TSTP Solution File: SWC045+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC045+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 : Tue Jul 19 22:01:20 EDT 2022
% Result : Theorem 33.93s 34.11s
% Output : Refutation 33.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of clauses : 73 ( 23 unt; 9 nHn; 73 RR)
% Number of literals : 169 ( 0 equ; 92 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC045+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC045+1.p',unknown),
[] ).
cnf(6,axiom,
cyclefreeP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(7,axiom,
totalorderP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(8,axiom,
strictorderP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderedP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderedP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(11,axiom,
duplicatefreeP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(12,axiom,
equalelemsP(nil),
file('SWC045+1.p',unknown),
[] ).
cnf(13,axiom,
ssList(skf44(u)),
file('SWC045+1.p',unknown),
[] ).
cnf(14,axiom,
equal(nil,skc5),
file('SWC045+1.p',unknown),
[] ).
cnf(53,axiom,
~ equal(nil,skc4),
file('SWC045+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC045+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC045+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| equal(nil,u)
| ssItem(hd(u)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| equal(nil,u)
| ssList(tl(u)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC045+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ ssList(u)
| ~ segmentP(nil,u)
| equal(nil,u) ),
file('SWC045+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC045+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,nil),v)
| singletonP(v) ),
file('SWC045+1.p',unknown),
[] ).
cnf(151,axiom,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| segmentP(skc5,app(app(cons(u,nil),skf44(u)),cons(u,nil))) ),
file('SWC045+1.p',unknown),
[] ).
cnf(184,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(x,cons(u,w)),v)
| memberP(v,u) ),
file('SWC045+1.p',unknown),
[] ).
cnf(194,plain,
equalelemsP(skc5),
inference(rew,[status(thm),theory(equality)],[14,12]),
[iquote('0:Rew:14.0,12.0')] ).
cnf(195,plain,
duplicatefreeP(skc5),
inference(rew,[status(thm),theory(equality)],[14,11]),
[iquote('0:Rew:14.0,11.0')] ).
cnf(196,plain,
strictorderedP(skc5),
inference(rew,[status(thm),theory(equality)],[14,10]),
[iquote('0:Rew:14.0,10.0')] ).
cnf(197,plain,
totalorderedP(skc5),
inference(rew,[status(thm),theory(equality)],[14,9]),
[iquote('0:Rew:14.0,9.0')] ).
cnf(198,plain,
strictorderP(skc5),
inference(rew,[status(thm),theory(equality)],[14,8]),
[iquote('0:Rew:14.0,8.0')] ).
cnf(199,plain,
totalorderP(skc5),
inference(rew,[status(thm),theory(equality)],[14,7]),
[iquote('0:Rew:14.0,7.0')] ).
cnf(200,plain,
cyclefreeP(skc5),
inference(rew,[status(thm),theory(equality)],[14,6]),
[iquote('0:Rew:14.0,6.0')] ).
cnf(203,plain,
~ equal(skc5,skc4),
inference(rew,[status(thm),theory(equality)],[14,53]),
[iquote('0:Rew:14.0,53.0')] ).
cnf(207,plain,
( ~ ssItem(u)
| equalelemsP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,76]),
[iquote('0:Rew:14.0,76.1')] ).
cnf(208,plain,
( ~ ssItem(u)
| duplicatefreeP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,75]),
[iquote('0:Rew:14.0,75.1')] ).
cnf(209,plain,
( ~ ssItem(u)
| strictorderedP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,74]),
[iquote('0:Rew:14.0,74.1')] ).
cnf(210,plain,
( ~ ssItem(u)
| totalorderedP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,73]),
[iquote('0:Rew:14.0,73.1')] ).
cnf(211,plain,
( ~ ssItem(u)
| strictorderP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,72]),
[iquote('0:Rew:14.0,72.1')] ).
cnf(212,plain,
( ~ ssItem(u)
| totalorderP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,71]),
[iquote('0:Rew:14.0,71.1')] ).
cnf(213,plain,
( ~ ssItem(u)
| cyclefreeP(cons(u,skc5)) ),
inference(rew,[status(thm),theory(equality)],[14,70]),
[iquote('0:Rew:14.0,70.1')] ).
cnf(214,plain,
( ~ ssItem(u)
| ~ memberP(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[14,69]),
[iquote('0:Rew:14.0,69.1')] ).
cnf(216,plain,
( ~ ssList(u)
| equal(app(skc5,u),u) ),
inference(rew,[status(thm),theory(equality)],[14,78]),
[iquote('0:Rew:14.0,78.1')] ).
cnf(217,plain,
( ~ ssList(u)
| ssList(tl(u))
| equal(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[14,83]),
[iquote('0:Rew:14.0,83.1')] ).
cnf(218,plain,
( ~ ssList(u)
| ssItem(hd(u))
| equal(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[14,82]),
[iquote('0:Rew:14.0,82.1')] ).
cnf(222,plain,
( ~ ssList(u)
| ~ segmentP(skc5,u)
| equal(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[14,93]),
[iquote('0:Rew:14.0,93.2,14.0,93.1')] ).
cnf(229,plain,
( ~ ssList(u)
| equal(skc5,u)
| equal(cons(hd(u),tl(u)),u) ),
inference(rew,[status(thm),theory(equality)],[14,114]),
[iquote('0:Rew:14.0,114.1')] ).
cnf(233,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,skc5),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[14,117]),
[iquote('0:Rew:14.0,117.2')] ).
cnf(244,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| segmentP(skc5,app(app(cons(u,skc5),skf44(u)),cons(u,skc5))) ),
inference(rew,[status(thm),theory(equality)],[14,151]),
[iquote('0:Rew:14.0,151.2')] ).
cnf(328,plain,
( equal(skc5,skc4)
| ssItem(hd(skc4)) ),
inference(res,[status(thm),theory(equality)],[2,218]),
[iquote('0:Res:2.0,218.0')] ).
cnf(492,plain,
( ~ ssItem(u)
| ssList(cons(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[1,87]),
[iquote('0:Res:1.0,87.0')] ).
cnf(598,plain,
ssItem(hd(skc4)),
inference(mrr,[status(thm)],[328,203]),
[iquote('0:MRR:328.0,203.0')] ).
cnf(1333,plain,
( ~ ssList(cons(u,skc5))
| ~ ssItem(u)
| singletonP(cons(u,skc5)) ),
inference(eqr,[status(thm),theory(equality)],[233]),
[iquote('0:EqR:233.2')] ).
cnf(1337,plain,
( ~ ssItem(u)
| singletonP(cons(u,skc5)) ),
inference(ssi,[status(thm)],[1333,207,208,211,212,213,209,210,492]),
[iquote('0:SSi:1333.0,207.1,208.1,211.1,212.1,213.1,209.1,210.1,492.1')] ).
cnf(3609,plain,
( ~ ssItem(u)
| ~ ssList(app(app(cons(u,skc5),skf44(u)),cons(u,skc5)))
| ~ memberP(skc4,u)
| equal(app(app(cons(u,skc5),skf44(u)),cons(u,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[244,222]),
[iquote('0:Res:244.2,222.1')] ).
cnf(3618,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| equal(app(app(cons(u,skc5),skf44(u)),cons(u,skc5)),skc5) ),
inference(ssi,[status(thm)],[3609,88,207,208,211,212,213,209,210,492,1337,13]),
[iquote('0:SSi:3609.1,88.1,88.1,207.1,208.1,211.1,212.1,213.1,209.1,210.1,492.0,1337.1,13.1,207.1,208.1,211.1,212.1,213.1,209.1,210.1,492.2,1337.2')] ).
cnf(6448,plain,
( ~ ssItem(u)
| ~ ssList(app(v,cons(u,w)))
| ~ ssList(w)
| ~ ssList(v)
| memberP(app(v,cons(u,w)),u) ),
inference(eqr,[status(thm),theory(equality)],[184]),
[iquote('0:EqR:184.4')] ).
cnf(6469,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| memberP(app(w,cons(u,v)),u) ),
inference(ssi,[status(thm)],[6448,88,87]),
[iquote('0:SSi:6448.1,88.2,87.2')] ).
cnf(14221,plain,
( ~ ssList(cons(u,v))
| ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(skc5)
| memberP(cons(u,v),u) ),
inference(spr,[status(thm),theory(equality)],[216,6469]),
[iquote('0:SpR:216.1,6469.3')] ).
cnf(14244,plain,
( ~ ssItem(u)
| ~ ssList(v)
| memberP(cons(u,v),u) ),
inference(ssi,[status(thm)],[14221,194,195,198,199,200,196,197,1,87]),
[iquote('0:SSi:14221.3,14221.0,194.2,195.0,198.0,199.0,200.0,196.0,197.0,1.0,87.0')] ).
cnf(14642,plain,
( ~ ssList(u)
| ~ ssItem(hd(u))
| ~ ssList(tl(u))
| equal(skc5,u)
| memberP(u,hd(u)) ),
inference(spr,[status(thm),theory(equality)],[229,14244]),
[iquote('0:SpR:229.2,14244.2')] ).
cnf(14654,plain,
( ~ ssList(u)
| equal(skc5,u)
| memberP(u,hd(u)) ),
inference(mrr,[status(thm)],[14642,218,217]),
[iquote('0:MRR:14642.1,14642.2,218.1,217.1')] ).
cnf(23910,plain,
( ~ ssItem(u)
| ~ ssItem(u)
| ~ ssList(skc5)
| ~ ssList(app(cons(u,skc5),skf44(u)))
| ~ memberP(skc4,u)
| memberP(skc5,u) ),
inference(spr,[status(thm),theory(equality)],[3618,6469]),
[iquote('0:SpR:3618.2,6469.3')] ).
cnf(23950,plain,
( ~ ssItem(u)
| ~ ssList(skc5)
| ~ ssList(app(cons(u,skc5),skf44(u)))
| ~ memberP(skc4,u)
| memberP(skc5,u) ),
inference(obv,[status(thm),theory(equality)],[23910]),
[iquote('0:Obv:23910.0')] ).
cnf(23951,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| memberP(skc5,u) ),
inference(ssi,[status(thm)],[23950,88,207,208,211,212,213,209,210,492,1337,13,194,195,198,199,200,196,197,1]),
[iquote('0:SSi:23950.2,23950.1,88.0,207.0,208.0,211.0,212.0,213.0,209.0,210.0,492.0,1337.1,13.1,194.1,195.1,198.1,199.1,200.1,196.1,197.1,1.2')] ).
cnf(23952,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u) ),
inference(mrr,[status(thm)],[23951,214]),
[iquote('0:MRR:23951.2,214.1')] ).
cnf(24041,plain,
( ~ ssList(skc4)
| ~ ssItem(hd(skc4))
| equal(skc5,skc4) ),
inference(res,[status(thm),theory(equality)],[14654,23952]),
[iquote('0:Res:14654.2,23952.1')] ).
cnf(26397,plain,
equal(skc5,skc4),
inference(ssi,[status(thm)],[24041,598,2]),
[iquote('0:SSi:24041.1,24041.0,598.0,2.0')] ).
cnf(26398,plain,
$false,
inference(mrr,[status(thm)],[26397,203]),
[iquote('0:MRR:26397.0,203.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC045+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 12:09:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 33.93/34.11
% 33.93/34.11 SPASS V 3.9
% 33.93/34.11 SPASS beiseite: Proof found.
% 33.93/34.11 % SZS status Theorem
% 33.93/34.11 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.93/34.11 SPASS derived 15308 clauses, backtracked 4628 clauses, performed 16 splits and kept 7214 clauses.
% 33.93/34.11 SPASS allocated 122674 KBytes.
% 33.93/34.11 SPASS spent 0:0:29.88 on the problem.
% 33.93/34.11 0:00:00.04 for the input.
% 33.93/34.11 0:00:00.06 for the FLOTTER CNF translation.
% 33.93/34.11 0:00:00.32 for inferences.
% 33.93/34.11 0:00:00.80 for the backtracking.
% 33.93/34.11 0:0:28.36 for the reduction.
% 33.93/34.11
% 33.93/34.11
% 33.93/34.11 Here is a proof with depth 4, length 73 :
% 33.93/34.11 % SZS output start Refutation
% See solution above
% 33.93/34.11 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax58 ax78 ax4 ax2 ax3
% 33.93/34.11
%------------------------------------------------------------------------------