TSTP Solution File: SWC247+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC247+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 22:02:47 EDT 2022
% Result : Theorem 24.12s 24.32s
% Output : Refutation 24.12s
% 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('SWC247+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC247+1.p',unknown),
[] ).
cnf(53,axiom,
~ equal(skc4,nil),
file('SWC247+1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skf44(u,v,w)),
file('SWC247+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC247+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC247+1.p',unknown),
[] ).
cnf(165,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(cons(u,v),w),cons(u,app(v,w))) ),
file('SWC247+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('SWC247+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(1542,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[118]),
[iquote('0:EqR:118.2')] ).
cnf(1545,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[1542,88,13,12,8,9,7,10,11,6,77,76,72,73,71,74,75]),
[iquote('0:SSi:1542.0,88.1,13.1,12.1,8.1,9.1,7.1,10.1,11.0,6.0,77.0,76.0,72.0,73.0,71.0,74.0,75.2')] ).
cnf(6449,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(6463,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)],[79,6449,165]),
[iquote('0:Rew:79.1,6449.4,165.3,6449.4')] ).
cnf(6464,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc4)
| memberP(nil,skf44(v,u,nil)) ),
inference(ssi,[status(thm)],[6463,13,12,8,9,7,10,11,6,88,77,76,72,73,71,74,75,1545]),
[iquote('0:SSi:6463.2,6463.0,13.1,12.1,8.1,9.1,7.1,10.1,11.1,6.1,88.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.2,77.0,76.0,72.0,73.0,71.0,74.0,75.0,1545.0')] ).
cnf(21573,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(skf44(v,u,nil))
| ~ equal(cons(v,u),skc4) ),
inference(res,[status(thm),theory(equality)],[6464,70]),
[iquote('0:Res:6464.3,70.1')] ).
cnf(21576,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc4) ),
inference(ssi,[status(thm)],[21573,61,13,12,8,9,7,10,11,6]),
[iquote('0:SSi:21573.2,61.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0')] ).
cnf(25404,plain,
( ~ ssList(tl(skc4))
| ~ ssItem(hd(skc4))
| ~ equal(skc4,skc4) ),
inference(spl,[status(thm),theory(equality)],[572,21576]),
[iquote('0:SpL:572.0,21576.2')] ).
cnf(25427,plain,
( ~ ssList(tl(skc4))
| ~ ssItem(hd(skc4)) ),
inference(obv,[status(thm),theory(equality)],[25404]),
[iquote('0:Obv:25404.2')] ).
cnf(25428,plain,
$false,
inference(ssi,[status(thm)],[25427,566,567]),
[iquote('0:SSi:25427.1,25427.0,566.0,567.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWC247+1 : TPTP v8.1.0. Released v2.4.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 13:24:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 24.12/24.32
% 24.12/24.32 SPASS V 3.9
% 24.12/24.32 SPASS beiseite: Proof found.
% 24.12/24.32 % SZS status Theorem
% 24.12/24.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.12/24.32 SPASS derived 15647 clauses, backtracked 1681 clauses, performed 18 splits and kept 5961 clauses.
% 24.12/24.32 SPASS allocated 121765 KBytes.
% 24.12/24.32 SPASS spent 0:0:20.67 on the problem.
% 24.12/24.32 0:00:00.04 for the input.
% 24.12/24.32 0:00:00.07 for the FLOTTER CNF translation.
% 24.12/24.32 0:00:00.26 for inferences.
% 24.12/24.32 0:00:00.57 for the backtracking.
% 24.12/24.32 0:0:19.46 for the reduction.
% 24.12/24.32
% 24.12/24.32
% 24.12/24.32 Here is a proof with depth 3, length 43 :
% 24.12/24.32 % SZS output start Refutation
% See solution above
% 24.12/24.32 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
% 24.12/24.32
%------------------------------------------------------------------------------