TSTP Solution File: SWC222+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC222+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:02:35 EDT 2022
% Result : Theorem 29.83s 30.07s
% Output : Refutation 29.83s
% 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(5,axiom,
ssList(skc7),
file('SWC222+1.p',unknown),
[] ).
cnf(8,axiom,
ssList(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(9,axiom,
cyclefreeP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(12,axiom,
totalorderedP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(13,axiom,
strictorderedP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(14,axiom,
duplicatefreeP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC222+1.p',unknown),
[] ).
cnf(54,axiom,
~ equal(skc7,nil),
file('SWC222+1.p',unknown),
[] ).
cnf(62,axiom,
ssItem(skf44(u,v,w)),
file('SWC222+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC222+1.p',unknown),
[] ).
cnf(166,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(cons(u,v),w),cons(u,app(v,w))) ),
file('SWC222+1.p',unknown),
[] ).
cnf(189,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),skc7)
| memberP(v,skf44(w,u,v)) ),
file('SWC222+1.p',unknown),
[] ).
cnf(255,plain,
( equal(skc7,nil)
| equal(cons(hd(skc7),tl(skc7)),skc7) ),
inference(res,[status(thm),theory(equality)],[5,117]),
[iquote('0:Res:5.0,117.0')] ).
cnf(280,plain,
( equal(skc7,nil)
| ssItem(hd(skc7)) ),
inference(res,[status(thm),theory(equality)],[5,84]),
[iquote('0:Res:5.0,84.0')] ).
cnf(281,plain,
( equal(skc7,nil)
| ssList(tl(skc7)) ),
inference(res,[status(thm),theory(equality)],[5,85]),
[iquote('0:Res:5.0,85.0')] ).
cnf(565,plain,
ssItem(hd(skc7)),
inference(mrr,[status(thm)],[280,54]),
[iquote('0:MRR:280.0,54.0')] ).
cnf(566,plain,
ssList(tl(skc7)),
inference(mrr,[status(thm)],[281,54]),
[iquote('0:MRR:281.0,54.0')] ).
cnf(571,plain,
equal(cons(hd(skc7),tl(skc7)),skc7),
inference(mrr,[status(thm)],[255,54]),
[iquote('0:MRR:255.0,54.0')] ).
cnf(1977,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[120]),
[iquote('0:EqR:120.2')] ).
cnf(1980,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[1977,89,15,14,11,10,9,13,12,8,78,77,74,73,72,76,75]),
[iquote('0:SSi:1977.0,89.1,15.1,14.1,11.1,10.1,9.1,13.1,12.0,8.0,78.0,77.0,74.0,73.0,72.0,76.0,75.2')] ).
cnf(6220,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(app(cons(u,nil),v),skc7)
| memberP(nil,skf44(u,v,nil)) ),
inference(spl,[status(thm),theory(equality)],[80,189]),
[iquote('0:SpL:80.1,189.3')] ).
cnf(6236,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ ssItem(u)
| ~ equal(cons(u,v),skc7)
| memberP(nil,skf44(u,v,nil)) ),
inference(rew,[status(thm),theory(equality)],[80,6220,166]),
[iquote('0:Rew:80.1,6220.4,166.3,6220.4')] ).
cnf(6237,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc7)
| memberP(nil,skf44(v,u,nil)) ),
inference(ssi,[status(thm)],[6236,15,14,11,10,9,13,12,8,89,78,77,74,73,72,76,75,1980]),
[iquote('0:SSi:6236.2,6236.0,15.1,14.1,11.1,10.1,9.1,13.1,12.1,8.1,89.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.2,78.0,77.0,74.0,73.0,72.0,76.0,75.0,1980.0')] ).
cnf(22257,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssItem(skf44(v,u,nil))
| ~ equal(cons(v,u),skc7) ),
inference(res,[status(thm),theory(equality)],[6237,71]),
[iquote('0:Res:6237.3,71.1')] ).
cnf(22260,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),skc7) ),
inference(ssi,[status(thm)],[22257,62,15,14,11,10,9,13,12,8]),
[iquote('0:SSi:22257.2,62.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0')] ).
cnf(29359,plain,
( ~ ssList(tl(skc7))
| ~ ssItem(hd(skc7))
| ~ equal(skc7,skc7) ),
inference(spl,[status(thm),theory(equality)],[571,22260]),
[iquote('0:SpL:571.0,22260.2')] ).
cnf(29427,plain,
( ~ ssList(tl(skc7))
| ~ ssItem(hd(skc7)) ),
inference(obv,[status(thm),theory(equality)],[29359]),
[iquote('0:Obv:29359.2')] ).
cnf(29428,plain,
$false,
inference(ssi,[status(thm)],[29427,565,566]),
[iquote('0:SSi:29427.1,29427.0,565.0,566.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC222+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n028.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Sun Jun 12 08:31:21 EDT 2022
% 0.12/0.32 % CPUTime :
% 29.83/30.07
% 29.83/30.07 SPASS V 3.9
% 29.83/30.07 SPASS beiseite: Proof found.
% 29.83/30.07 % SZS status Theorem
% 29.83/30.07 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.83/30.07 SPASS derived 18170 clauses, backtracked 2628 clauses, performed 26 splits and kept 7436 clauses.
% 29.83/30.07 SPASS allocated 124878 KBytes.
% 29.83/30.07 SPASS spent 0:0:25.30 on the problem.
% 29.83/30.07 0:00:00.04 for the input.
% 29.83/30.07 0:00:00.07 for the FLOTTER CNF translation.
% 29.83/30.07 0:00:00.29 for inferences.
% 29.83/30.07 0:00:00.75 for the backtracking.
% 29.83/30.07 0:0:23.84 for the reduction.
% 29.83/30.07
% 29.83/30.07
% 29.83/30.07 Here is a proof with depth 3, length 43 :
% 29.83/30.07 % SZS output start Refutation
% See solution above
% 29.83/30.07 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
% 29.83/30.07
%------------------------------------------------------------------------------