TSTP Solution File: SWC240+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC240+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:02:44 EDT 2022
% Result : Theorem 38.25s 38.49s
% Output : Refutation 38.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of clauses : 58 ( 18 unt; 10 nHn; 58 RR)
% Number of literals : 146 ( 0 equ; 84 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 : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssItem(skc7),
file('SWC240+1.p',unknown),
[] ).
cnf(3,axiom,
ssList(skc5),
file('SWC240+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC240+1.p',unknown),
[] ).
cnf(52,axiom,
~ equal(skc5,nil),
file('SWC240+1.p',unknown),
[] ).
cnf(60,axiom,
ssItem(skf44(u,v,w)),
file('SWC240+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| ~ memberP(skc5,u)
| equal(skc7,u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(164,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(cons(u,v),w),cons(u,app(v,w))) ),
file('SWC240+1.p',unknown),
[] ).
cnf(183,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(x,cons(u,w)),v)
| memberP(v,u) ),
file('SWC240+1.p',unknown),
[] ).
cnf(186,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),skc5)
| memberP(v,skf44(w,u,v)) ),
file('SWC240+1.p',unknown),
[] ).
cnf(250,plain,
( equal(skc5,nil)
| equal(cons(hd(skc5),tl(skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[3,115]),
[iquote('0:Res:3.0,115.0')] ).
cnf(275,plain,
( equal(skc5,nil)
| ssItem(hd(skc5)) ),
inference(res,[status(thm),theory(equality)],[3,82]),
[iquote('0:Res:3.0,82.0')] ).
cnf(276,plain,
( equal(skc5,nil)
| ssList(tl(skc5)) ),
inference(res,[status(thm),theory(equality)],[3,83]),
[iquote('0:Res:3.0,83.0')] ).
cnf(560,plain,
ssItem(hd(skc5)),
inference(mrr,[status(thm)],[275,52]),
[iquote('0:MRR:275.0,52.0')] ).
cnf(561,plain,
ssList(tl(skc5)),
inference(mrr,[status(thm)],[276,52]),
[iquote('0:MRR:276.0,52.0')] ).
cnf(566,plain,
equal(cons(hd(skc5),tl(skc5)),skc5),
inference(mrr,[status(thm)],[250,52]),
[iquote('0:MRR:250.0,52.0')] ).
cnf(1988,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[118]),
[iquote('0:EqR:118.2')] ).
cnf(1991,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[1988,88,13,12,9,8,7,11,10,6,76,75,72,71,70,74,73]),
[iquote('0:SSi:1988.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,76.0,75.0,72.0,71.0,70.0,74.0,73.2')] ).
cnf(5624,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)],[183]),
[iquote('0:EqR:183.4')] ).
cnf(5650,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| memberP(app(w,cons(u,v)),u) ),
inference(ssi,[status(thm)],[5624,89,88]),
[iquote('0:SSi:5624.1,89.2,88.2')] ).
cnf(6062,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(app(cons(u,nil),v),skc5)
| memberP(nil,skf44(u,v,nil)) ),
inference(spl,[status(thm),theory(equality)],[78,186]),
[iquote('0:SpL:78.1,186.3')] ).
cnf(6078,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(cons(u,v),skc5)
| memberP(nil,skf44(u,v,nil)) ),
inference(rew,[status(thm),theory(equality)],[78,6062,164]),
[iquote('0:Rew:78.1,6062.4,164.3,6062.4')] ).
cnf(6079,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc5)
| memberP(nil,skf44(v,u,nil)) ),
inference(ssi,[status(thm)],[6078,13,12,9,8,7,11,10,6,88,76,75,72,71,70,74,73,1991]),
[iquote('0:SSi:6078.2,6078.0,13.1,12.1,9.1,8.1,7.1,11.1,10.1,6.1,88.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.2,76.0,75.0,72.0,71.0,70.0,74.0,73.0,1991.0')] ).
cnf(15846,plain,
( ~ ssList(cons(u,v))
| ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(nil)
| memberP(cons(u,v),u) ),
inference(spr,[status(thm),theory(equality)],[78,5650]),
[iquote('0:SpR:78.1,5650.3')] ).
cnf(15875,plain,
( ~ ssItem(u)
| ~ ssList(v)
| memberP(cons(u,v),u) ),
inference(ssi,[status(thm)],[15846,13,12,9,8,7,11,10,6,88]),
[iquote('0:SSi:15846.3,15846.0,13.2,12.0,9.0,8.0,7.0,11.0,10.0,6.0,88.0')] ).
cnf(17851,plain,
( ~ ssList(u)
| ~ ssItem(hd(u))
| ~ ssList(tl(u))
| equal(nil,u)
| memberP(u,hd(u)) ),
inference(spr,[status(thm),theory(equality)],[115,15875]),
[iquote('0:SpR:115.2,15875.2')] ).
cnf(17862,plain,
( ~ ssList(u)
| equal(nil,u)
| memberP(u,hd(u)) ),
inference(mrr,[status(thm)],[17851,82,83]),
[iquote('0:MRR:17851.1,17851.2,82.1,83.1')] ).
cnf(17946,plain,
( ~ ssList(skc5)
| ~ ssItem(hd(skc5))
| equal(skc5,nil)
| equal(hd(skc5),skc7) ),
inference(res,[status(thm),theory(equality)],[17862,84]),
[iquote('0:Res:17862.2,84.1')] ).
cnf(22661,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(skf44(v,u,nil))
| ~ equal(cons(v,u),skc5) ),
inference(res,[status(thm),theory(equality)],[6079,69]),
[iquote('0:Res:6079.3,69.1')] ).
cnf(22664,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc5) ),
inference(ssi,[status(thm)],[22661,60,13,12,9,8,7,11,10,6]),
[iquote('0:SSi:22661.2,60.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).
cnf(31973,plain,
( ~ ssItem(hd(skc5))
| equal(skc5,nil)
| equal(hd(skc5),skc7) ),
inference(ssi,[status(thm)],[17946,3]),
[iquote('0:SSi:17946.0,3.0')] ).
cnf(31974,plain,
( ~ ssItem(hd(skc5))
| equal(hd(skc5),skc7) ),
inference(mrr,[status(thm)],[31973,52]),
[iquote('0:MRR:31973.1,52.0')] ).
cnf(31975,plain,
equal(hd(skc5),skc7),
inference(mrr,[status(thm)],[31974,560]),
[iquote('0:MRR:31974.0,560.0')] ).
cnf(31977,plain,
equal(cons(skc7,tl(skc5)),skc5),
inference(rew,[status(thm),theory(equality)],[31975,566]),
[iquote('0:Rew:31975.0,566.0')] ).
cnf(32579,plain,
( ~ ssList(tl(skc5))
| ~ ssItem(skc7)
| ~ equal(skc5,skc5) ),
inference(spl,[status(thm),theory(equality)],[31977,22664]),
[iquote('0:SpL:31977.0,22664.2')] ).
cnf(32601,plain,
( ~ ssList(tl(skc5))
| ~ ssItem(skc7) ),
inference(obv,[status(thm),theory(equality)],[32579]),
[iquote('0:Obv:32579.2')] ).
cnf(32602,plain,
$false,
inference(ssi,[status(thm)],[32601,1,561]),
[iquote('0:SSi:32601.1,32601.0,1.0,561.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC240+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 00:10:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 38.25/38.49
% 38.25/38.49 SPASS V 3.9
% 38.25/38.49 SPASS beiseite: Proof found.
% 38.25/38.49 % SZS status Theorem
% 38.25/38.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.25/38.49 SPASS derived 18545 clauses, backtracked 5079 clauses, performed 50 splits and kept 9300 clauses.
% 38.25/38.49 SPASS allocated 126434 KBytes.
% 38.25/38.49 SPASS spent 0:0:32.83 on the problem.
% 38.25/38.49 0:00:00.04 for the input.
% 38.25/38.49 0:00:00.07 for the FLOTTER CNF translation.
% 38.25/38.49 0:00:00.32 for inferences.
% 38.25/38.49 0:00:00.98 for the backtracking.
% 38.25/38.49 0:0:31.07 for the reduction.
% 38.25/38.49
% 38.25/38.49
% 38.25/38.49 Here is a proof with depth 4, length 58 :
% 38.25/38.49 % SZS output start Refutation
% See solution above
% 38.25/38.49 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 ax26 ax78 ax4 ax27 ax3
% 38.25/38.49
%------------------------------------------------------------------------------