into,[status(thm),theory(equality)],[53,409]),
[iquote('para_into,53.1.1.1.2,408.1.1')] ).
cnf(633,plain,
join(top,join(complement(A),meet(zero,A))) = top,
inference(para_into,[status(thm),theory(equality)],[55,409]),
[iquote('para_into,55.1.1.1,408.1.1')] ).
cnf(662,plain,
join(complement(A),top) = top,
inference(para_into,[status(thm),theory(equality)],[55,337]),
[iquote('para_into,55.1.1.2,337.1.1')] ).
cnf(668,plain,
meet(A,zero) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[559]),662,389]),
[iquote('back_demod,559,demod,662,389')] ).
cnf(670,plain,
join(complement(A),zero) = complement(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[424]),668]),
[iquote('back_demod,424,demod,668')] ).
cnf(712,plain,
meet(zero,A) = zero,
inference(para_into,[status(thm),theory(equality)],[668,48]),
[iquote('para_into,667.1.1,48.1.1')] ).
cnf(713,plain,
join(top,complement(A)) = top,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[633]),712,670]),
[iquote('back_demod,633,demod,712,670')] ).
cnf(736,plain,
join(top,A) = top,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[713,268]),342]),
[iquote('para_into,713.1.1.2,267.1.1,demod,342')] ).
cnf(754,plain,
join(zero,join(A,top)) = top,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[137]),736]),
[iquote('back_demod,137,demod,736')] ).
cnf(788,plain,
join(A,top) = top,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[71,59]),754]),
[iquote('para_into,71.1.1.2,59.1.1,demod,754')] ).
cnf(797,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]),788])]),
[iquote('para_into,71.1.1.2,30.1.1,demod,788,flip.1')] ).
cnf(820,plain,
join(converse(top),converse(A)) = converse(top),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[736,23])]),
[iquote('para_from,735.1.1,23.1.1.1,flip.1')] ).
cnf(825,plain,
meet(A,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[670,268]),298,268])]),
[iquote('para_into,669.1.1.1,267.1.1,demod,298,268,flip.1')] ).
cnf(852,plain,
join(zero,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[495]),825,825,825]),
[iquote('back_demod,495,demod,825,825,825')] ).
cnf(860,plain,
join(converse(A),converse(zero)) = converse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[376]),825]),
[iquote('back_demod,376,demod,825')] ).
cnf(871,plain,
join(A,zero) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[299]),825,825]),
[iquote('back_demod,299,demod,825,825')] ).
cnf(900,plain,
composition(converse(dollar_c1),complement(dollar_c1)) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[205]),871]),
[iquote('back_demod,205,demod,871')] ).
cnf(955,plain,
composition(converse(complement(dollar_c1)),dollar_c1) = converse(zero),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[900,26]),22])]),
[iquote('para_from,900.1.1,25.1.1.1,demod,22,flip.1')] ).
cnf(1013,plain,
join(converse(top),A) = converse(top),
inference(para_into,[status(thm),theory(equality)],[820,22]),
[iquote('para_into,820.1.1.2,21.1.1')] ).
cnf(1028,plain,
converse(top) = top,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1013,797])]),
[iquote('para_into,1013.1.1,797.1.1,flip.1')] ).
cnf(1057,plain,
join(A,converse(zero)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[860,22]),22]),
[iquote('para_into,860.1.1.1,21.1.1,demod,22')] ).
cnf(1076,plain,
converse(zero) = zero,
inference(para_into,[status(thm),theory(equality)],[1057,852]),
[iquote('para_into,1057.1.1,852.1.1')] ).
cnf(1077,plain,
composition(converse(complement(dollar_c1)),dollar_c1) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[955]),1076]),
[iquote('back_demod,955,demod,1076')] ).
cnf(1241,plain,
composition(top,converse(complement(dollar_c1))) = converse(complement(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[221,1077]),409,1028,226,736]),
[iquote('para_into,221.1.1.1.1.1.1,1077.1.1,demod,409,1028,226,736')] ).
cnf(1243,plain,
composition(complement(dollar_c1),top) = complement(dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1241,26]),22,22,1028])]),
[iquote('para_from,1241.1.1,25.1.1.1,demod,22,22,1028,flip.1')] ).
cnf(1245,plain,
$false,
inference(binary,[status(thm)],[1243,1]),
[iquote('binary,1243.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:09:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.95 ----- Otter 3.3f, August 2004 -----
% 1.75/1.95 The process was started by sandbox on n018.cluster.edu,
% 1.75/1.95 Wed Jul 27 10:09:01 2022
% 1.75/1.95 The command was "./otter". The process ID is 22565.
% 1.75/1.95
% 1.75/1.95 set(prolog_style_variables).
% 1.75/1.95 set(auto).
% 1.75/1.95 dependent: set(auto1).
% 1.75/1.95 dependent: set(process_input).
% 1.75/1.95 dependent: clear(print_kept).
% 1.75/1.95 dependent: clear(print_new_demod).
% 1.75/1.95 dependent: clear(print_back_demod).
% 1.75/1.95 dependent: clear(print_back_sub).
% 1.75/1.95 dependent: set(control_memory).
% 1.75/1.95 dependent: assign(max_mem, 12000).
% 1.75/1.95 dependent: assign(pick_given_ratio, 4).
% 1.75/1.95 dependent: assign(stats_level, 1).
% 1.75/1.95 dependent: assign(max_seconds, 10800).
% 1.75/1.95 clear(print_given).
% 1.75/1.95
% 1.75/1.95 formula_list(usable).
% 1.75/1.95 all A (A=A).
% 1.75/1.95 all X0 X1 (join(X0,X1)=join(X1,X0)).
% 1.75/1.95 all X0 X1 X2 (join(X0,join(X1,X2))=join(join(X0,X1),X2)).
% 1.75/1.95 all X0 X1 (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))).
% 1.75/1.95 all X0 X1 (meet(X0,X1)=complement(join(complement(X0),complement(X1)))).
% 1.75/1.95 all X0 X1 X2 (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2)).
% 1.75/1.95 all X0 (composition(X0,one)=X0).
% 1.75/1.95 all X0 X1 X2 (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2))).
% 1.75/1.95 all X0 (converse(converse(X0))=X0).
% 1.75/1.95 all X0 X1 (converse(join(X0,X1))=join(converse(X0),converse(X1))).
% 1.75/1.95 all X0 X1 (converse(composition(X0,X1))=composition(converse(X1),converse(X0))).
% 1.75/1.95 all X0 X1 (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1)).
% 1.75/1.95 all X0 (top=join(X0,complement(X0))).
% 1.75/1.95 all X0 (zero=meet(X0,complement(X0))).
% 1.75/1.95 -(all X0 (composition(X0,top)=X0->composition(complement(X0),top)=complement(X0))).
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 -------> usable clausifies to:
% 1.75/1.95
% 1.75/1.95 list(usable).
% 1.75/1.95 0 [] A=A.
% 1.75/1.95 0 [] join(X0,X1)=join(X1,X0).
% 1.75/1.95 0 [] join(X0,join(X1,X2))=join(join(X0,X1),X2).
% 1.75/1.95 0 [] X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))).
% 1.75/1.95 0 [] meet(X0,X1)=complement(join(complement(X0),complement(X1))).
% 1.75/1.95 0 [] composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2).
% 1.75/1.95 0 [] composition(X0,one)=X0.
% 1.75/1.95 0 [] composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)).
% 1.75/1.95 0 [] converse(converse(X0))=X0.
% 1.75/1.95 0 [] converse(join(X0,X1))=join(converse(X0),converse(X1)).
% 1.75/1.95 0 [] converse(composition(X0,X1))=composition(converse(X1),converse(X0)).
% 1.75/1.95 0 [] join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1).
% 1.75/1.95 0 [] top=join(X0,complement(X0)).
% 1.75/1.95 0 [] zero=meet(X0,complement(X0)).
% 1.75/1.95 0 [] composition($c1,top)=$c1.
% 1.75/1.95 0 [] composition(complement($c1),top)!=complement($c1).
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.95
% 1.75/1.95 All clauses are units, and equality is present; the
% 1.75/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.95
% 1.75/1.95 dependent: set(knuth_bendix).
% 1.75/1.95 dependent: set(anl_eq).
% 1.75/1.95 dependent: set(para_from).
% 1.75/1.95 dependent: set(para_into).
% 1.75/1.95 dependent: clear(para_from_right).
% 1.75/1.95 dependent: clear(para_into_right).
% 1.75/1.95 dependent: set(para_from_vars).
% 1.75/1.95 dependent: set(eq_units_both_ways).
% 1.75/1.95 dependent: set(dynamic_demod_all).
% 1.75/1.95 dependent: set(dynamic_demod).
% 1.75/1.95 dependent: set(order_eq).
% 1.75/1.95 dependent: set(back_demod).
% 1.75/1.95 dependent: set(lrpo).
% 1.75/1.95
% 1.75/1.95 ------------> process usable:
% 1.75/1.95 ** KEPT (pick-wt=7): 1 [] composition(complement($c1),top)!=complement($c1).
% 1.75/1.95
% 1.75/1.95 ------------> process sos:
% 1.75/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.95 ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 1.75/1.95 ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 1.75/1.95 ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 1.75/1.95 ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.75/1.95 ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.75/1.95 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.75/1.95 ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.75/1.95 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.75/1.95 ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.82/2.00 ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 1.82/2.00 ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 1.82/2.00 ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.82/2.00 ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.82/2.00 ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 1.82/2.00 ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 1.82/2.00 ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 1.82/2.00 ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 1.82/2.00 ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.82/2.00 ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.82/2.00 ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.82/2.00 ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.82/2.00 ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 1.82/2.00 ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 1.82/2.00 ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 1.82/2.00 ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 1.82/2.00 ** KEPT (pick-wt=5): 35 [] composition($c1,top)=$c1.
% 1.82/2.00 ---> New Demodulator: 36 [new_demod,35] composition($c1,top)=$c1.
% 1.82/2.00 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.82/2.00 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 1.82/2.00 >>>> Starting back demodulation with 6.
% 1.82/2.00 >>>> Starting back demodulation with 9.
% 1.82/2.00 >>>> Starting back demodulation with 12.
% 1.82/2.00 >> back demodulating 8 with 12.
% 1.82/2.00 >>>> Starting back demodulation with 15.
% 1.82/2.00 >>>> Starting back demodulation with 17.
% 1.82/2.00 >>>> Starting back demodulation with 20.
% 1.82/2.00 >>>> Starting back demodulation with 22.
% 1.82/2.00 >>>> Starting back demodulation with 24.
% 1.82/2.00 >>>> Starting back demodulation with 26.
% 1.82/2.00 >>>> Starting back demodulation with 28.
% 1.82/2.00 >>>> Starting back demodulation with 31.
% 1.82/2.00 >>>> Starting back demodulation with 34.
% 1.82/2.00 >>>> Starting back demodulation with 36.
% 1.82/2.00 >>>> Starting back demodulation with 38.
% 1.82/2.00
% 1.82/2.00 ======= end of input processing =======
% 1.82/2.00
% 1.82/2.00 =========== start of search ===========
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Resetting weight limit to 9.
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Resetting weight limit to 9.
% 1.82/2.00
% 1.82/2.00 sos_size=188
% 1.82/2.00
% 1.82/2.00 -------- PROOF --------
% 1.82/2.00
% 1.82/2.00 ----> UNIT CONFLICT at 0.04 sec ----> 1245 [binary,1243.1,1.1] $F.
% 1.82/2.00
% 1.82/2.00 Length of proof is 82. Level of proof is 21.
% 1.82/2.00
% 1.82/2.00 ---------------- PROOF ----------------
% 1.82/2.00 % SZS status Theorem
% 1.82/2.00 % SZS output start Refutation
% See solution above
% 1.82/2.00 ------------ end of proof -------------
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00 ============ end of search ============
% 1.82/2.00
% 1.82/2.00 -------------- statistics -------------
% 1.82/2.00 clauses given 167
% 1.82/2.00 clauses generated 3528
% 1.82/2.00 clauses kept 645
% 1.82/2.00 clauses forward subsumed 2455
% 1.82/2.00 clauses back subsumed 1
% 1.82/2.00 Kbytes malloced 4882
% 1.82/2.00
% 1.82/2.00 ----------- times (seconds) -----------
% 1.82/2.00 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.82/2.00 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.82/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.00
% 1.82/2.00 That finishes the proof of the theorem.
% 1.82/2.00
% 1.82/2.00 Process 22565 finished Wed Jul 27 10:09:03 2022
% 1.82/2.00 Otter interrupted
% 1.82/2.00 PROOF FOUND
%------------------------------------------------------------------------------