TSTP Solution File: HWV006-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HWV006-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:58:03 EDT 2022
% Result : Unsatisfiable 2.06s 2.24s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 50
% Syntax : Number of clauses : 118 ( 70 unt; 12 nHn; 118 RR)
% Number of literals : 181 ( 0 equ; 59 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ connection(A,B)
| ~ zero(A)
| zero(B) ),
file('HWV006-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ connection(A,B)
| ~ one(A)
| one(B) ),
file('HWV006-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ connection(A,B)
| ~ zero(B)
| zero(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ connection(A,B)
| ~ one(B)
| one(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ zero(A)
| ~ one(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ and_ok(A)
| ~ zero(in1(A))
| zero(out1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ and_ok(A)
| ~ one(in1(A))
| ~ one(in2(A))
| one(out1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ and_ok(A)
| ~ one(out1(A))
| one(in2(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ logic_and(A)
| and_ok(A)
| abnormal(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(15,axiom,
( ~ or_ok(A)
| ~ one(in2(A))
| one(out1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(18,axiom,
( ~ or_ok(A)
| ~ zero(out1(A))
| zero(in1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(21,axiom,
( ~ logic_or(A)
| or_ok(A)
| abnormal(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(22,axiom,
( ~ not_ok(A)
| ~ zero(in1(A))
| one(out1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(23,axiom,
( ~ not_ok(A)
| ~ one(in1(A))
| zero(out1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(27,axiom,
( ~ logic_not(A)
| not_ok(A)
| abnormal(A) ),
file('HWV006-2.p',unknown),
[] ).
cnf(28,axiom,
( ~ halfadder(A)
| logic_and(and1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(29,axiom,
( ~ halfadder(A)
| logic_and(and2(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(30,axiom,
( ~ halfadder(A)
| logic_not(not1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(31,axiom,
( ~ halfadder(A)
| logic_or(or1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(33,axiom,
( ~ halfadder(A)
| connection(in2(A),in2(or1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(34,axiom,
( ~ halfadder(A)
| connection(in1(A),in1(and2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(35,axiom,
( ~ halfadder(A)
| connection(in2(A),in2(and2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(36,axiom,
( ~ halfadder(A)
| connection(outs(A),out1(and1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(37,axiom,
( ~ halfadder(A)
| connection(outc(A),out1(and2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(38,axiom,
( ~ halfadder(A)
| connection(out1(or1(A)),in1(and1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(39,axiom,
( ~ halfadder(A)
| connection(out1(and2(A)),in1(not1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(40,axiom,
( ~ halfadder(A)
| connection(out1(not1(A)),in2(and1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(41,axiom,
( ~ fulladder(A)
| halfadder(h1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(42,axiom,
( ~ fulladder(A)
| halfadder(h2(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(43,axiom,
( ~ fulladder(A)
| logic_or(or1(A)) ),
file('HWV006-2.p',unknown),
[] ).
cnf(44,axiom,
( ~ fulladder(A)
| connection(outs(h1(A)),in2(h2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(46,axiom,
( ~ fulladder(A)
| connection(outc(h2(A)),in1(or1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(47,axiom,
( ~ fulladder(A)
| connection(in1(A),in1(h2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(48,axiom,
( ~ fulladder(A)
| connection(in2(A),in1(h1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(49,axiom,
( ~ fulladder(A)
| connection(inc(A),in2(h1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(50,axiom,
( ~ fulladder(A)
| connection(outs(A),outs(h2(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(51,axiom,
( ~ fulladder(A)
| connection(outc(A),out1(or1(A))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(52,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(53,axiom,
~ abnormal(and2(h2(f))),
file('HWV006-2.p',unknown),
[] ).
cnf(54,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
file('HWV006-2.p',unknown),
[] ).
cnf(55,axiom,
~ abnormal(or1(h1(f))),
file('HWV006-2.p',unknown),
[] ).
cnf(56,axiom,
~ abnormal(not1(h1(f))),
file('HWV006-2.p',unknown),
[] ).
cnf(57,axiom,
~ abnormal(and2(h1(f))),
file('HWV006-2.p',unknown),
[] ).
cnf(58,axiom,
~ abnormal(and1(h1(f))),
file('HWV006-2.p',unknown),
[] ).
cnf(59,axiom,
fulladder(f),
file('HWV006-2.p',unknown),
[] ).
cnf(60,axiom,
one(in1(f)),
file('HWV006-2.p',unknown),
[] ).
cnf(61,axiom,
zero(in2(f)),
file('HWV006-2.p',unknown),
[] ).
cnf(62,axiom,
one(inc(f)),
file('HWV006-2.p',unknown),
[] ).
cnf(63,axiom,
one(outs(f)),
file('HWV006-2.p',unknown),
[] ).
cnf(64,axiom,
zero(outc(f)),
file('HWV006-2.p',unknown),
[] ).
cnf(65,plain,
connection(outc(f),out1(or1(f))),
inference(hyper,[status(thm)],[59,51]),
[iquote('hyper,59,51')] ).
cnf(66,plain,
connection(outs(f),outs(h2(f))),
inference(hyper,[status(thm)],[59,50]),
[iquote('hyper,59,50')] ).
cnf(67,plain,
connection(inc(f),in2(h1(f))),
inference(hyper,[status(thm)],[59,49]),
[iquote('hyper,59,49')] ).
cnf(68,plain,
connection(in2(f),in1(h1(f))),
inference(hyper,[status(thm)],[59,48]),
[iquote('hyper,59,48')] ).
cnf(69,plain,
connection(in1(f),in1(h2(f))),
inference(hyper,[status(thm)],[59,47]),
[iquote('hyper,59,47')] ).
cnf(70,plain,
connection(outc(h2(f)),in1(or1(f))),
inference(hyper,[status(thm)],[59,46]),
[iquote('hyper,59,46')] ).
cnf(72,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(hyper,[status(thm)],[59,44]),
[iquote('hyper,59,44')] ).
cnf(73,plain,
logic_or(or1(f)),
inference(hyper,[status(thm)],[59,43]),
[iquote('hyper,59,43')] ).
cnf(74,plain,
halfadder(h2(f)),
inference(hyper,[status(thm)],[59,42]),
[iquote('hyper,59,42')] ).
cnf(75,plain,
halfadder(h1(f)),
inference(hyper,[status(thm)],[59,41]),
[iquote('hyper,59,41')] ).
cnf(76,plain,
( or_ok(or1(f))
| abnormal(or1(f)) ),
inference(hyper,[status(thm)],[73,21]),
[iquote('hyper,73,21')] ).
cnf(77,plain,
connection(out1(not1(h2(f))),in2(and1(h2(f)))),
inference(hyper,[status(thm)],[74,40]),
[iquote('hyper,74,40')] ).
cnf(78,plain,
connection(out1(and2(h2(f))),in1(not1(h2(f)))),
inference(hyper,[status(thm)],[74,39]),
[iquote('hyper,74,39')] ).
cnf(80,plain,
connection(outc(h2(f)),out1(and2(h2(f)))),
inference(hyper,[status(thm)],[74,37]),
[iquote('hyper,74,37')] ).
cnf(81,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(hyper,[status(thm)],[74,36]),
[iquote('hyper,74,36')] ).
cnf(82,plain,
connection(in2(h2(f)),in2(and2(h2(f)))),
inference(hyper,[status(thm)],[74,35]),
[iquote('hyper,74,35')] ).
cnf(83,plain,
connection(in1(h2(f)),in1(and2(h2(f)))),
inference(hyper,[status(thm)],[74,34]),
[iquote('hyper,74,34')] ).
cnf(87,plain,
logic_not(not1(h2(f))),
inference(hyper,[status(thm)],[74,30]),
[iquote('hyper,74,30')] ).
cnf(88,plain,
logic_and(and2(h2(f))),
inference(hyper,[status(thm)],[74,29]),
[iquote('hyper,74,29')] ).
cnf(89,plain,
logic_and(and1(h2(f))),
inference(hyper,[status(thm)],[74,28]),
[iquote('hyper,74,28')] ).
cnf(90,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(hyper,[status(thm)],[75,40]),
[iquote('hyper,75,40')] ).
cnf(91,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(hyper,[status(thm)],[75,39]),
[iquote('hyper,75,39')] ).
cnf(92,plain,
connection(out1(or1(h1(f))),in1(and1(h1(f)))),
inference(hyper,[status(thm)],[75,38]),
[iquote('hyper,75,38')] ).
cnf(94,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(hyper,[status(thm)],[75,36]),
[iquote('hyper,75,36')] ).
cnf(96,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(hyper,[status(thm)],[75,34]),
[iquote('hyper,75,34')] ).
cnf(97,plain,
connection(in2(h1(f)),in2(or1(h1(f)))),
inference(hyper,[status(thm)],[75,33]),
[iquote('hyper,75,33')] ).
cnf(99,plain,
logic_or(or1(h1(f))),
inference(hyper,[status(thm)],[75,31]),
[iquote('hyper,75,31')] ).
cnf(100,plain,
logic_not(not1(h1(f))),
inference(hyper,[status(thm)],[75,30]),
[iquote('hyper,75,30')] ).
cnf(101,plain,
logic_and(and2(h1(f))),
inference(hyper,[status(thm)],[75,29]),
[iquote('hyper,75,29')] ).
cnf(102,plain,
logic_and(and1(h1(f))),
inference(hyper,[status(thm)],[75,28]),
[iquote('hyper,75,28')] ).
cnf(104,plain,
zero(out1(or1(f))),
inference(hyper,[status(thm)],[65,1,64]),
[iquote('hyper,65,1,64')] ).
cnf(105,plain,
( not_ok(not1(h2(f)))
| abnormal(not1(h2(f))) ),
inference(hyper,[status(thm)],[87,27]),
[iquote('hyper,87,27')] ).
cnf(106,plain,
and_ok(and2(h2(f))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[88,13]),53]),
[iquote('hyper,88,13,unit_del,53')] ).
cnf(107,plain,
( and_ok(and1(h2(f)))
| abnormal(and1(h2(f))) ),
inference(hyper,[status(thm)],[89,13]),
[iquote('hyper,89,13')] ).
cnf(108,plain,
or_ok(or1(h1(f))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[99,21]),55]),
[iquote('hyper,99,21,unit_del,55')] ).
cnf(109,plain,
one(outs(h2(f))),
inference(hyper,[status(thm)],[66,2,63]),
[iquote('hyper,66,2,63')] ).
cnf(110,plain,
not_ok(not1(h1(f))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[100,27]),56]),
[iquote('hyper,100,27,unit_del,56')] ).
cnf(111,plain,
and_ok(and2(h1(f))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[101,13]),57]),
[iquote('hyper,101,13,unit_del,57')] ).
cnf(112,plain,
and_ok(and1(h1(f))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[102,13]),58]),
[iquote('hyper,102,13,unit_del,58')] ).
cnf(113,plain,
one(in2(h1(f))),
inference(hyper,[status(thm)],[67,2,62]),
[iquote('hyper,67,2,62')] ).
cnf(114,plain,
zero(in1(h1(f))),
inference(hyper,[status(thm)],[68,1,61]),
[iquote('hyper,68,1,61')] ).
cnf(115,plain,
one(in1(h2(f))),
inference(hyper,[status(thm)],[69,2,60]),
[iquote('hyper,69,2,60')] ).
cnf(117,plain,
( abnormal(or1(f))
| zero(in1(or1(f))) ),
inference(hyper,[status(thm)],[76,18,104]),
[iquote('hyper,76,18,104')] ).
cnf(119,plain,
( abnormal(or1(f))
| zero(outc(h2(f))) ),
inference(hyper,[status(thm)],[117,3,70]),
[iquote('hyper,117,3,70')] ).
cnf(121,plain,
one(out1(and1(h2(f)))),
inference(hyper,[status(thm)],[81,2,109]),
[iquote('hyper,81,2,109')] ).
cnf(122,plain,
one(in1(and2(h2(f)))),
inference(hyper,[status(thm)],[83,2,115]),
[iquote('hyper,83,2,115')] ).
cnf(126,plain,
zero(in1(and2(h1(f)))),
inference(hyper,[status(thm)],[96,1,114]),
[iquote('hyper,96,1,114')] ).
cnf(127,plain,
zero(out1(and2(h1(f)))),
inference(hyper,[status(thm)],[126,6,111]),
[iquote('hyper,126,6,111')] ).
cnf(129,plain,
zero(in1(not1(h1(f)))),
inference(hyper,[status(thm)],[91,1,127]),
[iquote('hyper,91,1,127')] ).
cnf(131,plain,
one(out1(not1(h1(f)))),
inference(hyper,[status(thm)],[129,22,110]),
[iquote('hyper,129,22,110')] ).
cnf(132,plain,
one(in2(and1(h1(f)))),
inference(hyper,[status(thm)],[131,2,90]),
[iquote('hyper,131,2,90')] ).
cnf(133,plain,
one(in2(or1(h1(f)))),
inference(hyper,[status(thm)],[97,2,113]),
[iquote('hyper,97,2,113')] ).
cnf(134,plain,
one(out1(or1(h1(f)))),
inference(hyper,[status(thm)],[133,15,108]),
[iquote('hyper,133,15,108')] ).
cnf(135,plain,
one(in1(and1(h1(f)))),
inference(hyper,[status(thm)],[134,2,92]),
[iquote('hyper,134,2,92')] ).
cnf(137,plain,
one(out1(and1(h1(f)))),
inference(hyper,[status(thm)],[135,8,112,132]),
[iquote('hyper,135,8,112,132')] ).
cnf(138,plain,
one(outs(h1(f))),
inference(hyper,[status(thm)],[137,4,94]),
[iquote('hyper,137,4,94')] ).
cnf(139,plain,
one(in2(h2(f))),
inference(hyper,[status(thm)],[138,2,72]),
[iquote('hyper,138,2,72')] ).
cnf(142,plain,
one(in2(and2(h2(f)))),
inference(hyper,[status(thm)],[139,2,82]),
[iquote('hyper,139,2,82')] ).
cnf(143,plain,
one(out1(and2(h2(f)))),
inference(hyper,[status(thm)],[142,8,106,122]),
[iquote('hyper,142,8,106,122')] ).
cnf(144,plain,
one(outc(h2(f))),
inference(hyper,[status(thm)],[143,4,80]),
[iquote('hyper,143,4,80')] ).
cnf(145,plain,
one(in1(not1(h2(f)))),
inference(hyper,[status(thm)],[143,2,78]),
[iquote('hyper,143,2,78')] ).
cnf(146,plain,
abnormal(or1(f)),
inference(hyper,[status(thm)],[144,5,119]),
[iquote('hyper,144,5,119')] ).
cnf(148,plain,
( zero(out1(not1(h2(f))))
| abnormal(not1(h2(f))) ),
inference(hyper,[status(thm)],[145,23,105]),
[iquote('hyper,145,23,105')] ).
cnf(149,plain,
( abnormal(and1(h2(f)))
| one(in2(and1(h2(f)))) ),
inference(hyper,[status(thm)],[107,11,121]),
[iquote('hyper,107,11,121')] ).
cnf(152,plain,
( abnormal(not1(h2(f)))
| zero(in2(and1(h2(f)))) ),
inference(hyper,[status(thm)],[148,1,77]),
[iquote('hyper,148,1,77')] ).
cnf(156,plain,
( abnormal(not1(h2(f)))
| abnormal(and1(h2(f))) ),
inference(hyper,[status(thm)],[152,5,149]),
[iquote('hyper,152,5,149')] ).
cnf(157,plain,
abnormal(and1(h2(f))),
inference(hyper,[status(thm)],[156,52,146]),
[iquote('hyper,156,52,146')] ).
cnf(159,plain,
$false,
inference(hyper,[status(thm)],[157,54,146]),
[iquote('hyper,157,54,146')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : HWV006-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.08/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:50:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.06/2.24 ----- Otter 3.3f, August 2004 -----
% 2.06/2.24 The process was started by sandbox on n026.cluster.edu,
% 2.06/2.24 Wed Jul 27 06:50:54 2022
% 2.06/2.24 The command was "./otter". The process ID is 11982.
% 2.06/2.24
% 2.06/2.24 set(prolog_style_variables).
% 2.06/2.24 set(auto).
% 2.06/2.24 dependent: set(auto1).
% 2.06/2.24 dependent: set(process_input).
% 2.06/2.24 dependent: clear(print_kept).
% 2.06/2.24 dependent: clear(print_new_demod).
% 2.06/2.24 dependent: clear(print_back_demod).
% 2.06/2.24 dependent: clear(print_back_sub).
% 2.06/2.24 dependent: set(control_memory).
% 2.06/2.24 dependent: assign(max_mem, 12000).
% 2.06/2.24 dependent: assign(pick_given_ratio, 4).
% 2.06/2.24 dependent: assign(stats_level, 1).
% 2.06/2.24 dependent: assign(max_seconds, 10800).
% 2.06/2.24 clear(print_given).
% 2.06/2.24
% 2.06/2.24 list(usable).
% 2.06/2.24 0 [] -connection(P1,P2)| -zero(P1)|zero(P2).
% 2.06/2.24 0 [] -connection(P1,P2)| -one(P1)|one(P2).
% 2.06/2.24 0 [] -connection(P1,P2)| -zero(P2)|zero(P1).
% 2.06/2.24 0 [] -connection(P1,P2)| -one(P2)|one(P1).
% 2.06/2.24 0 [] -zero(P)| -one(P).
% 2.06/2.24 0 [] -and_ok(K)| -zero(in1(K))|zero(out1(K)).
% 2.06/2.24 0 [] -and_ok(K)| -zero(in2(K))|zero(out1(K)).
% 2.06/2.24 0 [] -and_ok(K)| -one(in1(K))| -one(in2(K))|one(out1(K)).
% 2.06/2.24 0 [] -and_ok(K)| -zero(out1(K))|zero(in1(K))|zero(in2(K)).
% 2.06/2.24 0 [] -and_ok(K)| -one(out1(K))|one(in1(K)).
% 2.06/2.24 0 [] -and_ok(K)| -one(out1(K))|one(in2(K)).
% 2.06/2.24 0 [] -and_ok(K)| -abnormal(K).
% 2.06/2.24 0 [] -logic_and(K)|and_ok(K)|abnormal(K).
% 2.06/2.24 0 [] -or_ok(K)| -one(in1(K))|one(out1(K)).
% 2.06/2.24 0 [] -or_ok(K)| -one(in2(K))|one(out1(K)).
% 2.06/2.24 0 [] -or_ok(K)| -zero(in1(K))| -zero(in2(K))|zero(out1(K)).
% 2.06/2.24 0 [] -or_ok(K)| -one(out1(K))|one(in1(K))|one(in2(K)).
% 2.06/2.24 0 [] -or_ok(K)| -zero(out1(K))|zero(in1(K)).
% 2.06/2.24 0 [] -or_ok(K)| -zero(out1(K))|zero(in2(K)).
% 2.06/2.24 0 [] -or_ok(K)| -abnormal(K).
% 2.06/2.24 0 [] -logic_or(K)|or_ok(K)|abnormal(K).
% 2.06/2.24 0 [] -not_ok(K)| -zero(in1(K))|one(out1(K)).
% 2.06/2.24 0 [] -not_ok(K)| -one(in1(K))|zero(out1(K)).
% 2.06/2.24 0 [] -not_ok(K)| -zero(out1(K))|one(in1(K)).
% 2.06/2.24 0 [] -not_ok(K)| -one(out1(K))|zero(in1(K)).
% 2.06/2.24 0 [] -not_ok(K)| -abnormal(K).
% 2.06/2.24 0 [] -logic_not(K)|not_ok(K)|abnormal(K).
% 2.06/2.24 0 [] -halfadder(X)|logic_and(and1(X)).
% 2.06/2.24 0 [] -halfadder(X)|logic_and(and2(X)).
% 2.06/2.24 0 [] -halfadder(X)|logic_not(not1(X)).
% 2.06/2.24 0 [] -halfadder(X)|logic_or(or1(X)).
% 2.06/2.24 0 [] -halfadder(X)|connection(in1(X),in1(or1(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(in2(X),in2(or1(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(in1(X),in1(and2(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(in2(X),in2(and2(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(outs(X),out1(and1(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(outc(X),out1(and2(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(out1(or1(X)),in1(and1(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(out1(and2(X)),in1(not1(X))).
% 2.06/2.24 0 [] -halfadder(X)|connection(out1(not1(X)),in2(and1(X))).
% 2.06/2.24 0 [] -fulladder(X)|halfadder(h1(X)).
% 2.06/2.24 0 [] -fulladder(X)|halfadder(h2(X)).
% 2.06/2.24 0 [] -fulladder(X)|logic_or(or1(X)).
% 2.06/2.24 0 [] -fulladder(X)|connection(outs(h1(X)),in2(h2(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(outc(h1(X)),in2(or1(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(outc(h2(X)),in1(or1(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(in1(X),in1(h2(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(in2(X),in1(h1(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(inc(X),in2(h1(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(outs(X),outs(h2(X))).
% 2.06/2.24 0 [] -fulladder(X)|connection(outc(X),out1(or1(X))).
% 2.06/2.24 0 [] fulladder(f).
% 2.06/2.24 0 [] one(in1(f)).
% 2.06/2.24 0 [] zero(in2(f)).
% 2.06/2.24 0 [] one(inc(f)).
% 2.06/2.24 0 [] one(outs(f)).
% 2.06/2.24 0 [] zero(outc(f)).
% 2.06/2.24 0 [] -abnormal(or1(f))| -abnormal(not1(h2(f))).
% 2.06/2.24 0 [] -abnormal(and2(h2(f))).
% 2.06/2.24 0 [] -abnormal(or1(f))| -abnormal(and1(h2(f))).
% 2.06/2.24 0 [] -abnormal(or1(h1(f))).
% 2.06/2.24 0 [] -abnormal(not1(h1(f))).
% 2.06/2.24 0 [] -abnormal(and2(h1(f))).
% 2.06/2.24 0 [] -abnormal(and1(h1(f))).
% 2.06/2.24 end_of_list.
% 2.06/2.24
% 2.06/2.24 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 2.06/2.24
% 2.06/2.24 This is a non-Horn set without equality. The strategy will
% 2.06/2.24 be ordered hyper_res, unit deletion, and factoring, with
% 2.06/2.24 satellites in sos and with nuclei in usable.
% 2.06/2.24
% 2.06/2.24 dependent: set(hyper_res).
% 2.06/2.24 dependent: set(factor).
% 2.06/2.24 dependent: set(unit_deletion).
% 2.06/2.24
% 2.06/2.24 ------------> process usable:
% 2.06/2.24 ** KEPT (pick-wt=7): 1 [] -connection(A,B)| -zero(A)|zero(B).
% 2.06/2.24 ** KEPT (pick-wt=7): 2 [] -connection(A,B)| -one(A)|one(B).
% 2.06/2.24 ** KEPT (pick-wt=7): 3 [] -connection(A,B)| -zero(B)|zero(A).
% 2.06/2.24 ** KEPT (pick-wt=7): 4 [] -connection(A,B)| -one(B)|one(A).
% 2.06/2.24 ** KEPT (pick-wt=4): 5 [] -zero(A)| -one(A).
% 2.06/2.24 ** KEPT (pick-wt=8): 6 [] -and_ok(A)| -zero(in1(A))|zero(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 7 [] -and_ok(A)| -zero(in2(A))|zero(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=11): 8 [] -and_ok(A)| -one(in1(A))| -one(in2(A))|one(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=11): 9 [] -and_ok(A)| -zero(out1(A))|zero(in1(A))|zero(in2(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 10 [] -and_ok(A)| -one(out1(A))|one(in1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 11 [] -and_ok(A)| -one(out1(A))|one(in2(A)).
% 2.06/2.24 ** KEPT (pick-wt=4): 12 [] -and_ok(A)| -abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=6): 13 [] -logic_and(A)|and_ok(A)|abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=8): 14 [] -or_ok(A)| -one(in1(A))|one(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 15 [] -or_ok(A)| -one(in2(A))|one(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=11): 16 [] -or_ok(A)| -zero(in1(A))| -zero(in2(A))|zero(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=11): 17 [] -or_ok(A)| -one(out1(A))|one(in1(A))|one(in2(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 18 [] -or_ok(A)| -zero(out1(A))|zero(in1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 19 [] -or_ok(A)| -zero(out1(A))|zero(in2(A)).
% 2.06/2.24 ** KEPT (pick-wt=4): 20 [] -or_ok(A)| -abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=6): 21 [] -logic_or(A)|or_ok(A)|abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=8): 22 [] -not_ok(A)| -zero(in1(A))|one(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 23 [] -not_ok(A)| -one(in1(A))|zero(out1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 24 [] -not_ok(A)| -zero(out1(A))|one(in1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 25 [] -not_ok(A)| -one(out1(A))|zero(in1(A)).
% 2.06/2.24 ** KEPT (pick-wt=4): 26 [] -not_ok(A)| -abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=6): 27 [] -logic_not(A)|not_ok(A)|abnormal(A).
% 2.06/2.24 ** KEPT (pick-wt=5): 28 [] -halfadder(A)|logic_and(and1(A)).
% 2.06/2.24 ** KEPT (pick-wt=5): 29 [] -halfadder(A)|logic_and(and2(A)).
% 2.06/2.24 ** KEPT (pick-wt=5): 30 [] -halfadder(A)|logic_not(not1(A)).
% 2.06/2.24 ** KEPT (pick-wt=5): 31 [] -halfadder(A)|logic_or(or1(A)).
% 2.06/2.24 ** KEPT (pick-wt=8): 32 [] -halfadder(A)|connection(in1(A),in1(or1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 33 [] -halfadder(A)|connection(in2(A),in2(or1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 34 [] -halfadder(A)|connection(in1(A),in1(and2(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 35 [] -halfadder(A)|connection(in2(A),in2(and2(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 36 [] -halfadder(A)|connection(outs(A),out1(and1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 37 [] -halfadder(A)|connection(outc(A),out1(and2(A))).
% 2.06/2.24 ** KEPT (pick-wt=9): 38 [] -halfadder(A)|connection(out1(or1(A)),in1(and1(A))).
% 2.06/2.24 ** KEPT (pick-wt=9): 39 [] -halfadder(A)|connection(out1(and2(A)),in1(not1(A))).
% 2.06/2.24 ** KEPT (pick-wt=9): 40 [] -halfadder(A)|connection(out1(not1(A)),in2(and1(A))).
% 2.06/2.24 ** KEPT (pick-wt=5): 41 [] -fulladder(A)|halfadder(h1(A)).
% 2.06/2.24 ** KEPT (pick-wt=5): 42 [] -fulladder(A)|halfadder(h2(A)).
% 2.06/2.24 ** KEPT (pick-wt=5): 43 [] -fulladder(A)|logic_or(or1(A)).
% 2.06/2.24 ** KEPT (pick-wt=9): 44 [] -fulladder(A)|connection(outs(h1(A)),in2(h2(A))).
% 2.06/2.24 ** KEPT (pick-wt=9): 45 [] -fulladder(A)|connection(outc(h1(A)),in2(or1(A))).
% 2.06/2.24 ** KEPT (pick-wt=9): 46 [] -fulladder(A)|connection(outc(h2(A)),in1(or1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 47 [] -fulladder(A)|connection(in1(A),in1(h2(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 48 [] -fulladder(A)|connection(in2(A),in1(h1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 49 [] -fulladder(A)|connection(inc(A),in2(h1(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 50 [] -fulladder(A)|connection(outs(A),outs(h2(A))).
% 2.06/2.24 ** KEPT (pick-wt=8): 51 [] -fulladder(A)|connection(outc(A),out1(or1(A))).
% 2.06/2.24 ** KEPT (pick-wt=7): 52 [] -abnormal(or1(f))| -abnormal(not1(h2(f))).
% 2.06/2.24 ** KEPT (pick-wt=4): 53 [] -abnormal(and2(h2(f))).
% 2.06/2.24 ** KEPT (pick-wt=7): 54 [] -abnormal(or1(f))| -abnormal(and1(h2(f))).
% 2.06/2.24 ** KEPT (pick-wt=4): 55 [] -abnormal(or1(h1(f))).
% 2.06/2.24 ** KEPT (pick-wt=4): 56 [] -abnormal(not1(h1(f))).
% 2.06/2.24 ** KEPT (pick-wt=4): 57 [] -abnormal(and2(h1(f))).
% 2.06/2.24 ** KEPT (pick-wt=4): 58 [] -abnormal(and1(h1(f))).
% 2.06/2.24
% 2.06/2.24 ------------> process sos:
% 2.06/2.24 ** KEPT (pick-wt=2): 59 [] fulladder(f).
% 2.06/2.24 ** KEPT (pick-wt=3): 60 [] one(in1(f)).
% 2.06/2.24 ** KEPT (pick-wt=3): 61 [] zero(in2(f)).
% 2.06/2.24 ** KEPT (pick-wt=3): 62 [] one(inc(f)).
% 2.06/2.24 ** KEPT (pick-wt=3): 63 [] one(outs(f)).
% 2.06/2.24 ** KEPT (pick-wt=3): 64 [] zero(outc(f)).
% 2.06/2.24
% 2.06/2.24 ======= end of input processing =======
% 2.06/2.24
% 2.06/2.24 =========== start of search ===========
% 2.06/2.24
% 2.06/2.24 -------- PROOF --------
% 2.06/2.24
% 2.06/2.24 -----> EMPTY CLAUSE at 0.00 sec ----> 159 [hyper,157,54,146] $F.
% 2.06/2.24
% 2.06/2.24 Length of proof is 67. Level of proof is 17.
% 2.06/2.24
% 2.06/2.24 ---------------- PROOF ----------------
% 2.06/2.24 % SZS status Unsatisfiable
% 2.06/2.24 % SZS output start Refutation
% See solution above
% 2.06/2.24 ------------ end of proof -------------
% 2.06/2.24
% 2.06/2.24
% 2.06/2.24 Search stopped by max_proofs option.
% 2.06/2.24
% 2.06/2.24
% 2.06/2.24 Search stopped by max_proofs option.
% 2.06/2.24
% 2.06/2.24 ============ end of search ============
% 2.06/2.24
% 2.06/2.24 -------------- statistics -------------
% 2.06/2.24 clauses given 94
% 2.06/2.24 clauses generated 139
% 2.06/2.24 clauses kept 158
% 2.06/2.24 clauses forward subsumed 44
% 2.06/2.24 clauses back subsumed 17
% 2.06/2.24 Kbytes malloced 1953
% 2.06/2.24
% 2.06/2.24 ----------- times (seconds) -----------
% 2.06/2.24 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.06/2.24 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.06/2.24 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.06/2.24
% 2.06/2.24 That finishes the proof of the theorem.
% 2.06/2.24
% 2.06/2.24 Process 11982 finished Wed Jul 27 06:50:56 2022
% 2.06/2.24 Otter interrupted
% 2.06/2.24 PROOF FOUND
%------------------------------------------------------------------------------