TSTP Solution File: HWV008-1.002 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 19:14:42 EDT 2022
% Result : Unsatisfiable 1.01s 1.21s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 29
% Syntax : Number of clauses : 90 ( 19 unt; 5 nHn; 90 RR)
% Number of literals : 199 ( 0 equ; 117 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 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(2,axiom,
( ~ type(u,nbit_adder(n2))
| type(f(n2,u),fulladder) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(5,axiom,
( ~ type(u,nbit_adder(n2))
| connection(out(c,u),out(c,f(n2,u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(8,axiom,
( ~ type(u,nbit_adder(n2))
| connection(in(a2,u),in(n1,f(n2,u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(9,axiom,
( ~ type(u,nbit_adder(n2))
| connection(in(b2,u),in(n2,f(n2,u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(12,axiom,
type(a,nbit_adder(n2)),
file('HWV008-1.002.p',unknown),
[] ).
cnf(14,axiom,
value(in(a2,a),n0),
file('HWV008-1.002.p',unknown),
[] ).
cnf(16,axiom,
value(in(b2,a),n0),
file('HWV008-1.002.p',unknown),
[] ).
cnf(20,axiom,
value(out(c,a),n1),
file('HWV008-1.002.p',unknown),
[] ).
cnf(21,axiom,
~ mode(or1(f(n2,a)),abnormal),
file('HWV008-1.002.p',unknown),
[] ).
cnf(22,axiom,
~ mode(and2(h1(f(n2,a))),abnormal),
file('HWV008-1.002.p',unknown),
[] ).
cnf(23,axiom,
~ mode(and2(h2(f(n2,a))),abnormal),
file('HWV008-1.002.p',unknown),
[] ).
cnf(24,axiom,
( ~ value(u,v)
| ~ connection(u,w)
| value(w,v) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(25,axiom,
( ~ value(u,v)
| ~ connection(w,u)
| value(w,v) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(26,axiom,
( ~ value(u,v)
| ~ value(u,w)
| equal_value(w,v) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(27,axiom,
~ equal_value(n0,n1),
file('HWV008-1.002.p',unknown),
[] ).
cnf(30,axiom,
( ~ type(u,v)
| mode(u,abnormal)
| mode(u,ok) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(31,axiom,
( ~ type(u,and__dfg)
| ~ mode(u,ok)
| ~ value(in(v,u),n0)
| value(out(n1,u),n0) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(38,axiom,
( ~ type(u,or__dfg)
| ~ mode(u,ok)
| ~ value(out(n1,u),n1)
| value(in(n1,u),n1)
| value(in(n2,u),n1) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(46,axiom,
( ~ type(u,halfadder)
| type(and2(u),and__dfg) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(51,axiom,
( ~ type(u,halfadder)
| connection(in(n1,u),in(n1,and2(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(54,axiom,
( ~ type(u,halfadder)
| connection(out(c,u),out(n1,and2(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(58,axiom,
( ~ type(u,fulladder)
| type(h1(u),halfadder) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(59,axiom,
( ~ type(u,fulladder)
| type(h2(u),halfadder) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(60,axiom,
( ~ type(u,fulladder)
| type(or1(u),or__dfg) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(62,axiom,
( ~ type(u,fulladder)
| connection(out(c,h1(u)),in(n2,or1(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(63,axiom,
( ~ type(u,fulladder)
| connection(out(c,h2(u)),in(n1,or1(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(64,axiom,
( ~ type(u,fulladder)
| connection(in(n1,u),in(n1,h2(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(65,axiom,
( ~ type(u,fulladder)
| connection(in(n2,u),in(n1,h1(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(68,axiom,
( ~ type(u,fulladder)
| connection(out(c,u),out(n1,or1(u))) ),
file('HWV008-1.002.p',unknown),
[] ).
cnf(70,plain,
( ~ type(and2(h2(f(n2,a))),u)
| mode(and2(h2(f(n2,a))),ok) ),
inference(res,[status(thm),theory(equality)],[30,23]),
[iquote('0:Res:30.2,23.0')] ).
cnf(71,plain,
( ~ type(and2(h1(f(n2,a))),u)
| mode(and2(h1(f(n2,a))),ok) ),
inference(res,[status(thm),theory(equality)],[30,22]),
[iquote('0:Res:30.2,22.0')] ).
cnf(74,plain,
( ~ type(u,fulladder)
| mode(or1(u),abnormal)
| mode(or1(u),ok) ),
inference(res,[status(thm),theory(equality)],[60,30]),
[iquote('0:Res:60.1,30.0')] ).
cnf(103,plain,
( ~ connection(out(c,a),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[20,24]),
[iquote('0:Res:20.0,24.0')] ).
cnf(107,plain,
( ~ connection(in(b2,a),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[16,24]),
[iquote('0:Res:16.0,24.0')] ).
cnf(109,plain,
( ~ connection(in(a2,a),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[14,24]),
[iquote('0:Res:14.0,24.0')] ).
cnf(129,plain,
( ~ type(f(n2,a),fulladder)
| mode(or1(f(n2,a)),ok) ),
inference(res,[status(thm),theory(equality)],[74,21]),
[iquote('0:Res:74.1,21.0')] ).
cnf(144,plain,
( ~ type(a,nbit_adder(n2))
| value(in(n1,f(n2,a)),n0) ),
inference(res,[status(thm),theory(equality)],[8,109]),
[iquote('0:Res:8.1,109.0')] ).
cnf(145,plain,
value(in(n1,f(n2,a)),n0),
inference(mrr,[status(thm)],[144,12]),
[iquote('0:MRR:144.0,12.0')] ).
cnf(146,plain,
( ~ connection(in(n1,f(n2,a)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[145,24]),
[iquote('0:Res:145.0,24.0')] ).
cnf(149,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n1,h2(f(n2,a))),n0) ),
inference(res,[status(thm),theory(equality)],[64,146]),
[iquote('0:Res:64.1,146.0')] ).
cnf(183,plain,
( ~ type(a,nbit_adder(n2))
| value(in(n2,f(n2,a)),n0) ),
inference(res,[status(thm),theory(equality)],[9,107]),
[iquote('0:Res:9.1,107.0')] ).
cnf(184,plain,
value(in(n2,f(n2,a)),n0),
inference(mrr,[status(thm)],[183,12]),
[iquote('0:MRR:183.0,12.0')] ).
cnf(185,plain,
( ~ connection(in(n2,f(n2,a)),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[184,24]),
[iquote('0:Res:184.0,24.0')] ).
cnf(188,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n1,h1(f(n2,a))),n0) ),
inference(res,[status(thm),theory(equality)],[65,185]),
[iquote('0:Res:65.1,185.0')] ).
cnf(200,plain,
( ~ type(a,nbit_adder(n2))
| value(out(c,f(n2,a)),n1) ),
inference(res,[status(thm),theory(equality)],[5,103]),
[iquote('0:Res:5.1,103.0')] ).
cnf(201,plain,
value(out(c,f(n2,a)),n1),
inference(mrr,[status(thm)],[200,12]),
[iquote('0:MRR:200.0,12.0')] ).
cnf(202,plain,
( ~ connection(out(c,f(n2,a)),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[201,24]),
[iquote('0:Res:201.0,24.0')] ).
cnf(205,plain,
( ~ type(f(n2,a),fulladder)
| value(out(n1,or1(f(n2,a))),n1) ),
inference(res,[status(thm),theory(equality)],[68,202]),
[iquote('0:Res:68.1,202.0')] ).
cnf(220,plain,
( ~ type(f(n2,a),fulladder)
| ~ connection(in(n1,h2(f(n2,a))),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[149,24]),
[iquote('0:Res:149.1,24.0')] ).
cnf(264,plain,
( ~ type(f(n2,a),fulladder)
| ~ connection(in(n1,h1(f(n2,a))),u)
| value(u,n0) ),
inference(res,[status(thm),theory(equality)],[188,24]),
[iquote('0:Res:188.1,24.0')] ).
cnf(441,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(or1(f(n2,a)),or__dfg)
| ~ mode(or1(f(n2,a)),ok)
| value(in(n1,or1(f(n2,a))),n1)
| value(in(n2,or1(f(n2,a))),n1) ),
inference(res,[status(thm),theory(equality)],[205,38]),
[iquote('0:Res:205.1,38.2')] ).
cnf(447,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n1,or1(f(n2,a))),n1)
| value(in(n2,or1(f(n2,a))),n1) ),
inference(mrr,[status(thm)],[441,60,129]),
[iquote('0:MRR:441.1,441.2,60.1,129.1')] ).
cnf(951,plain,
( ~ type(h2(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder)
| value(in(n1,and2(h2(f(n2,a)))),n0) ),
inference(res,[status(thm),theory(equality)],[51,220]),
[iquote('0:Res:51.1,220.1')] ).
cnf(954,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n1,and2(h2(f(n2,a)))),n0) ),
inference(mrr,[status(thm)],[951,59]),
[iquote('0:MRR:951.0,59.1')] ).
cnf(991,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h2(f(n2,a))),and__dfg)
| ~ mode(and2(h2(f(n2,a))),ok)
| value(out(n1,and2(h2(f(n2,a)))),n0) ),
inference(res,[status(thm),theory(equality)],[954,31]),
[iquote('0:Res:954.1,31.2')] ).
cnf(995,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h2(f(n2,a))),and__dfg)
| value(out(n1,and2(h2(f(n2,a)))),n0) ),
inference(mrr,[status(thm)],[991,70]),
[iquote('0:MRR:991.2,70.1')] ).
cnf(1291,plain,
( ~ type(h1(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder)
| value(in(n1,and2(h1(f(n2,a)))),n0) ),
inference(res,[status(thm),theory(equality)],[51,264]),
[iquote('0:Res:51.1,264.1')] ).
cnf(1294,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n1,and2(h1(f(n2,a)))),n0) ),
inference(mrr,[status(thm)],[1291,58]),
[iquote('0:MRR:1291.0,58.1')] ).
cnf(1327,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h1(f(n2,a))),and__dfg)
| ~ mode(and2(h1(f(n2,a))),ok)
| value(out(n1,and2(h1(f(n2,a)))),n0) ),
inference(res,[status(thm),theory(equality)],[1294,31]),
[iquote('0:Res:1294.1,31.2')] ).
cnf(1331,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h1(f(n2,a))),and__dfg)
| value(out(n1,and2(h1(f(n2,a)))),n0) ),
inference(mrr,[status(thm)],[1327,71]),
[iquote('0:MRR:1327.2,71.1')] ).
cnf(2597,plain,
value(in(n1,or1(f(n2,a))),n1),
inference(spt,[spt(split,[position(s1)])],[447]),
[iquote('1:Spt:447.1')] ).
cnf(2608,plain,
( ~ connection(u,in(n1,or1(f(n2,a))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[2597,25]),
[iquote('1:Res:2597.0,25.0')] ).
cnf(2622,plain,
( ~ type(f(n2,a),fulladder)
| value(out(c,h2(f(n2,a))),n1) ),
inference(res,[status(thm),theory(equality)],[63,2608]),
[iquote('1:Res:63.1,2608.0')] ).
cnf(2632,plain,
( ~ type(f(n2,a),fulladder)
| ~ connection(out(c,h2(f(n2,a))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[2622,24]),
[iquote('1:Res:2622.1,24.0')] ).
cnf(2693,plain,
( ~ type(h2(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder)
| value(out(n1,and2(h2(f(n2,a)))),n1) ),
inference(res,[status(thm),theory(equality)],[54,2632]),
[iquote('1:Res:54.1,2632.1')] ).
cnf(2697,plain,
( ~ type(f(n2,a),fulladder)
| value(out(n1,and2(h2(f(n2,a)))),n1) ),
inference(mrr,[status(thm)],[2693,59]),
[iquote('1:MRR:2693.0,59.1')] ).
cnf(2708,plain,
( ~ type(f(n2,a),fulladder)
| ~ value(out(n1,and2(h2(f(n2,a)))),u)
| equal_value(u,n1) ),
inference(res,[status(thm),theory(equality)],[2697,26]),
[iquote('1:Res:2697.1,26.0')] ).
cnf(3990,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h2(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder)
| equal_value(n0,n1) ),
inference(res,[status(thm),theory(equality)],[995,2708]),
[iquote('1:Res:995.2,2708.1')] ).
cnf(3998,plain,
( ~ type(and2(h2(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder)
| equal_value(n0,n1) ),
inference(obv,[status(thm),theory(equality)],[3990]),
[iquote('1:Obv:3990.0')] ).
cnf(3999,plain,
( ~ type(and2(h2(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder) ),
inference(mrr,[status(thm)],[3998,27]),
[iquote('1:MRR:3998.2,27.0')] ).
cnf(4002,plain,
( ~ type(h2(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder) ),
inference(res,[status(thm),theory(equality)],[46,3999]),
[iquote('1:Res:46.1,3999.0')] ).
cnf(4003,plain,
~ type(f(n2,a),fulladder),
inference(mrr,[status(thm)],[4002,59]),
[iquote('1:MRR:4002.0,59.1')] ).
cnf(4004,plain,
~ type(a,nbit_adder(n2)),
inference(res,[status(thm),theory(equality)],[2,4003]),
[iquote('1:Res:2.1,4003.0')] ).
cnf(4005,plain,
$false,
inference(mrr,[status(thm)],[4004,12]),
[iquote('1:MRR:4004.0,12.0')] ).
cnf(4006,plain,
~ value(in(n1,or1(f(n2,a))),n1),
inference(spt,[spt(split,[position(sa)])],[4005,2597]),
[iquote('1:Spt:4005.0,447.1,2597.0')] ).
cnf(4007,plain,
( ~ type(f(n2,a),fulladder)
| value(in(n2,or1(f(n2,a))),n1) ),
inference(spt,[spt(split,[position(s2)])],[447]),
[iquote('1:Spt:4005.0,447.0,447.2')] ).
cnf(4016,plain,
( ~ type(f(n2,a),fulladder)
| ~ connection(u,in(n2,or1(f(n2,a))))
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4007,25]),
[iquote('1:Res:4007.1,25.0')] ).
cnf(4111,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(f(n2,a),fulladder)
| value(out(c,h1(f(n2,a))),n1) ),
inference(res,[status(thm),theory(equality)],[62,4016]),
[iquote('1:Res:62.1,4016.1')] ).
cnf(4112,plain,
( ~ type(f(n2,a),fulladder)
| value(out(c,h1(f(n2,a))),n1) ),
inference(obv,[status(thm),theory(equality)],[4111]),
[iquote('1:Obv:4111.0')] ).
cnf(4127,plain,
( ~ type(f(n2,a),fulladder)
| ~ connection(out(c,h1(f(n2,a))),u)
| value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4112,24]),
[iquote('1:Res:4112.1,24.0')] ).
cnf(4135,plain,
( ~ type(h1(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder)
| value(out(n1,and2(h1(f(n2,a)))),n1) ),
inference(res,[status(thm),theory(equality)],[54,4127]),
[iquote('1:Res:54.1,4127.1')] ).
cnf(4139,plain,
( ~ type(f(n2,a),fulladder)
| value(out(n1,and2(h1(f(n2,a)))),n1) ),
inference(mrr,[status(thm)],[4135,58]),
[iquote('1:MRR:4135.0,58.1')] ).
cnf(4150,plain,
( ~ type(f(n2,a),fulladder)
| ~ value(out(n1,and2(h1(f(n2,a)))),u)
| equal_value(u,n1) ),
inference(res,[status(thm),theory(equality)],[4139,26]),
[iquote('1:Res:4139.1,26.0')] ).
cnf(4436,plain,
( ~ type(f(n2,a),fulladder)
| ~ type(and2(h1(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder)
| equal_value(n0,n1) ),
inference(res,[status(thm),theory(equality)],[1331,4150]),
[iquote('1:Res:1331.2,4150.1')] ).
cnf(4444,plain,
( ~ type(and2(h1(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder)
| equal_value(n0,n1) ),
inference(obv,[status(thm),theory(equality)],[4436]),
[iquote('1:Obv:4436.0')] ).
cnf(4445,plain,
( ~ type(and2(h1(f(n2,a))),and__dfg)
| ~ type(f(n2,a),fulladder) ),
inference(mrr,[status(thm)],[4444,27]),
[iquote('1:MRR:4444.2,27.0')] ).
cnf(4448,plain,
( ~ type(h1(f(n2,a)),halfadder)
| ~ type(f(n2,a),fulladder) ),
inference(res,[status(thm),theory(equality)],[46,4445]),
[iquote('1:Res:46.1,4445.0')] ).
cnf(4449,plain,
~ type(f(n2,a),fulladder),
inference(mrr,[status(thm)],[4448,58]),
[iquote('1:MRR:4448.0,58.1')] ).
cnf(4450,plain,
~ type(a,nbit_adder(n2)),
inference(res,[status(thm),theory(equality)],[2,4449]),
[iquote('1:Res:2.1,4449.0')] ).
cnf(4451,plain,
$false,
inference(mrr,[status(thm)],[4450,12]),
[iquote('1:MRR:4450.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 : 600
% 0.13/0.34 % DateTime : Thu Jun 16 21:29:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.01/1.21
% 1.01/1.21 SPASS V 3.9
% 1.01/1.21 SPASS beiseite: Proof found.
% 1.01/1.21 % SZS status Theorem
% 1.01/1.21 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/1.21 SPASS derived 3439 clauses, backtracked 135 clauses, performed 3 splits and kept 2438 clauses.
% 1.01/1.21 SPASS allocated 68320 KBytes.
% 1.01/1.21 SPASS spent 0:00:00.86 on the problem.
% 1.01/1.21 0:00:00.04 for the input.
% 1.01/1.21 0:00:00.00 for the FLOTTER CNF translation.
% 1.01/1.21 0:00:00.08 for inferences.
% 1.01/1.21 0:00:00.04 for the backtracking.
% 1.01/1.21 0:00:00.63 for the reduction.
% 1.01/1.21
% 1.01/1.21
% 1.01/1.21 Here is a proof with depth 14, length 90 :
% 1.01/1.21 % SZS output start Refutation
% See solution above
% 1.01/1.21 Formulae used in the proof : nbit_adder_fulladder2 nbit_adder_connection_outc_outcf1 nbit_adder_connection_ina2_in1f2 nbit_adder_connection_inb2_in2f2 a_isa_2bit_adder ina2_0 inb2_0 outc_1 diagnosis_or1f2a diagnosis_and2h2f2a diagnosis_and2h1f2a value_propagation1 value_propagation2 unique_value equal_value1 ok_or_abnormal and_0x_0 or_1_11 halfadder_and2 halfadder_connection_in1_in1and2 halfadder_connection_outc_out1and2 fulladder_halfadder1 fulladder_halfadder2 fulladder_or1 fulladder_connection_outch1_in2or1 fulladder_connection_outch2_in1or1 fulladder_connection_in1_in1h2 fulladder_connection_in2_in1h1 fulladder_connection_outc_out1or1
% 1.08/1.24
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