TSTP Solution File: SWC249+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC249+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 22:02:49 EDT 2022
% Result : Theorem 27.05s 27.25s
% Output : Refutation 27.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of clauses : 43 ( 15 unt; 6 nHn; 43 RR)
% Number of literals : 97 ( 0 equ; 54 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(2,axiom,
ssList(skc4),
file('SWC249+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC249+1.p',unknown),
[] ).
cnf(53,axiom,
~ equal(skc4,nil),
file('SWC249+1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skf44(u,v,w)),
file('SWC249+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC249+1.p',unknown),
[] ).
cnf(165,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(cons(u,v),w),cons(u,app(v,w))) ),
file('SWC249+1.p',unknown),
[] ).
cnf(187,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),skc4)
| memberP(v,skf44(w,u,v)) ),
file('SWC249+1.p',unknown),
[] ).
cnf(255,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(280,plain,
( equal(skc4,nil)
| ssItem(hd(skc4)) ),
inference(res,[status(thm),theory(equality)],[2,83]),
[iquote('0:Res:2.0,83.0')] ).
cnf(281,plain,
( equal(skc4,nil)
| ssList(tl(skc4)) ),
inference(res,[status(thm),theory(equality)],[2,84]),
[iquote('0:Res:2.0,84.0')] ).
cnf(566,plain,
ssItem(hd(skc4)),
inference(mrr,[status(thm)],[280,53]),
[iquote('0:MRR:280.0,53.0')] ).
cnf(567,plain,
ssList(tl(skc4)),
inference(mrr,[status(thm)],[281,53]),
[iquote('0:MRR:281.0,53.0')] ).
cnf(572,plain,
equal(cons(hd(skc4),tl(skc4)),skc4),
inference(mrr,[status(thm)],[255,53]),
[iquote('0:MRR:255.0,53.0')] ).
cnf(1511,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[118]),
[iquote('0:EqR:118.2')] ).
cnf(1514,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[1511,88,13,12,9,8,7,11,10,6,77,76,73,72,71,75,74]),
[iquote('0:SSi:1511.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,77.0,76.0,73.0,72.0,71.0,75.0,74.2')] ).
cnf(6337,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(app(cons(u,nil),v),skc4)
| memberP(nil,skf44(u,v,nil)) ),
inference(spl,[status(thm),theory(equality)],[79,187]),
[iquote('0:SpL:79.1,187.3')] ).
cnf(6351,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(cons(u,v),skc4)
| memberP(nil,skf44(u,v,nil)) ),
inference(rew,[status(thm),theory(equality)],[79,6337,165]),
[iquote('0:Rew:79.1,6337.4,165.3,6337.4')] ).
cnf(6352,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc4)
| memberP(nil,skf44(v,u,nil)) ),
inference(ssi,[status(thm)],[6351,13,12,9,8,7,11,10,6,88,77,76,73,72,71,75,74,1514]),
[iquote('0:SSi:6351.2,6351.0,13.1,12.1,9.1,8.1,7.1,11.1,10.1,6.1,88.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.2,77.0,76.0,73.0,72.0,71.0,75.0,74.0,1514.0')] ).
cnf(20720,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(skf44(v,u,nil))
| ~ equal(cons(v,u),skc4) ),
inference(res,[status(thm),theory(equality)],[6352,70]),
[iquote('0:Res:6352.3,70.1')] ).
cnf(20723,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc4) ),
inference(ssi,[status(thm)],[20720,61,13,12,9,8,7,11,10,6]),
[iquote('0:SSi:20720.2,61.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).
cnf(26532,plain,
( ~ ssList(tl(skc4))
| ~ ssItem(hd(skc4))
| ~ equal(skc4,skc4) ),
inference(spl,[status(thm),theory(equality)],[572,20723]),
[iquote('0:SpL:572.0,20723.2')] ).
cnf(26555,plain,
( ~ ssList(tl(skc4))
| ~ ssItem(hd(skc4)) ),
inference(obv,[status(thm),theory(equality)],[26532]),
[iquote('0:Obv:26532.2')] ).
cnf(26556,plain,
$false,
inference(ssi,[status(thm)],[26555,566,567]),
[iquote('0:SSi:26555.1,26555.0,566.0,567.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC249+1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 18:06:31 EDT 2022
% 0.21/0.34 % CPUTime :
% 27.05/27.25
% 27.05/27.25 SPASS V 3.9
% 27.05/27.25 SPASS beiseite: Proof found.
% 27.05/27.25 % SZS status Theorem
% 27.05/27.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.05/27.25 SPASS derived 16241 clauses, backtracked 1713 clauses, performed 17 splits and kept 6215 clauses.
% 27.05/27.25 SPASS allocated 122730 KBytes.
% 27.05/27.25 SPASS spent 0:0:23.22 on the problem.
% 27.05/27.25 0:00:00.04 for the input.
% 27.05/27.25 0:00:00.07 for the FLOTTER CNF translation.
% 27.05/27.25 0:00:00.30 for inferences.
% 27.05/27.25 0:00:00.61 for the backtracking.
% 27.05/27.25 0:0:21.91 for the reduction.
% 27.05/27.25
% 27.05/27.25
% 27.05/27.25 Here is a proof with depth 3, length 43 :
% 27.05/27.25 % SZS output start Refutation
% See solution above
% 27.05/27.25 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 ax27
% 27.05/27.25
%------------------------------------------------------------------------------