TSTP Solution File: SWC200+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC200+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 22:02:26 EDT 2022
% Result : Theorem 1.91s 2.09s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of clauses : 66 ( 31 unt; 9 nHn; 66 RR)
% Number of literals : 124 ( 0 equ; 55 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
ssList(skc4),
file('SWC200+1.p',unknown),
[] ).
cnf(3,axiom,
singletonP(skc4),
file('SWC200+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(14,axiom,
ssItem(skf44(u)),
file('SWC200+1.p',unknown),
[] ).
cnf(15,axiom,
ssItem(skf47(u)),
file('SWC200+1.p',unknown),
[] ).
cnf(52,axiom,
~ singletonP(nil),
file('SWC200+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ ssItem(u)
| memberP(skc4,skf44(u)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC200+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| ~ equal(skf44(u),u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ singletonP(u)
| equal(cons(skf47(u),nil),u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(tl(cons(u,v)),v) ),
file('SWC200+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(150,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ strictorderedP(cons(v,u))
| lt(v,hd(u))
| equal(nil,u) ),
file('SWC200+1.p',unknown),
[] ).
cnf(167,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(w)
| ~ memberP(cons(v,u),w)
| memberP(u,w)
| equal(w,v) ),
file('SWC200+1.p',unknown),
[] ).
cnf(198,plain,
( ~ ssList(skc4)
| equal(cons(skf47(skc4),nil),skc4) ),
inference(res,[status(thm),theory(equality)],[3,104]),
[iquote('0:Res:3.0,104.0')] ).
cnf(247,plain,
( equal(skc4,nil)
| equal(cons(hd(skc4),tl(skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[2,115]),
[iquote('0:Res:2.0,115.0')] ).
cnf(272,plain,
( ssItem(hd(skc4))
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[2,83]),
[iquote('0:Res:2.0,83.0')] ).
cnf(305,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc4))
| lt(u,hd(skc4))
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[2,150]),
[iquote('0:Res:2.0,150.1')] ).
cnf(541,plain,
equal(cons(skf47(skc4),nil),skc4),
inference(mrr,[status(thm)],[198,2]),
[iquote('0:MRR:198.0,2.0')] ).
cnf(550,plain,
equal(skc4,nil),
inference(spt,[spt(split,[position(s1)])],[305]),
[iquote('1:Spt:305.3')] ).
cnf(652,plain,
singletonP(nil),
inference(rew,[status(thm),theory(equality)],[550,3]),
[iquote('1:Rew:550.0,3.0')] ).
cnf(702,plain,
$false,
inference(mrr,[status(thm)],[652,52]),
[iquote('1:MRR:652.0,52.0')] ).
cnf(805,plain,
~ equal(skc4,nil),
inference(spt,[spt(split,[position(sa)])],[702,550]),
[iquote('1:Spt:702.0,305.3,550.0')] ).
cnf(806,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc4))
| lt(u,hd(skc4)) ),
inference(spt,[spt(split,[position(s2)])],[305]),
[iquote('1:Spt:702.0,305.0,305.1,305.2')] ).
cnf(808,plain,
ssItem(hd(skc4)),
inference(mrr,[status(thm)],[272,805]),
[iquote('1:MRR:272.1,805.0')] ).
cnf(812,plain,
equal(cons(hd(skc4),tl(skc4)),skc4),
inference(mrr,[status(thm)],[247,805]),
[iquote('1:MRR:247.0,805.0')] ).
cnf(1094,plain,
( ~ ssItem(skf47(skc4))
| equalelemsP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,76]),
[iquote('0:SpR:541.0,76.1')] ).
cnf(1097,plain,
( ~ ssItem(skf47(skc4))
| duplicatefreeP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,75]),
[iquote('0:SpR:541.0,75.1')] ).
cnf(1098,plain,
( ~ ssItem(skf47(skc4))
| strictorderP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,72]),
[iquote('0:SpR:541.0,72.1')] ).
cnf(1099,plain,
( ~ ssItem(skf47(skc4))
| totalorderP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,71]),
[iquote('0:SpR:541.0,71.1')] ).
cnf(1100,plain,
( ~ ssItem(skf47(skc4))
| cyclefreeP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,70]),
[iquote('0:SpR:541.0,70.1')] ).
cnf(1101,plain,
( ~ ssItem(skf47(skc4))
| strictorderedP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,74]),
[iquote('0:SpR:541.0,74.1')] ).
cnf(1102,plain,
( ~ ssItem(skf47(skc4))
| totalorderedP(skc4) ),
inference(spr,[status(thm),theory(equality)],[541,73]),
[iquote('0:SpR:541.0,73.1')] ).
cnf(1776,plain,
duplicatefreeP(skc4),
inference(ssi,[status(thm)],[1097,15,2,3]),
[iquote('0:SSi:1097.0,15.0,2.0,3.0')] ).
cnf(1777,plain,
totalorderP(skc4),
inference(ssi,[status(thm)],[1099,15,2,3]),
[iquote('0:SSi:1099.0,15.0,2.0,3.0')] ).
cnf(1778,plain,
equalelemsP(skc4),
inference(ssi,[status(thm)],[1094,15,2,3]),
[iquote('0:SSi:1094.0,15.0,2.0,3.0')] ).
cnf(1779,plain,
strictorderP(skc4),
inference(ssi,[status(thm)],[1098,15,2,3]),
[iquote('0:SSi:1098.0,15.0,2.0,3.0')] ).
cnf(1780,plain,
cyclefreeP(skc4),
inference(ssi,[status(thm)],[1100,15,2,3]),
[iquote('0:SSi:1100.0,15.0,2.0,3.0')] ).
cnf(1781,plain,
totalorderedP(skc4),
inference(ssi,[status(thm)],[1102,15,2,3]),
[iquote('0:SSi:1102.0,15.0,2.0,3.0')] ).
cnf(1782,plain,
strictorderedP(skc4),
inference(ssi,[status(thm)],[1101,15,2,3]),
[iquote('0:SSi:1101.0,15.0,2.0,3.0')] ).
cnf(1887,plain,
( ~ ssItem(skf47(skc4))
| ~ ssList(nil)
| equal(tl(skc4),nil) ),
inference(spr,[status(thm),theory(equality)],[541,109]),
[iquote('0:SpR:541.0,109.2')] ).
cnf(1893,plain,
equal(tl(skc4),nil),
inference(ssi,[status(thm)],[1887,13,12,9,8,7,11,10,6,15,2,3,1776,1777,1778,1779,1780,1781,1782]),
[iquote('0:SSi:1887.1,1887.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0,15.0,2.0,3.0,1776.0,1777.0,1778.0,1779.0,1780.0,1781.0,1782.0')] ).
cnf(1895,plain,
equal(cons(hd(skc4),nil),skc4),
inference(rew,[status(thm),theory(equality)],[1893,812]),
[iquote('1:Rew:1893.0,812.0')] ).
cnf(6178,plain,
( ~ ssList(nil)
| ~ ssItem(hd(skc4))
| ~ ssItem(u)
| ~ memberP(skc4,u)
| memberP(nil,u)
| equal(u,hd(skc4)) ),
inference(spl,[status(thm),theory(equality)],[1895,167]),
[iquote('1:SpL:1895.0,167.3')] ).
cnf(6191,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| memberP(nil,u)
| equal(u,hd(skc4)) ),
inference(ssi,[status(thm)],[6178,808,13,12,9,8,7,11,10,6]),
[iquote('1:SSi:6178.1,6178.0,808.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).
cnf(6192,plain,
( ~ ssItem(u)
| ~ memberP(skc4,u)
| equal(u,hd(skc4)) ),
inference(mrr,[status(thm)],[6191,69]),
[iquote('1:MRR:6191.2,69.1')] ).
cnf(6210,plain,
( ~ ssItem(u)
| ~ ssItem(skf44(u))
| equal(skf44(u),hd(skc4)) ),
inference(res,[status(thm),theory(equality)],[68,6192]),
[iquote('1:Res:68.1,6192.1')] ).
cnf(6212,plain,
( ~ ssItem(u)
| equal(skf44(u),hd(skc4)) ),
inference(ssi,[status(thm)],[6210,14]),
[iquote('1:SSi:6210.1,14.0')] ).
cnf(6214,plain,
( ~ ssItem(u)
| ~ equal(hd(skc4),u) ),
inference(rew,[status(thm),theory(equality)],[6212,78]),
[iquote('1:Rew:6212.1,78.1')] ).
cnf(6240,plain,
~ ssItem(hd(skc4)),
inference(eqr,[status(thm),theory(equality)],[6214]),
[iquote('1:EqR:6214.1')] ).
cnf(6243,plain,
$false,
inference(ssi,[status(thm)],[6240,808]),
[iquote('1:SSi:6240.0,808.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWC200+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n019.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Sun Jun 12 15:11:25 EDT 2022
% 0.14/0.37 % CPUTime :
% 1.91/2.09
% 1.91/2.09 SPASS V 3.9
% 1.91/2.09 SPASS beiseite: Proof found.
% 1.91/2.09 % SZS status Theorem
% 1.91/2.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.91/2.09 SPASS derived 4134 clauses, backtracked 499 clauses, performed 19 splits and kept 2238 clauses.
% 1.91/2.09 SPASS allocated 103210 KBytes.
% 1.91/2.09 SPASS spent 0:00:01.63 on the problem.
% 1.91/2.09 0:00:00.04 for the input.
% 1.91/2.09 0:00:00.06 for the FLOTTER CNF translation.
% 1.91/2.09 0:00:00.04 for inferences.
% 1.91/2.09 0:00:00.02 for the backtracking.
% 1.91/2.09 0:00:01.28 for the reduction.
% 1.91/2.09
% 1.91/2.09
% 1.91/2.09 Here is a proof with depth 3, length 66 :
% 1.91/2.09 % SZS output start Refutation
% See solution above
% 1.91/2.09 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax39 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax75 ax25 ax78 ax70 ax37
% 1.91/2.09
%------------------------------------------------------------------------------