TSTP Solution File: SWC248+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC248+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 22:02:48 EDT 2022
% Result : Theorem 29.10s 29.31s
% Output : Refutation 29.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of clauses : 55 ( 21 unt; 10 nHn; 55 RR)
% Number of literals : 123 ( 0 equ; 67 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
ssList(skc6),
file('SWC248+1.p',unknown),
[] ).
cnf(5,axiom,
totalorderedP(skc6),
file('SWC248+1.p',unknown),
[] ).
cnf(8,axiom,
ssList(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(9,axiom,
cyclefreeP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(12,axiom,
totalorderedP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(13,axiom,
strictorderedP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(14,axiom,
duplicatefreeP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC248+1.p',unknown),
[] ).
cnf(54,axiom,
~ equal(skc6,nil),
file('SWC248+1.p',unknown),
[] ).
cnf(62,axiom,
ssItem(skf44(u,v,w)),
file('SWC248+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ totalorderedP(cons(v,u))
| totalorderedP(u)
| equal(nil,u) ),
file('SWC248+1.p',unknown),
[] ).
cnf(166,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(cons(u,v),w),cons(u,app(v,w))) ),
file('SWC248+1.p',unknown),
[] ).
cnf(188,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),skc6)
| memberP(v,skf44(w,u,v)) ),
file('SWC248+1.p',unknown),
[] ).
cnf(258,plain,
( equal(skc6,nil)
| equal(cons(hd(skc6),tl(skc6)),skc6) ),
inference(res,[status(thm),theory(equality)],[4,117]),
[iquote('0:Res:4.0,117.0')] ).
cnf(283,plain,
( equal(skc6,nil)
| ssItem(hd(skc6)) ),
inference(res,[status(thm),theory(equality)],[4,85]),
[iquote('0:Res:4.0,85.0')] ).
cnf(284,plain,
( equal(skc6,nil)
| ssList(tl(skc6)) ),
inference(res,[status(thm),theory(equality)],[4,86]),
[iquote('0:Res:4.0,86.0')] ).
cnf(576,plain,
ssItem(hd(skc6)),
inference(mrr,[status(thm)],[283,54]),
[iquote('0:MRR:283.0,54.0')] ).
cnf(577,plain,
ssList(tl(skc6)),
inference(mrr,[status(thm)],[284,54]),
[iquote('0:MRR:284.0,54.0')] ).
cnf(582,plain,
equal(cons(hd(skc6),tl(skc6)),skc6),
inference(mrr,[status(thm)],[258,54]),
[iquote('0:MRR:258.0,54.0')] ).
cnf(2034,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[120]),
[iquote('0:EqR:120.2')] ).
cnf(2037,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[2034,90,15,14,10,11,9,12,13,8,79,78,74,75,73,76,77]),
[iquote('0:SSi:2034.0,90.1,15.1,14.1,10.1,11.1,9.1,12.1,13.0,8.0,79.0,78.0,74.0,75.0,73.0,76.0,77.2')] ).
cnf(2401,plain,
( ~ ssList(tl(skc6))
| ~ ssItem(hd(skc6))
| ~ totalorderedP(skc6)
| totalorderedP(tl(skc6))
| equal(tl(skc6),nil) ),
inference(spl,[status(thm),theory(equality)],[582,130]),
[iquote('0:SpL:582.0,130.2')] ).
cnf(2413,plain,
( ~ totalorderedP(skc6)
| totalorderedP(tl(skc6))
| equal(tl(skc6),nil) ),
inference(ssi,[status(thm)],[2401,576,577]),
[iquote('0:SSi:2401.1,2401.0,576.0,577.0')] ).
cnf(2414,plain,
( totalorderedP(tl(skc6))
| equal(tl(skc6),nil) ),
inference(mrr,[status(thm)],[2413,5]),
[iquote('0:MRR:2413.0,5.0')] ).
cnf(2418,plain,
equal(tl(skc6),nil),
inference(spt,[spt(split,[position(s1)])],[2414]),
[iquote('1:Spt:2414.1')] ).
cnf(2420,plain,
equal(cons(hd(skc6),nil),skc6),
inference(rew,[status(thm),theory(equality)],[2418,582]),
[iquote('1:Rew:2418.0,582.0')] ).
cnf(6721,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(app(cons(u,nil),v),skc6)
| memberP(nil,skf44(u,v,nil)) ),
inference(spl,[status(thm),theory(equality)],[81,188]),
[iquote('0:SpL:81.1,188.3')] ).
cnf(6735,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(cons(u,v),skc6)
| memberP(nil,skf44(u,v,nil)) ),
inference(rew,[status(thm),theory(equality)],[81,6721,166]),
[iquote('0:Rew:81.1,6721.4,166.3,6721.4')] ).
cnf(6736,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc6)
| memberP(nil,skf44(v,u,nil)) ),
inference(ssi,[status(thm)],[6735,15,14,10,11,9,12,13,8,90,79,78,74,75,73,76,77,2037]),
[iquote('0:SSi:6735.2,6735.0,15.1,14.1,10.1,11.1,9.1,12.1,13.1,8.1,90.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.2,79.0,78.0,74.0,75.0,73.0,76.0,77.0,2037.0')] ).
cnf(22325,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(skf44(v,u,nil))
| ~ equal(cons(v,u),skc6) ),
inference(res,[status(thm),theory(equality)],[6736,72]),
[iquote('0:Res:6736.3,72.1')] ).
cnf(22328,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc6) ),
inference(ssi,[status(thm)],[22325,62,15,14,10,11,9,12,13,8]),
[iquote('0:SSi:22325.2,62.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.0')] ).
cnf(27192,plain,
( ~ ssList(nil)
| ~ ssItem(hd(skc6))
| ~ equal(skc6,skc6) ),
inference(spl,[status(thm),theory(equality)],[2420,22328]),
[iquote('1:SpL:2420.0,22328.2')] ).
cnf(27194,plain,
( ~ ssList(nil)
| ~ ssItem(hd(skc6)) ),
inference(obv,[status(thm),theory(equality)],[27192]),
[iquote('1:Obv:27192.2')] ).
cnf(27195,plain,
$false,
inference(ssi,[status(thm)],[27194,576,15,14,10,11,9,12,13,8]),
[iquote('1:SSi:27194.1,27194.0,576.0,15.0,14.0,10.0,11.0,9.0,12.0,13.0,8.0')] ).
cnf(27204,plain,
~ equal(tl(skc6),nil),
inference(spt,[spt(split,[position(sa)])],[27195,2418]),
[iquote('1:Spt:27195.0,2414.1,2418.0')] ).
cnf(27205,plain,
totalorderedP(tl(skc6)),
inference(spt,[spt(split,[position(s2)])],[2414]),
[iquote('1:Spt:27195.0,2414.0')] ).
cnf(28390,plain,
( ~ ssList(tl(skc6))
| ~ ssItem(hd(skc6))
| ~ equal(skc6,skc6) ),
inference(spl,[status(thm),theory(equality)],[582,22328]),
[iquote('0:SpL:582.0,22328.2')] ).
cnf(28413,plain,
( ~ ssList(tl(skc6))
| ~ ssItem(hd(skc6)) ),
inference(obv,[status(thm),theory(equality)],[28390]),
[iquote('0:Obv:28390.2')] ).
cnf(28414,plain,
$false,
inference(ssi,[status(thm)],[28413,576,27205,577]),
[iquote('1:SSi:28413.1,28413.0,576.0,27205.0,577.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC248+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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 : Sun Jun 12 01:55:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 29.10/29.31
% 29.10/29.31 SPASS V 3.9
% 29.10/29.31 SPASS beiseite: Proof found.
% 29.10/29.31 % SZS status Theorem
% 29.10/29.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.10/29.31 SPASS derived 17679 clauses, backtracked 1633 clauses, performed 22 splits and kept 6621 clauses.
% 29.10/29.31 SPASS allocated 124372 KBytes.
% 29.10/29.31 SPASS spent 0:0:24.85 on the problem.
% 29.10/29.31 0:00:00.04 for the input.
% 29.10/29.31 0:00:00.07 for the FLOTTER CNF translation.
% 29.10/29.31 0:00:00.34 for inferences.
% 29.10/29.31 0:00:00.70 for the backtracking.
% 29.10/29.31 0:0:23.37 for the reduction.
% 29.10/29.31
% 29.10/29.31
% 29.10/29.31 Here is a proof with depth 3, length 55 :
% 29.10/29.31 % SZS output start Refutation
% See solution above
% 29.10/29.31 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax78 ax4 ax67 ax27
% 29.10/29.31
%------------------------------------------------------------------------------