TSTP Solution File: REL015+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:11:50 EDT 2022
% Result : Theorem 1.81s 1.99s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 18 RR)
% Number of literals : 89 ( 88 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
composition(top,top) != top,
file('REL015+1.p',unknown),
[] ).
cnf(3,axiom,
join(A,B) = join(B,A),
file('REL015+1.p',unknown),
[] ).
cnf(4,axiom,
join(A,join(B,C)) = join(join(A,B),C),
file('REL015+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('REL015+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('REL015+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('REL015+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('REL015+1.p',unknown),
[] ).
cnf(18,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('REL015+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('REL015+1.p',unknown),
[] ).
cnf(23,axiom,
converse(join(A,B)) = join(converse(A),converse(B)),
file('REL015+1.p',unknown),
[] ).
cnf(25,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)),
file('REL015+1.p',unknown),
[] ).
cnf(27,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('REL015+1.p',unknown),
[] ).
cnf(29,axiom,
top = join(A,complement(A)),
file('REL015+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('REL015+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(39,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(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(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(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(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(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(383,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)],[383,39]),
[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(555,plain,
meet(join(complement(A),top),meet(A,zero)) = zero,
inference(para_into,[status(thm),theory(equality)],[51,383]),
[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)],[53,383]),
[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(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(860,plain,
complement(complement(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[242]),811]),
[iquote('back_demod,241,demod,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(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(1143,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(1159,plain,
complement(composition(top,top)) = zero,
inference(para_into,[status(thm),theory(equality)],[1143,174]),
[iquote('para_into,1143.1.1,173.1.1')] ).
cnf(1169,plain,
composition(top,top) = top,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1159,860]),383])]),
[iquote('para_from,1159.1.1,860.1.1.1,demod,383,flip.1')] ).
cnf(1171,plain,
$false,
inference(binary,[status(thm)],[1169,1]),
[iquote('binary,1169.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL015+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.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 10:07:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n019.cluster.edu,
% 1.75/1.96 Wed Jul 27 10:07:22 2022
% 1.75/1.96 The command was "./otter". The process ID is 3164.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 all X0 X1 (join(X0,X1)=join(X1,X0)).
% 1.75/1.96 all X0 X1 X2 (join(X0,join(X1,X2))=join(join(X0,X1),X2)).
% 1.75/1.96 all X0 X1 (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))).
% 1.75/1.96 all X0 X1 (meet(X0,X1)=complement(join(complement(X0),complement(X1)))).
% 1.75/1.96 all X0 X1 X2 (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2)).
% 1.75/1.96 all X0 (composition(X0,one)=X0).
% 1.75/1.96 all X0 X1 X2 (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2))).
% 1.75/1.96 all X0 (converse(converse(X0))=X0).
% 1.75/1.96 all X0 X1 (converse(join(X0,X1))=join(converse(X0),converse(X1))).
% 1.75/1.96 all X0 X1 (converse(composition(X0,X1))=composition(converse(X1),converse(X0))).
% 1.75/1.96 all X0 X1 (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1)).
% 1.75/1.96 all X0 (top=join(X0,complement(X0))).
% 1.75/1.96 all X0 (zero=meet(X0,complement(X0))).
% 1.75/1.96 composition(top,top)!=top.
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] join(X0,X1)=join(X1,X0).
% 1.75/1.96 0 [] join(X0,join(X1,X2))=join(join(X0,X1),X2).
% 1.75/1.96 0 [] X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))).
% 1.75/1.96 0 [] meet(X0,X1)=complement(join(complement(X0),complement(X1))).
% 1.75/1.96 0 [] composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2).
% 1.75/1.96 0 [] composition(X0,one)=X0.
% 1.75/1.96 0 [] composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)).
% 1.75/1.96 0 [] converse(converse(X0))=X0.
% 1.75/1.96 0 [] converse(join(X0,X1))=join(converse(X0),converse(X1)).
% 1.75/1.96 0 [] converse(composition(X0,X1))=composition(converse(X1),converse(X0)).
% 1.75/1.96 0 [] join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1).
% 1.75/1.96 0 [] top=join(X0,complement(X0)).
% 1.75/1.96 0 [] zero=meet(X0,complement(X0)).
% 1.75/1.96 0 [] composition(top,top)!=top.
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.96
% 1.75/1.96 All clauses are units, and equality is present; the
% 1.75/1.96 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=5): 1 [] composition(top,top)!=top.
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 1.75/1.96 ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 1.75/1.96 ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 1.75/1.96 ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.75/1.96 ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.75/1.96 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.75/1.96 ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.75/1.96 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.75/1.96 ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.75/1.96 ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 1.75/1.96 ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 1.81/1.99 ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.81/1.99 ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.81/1.99 ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 1.81/1.99 ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 1.81/1.99 ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 1.81/1.99 ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 1.81/1.99 ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.81/1.99 ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.81/1.99 ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.81/1.99 ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.81/1.99 ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 1.81/1.99 ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 1.81/1.99 ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 1.81/1.99 ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 1.81/1.99 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.81/1.99 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 1.81/1.99 >>>> Starting back demodulation with 6.
% 1.81/1.99 >>>> Starting back demodulation with 9.
% 1.81/1.99 >>>> Starting back demodulation with 12.
% 1.81/1.99 >> back demodulating 8 with 12.
% 1.81/1.99 >>>> Starting back demodulation with 15.
% 1.81/1.99 >>>> Starting back demodulation with 17.
% 1.81/1.99 >>>> Starting back demodulation with 20.
% 1.81/1.99 >>>> Starting back demodulation with 22.
% 1.81/1.99 >>>> Starting back demodulation with 24.
% 1.81/1.99 >>>> Starting back demodulation with 26.
% 1.81/1.99 >>>> Starting back demodulation with 28.
% 1.81/1.99 >>>> Starting back demodulation with 31.
% 1.81/1.99 >>>> Starting back demodulation with 34.
% 1.81/1.99 >>>> Starting back demodulation with 36.
% 1.81/1.99
% 1.81/1.99 ======= end of input processing =======
% 1.81/1.99
% 1.81/1.99 =========== start of search ===========
% 1.81/1.99
% 1.81/1.99
% 1.81/1.99 Resetting weight limit to 10.
% 1.81/1.99
% 1.81/1.99
% 1.81/1.99 Resetting weight limit to 10.
% 1.81/1.99
% 1.81/1.99 sos_size=185
% 1.81/1.99
% 1.81/1.99 -------- PROOF --------
% 1.81/1.99
% 1.81/1.99 ----> UNIT CONFLICT at 0.03 sec ----> 1171 [binary,1169.1,1.1] $F.
% 1.81/1.99
% 1.81/1.99 Length of proof is 74. Level of proof is 22.
% 1.81/1.99
% 1.81/1.99 ---------------- PROOF ----------------
% 1.81/1.99 % SZS status Theorem
% 1.81/1.99 % SZS output start Refutation
% See solution above
% 1.81/1.99 ------------ end of proof -------------
% 1.81/1.99
% 1.81/1.99
% 1.81/1.99 Search stopped by max_proofs option.
% 1.81/1.99
% 1.81/1.99
% 1.81/1.99 Search stopped by max_proofs option.
% 1.81/1.99
% 1.81/1.99 ============ end of search ============
% 1.81/1.99
% 1.81/1.99 -------------- statistics -------------
% 1.81/1.99 clauses given 113
% 1.81/1.99 clauses generated 1797
% 1.81/1.99 clauses kept 609
% 1.81/1.99 clauses forward subsumed 1519
% 1.81/1.99 clauses back subsumed 1
% 1.81/1.99 Kbytes malloced 4882
% 1.81/1.99
% 1.81/1.99 ----------- times (seconds) -----------
% 1.81/1.99 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.81/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/1.99 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.81/1.99
% 1.81/1.99 That finishes the proof of the theorem.
% 1.81/1.99
% 1.81/1.99 Process 3164 finished Wed Jul 27 10:07:23 2022
% 1.81/1.99 Otter interrupted
% 1.81/1.99 PROOF FOUND
%------------------------------------------------------------------------------