TSTP Solution File: HWV007-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV007-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 19:14:41 EDT 2022
% Result : Unsatisfiable 0.43s 0.59s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 46
% Syntax : Number of clauses : 145 ( 26 unt; 7 nHn; 145 RR)
% Number of literals : 346 ( 0 equ; 215 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('HWV007-1.p',unknown),
[] ).
cnf(2,axiom,
value(in(n1,f),n0),
file('HWV007-1.p',unknown),
[] ).
cnf(3,axiom,
value(in(n2,f),n1),
file('HWV007-1.p',unknown),
[] ).
cnf(4,axiom,
value(in(c,f),n1),
file('HWV007-1.p',unknown),
[] ).
cnf(5,axiom,
value(out(s,f),n1),
file('HWV007-1.p',unknown),
[] ).
cnf(6,axiom,
value(out(c,f),n0),
file('HWV007-1.p',unknown),
[] ).
cnf(7,axiom,
~ mode(and2(h1(f)),abnormal),
file('HWV007-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h1(f)),abnormal) ),
file('HWV007-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(not1(h1(f)),abnormal) ),
file('HWV007-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h2(f)),abnormal) ),
file('HWV007-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(or1(h2(f)),abnormal) ),
file('HWV007-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ value(u,v)
| ~ connection(u,w)
| value(w,v) ),
file('HWV007-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ value(u,v)
| ~ connection(w,u)
| value(w,v) ),
file('HWV007-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ value(u,v)
| ~ value(u,w)
| equal_value(w,v) ),
file('HWV007-1.p',unknown),
[] ).
cnf(16,axiom,
~ equal_value(n1,n0),
file('HWV007-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ type(u,v)
| mode(u,abnormal)
| mode(u,ok) ),
file('HWV007-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(in(v,u),n0)
| value(out(n1,u),n0) ),
file('HWV007-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(in(n1,u),n1)
| ~ value(in(n2,u),n1)
| value(out(n1,u),n1) ),
file('HWV007-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| value(in(n1,u),n1) ),
file('HWV007-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(in(n2,u),n0)
| ~ value(in(n1,u),n0)
| value(out(n1,u),n0) ),
file('HWV007-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| value(in(n1,u),n1)
| value(in(n2,u),n1) ),
file('HWV007-1.p',unknown),
[] ).
cnf(28,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n0)
| value(in(n2,u),n0) ),
file('HWV007-1.p',unknown),
[] ).
cnf(30,axiom,
( ~ type(u,not__dfg)
| ~ mode(u,ok)
| ~ value(in(n1,u),n1)
| value(out(n1,u),n0) ),
file('HWV007-1.p',unknown),
[] ).
cnf(33,axiom,
( ~ type(u,halfadder)
| type(and1(u),and__dfg) ),
file('HWV007-1.p',unknown),
[] ).
cnf(34,axiom,
( ~ type(u,halfadder)
| type(and2(u),and__dfg) ),
file('HWV007-1.p',unknown),
[] ).
cnf(35,axiom,
( ~ type(u,halfadder)
| type(not1(u),not__dfg) ),
file('HWV007-1.p',unknown),
[] ).
cnf(36,axiom,
( ~ type(u,halfadder)
| type(or1(u),or__dfg) ),
file('HWV007-1.p',unknown),
[] ).
cnf(37,axiom,
( ~ type(u,halfadder)
| connection(in(n1,u),in(n1,or1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(38,axiom,
( ~ type(u,halfadder)
| connection(in(n2,u),in(n2,or1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(39,axiom,
( ~ type(u,halfadder)
| connection(in(n1,u),in(n1,and2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ type(u,halfadder)
| connection(in(n2,u),in(n2,and2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ type(u,halfadder)
| connection(out(s,u),out(n1,and1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(42,axiom,
( ~ type(u,halfadder)
| connection(out(c,u),out(n1,and2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(43,axiom,
( ~ type(u,halfadder)
| connection(out(n1,or1(u)),in(n1,and1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(44,axiom,
( ~ type(u,halfadder)
| connection(out(n1,and2(u)),in(n1,not1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(45,axiom,
( ~ type(u,halfadder)
| connection(out(n1,not1(u)),in(n2,and1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(46,axiom,
( ~ type(u,fulladder)
| type(h1(u),halfadder) ),
file('HWV007-1.p',unknown),
[] ).
cnf(47,axiom,
( ~ type(u,fulladder)
| type(h2(u),halfadder) ),
file('HWV007-1.p',unknown),
[] ).
cnf(48,axiom,
( ~ type(u,fulladder)
| type(or1(u),or__dfg) ),
file('HWV007-1.p',unknown),
[] ).
cnf(49,axiom,
( ~ type(u,fulladder)
| connection(out(s,h1(u)),in(n2,h2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(50,axiom,
( ~ type(u,fulladder)
| connection(out(c,h1(u)),in(n2,or1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ type(u,fulladder)
| connection(in(n1,u),in(n1,h2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(53,axiom,
( ~ type(u,fulladder)
| connection(in(n2,u),in(n1,h1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(54,axiom,
( ~ type(u,fulladder)
| connection(in(c,u),in(n2,h1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ type(u,fulladder)
| connection(out(s,u),out(s,h2(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(56,axiom,
( ~ type(u,fulladder)
| connection(out(c,u),out(n1,or1(u))) ),
file('HWV007-1.p',unknown),
[] ).
cnf(57,plain,
( ~ type(and2(h1(f)),u)
| mode(and2(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[18,7]),
[iquote('0:Res:18.2,7.0')] ).
cnf(58,plain,
~ mode(or1(f),abnormal),
inference(spt,[spt(split,[position(s1)])],[10]),
[iquote('1:Spt:10.0')] ).
cnf(60,plain,
( ~ type(u,halfadder)
| mode(or1(u),abnormal)
| mode(or1(u),ok) ),
inference(res,[status(thm),theory(equality)],[36,18]),
[iquote('0:Res:36.1,18.0')] ).
cnf(61,plain,
( ~ type(u,fulladder)
| mode(or1(u),abnormal)
| mode(or1(u),ok) ),
inference(res,[status(thm),theory(equality)],[48,18]),
[iquote('0:Res:48.1,18.0')] ).
cnf(64,plain,
( ~ type(u,halfadder)
| mode(not1(u),abnormal)
| mode(not1(u),ok) ),
inference(res,[status(thm),theory(equality)],[35,18]),
[iquote('0:Res:35.1,18.0')] ).
cnf(66,plain,
( ~ type(u,halfadder)
| mode(and1(u),abnormal)
| mode(and1(u),ok) ),
inference(res,[status(thm),theory(equality)],[33,18]),
[iquote('0:Res:33.1,18.0')] ).
cnf(83,plain,
( ~ connection(out(c,f),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[6,12]),
[iquote('0:Res:6.0,12.0')] ).
cnf(84,plain,
( ~ connection(out(s,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.0,12.0')] ).
cnf(85,plain,
( ~ connection(in(c,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.0')] ).
cnf(86,plain,
( ~ connection(in(n2,f),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.0')] ).
cnf(87,plain,
( ~ connection(in(n1,f),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(88,plain,
( ~ type(f,fulladder)
| value(out(n1,or1(f)),n0) ),
inference(res,[status(thm),theory(equality)],[56,83]),
[iquote('0:Res:56.1,83.0')] ).
cnf(89,plain,
value(out(n1,or1(f)),n0),
inference(mrr,[status(thm)],[88,1]),
[iquote('0:MRR:88.0,1.0')] ).
cnf(93,plain,
( ~ type(f,fulladder)
| value(in(n2,h1(f)),n1) ),
inference(res,[status(thm),theory(equality)],[54,85]),
[iquote('0:Res:54.1,85.0')] ).
cnf(94,plain,
value(in(n2,h1(f)),n1),
inference(mrr,[status(thm)],[93,1]),
[iquote('0:MRR:93.0,1.0')] ).
cnf(95,plain,
( ~ connection(in(n2,h1(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[94,12]),
[iquote('0:Res:94.0,12.0')] ).
cnf(98,plain,
( ~ type(f,fulladder)
| value(in(n1,h1(f)),n1) ),
inference(res,[status(thm),theory(equality)],[53,86]),
[iquote('0:Res:53.1,86.0')] ).
cnf(99,plain,
value(in(n1,h1(f)),n1),
inference(mrr,[status(thm)],[98,1]),
[iquote('0:MRR:98.0,1.0')] ).
cnf(100,plain,
( ~ connection(in(n1,h1(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[99,12]),
[iquote('0:Res:99.0,12.0')] ).
cnf(118,plain,
( ~ type(h1(f),halfadder)
| mode(and2(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[34,57]),
[iquote('0:Res:34.1,57.0')] ).
cnf(119,plain,
( ~ type(f,fulladder)
| value(out(s,h2(f)),n1) ),
inference(res,[status(thm),theory(equality)],[55,84]),
[iquote('0:Res:55.1,84.0')] ).
cnf(120,plain,
value(out(s,h2(f)),n1),
inference(mrr,[status(thm)],[119,1]),
[iquote('0:MRR:119.0,1.0')] ).
cnf(121,plain,
( ~ connection(out(s,h2(f)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[120,12]),
[iquote('0:Res:120.0,12.0')] ).
cnf(124,plain,
( ~ type(h2(f),halfadder)
| value(out(n1,and1(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[41,121]),
[iquote('0:Res:41.1,121.0')] ).
cnf(127,plain,
( ~ type(f,fulladder)
| value(in(n1,h2(f)),n0) ),
inference(res,[status(thm),theory(equality)],[52,87]),
[iquote('0:Res:52.1,87.0')] ).
cnf(129,plain,
value(in(n1,h2(f)),n0),
inference(mrr,[status(thm)],[127,1]),
[iquote('0:MRR:127.0,1.0')] ).
cnf(130,plain,
( ~ connection(in(n1,h2(f)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[129,12]),
[iquote('0:Res:129.0,12.0')] ).
cnf(137,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,and2(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[40,95]),
[iquote('0:Res:40.1,95.0')] ).
cnf(149,plain,
( ~ type(h1(f),halfadder)
| value(in(n1,and2(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[39,100]),
[iquote('0:Res:39.1,100.0')] ).
cnf(179,plain,
( ~ type(h2(f),halfadder)
| value(in(n1,or1(h2(f))),n0) ),
inference(res,[status(thm),theory(equality)],[37,130]),
[iquote('0:Res:37.1,130.0')] ).
cnf(191,plain,
( ~ type(h2(f),halfadder)
| ~ value(in(n1,or1(h2(f))),u)
| equal_value(u,n0) ),
inference(res,[status(thm),theory(equality)],[179,14]),
[iquote('0:Res:179.1,14.0')] ).
cnf(194,plain,
( ~ type(f,fulladder)
| mode(or1(f),ok) ),
inference(res,[status(thm),theory(equality)],[61,58]),
[iquote('1:Res:61.1,58.0')] ).
cnf(196,plain,
mode(or1(f),ok),
inference(mrr,[status(thm)],[194,1]),
[iquote('1:MRR:194.0,1.0')] ).
cnf(207,plain,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n0)
| ~ connection(v,in(n2,u))
| value(v,n0) ),
inference(res,[status(thm),theory(equality)],[28,13]),
[iquote('0:Res:28.3,13.0')] ).
cnf(208,plain,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n0)
| ~ value(in(n2,u),v)
| equal_value(v,n0) ),
inference(res,[status(thm),theory(equality)],[28,14]),
[iquote('0:Res:28.3,14.0')] ).
cnf(329,plain,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| ~ connection(v,in(n1,u))
| value(v,n1) ),
inference(res,[status(thm),theory(equality)],[22,13]),
[iquote('0:Res:22.3,13.0')] ).
cnf(450,plain,
( ~ type(h2(f),halfadder)
| ~ type(or1(h2(f)),or__dfg)
| ~ mode(or1(h2(f)),ok)
| ~ value(in(n2,or1(h2(f))),n0)
| value(out(n1,or1(h2(f))),n0) ),
inference(res,[status(thm),theory(equality)],[179,25]),
[iquote('0:Res:179.1,25.3')] ).
cnf(455,plain,
( ~ type(h2(f),halfadder)
| ~ mode(or1(h2(f)),ok)
| ~ value(in(n2,or1(h2(f))),n0)
| value(out(n1,or1(h2(f))),n0) ),
inference(mrr,[status(thm)],[450,36]),
[iquote('0:MRR:450.1,36.1')] ).
cnf(484,plain,
( ~ type(h1(f),halfadder)
| ~ type(and2(h1(f)),and__dfg)
| ~ mode(and2(h1(f)),ok)
| ~ value(in(n2,and2(h1(f))),n1)
| value(out(n1,and2(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[149,20]),
[iquote('0:Res:149.1,20.2')] ).
cnf(494,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,and2(h1(f))),n1) ),
inference(mrr,[status(thm)],[484,34,118,137]),
[iquote('0:MRR:484.1,484.2,484.3,34.1,118.1,137.1')] ).
cnf(496,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(n1,and2(h1(f))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[494,12]),
[iquote('0:Res:494.1,12.0')] ).
cnf(497,plain,
( ~ type(h1(f),halfadder)
| ~ connection(u,out(n1,and2(h1(f))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[494,13]),
[iquote('0:Res:494.1,13.0')] ).
cnf(586,plain,
( ~ type(or1(f),or__dfg)
| ~ mode(or1(f),ok)
| ~ connection(u,in(n2,or1(f)))
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[89,207]),
[iquote('0:Res:89.0,207.2')] ).
cnf(590,plain,
( ~ type(or1(f),or__dfg)
| ~ connection(u,in(n2,or1(f)))
| value(u,n0) ),
inference(mrr,[status(thm)],[586,196]),
[iquote('1:MRR:586.1,196.0')] ).
cnf(594,plain,
( ~ type(f,fulladder)
| ~ type(or1(f),or__dfg)
| value(out(c,h1(f)),n0) ),
inference(res,[status(thm),theory(equality)],[50,590]),
[iquote('1:Res:50.1,590.1')] ).
cnf(596,plain,
( ~ type(or1(f),or__dfg)
| value(out(c,h1(f)),n0) ),
inference(mrr,[status(thm)],[594,1]),
[iquote('1:MRR:594.0,1.0')] ).
cnf(599,plain,
( ~ type(or1(f),or__dfg)
| ~ value(out(c,h1(f)),u)
| equal_value(u,n0) ),
inference(res,[status(thm),theory(equality)],[596,14]),
[iquote('1:Res:596.1,14.0')] ).
cnf(804,plain,
( ~ type(or1(h2(f)),or__dfg)
| ~ mode(or1(h2(f)),ok)
| ~ value(out(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder)
| value(in(n2,or1(h2(f))),n1)
| equal_value(n1,n0) ),
inference(res,[status(thm),theory(equality)],[26,191]),
[iquote('0:Res:26.3,191.1')] ).
cnf(810,plain,
( ~ mode(or1(h2(f)),ok)
| ~ value(out(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder)
| value(in(n2,or1(h2(f))),n1) ),
inference(mrr,[status(thm)],[804,36,16]),
[iquote('0:MRR:804.0,804.5,36.1,16.0')] ).
cnf(811,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n1,not1(h1(f))),n1) ),
inference(res,[status(thm),theory(equality)],[44,496]),
[iquote('0:Res:44.1,496.1')] ).
cnf(812,plain,
( ~ type(h1(f),halfadder)
| value(in(n1,not1(h1(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[811]),
[iquote('0:Obv:811.0')] ).
cnf(814,plain,
( ~ type(h1(f),halfadder)
| ~ type(not1(h1(f)),not__dfg)
| ~ mode(not1(h1(f)),ok)
| value(out(n1,not1(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[812,30]),
[iquote('0:Res:812.1,30.2')] ).
cnf(821,plain,
( ~ type(h1(f),halfadder)
| ~ mode(not1(h1(f)),ok)
| value(out(n1,not1(h1(f))),n0) ),
inference(mrr,[status(thm)],[814,35]),
[iquote('0:MRR:814.1,35.1')] ).
cnf(839,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(out(c,h1(f)),n1) ),
inference(res,[status(thm),theory(equality)],[42,497]),
[iquote('0:Res:42.1,497.1')] ).
cnf(840,plain,
( ~ type(h1(f),halfadder)
| value(out(c,h1(f)),n1) ),
inference(obv,[status(thm),theory(equality)],[839]),
[iquote('0:Obv:839.0')] ).
cnf(841,plain,
( ~ type(h1(f),halfadder)
| ~ type(or1(f),or__dfg)
| equal_value(n1,n0) ),
inference(res,[status(thm),theory(equality)],[840,599]),
[iquote('1:Res:840.1,599.1')] ).
cnf(845,plain,
( ~ type(h1(f),halfadder)
| ~ type(or1(f),or__dfg) ),
inference(mrr,[status(thm)],[841,16]),
[iquote('1:MRR:841.2,16.0')] ).
cnf(846,plain,
( ~ type(f,fulladder)
| ~ type(or1(f),or__dfg) ),
inference(res,[status(thm),theory(equality)],[46,845]),
[iquote('1:Res:46.1,845.0')] ).
cnf(847,plain,
~ type(or1(f),or__dfg),
inference(mrr,[status(thm)],[846,1]),
[iquote('1:MRR:846.0,1.0')] ).
cnf(849,plain,
~ type(f,fulladder),
inference(res,[status(thm),theory(equality)],[48,847]),
[iquote('1:Res:48.1,847.0')] ).
cnf(850,plain,
$false,
inference(mrr,[status(thm)],[849,1]),
[iquote('1:MRR:849.0,1.0')] ).
cnf(851,plain,
mode(or1(f),abnormal),
inference(spt,[spt(split,[position(sa)])],[850,58]),
[iquote('1:Spt:850.0,10.0,58.0')] ).
cnf(852,plain,
~ mode(and1(h2(f)),abnormal),
inference(spt,[spt(split,[position(s2)])],[10]),
[iquote('1:Spt:850.0,10.1')] ).
cnf(853,plain,
~ mode(or1(h2(f)),abnormal),
inference(mrr,[status(thm)],[11,851]),
[iquote('1:MRR:11.0,851.0')] ).
cnf(854,plain,
~ mode(not1(h1(f)),abnormal),
inference(mrr,[status(thm)],[9,851]),
[iquote('1:MRR:9.0,851.0')] ).
cnf(855,plain,
~ mode(and1(h1(f)),abnormal),
inference(mrr,[status(thm)],[8,851]),
[iquote('1:MRR:8.0,851.0')] ).
cnf(857,plain,
( ~ type(h2(f),halfadder)
| mode(and1(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[66,852]),
[iquote('1:Res:66.1,852.0')] ).
cnf(861,plain,
( ~ type(h2(f),halfadder)
| mode(or1(h2(f)),ok) ),
inference(res,[status(thm),theory(equality)],[60,853]),
[iquote('1:Res:60.1,853.0')] ).
cnf(864,plain,
( ~ type(h2(f),halfadder)
| ~ value(in(n2,or1(h2(f))),n0)
| value(out(n1,or1(h2(f))),n0) ),
inference(mrr,[status(thm)],[455,861]),
[iquote('1:MRR:455.1,861.1')] ).
cnf(867,plain,
( ~ value(out(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder)
| value(in(n2,or1(h2(f))),n1) ),
inference(mrr,[status(thm)],[810,861]),
[iquote('1:MRR:810.0,861.1')] ).
cnf(868,plain,
( ~ type(h1(f),halfadder)
| mode(not1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[64,854]),
[iquote('1:Res:64.1,854.0')] ).
cnf(869,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,not1(h1(f))),n0) ),
inference(mrr,[status(thm)],[821,868]),
[iquote('1:MRR:821.1,868.1')] ).
cnf(873,plain,
( ~ type(h1(f),halfadder)
| mode(and1(h1(f)),ok) ),
inference(res,[status(thm),theory(equality)],[66,855]),
[iquote('1:Res:66.1,855.0')] ).
cnf(995,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(n1,not1(h1(f))),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[869,12]),
[iquote('1:Res:869.1,12.0')] ).
cnf(1154,plain,
( ~ type(h2(f),halfadder)
| ~ type(and1(h2(f)),and__dfg)
| ~ mode(and1(h2(f)),ok)
| ~ connection(u,in(n1,and1(h2(f))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[124,329]),
[iquote('0:Res:124.1,329.2')] ).
cnf(1165,plain,
( ~ type(h2(f),halfadder)
| ~ connection(u,in(n1,and1(h2(f))))
| value(u,n1) ),
inference(mrr,[status(thm)],[1154,33,857]),
[iquote('1:MRR:1154.1,1154.2,33.1,857.1')] ).
cnf(1751,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n2,and1(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[45,995]),
[iquote('1:Res:45.1,995.1')] ).
cnf(1752,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,and1(h1(f))),n0) ),
inference(obv,[status(thm),theory(equality)],[1751]),
[iquote('1:Obv:1751.0')] ).
cnf(1756,plain,
( ~ type(h1(f),halfadder)
| ~ type(and1(h1(f)),and__dfg)
| ~ mode(and1(h1(f)),ok)
| value(out(n1,and1(h1(f))),n0) ),
inference(res,[status(thm),theory(equality)],[1752,19]),
[iquote('1:Res:1752.1,19.2')] ).
cnf(1760,plain,
( ~ type(h1(f),halfadder)
| value(out(n1,and1(h1(f))),n0) ),
inference(mrr,[status(thm)],[1756,33,873]),
[iquote('1:MRR:1756.1,1756.2,33.1,873.1')] ).
cnf(1771,plain,
( ~ type(h1(f),halfadder)
| ~ connection(u,out(n1,and1(h1(f))))
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[1760,13]),
[iquote('1:Res:1760.1,13.0')] ).
cnf(1788,plain,
( ~ type(h2(f),halfadder)
| ~ type(h2(f),halfadder)
| value(out(n1,or1(h2(f))),n1) ),
inference(res,[status(thm),theory(equality)],[43,1165]),
[iquote('1:Res:43.1,1165.1')] ).
cnf(1789,plain,
( ~ type(h2(f),halfadder)
| value(out(n1,or1(h2(f))),n1) ),
inference(obv,[status(thm),theory(equality)],[1788]),
[iquote('1:Obv:1788.0')] ).
cnf(1791,plain,
( ~ type(h2(f),halfadder)
| value(in(n2,or1(h2(f))),n1) ),
inference(mrr,[status(thm)],[867,1789]),
[iquote('1:MRR:867.0,1789.1')] ).
cnf(1805,plain,
( ~ type(h2(f),halfadder)
| ~ type(or1(h2(f)),or__dfg)
| ~ mode(or1(h2(f)),ok)
| ~ value(out(n1,or1(h2(f))),n0)
| equal_value(n1,n0) ),
inference(res,[status(thm),theory(equality)],[1791,208]),
[iquote('1:Res:1791.1,208.3')] ).
cnf(1810,plain,
( ~ type(h2(f),halfadder)
| ~ value(out(n1,or1(h2(f))),n0) ),
inference(mrr,[status(thm)],[1805,36,861,16]),
[iquote('1:MRR:1805.1,1805.2,1805.4,36.1,861.1,16.0')] ).
cnf(1811,plain,
( ~ type(h2(f),halfadder)
| ~ value(in(n2,or1(h2(f))),n0) ),
inference(mrr,[status(thm)],[864,1810]),
[iquote('1:MRR:864.2,1810.1')] ).
cnf(1863,plain,
( ~ type(h1(f),halfadder)
| ~ type(h1(f),halfadder)
| value(out(s,h1(f)),n0) ),
inference(res,[status(thm),theory(equality)],[41,1771]),
[iquote('1:Res:41.1,1771.1')] ).
cnf(1864,plain,
( ~ type(h1(f),halfadder)
| value(out(s,h1(f)),n0) ),
inference(obv,[status(thm),theory(equality)],[1863]),
[iquote('1:Obv:1863.0')] ).
cnf(1885,plain,
( ~ type(h1(f),halfadder)
| ~ connection(out(s,h1(f)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[1864,12]),
[iquote('1:Res:1864.1,12.0')] ).
cnf(1890,plain,
( ~ type(f,fulladder)
| ~ type(h1(f),halfadder)
| value(in(n2,h2(f)),n0) ),
inference(res,[status(thm),theory(equality)],[49,1885]),
[iquote('1:Res:49.1,1885.1')] ).
cnf(1891,plain,
( ~ type(h1(f),halfadder)
| value(in(n2,h2(f)),n0) ),
inference(mrr,[status(thm)],[1890,1]),
[iquote('1:MRR:1890.0,1.0')] ).
cnf(1920,plain,
( ~ type(h1(f),halfadder)
| ~ connection(in(n2,h2(f)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[1891,12]),
[iquote('1:Res:1891.1,12.0')] ).
cnf(1928,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder)
| value(in(n2,or1(h2(f))),n0) ),
inference(res,[status(thm),theory(equality)],[38,1920]),
[iquote('1:Res:38.1,1920.1')] ).
cnf(1929,plain,
( ~ type(h2(f),halfadder)
| ~ type(h1(f),halfadder) ),
inference(mrr,[status(thm)],[1928,1811]),
[iquote('1:MRR:1928.2,1811.1')] ).
cnf(1952,plain,
( ~ type(f,fulladder)
| ~ type(h2(f),halfadder) ),
inference(res,[status(thm),theory(equality)],[46,1929]),
[iquote('1:Res:46.1,1929.1')] ).
cnf(1953,plain,
~ type(h2(f),halfadder),
inference(mrr,[status(thm)],[1952,1]),
[iquote('1:MRR:1952.0,1.0')] ).
cnf(1954,plain,
~ type(f,fulladder),
inference(res,[status(thm),theory(equality)],[47,1953]),
[iquote('1:Res:47.1,1953.0')] ).
cnf(1955,plain,
$false,
inference(mrr,[status(thm)],[1954,1]),
[iquote('1:MRR:1954.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV007-1 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 22:54:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.59
% 0.43/0.59 SPASS V 3.9
% 0.43/0.59 SPASS beiseite: Proof found.
% 0.43/0.59 % SZS status Theorem
% 0.43/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.59 SPASS derived 1452 clauses, backtracked 57 clauses, performed 1 splits and kept 848 clauses.
% 0.43/0.59 SPASS allocated 64992 KBytes.
% 0.43/0.59 SPASS spent 0:00:00.25 on the problem.
% 0.43/0.59 0:00:00.03 for the input.
% 0.43/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.43/0.59 0:00:00.03 for inferences.
% 0.43/0.59 0:00:00.00 for the backtracking.
% 0.43/0.59 0:00:00.15 for the reduction.
% 0.43/0.59
% 0.43/0.59
% 0.43/0.59 Here is a proof with depth 19, length 145 :
% 0.43/0.59 % SZS output start Refutation
% See solution above
% 0.43/0.60 Formulae used in the proof : f_isa_fulladder in1_1 in2_0 inc_1 outs_1 outc_0 diagnosis_and2h1 diagnosis_or1_and1h1 diagnosis_or1_not1h1 diagnosis_or1_and1h2 diagnosis_or1_or1h2 value_propagation1 value_propagation2 unique_value equal_value2 ok_or_abnormal and_0x_0 and_11_1 and_1_1x or_00_0 or_1_11 or_0_01 not_1_0_fw halfadder_and1 halfadder_and2 halfadder_not1 halfadder_or1 halfadder_connection_in1_in1or1 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_outch1_in2or1 fulladder_connection_in1_in1h2 fulladder_connection_in2_in1h1 fulladder_connection_inc_in2h1 fulladder_connection_outs_outsh2 fulladder_connection_outc_out1or1
% 0.43/0.60
%------------------------------------------------------------------------------