TSTP Solution File: HWV005-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of clauses : 60 ( 20 unt; 4 nHn; 60 RR)
% Number of literals : 116 ( 0 equ; 56 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
halfadder(h),
file('HWV005-2.p',unknown),
[] ).
cnf(2,axiom,
one(in1(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(4,axiom,
zero(outs(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(5,axiom,
zero(outc(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(6,axiom,
~ abnormal(and1(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(7,axiom,
~ abnormal(not1(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(8,axiom,
~ abnormal(or1(h)),
file('HWV005-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ zero(u)
| ~ connection(u,v)
| zero(v) ),
file('HWV005-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ one(u)
| ~ connection(u,v)
| one(v) ),
file('HWV005-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ one(u)
| ~ zero(u) ),
file('HWV005-2.p',unknown),
[] ).
cnf(17,axiom,
( ~ and_ok(u)
| ~ zero(out1(u))
| zero(in2(u))
| zero(in1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(21,axiom,
( ~ logic_and(u)
| abnormal(u)
| and_ok(u) ),
file('HWV005-2.p',unknown),
[] ).
cnf(22,axiom,
( ~ or_ok(u)
| ~ one(in1(u))
| one(out1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(29,axiom,
( ~ logic_or(u)
| abnormal(u)
| or_ok(u) ),
file('HWV005-2.p',unknown),
[] ).
cnf(30,axiom,
( ~ not_ok(u)
| ~ zero(in1(u))
| one(out1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(35,axiom,
( ~ logic_not(u)
| abnormal(u)
| not_ok(u) ),
file('HWV005-2.p',unknown),
[] ).
cnf(36,axiom,
( ~ halfadder(u)
| logic_and(and1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(38,axiom,
( ~ halfadder(u)
| logic_not(not1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(39,axiom,
( ~ halfadder(u)
| logic_or(or1(u)) ),
file('HWV005-2.p',unknown),
[] ).
cnf(40,axiom,
( ~ halfadder(u)
| connection(in1(u),in1(or1(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(44,axiom,
( ~ halfadder(u)
| connection(outs(u),out1(and1(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(45,axiom,
( ~ halfadder(u)
| connection(outc(u),out1(and2(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(46,axiom,
( ~ halfadder(u)
| connection(out1(or1(u)),in1(and1(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(47,axiom,
( ~ halfadder(u)
| connection(out1(and2(u)),in1(not1(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(48,axiom,
( ~ halfadder(u)
| connection(out1(not1(u)),in2(and1(u))) ),
file('HWV005-2.p',unknown),
[] ).
cnf(50,plain,
( ~ logic_or(or1(h))
| or_ok(or1(h)) ),
inference(res,[status(thm),theory(equality)],[29,8]),
[iquote('0:Res:29.2,8.0')] ).
cnf(54,plain,
( ~ logic_not(not1(h))
| not_ok(not1(h)) ),
inference(res,[status(thm),theory(equality)],[35,7]),
[iquote('0:Res:35.2,7.0')] ).
cnf(55,plain,
( ~ logic_and(and1(h))
| and_ok(and1(h)) ),
inference(res,[status(thm),theory(equality)],[21,6]),
[iquote('0:Res:21.2,6.0')] ).
cnf(95,plain,
( ~ halfadder(h)
| not_ok(not1(h)) ),
inference(sor,[status(thm)],[54,38]),
[iquote('0:SoR:54.0,38.1')] ).
cnf(96,plain,
not_ok(not1(h)),
inference(ssi,[status(thm)],[95,1]),
[iquote('0:SSi:95.0,1.0')] ).
cnf(101,plain,
( ~ halfadder(h)
| or_ok(or1(h)) ),
inference(sor,[status(thm)],[50,39]),
[iquote('0:SoR:50.0,39.1')] ).
cnf(102,plain,
or_ok(or1(h)),
inference(ssi,[status(thm)],[101,1]),
[iquote('0:SSi:101.0,1.0')] ).
cnf(109,plain,
( ~ halfadder(h)
| and_ok(and1(h)) ),
inference(sor,[status(thm)],[55,36]),
[iquote('0:SoR:55.0,36.1')] ).
cnf(110,plain,
and_ok(and1(h)),
inference(ssi,[status(thm)],[109,1]),
[iquote('0:SSi:109.0,1.0')] ).
cnf(130,plain,
( ~ halfadder(u)
| ~ one(in1(u))
| one(in1(or1(u))) ),
inference(res,[status(thm),theory(equality)],[40,10]),
[iquote('0:Res:40.1,10.1')] ).
cnf(137,plain,
( ~ halfadder(u)
| ~ zero(outc(u))
| zero(out1(and2(u))) ),
inference(res,[status(thm),theory(equality)],[45,9]),
[iquote('0:Res:45.1,9.1')] ).
cnf(138,plain,
( ~ halfadder(u)
| ~ zero(outs(u))
| zero(out1(and1(u))) ),
inference(res,[status(thm),theory(equality)],[44,9]),
[iquote('0:Res:44.1,9.1')] ).
cnf(146,plain,
( ~ halfadder(u)
| ~ one(out1(not1(u)))
| one(in2(and1(u))) ),
inference(res,[status(thm),theory(equality)],[48,10]),
[iquote('0:Res:48.1,10.1')] ).
cnf(149,plain,
( ~ halfadder(u)
| ~ zero(out1(and2(u)))
| zero(in1(not1(u))) ),
inference(res,[status(thm),theory(equality)],[47,9]),
[iquote('0:Res:47.1,9.1')] ).
cnf(154,plain,
( ~ halfadder(u)
| ~ one(out1(or1(u)))
| one(in1(and1(u))) ),
inference(res,[status(thm),theory(equality)],[46,10]),
[iquote('0:Res:46.1,10.1')] ).
cnf(208,plain,
( ~ halfadder(h)
| one(in1(or1(h))) ),
inference(sor,[status(thm)],[130,2]),
[iquote('0:SoR:130.1,2.0')] ).
cnf(209,plain,
one(in1(or1(h))),
inference(ssi,[status(thm)],[208,1]),
[iquote('0:SSi:208.0,1.0')] ).
cnf(217,plain,
( ~ or_ok(or1(h))
| one(out1(or1(h))) ),
inference(res,[status(thm),theory(equality)],[209,22]),
[iquote('0:Res:209.0,22.1')] ).
cnf(218,plain,
one(out1(or1(h))),
inference(ssi,[status(thm)],[217,102,39,1]),
[iquote('0:SSi:217.0,102.0,39.1,1.0')] ).
cnf(238,plain,
( ~ halfadder(h)
| zero(out1(and2(h))) ),
inference(sor,[status(thm)],[137,5]),
[iquote('0:SoR:137.1,5.0')] ).
cnf(239,plain,
zero(out1(and2(h))),
inference(ssi,[status(thm)],[238,1]),
[iquote('0:SSi:238.0,1.0')] ).
cnf(243,plain,
( ~ halfadder(h)
| zero(out1(and1(h))) ),
inference(sor,[status(thm)],[138,4]),
[iquote('0:SoR:138.1,4.0')] ).
cnf(244,plain,
zero(out1(and1(h))),
inference(ssi,[status(thm)],[243,1]),
[iquote('0:SSi:243.0,1.0')] ).
cnf(280,plain,
( ~ halfadder(h)
| zero(in1(not1(h))) ),
inference(sor,[status(thm)],[149,239]),
[iquote('0:SoR:149.1,239.0')] ).
cnf(282,plain,
zero(in1(not1(h))),
inference(ssi,[status(thm)],[280,1]),
[iquote('0:SSi:280.0,1.0')] ).
cnf(290,plain,
( ~ not_ok(not1(h))
| one(out1(not1(h))) ),
inference(res,[status(thm),theory(equality)],[282,30]),
[iquote('0:Res:282.0,30.1')] ).
cnf(291,plain,
one(out1(not1(h))),
inference(ssi,[status(thm)],[290,96,38,1]),
[iquote('0:SSi:290.0,96.0,38.1,1.0')] ).
cnf(295,plain,
( ~ halfadder(h)
| one(in2(and1(h))) ),
inference(sor,[status(thm)],[146,291]),
[iquote('0:SoR:146.1,291.0')] ).
cnf(296,plain,
one(in2(and1(h))),
inference(ssi,[status(thm)],[295,1]),
[iquote('0:SSi:295.0,1.0')] ).
cnf(314,plain,
( ~ halfadder(h)
| one(in1(and1(h))) ),
inference(sor,[status(thm)],[154,218]),
[iquote('0:SoR:154.1,218.0')] ).
cnf(315,plain,
one(in1(and1(h))),
inference(ssi,[status(thm)],[314,1]),
[iquote('0:SSi:314.0,1.0')] ).
cnf(318,plain,
( ~ and_ok(and1(h))
| ~ zero(out1(and1(h)))
| zero(in2(and1(h))) ),
inference(ems,[status(thm)],[13,315,17]),
[iquote('0:EmS:13.0,13.1,315.0,17.3')] ).
cnf(325,plain,
( ~ zero(out1(and1(h)))
| zero(in2(and1(h))) ),
inference(ssi,[status(thm)],[318,110,36,1]),
[iquote('0:SSi:318.0,110.0,36.1,1.0')] ).
cnf(326,plain,
zero(in2(and1(h))),
inference(mrr,[status(thm)],[325,244]),
[iquote('0:MRR:325.0,244.0')] ).
cnf(329,plain,
$false,
inference(ems,[status(thm)],[13,296,326]),
[iquote('0:EmS:13.0,13.1,296.0,326.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n010.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 07:53:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 214 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.18/0.43 SPASS allocated 75854 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.02 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 6, length 60 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.44 Formulae used in the proof : h_isa_halfadder in1_1 outs_0 outc_0 diagnosis_and1 diagnosis_not1 diagnosis_or1 value_propagation_zero1 value_propagation_one1 unique_value and_0_00 and_ok_or_abnormal or_1x_1 or_ok_or_abnormal not_0_1_fw not_ok_or_abnormal halfadder_and1 halfadder_not1 halfadder_or1 halfadder_connection_in1_in1or1 halfadder_connection_outs_out1and1 halfadder_connection_outc_out1and2 halfadder_connection_out1or1_in1_and1 halfadder_connection_out1and2_in1not1 halfadder_connection_out1not1_in2and1
% 0.18/0.44
%------------------------------------------------------------------------------