TSTP Solution File: HWV006-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV006-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 19:14:40 EDT 2022
% Result : Unsatisfiable 1.32s 1.49s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 48
% Syntax : Number of clauses : 152 ( 21 unt; 4 nHn; 152 RR)
% Number of literals : 399 ( 0 equ; 263 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
type(f,fulladder),
file('HWV006-1.p',unknown),
[] ).
cnf(2,axiom,
value(in(n1,f),n1),
file('HWV006-1.p',unknown),
[] ).
cnf(3,axiom,
value(in(n2,f),n0),
file('HWV006-1.p',unknown),
[] ).
cnf(4,axiom,
value(in(c,f),n1),
file('HWV006-1.p',unknown),
[] ).
cnf(5,axiom,
value(out(s,f),n1),
file('HWV006-1.p',unknown),
[] ).
cnf(6,axiom,
value(out(c,f),n0),
file('HWV006-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(not1(h2(f)),abnormal) ),
file('HWV006-1.p',unknown),
[] ).
cnf(8,axiom,
~ mode(and2(h2(f)),abnormal),
file('HWV006-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h2(f)),abnormal) ),
file('HWV006-1.p',unknown),
[] ).
cnf(10,axiom,
~ mode(or1(h1(f)),abnormal),
file('HWV006-1.p',unknown),
[] ).
cnf(11,axiom,
~ mode(not1(h1(f)),abnormal),
file('HWV006-1.p',unknown),
[] ).
cnf(12,axiom,
~ mode(and2(h1(f)),abnormal),
file('HWV006-1.p',unknown),
[] ).
cnf(13,axiom,
~ mode(and1(h1(f)),abnormal),
file('HWV006-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ value(u,v)
| ~ connection(u,w)
| value(w,v) ),
file('HWV006-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ value(u,v)
| ~ connection(w,u)
| value(w,v) ),
file('HWV006-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ value(u,v)
| ~ value(u,w)
| equal_value(w,v) ),
file('HWV006-1.p',unknown),
[] ).
cnf(17,axiom,
~ equal_value(n0,n1),
file('HWV006-1.p',unknown),
[] ).
cnf(18,axiom,
~ equal_value(n1,n0),
file('HWV006-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ type(u,v)
| mode(u,abnormal)
| mode(u,ok) ),
file('HWV006-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(in(v,u),n0)
| value(out(n1,u),n0) ),
file('HWV006-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(in(n1,u),n1)
| ~ value(in(n2,u),n1)
| value(out(n1,u),n1) ),
file('HWV006-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| value(in(n2,u),n1) ),
file('HWV006-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(in(v,u),n1)
| value(out(n1,u),n1) ),
file('HWV006-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n0)
| value(in(n1,u),n0) ),
file('HWV006-1.p',unknown),
[] ).
cnf(31,axiom,
( ~ type(u,not__dfg)
| ~ mode(u,ok)
| ~ value(in(n1,u),n0)
| value(out(n1,u),n1) ),
file('HWV006-1.p',unknown),
[] ).
cnf(32,axiom,
( ~ type(u,not__dfg)
| ~ mode(u,ok)
| ~ value(in(n1,u),n1)
| value(out(n1,u),n0) ),
file('HWV006-1.p',unknown),
[] ).
cnf(35,axiom,
( ~ type(u,halfadder)
| type(and1(u),and__dfg) ),
file('HWV006-1.p',unknown),
[] ).
cnf(36,axiom,
( ~ type(u,halfadder)
| type(and2(u),and__dfg) ),
file('HWV006-1.p',unknown),
[] ).
cnf(37,axiom,
( ~ type(u,halfadder)
| type(not1(u),not__dfg) ),
file('HWV006-1.p',unknown),
[] ).
cnf(38,axiom,
( ~ type(u,halfadder)
| type(or1(u),or__dfg) ),
file('HWV006-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ type(u,halfadder)
| connection(in(n2,u),in(n2,or1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ type(u,halfadder)
| connection(in(n1,u),in(n1,and2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(42,axiom,
( ~ type(u,halfadder)
| connection(in(n2,u),in(n2,and2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(43,axiom,
( ~ type(u,halfadder)
| connection(out(s,u),out(n1,and1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(44,axiom,
( ~ type(u,halfadder)
| connection(out(c,u),out(n1,and2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(45,axiom,
( ~ type(u,halfadder)
| connection(out(n1,or1(u)),in(n1,and1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(46,axiom,
( ~ type(u,halfadder)
| connection(out(n1,and2(u)),in(n1,not1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(47,axiom,
( ~ type(u,halfadder)
| connection(out(n1,not1(u)),in(n2,and1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(48,axiom,
( ~ type(u,fulladder)
| type(h1(u),halfadder) ),
file('HWV006-1.p',unknown),
[] ).
cnf(49,axiom,
( ~ type(u,fulladder)
| type(h2(u),halfadder) ),
file('HWV006-1.p',unknown),
[] ).
cnf(50,axiom,
( ~ type(u,fulladder)
| type(or1(u),or__dfg) ),
file('HWV006-1.p',unknown),
[] ).
cnf(51,axiom,
( ~ type(u,fulladder)
| connection(out(s,h1(u)),in(n2,h2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(53,axiom,
( ~ type(u,fulladder)
| connection(out(c,h2(u)),in(n1,or1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(54,axiom,
( ~ type(u,fulladder)
| connection(in(n1,u),in(n1,h2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ type(u,fulladder)
| connection(in(n2,u),in(n1,h1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(56,axiom,
( ~ type(u,fulladder)
| connection(in(c,u),in(n2,h1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(57,axiom,
( ~ type(u,fulladder)
| connection(out(s,u),out(s,h2(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(58,axiom,
( ~ type(u,fulladder)
| connection(out(c,u),out(n1,or1(u))) ),
file('HWV006-1.p',unknown),
[] ).
cnf(59,plain,
( ~ type(and1(h1(f)),u)
| mode(and1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[20,13]),
[iquote('0:Res:20.2,13.0')] ).
cnf(60,plain,
( ~ type(and2(h1(f)),u)
| mode(and2(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[20,12]),
[iquote('0:Res:20.2,12.0')] ).
cnf(61,plain,
( ~ type(not1(h1(f)),u)
| mode(not1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[20,11]),
[iquote('0:Res:20.2,11.0')] ).
cnf(62,plain,
( ~ type(or1(h1(f)),u)
| mode(or1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[20,10]),
[iquote('0:Res:20.2,10.0')] ).
cnf(63,plain,
( ~ type(and2(h2(f)),u)
| mode(and2(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[20,8]),
[iquote('0:Res:20.2,8.0')] ).
cnf(66,plain,
( ~ type(u,fulladder)
| mode(or1(u),abnormal)
| mode(or1(u),ok) ),
inference(res,[status(thm),theory(equality)],[50,20]),
[iquote('0:Res:50.1,20.0')] ).
cnf(69,plain,
( ~ type(u,halfadder)
| mode(not1(u),abnormal)
| mode(not1(u),ok) ),
inference(res,[status(thm),theory(equality)],[37,20]),
[iquote('0:Res:37.1,20.0')] ).
cnf(71,plain,
( ~ type(u,halfadder)
| mode(and1(u),abnormal)
| mode(and1(u),ok) ),
inference(res,[status(thm),theory(equality)],[35,20]),
[iquote('0:Res:35.1,20.0')] ).
cnf(73,plain,
( ~ type(h2(f),halfadder)
| mode(and2(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[36,63]),
[iquote('0:Res:36.1,63.0')] ).
cnf(74,plain,
( ~ type(h1(f),halfadder)
| mode(or1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[38,62]),
[iquote('0:Res:38.1,62.0')] ).
cnf(91,plain,
( ~ connection(out(c,f),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[6,14]),
[iquote('0:Res:6.0,14.0')] ).
cnf(92,plain,
( ~ connection(out(s,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.0,14.0')] ).
cnf(93,plain,
( ~ connection(in(c,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4,14]),
[iquote('0:Res:4.0,14.0')] ).
cnf(94,plain,
( ~ connection(in(n1,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.0')] ).
cnf(95,plain,
( ~ connection(in(n2,f),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.0,14.0')] ).
cnf(96,plain,
( ~ type(f,fulladder)
| value(out(n1,or1(f)),n0) ),
inference(res,[status(thm),theory(equality)],[58,91]),
[iquote('0:Res:58.1,91.0')] ).
cnf(97,plain,
value(out(n1,or1(f)),n0),
inference(mrr,[status(thm)],[96,1]),
[iquote('0:MRR:96.0,1.0')] ).
cnf(101,plain,
( ~ type(f,fulladder)
| value(in(n2,h1(f)),n1) ),
inference(res,[status(thm),theory(equality)],[56,93]),
[iquote('0:Res:56.1,93.0')] ).
cnf(102,plain,
value(in(n2,h1(f)),n1),
inference(mrr,[status(thm)],[101,1]),
[iquote('0:MRR:101.0,1.0')] ).
cnf(103,plain,
( ~ connection(in(n2,h1(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[102,14]),
[iquote('0:Res:102.0,14.0')] ).
cnf(106,plain,
( ~ type(f,fulladder)
| value(in(n1,h1(f)),n0) ),
inference(res,[status(thm),theory(equality)],[55,95]),
[iquote('0:Res:55.1,95.0')] ).
cnf(107,plain,
value(in(n1,h1(f)),n0),
inference(mrr,[status(thm)],[106,1]),
[iquote('0:MRR:106.0,1.0')] ).
cnf(108,plain,
( ~ connection(in(n1,h1(f)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[107,14]),
[iquote('0:Res:107.0,14.0')] ).
cnf(126,plain,
( ~ type(f,fulladder)
| value(out(s,h2(f)),n1) ),
inference(res,[status(thm),theory(equality)],[57,92]),
[iquote('0:Res:57.1,92.0')] ).
cnf(127,plain,
value(out(s,h2(f)),n1),
inference(mrr,[status(thm)],[126,1]),
[iquote('0:MRR:126.0,1.0')] ).
cnf(128,plain,
( ~ connection(out(s,h2(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[127,14]),
[iquote('0:Res:127.0,14.0')] ).
cnf(131,plain,
( ~ type(h2(f),halfadder)
| value(out(n1,and1(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[43,128]),
[iquote('0:Res:43.1,128.0')] ).
cnf(135,plain,
( ~ type(f,fulladder)
| value(in(n1,h2(f)),n1) ),
inference(res,[status(thm),theory(equality)],[54,94]),
[iquote('0:Res:54.1,94.0')] ).
cnf(137,plain,
value(in(n1,h2(f)),n1),
inference(mrr,[status(thm)],[135,1]),
[iquote('0:MRR:135.0,1.0')] ).
cnf(138,plain,
( ~ connection(in(n1,h2(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[137,14]),
[iquote('0:Res:137.0,14.0')] ).
cnf(149,plain,
( ~ type(h1(f),halfadder)
| mode(not1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[37,61]),
[iquote('0:Res:37.1,61.0')] ).
cnf(150,plain,
( ~ type(h1(f),halfadder)
| mode(and2(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[36,60]),
[iquote('0:Res:36.1,60.0')] ).
cnf(152,plain,
( ~ type(h1(f),halfadder)
| value(in(n1,and2(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[41,108]),
[iquote('0:Res:41.1,108.0')] ).
cnf(153,plain,
( ~ type(h2(f),halfadder)
| value(in(n1,and2(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[41,138]),
[iquote('0:Res:41.1,138.0')] ).
cnf(157,plain,
( ~ type(h1(f),halfadder)
| mode(and1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[35,59]),
[iquote('0:Res:35.1,59.0')] ).
cnf(159,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,or1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[40,103]),
[iquote('0:Res:40.1,103.0')] ).
cnf(209,plain,
( ~ type(h2(f),halfadder)
| ~ mode(or1(f),abnormal)
| mode(not1(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[69,7]),
[iquote('0:Res:69.1,7.1')] ).
cnf(215,plain,
( ~ type(h2(f),halfadder)
| ~ mode(or1(f),abnormal)
| mode(and1(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[71,9]),
[iquote('0:Res:71.1,9.1')] ).
cnf(240,plain,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n0)
| ~ connection(v,in(n1,u))
| value(v,n0) ),
inference(res,[status(thm),theory(equality)],[29,15]),
[iquote('0:Res:29.3,15.0')] ).
cnf(293,plain,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| ~ connection(v,in(n2,u))
| value(v,n1) ),
inference(res,[status(thm),theory(equality)],[25,15]),
[iquote('0:Res:25.3,15.0')] ).
cnf(377,plain,
( ~ type(h1(f),halfadder)
| ~ type(and2(h1(f)),and__dfg)
| ~ mode(and2(h1(f)),ok)
| value(out(n1,and2(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[152,21]),
[iquote('0:Res:152.1,21.2')] ).
cnf(387,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,and2(h1(f))),n0) ),
inference(mrr,[status(thm)],[377,36,150]),
[iquote('0:MRR:377.1,377.2,36.1,150.1')] ).
cnf(389,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(n1,and2(h1(f))),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[387,14]),
[iquote('0:Res:387.1,14.0')] ).
cnf(412,plain,
( ~ type(h1(f),halfadder)
| ~ type(or1(h1(f)),or__dfg)
| ~ mode(or1(h1(f)),ok)
| value(out(n1,or1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[159,26]),
[iquote('0:Res:159.1,26.2')] ).
cnf(414,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,or1(h1(f))),n1) ),
inference(mrr,[status(thm)],[412,38,74]),
[iquote('0:MRR:412.1,412.2,38.1,74.1')] ).
cnf(419,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(n1,or1(h1(f))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[414,14]),
[iquote('0:Res:414.1,14.0')] ).
cnf(513,plain,
( ~ type(h2(f),halfadder)
| ~ type(and2(h2(f)),and__dfg)
| ~ mode(and2(h2(f)),ok)
| ~ value(in(n2,and2(h2(f))),n1)
| value(out(n1,and2(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[153,22]),
[iquote('0:Res:153.1,22.2')] ).
cnf(520,plain,
( ~ type(h2(f),halfadder)
| ~ value(in(n2,and2(h2(f))),n1)
| value(out(n1,and2(h2(f))),n1) ),
inference(mrr,[status(thm)],[513,36,73]),
[iquote('0:MRR:513.1,513.2,36.1,73.1')] ).
cnf(794,plain,
( ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| ~ connection(u,in(n1,or1(f)))
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[97,240]),
[iquote('0:Res:97.0,240.2')] ).
cnf(1074,plain,
( ~ type(h2(f),halfadder)
| ~ type(and1(h2(f)),and__dfg)
| ~ mode(and1(h2(f)),ok)
| ~ connection(u,in(n2,and1(h2(f))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[131,293]),
[iquote('0:Res:131.1,293.2')] ).
cnf(1085,plain,
( ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| ~ connection(u,in(n2,and1(h2(f))))
| value(u,n1) ),
inference(mrr,[status(thm)],[1074,35]),
[iquote('0:MRR:1074.1,35.1')] ).
cnf(1244,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n1,not1(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[46,389]),
[iquote('0:Res:46.1,389.1')] ).
cnf(1245,plain,
( ~ type(h1(f),halfadder)
| value(in(n1,not1(h1(f))),n0) ),
inference(obv,[status(thm),theory(equality)],[1244]),
[iquote('0:Obv:1244.0')] ).
cnf(1247,plain,
( ~ type(h1(f),halfadder)
| ~ type(not1(h1(f)),not__dfg)
| ~ mode(not1(h1(f)),ok)
| value(out(n1,not1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[1245,31]),
[iquote('0:Res:1245.1,31.2')] ).
cnf(1256,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,not1(h1(f))),n1) ),
inference(mrr,[status(thm)],[1247,37,149]),
[iquote('0:MRR:1247.1,1247.2,37.1,149.1')] ).
cnf(1278,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(n1,not1(h1(f))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[1256,14]),
[iquote('0:Res:1256.1,14.0')] ).
cnf(1412,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n1,and1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[45,419]),
[iquote('0:Res:45.1,419.1')] ).
cnf(1413,plain,
( ~ type(h1(f),halfadder)
| value(in(n1,and1(h1(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[1412]),
[iquote('0:Obv:1412.0')] ).
cnf(1426,plain,
( ~ type(h1(f),halfadder)
| ~ type(and1(h1(f)),and__dfg)
| ~ mode(and1(h1(f)),ok)
| ~ value(in(n2,and1(h1(f))),n1)
| value(out(n1,and1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[1413,22]),
[iquote('0:Res:1413.1,22.2')] ).
cnf(1440,plain,
( ~ type(h1(f),halfadder)
| ~ value(in(n2,and1(h1(f))),n1)
| value(out(n1,and1(h1(f))),n1) ),
inference(mrr,[status(thm)],[1426,35,157]),
[iquote('0:MRR:1426.1,1426.2,35.1,157.1')] ).
cnf(1466,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n2,and1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[47,1278]),
[iquote('0:Res:47.1,1278.1')] ).
cnf(1467,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,and1(h1(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[1466]),
[iquote('0:Obv:1466.0')] ).
cnf(1468,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,and1(h1(f))),n1) ),
inference(mrr,[status(thm)],[1440,1467]),
[iquote('0:MRR:1440.1,1467.1')] ).
cnf(1539,plain,
( ~ type(h1(f),halfadder)
| ~ connection(u,out(n1,and1(h1(f))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[1468,15]),
[iquote('0:Res:1468.1,15.0')] ).
cnf(1591,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(out(s,h1(f)),n1) ),
inference(res,[status(thm),theory(equality)],[43,1539]),
[iquote('0:Res:43.1,1539.1')] ).
cnf(1592,plain,
( ~ type(h1(f),halfadder)
| value(out(s,h1(f)),n1) ),
inference(obv,[status(thm),theory(equality)],[1591]),
[iquote('0:Obv:1591.0')] ).
cnf(1649,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(s,h1(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[1592,14]),
[iquote('0:Res:1592.1,14.0')] ).
cnf(1654,plain,
( ~ type(f,fulladder)
| ~ type(h1(f),halfadder)
| value(in(n2,h2(f)),n1) ),
inference(res,[status(thm),theory(equality)],[51,1649]),
[iquote('0:Res:51.1,1649.1')] ).
cnf(1655,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,h2(f)),n1) ),
inference(mrr,[status(thm)],[1654,1]),
[iquote('0:MRR:1654.0,1.0')] ).
cnf(1661,plain,
( ~ type(h1(f),halfadder)
| ~ connection(in(n2,h2(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[1655,14]),
[iquote('0:Res:1655.1,14.0')] ).
cnf(1687,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n2,and2(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[42,1661]),
[iquote('0:Res:42.1,1661.1')] ).
cnf(2230,plain,
( ~ type(f,fulladder)
| ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| value(out(c,h2(f)),n0) ),
inference(res,[status(thm),theory(equality)],[53,794]),
[iquote('0:Res:53.1,794.2')] ).
cnf(2232,plain,
( ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| value(out(c,h2(f)),n0) ),
inference(mrr,[status(thm)],[2230,1]),
[iquote('0:MRR:2230.0,1.0')] ).
cnf(2236,plain,
( ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| ~ value(out(c,h2(f)),u)
| equal_value(u,n0) ),
inference(res,[status(thm),theory(equality)],[2232,16]),
[iquote('0:Res:2232.2,16.0')] ).
cnf(4072,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(out(n1,and2(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[1687,520]),
[iquote('0:Res:1687.2,520.1')] ).
cnf(4073,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(out(n1,and2(h2(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[4072]),
[iquote('0:Obv:4072.0')] ).
cnf(4086,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ connection(out(n1,and2(h2(f))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4073,14]),
[iquote('0:Res:4073.2,14.0')] ).
cnf(4087,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ connection(u,out(n1,and2(h2(f))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4073,15]),
[iquote('0:Res:4073.2,15.0')] ).
cnf(5643,plain,
( ~ type(h2(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| value(out(n1,not1(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[47,1085]),
[iquote('0:Res:47.1,1085.2')] ).
cnf(5644,plain,
( ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| value(out(n1,not1(h2(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[5643]),
[iquote('0:Obv:5643.0')] ).
cnf(5658,plain,
( ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| ~ value(out(n1,not1(h2(f))),u)
| equal_value(u,n1) ),
inference(res,[status(thm),theory(equality)],[5644,16]),
[iquote('0:Res:5644.2,16.0')] ).
cnf(5915,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(out(c,h2(f)),n1) ),
inference(res,[status(thm),theory(equality)],[44,4087]),
[iquote('0:Res:44.1,4087.2')] ).
cnf(5916,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(out(c,h2(f)),n1) ),
inference(obv,[status(thm),theory(equality)],[5915]),
[iquote('0:Obv:5915.0')] ).
cnf(5917,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| equal_value(n1,n0) ),
inference(res,[status(thm),theory(equality)],[5916,2236]),
[iquote('0:Res:5916.2,2236.2')] ).
cnf(5923,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok) ),
inference(mrr,[status(thm)],[5917,18]),
[iquote('0:MRR:5917.4,18.0')] ).
cnf(6016,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(in(n1,not1(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[46,4086]),
[iquote('0:Res:46.1,4086.2')] ).
cnf(6017,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| value(in(n1,not1(h2(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[6016]),
[iquote('0:Obv:6016.0')] ).
cnf(6044,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ type(not1(h2(f)),not__dfg)
| ~ mode(not1(h2(f)),ok)
| value(out(n1,not1(h2(f))),n0) ),
inference(res,[status(thm),theory(equality)],[6017,32]),
[iquote('0:Res:6017.2,32.2')] ).
cnf(6057,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ mode(not1(h2(f)),ok)
| value(out(n1,not1(h2(f))),n0) ),
inference(mrr,[status(thm)],[6044,37]),
[iquote('0:MRR:6044.2,37.1')] ).
cnf(7865,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ mode(not1(h2(f)),ok)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| equal_value(n0,n1) ),
inference(res,[status(thm),theory(equality)],[6057,5658]),
[iquote('0:Res:6057.3,5658.2')] ).
cnf(7869,plain,
( ~ type(h1(f),halfadder)
| ~ mode(not1(h2(f)),ok)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok)
| equal_value(n0,n1) ),
inference(obv,[status(thm),theory(equality)],[7865]),
[iquote('0:Obv:7865.1')] ).
cnf(7870,plain,
( ~ type(h1(f),halfadder)
| ~ mode(not1(h2(f)),ok)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok) ),
inference(mrr,[status(thm)],[7869,17]),
[iquote('0:MRR:7869.4,17.0')] ).
cnf(7884,plain,
( ~ type(h2(f),halfadder)
| ~ mode(or1(f),abnormal)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[209,7870]),
[iquote('0:Res:209.2,7870.1')] ).
cnf(7885,plain,
( ~ mode(or1(f),abnormal)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ mode(and1(h2(f)),ok) ),
inference(obv,[status(thm),theory(equality)],[7884]),
[iquote('0:Obv:7884.0')] ).
cnf(7886,plain,
( ~ mode(or1(f),abnormal)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder) ),
inference(mrr,[status(thm)],[7885,215]),
[iquote('0:MRR:7885.3,215.2')] ).
cnf(7887,plain,
( ~ type(f,fulladder)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| mode(or1(f),ok) ),
inference(res,[status(thm),theory(equality)],[66,7886]),
[iquote('0:Res:66.1,7886.0')] ).
cnf(7889,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| mode(or1(f),ok) ),
inference(mrr,[status(thm)],[7887,1]),
[iquote('0:MRR:7887.0,1.0')] ).
cnf(7890,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder)
| ~ type(or1(f),or__dfg) ),
inference(mrr,[status(thm)],[5923,7889]),
[iquote('0:MRR:5923.3,7889.2')] ).
cnf(7896,plain,
( ~ type(f,fulladder)
| ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder) ),
inference(res,[status(thm),theory(equality)],[50,7890]),
[iquote('0:Res:50.1,7890.2')] ).
cnf(7897,plain,
( ~ type(h1(f),halfadder)
| ~ type(h2(f),halfadder) ),
inference(mrr,[status(thm)],[7896,1]),
[iquote('0:MRR:7896.0,1.0')] ).
cnf(7898,plain,
( ~ type(f,fulladder)
| ~ type(h1(f),halfadder) ),
inference(res,[status(thm),theory(equality)],[49,7897]),
[iquote('0:Res:49.1,7897.1')] ).
cnf(7899,plain,
~ type(h1(f),halfadder),
inference(mrr,[status(thm)],[7898,1]),
[iquote('0:MRR:7898.0,1.0')] ).
cnf(7900,plain,
~ type(f,fulladder),
inference(res,[status(thm),theory(equality)],[48,7899]),
[iquote('0:Res:48.1,7899.0')] ).
cnf(7901,plain,
$false,
inference(mrr,[status(thm)],[7900,1]),
[iquote('0:MRR:7900.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV006-1 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 01:31:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.32/1.49
% 1.32/1.49 SPASS V 3.9
% 1.32/1.49 SPASS beiseite: Proof found.
% 1.32/1.49 % SZS status Theorem
% 1.32/1.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.32/1.49 SPASS derived 6088 clauses, backtracked 571 clauses, performed 2 splits and kept 2945 clauses.
% 1.32/1.49 SPASS allocated 70268 KBytes.
% 1.32/1.49 SPASS spent 0:00:01.14 on the problem.
% 1.32/1.49 0:00:00.03 for the input.
% 1.32/1.49 0:00:00.00 for the FLOTTER CNF translation.
% 1.32/1.49 0:00:00.11 for inferences.
% 1.32/1.49 0:00:00.00 for the backtracking.
% 1.32/1.49 0:00:00.91 for the reduction.
% 1.32/1.49
% 1.32/1.49
% 1.32/1.49 Here is a proof with depth 21, length 152 :
% 1.32/1.49 % SZS output start Refutation
% See solution above
% 1.45/1.62 Formulae used in the proof : f_isa_fulladder in1_1 in2_0 inc_1 outs_1 outc_0 diagnosis_or1_not1h2 diagnosis_and2 diagnosis_or1_and1h2 diagnosis_or1h1 diagnosis_not1h1 diagnosis_and2h1 diagnosis_and1h1 value_propagation1 value_propagation2 unique_value equal_value1 equal_value2 ok_or_abnormal and_0x_0 and_11_1 and_1_x1 or_1x_1 or_0_0x not_0_1_fw not_1_0_fw halfadder_and1 halfadder_and2 halfadder_not1 halfadder_or1 halfadder_connection_in2_in2or1 halfadder_connection_in1_in1and2 halfadder_connection_in2_in2and2 halfadder_connection_outs_out1and1 halfadder_connection_outc_out1and2 halfadder_connection_out1or1_in1_and1 halfadder_connection_out1and2_in1not1 halfadder_connection_out1not1_in2and1 fulladder_halfadder1 fulladder_halfadder2 fulladder_or1 fulladder_connection_outsh1_in2h2 fulladder_connection_outch2_in1or1 fulladder_connection_in1_in1h2 fulladder_connection_in2_in1h1 fulladder_connection_inc_in2h1 fulladder_connection_outs_outsh2 fulladder_connection_outc_out1or1
% 1.45/1.62
%------------------------------------------------------------------------------