TSTP Solution File: SWC021+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC021+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 22:01:09 EDT 2022
% Result : Theorem 2.01s 2.26s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 33
% Syntax : Number of clauses : 73 ( 23 unt; 10 nHn; 73 RR)
% Number of literals : 166 ( 0 equ; 100 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC021+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC021+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC021+1.p',unknown),
[] ).
cnf(14,axiom,
frontsegP(skc5,skc4),
file('SWC021+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ ssList(u)
| frontsegP(u,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC021+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ equal(skc4,nil)
| ~ equal(skc5,nil) ),
file('SWC021+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,v),nil) ),
file('SWC021+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ frontsegP(skc4,u)
| ~ frontsegP(skc5,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(app(cons(u,nil),v),cons(u,v)) ),
file('SWC021+1.p',unknown),
[] ).
cnf(140,axiom,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ segmentP(u,skc4)
| ~ neq(skc4,u)
| ~ frontsegP(skc5,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(u,w),v)
| frontsegP(v,u) ),
file('SWC021+1.p',unknown),
[] ).
cnf(246,plain,
( ~ neq(skc4,nil)
| ~ frontsegP(skc5,skc4)
| ~ frontsegP(skc4,skc4) ),
inference(res,[status(thm),theory(equality)],[2,124]),
[iquote('0:Res:2.0,124.0')] ).
cnf(254,plain,
( ~ ssList(u)
| neq(skc4,u)
| equal(skc4,u) ),
inference(res,[status(thm),theory(equality)],[2,104]),
[iquote('0:Res:2.0,104.0')] ).
cnf(256,plain,
( ~ ssItem(u)
| ~ equal(cons(u,skc4),nil) ),
inference(res,[status(thm),theory(equality)],[2,106]),
[iquote('0:Res:2.0,106.0')] ).
cnf(269,plain,
( ~ ssItem(u)
| ssList(cons(u,skc4)) ),
inference(res,[status(thm),theory(equality)],[2,87]),
[iquote('0:Res:2.0,87.0')] ).
cnf(281,plain,
frontsegP(skc4,skc4),
inference(res,[status(thm),theory(equality)],[2,61]),
[iquote('0:Res:2.0,61.0')] ).
cnf(425,plain,
( equal(skc5,nil)
| equal(cons(hd(skc5),tl(skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[1,114]),
[iquote('0:Res:1.0,114.0')] ).
cnf(450,plain,
( ssItem(hd(skc5))
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,82]),
[iquote('0:Res:1.0,82.0')] ).
cnf(451,plain,
( ssList(tl(skc5))
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,83]),
[iquote('0:Res:1.0,83.0')] ).
cnf(548,plain,
~ neq(skc4,nil),
inference(mrr,[status(thm)],[246,14,281]),
[iquote('0:MRR:246.1,246.2,14.0,281.0')] ).
cnf(2124,plain,
( ~ ssList(nil)
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[254,548]),
[iquote('0:Res:254.1,548.0')] ).
cnf(2125,plain,
equal(skc4,nil),
inference(ssi,[status(thm)],[2124,13,12,9,8,7,11,10,6]),
[iquote('0:SSi:2124.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).
cnf(2128,plain,
( ~ ssList(u)
| neq(skc4,u)
| equal(nil,u) ),
inference(rew,[status(thm),theory(equality)],[2125,254]),
[iquote('0:Rew:2125.0,254.2')] ).
cnf(2142,plain,
( ~ ssItem(u)
| ssList(cons(u,nil)) ),
inference(rew,[status(thm),theory(equality)],[2125,269]),
[iquote('0:Rew:2125.0,269.1')] ).
cnf(2143,plain,
( ~ ssItem(u)
| ~ equal(cons(u,nil),nil) ),
inference(rew,[status(thm),theory(equality)],[2125,256]),
[iquote('0:Rew:2125.0,256.1')] ).
cnf(2176,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ segmentP(u,skc4)
| ~ neq(nil,u)
| ~ frontsegP(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[2125,140]),
[iquote('0:Rew:2125.0,140.3')] ).
cnf(2270,plain,
( ~ equal(nil,nil)
| ~ equal(skc5,nil) ),
inference(rew,[status(thm),theory(equality)],[2125,77]),
[iquote('0:Rew:2125.0,77.0')] ).
cnf(2271,plain,
~ equal(skc5,nil),
inference(obv,[status(thm),theory(equality)],[2270]),
[iquote('0:Obv:2270.0')] ).
cnf(2272,plain,
ssList(tl(skc5)),
inference(mrr,[status(thm)],[451,2271]),
[iquote('0:MRR:451.1,2271.0')] ).
cnf(2273,plain,
ssItem(hd(skc5)),
inference(mrr,[status(thm)],[450,2271]),
[iquote('0:MRR:450.1,2271.0')] ).
cnf(2280,plain,
( ~ ssList(u)
| neq(nil,u)
| equal(nil,u) ),
inference(rew,[status(thm),theory(equality)],[2125,2128]),
[iquote('0:Rew:2125.0,2128.1')] ).
cnf(2282,plain,
equal(cons(hd(skc5),tl(skc5)),skc5),
inference(mrr,[status(thm)],[425,2271]),
[iquote('0:MRR:425.0,2271.0')] ).
cnf(2370,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ segmentP(u,nil)
| ~ neq(nil,u)
| ~ frontsegP(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[2125,2176]),
[iquote('0:Rew:2125.0,2176.2')] ).
cnf(2371,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ neq(nil,u)
| ~ frontsegP(skc5,u) ),
inference(mrr,[status(thm)],[2370,66]),
[iquote('0:MRR:2370.2,66.1')] ).
cnf(3000,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[117]),
[iquote('0:EqR:117.2')] ).
cnf(3002,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[3000,75,74,71,70,69,73,72,2142]),
[iquote('0:SSi:3000.0,75.1,74.1,71.1,70.1,69.1,73.1,72.1,2142.1')] ).
cnf(4652,plain,
( ~ ssList(u)
| ~ ssList(app(u,v))
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[141]),
[iquote('0:EqR:141.3')] ).
cnf(4671,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[4652,88]),
[iquote('0:SSi:4652.1,88.2')] ).
cnf(5035,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(cons(u,nil))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(spr,[status(thm),theory(equality)],[125,4671]),
[iquote('0:SpR:125.2,4671.2')] ).
cnf(5055,plain,
( ~ ssItem(u)
| ~ ssList(cons(u,nil))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(obv,[status(thm),theory(equality)],[5035]),
[iquote('0:Obv:5035.1')] ).
cnf(5056,plain,
( ~ ssItem(u)
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(ssi,[status(thm)],[5055,75,74,71,70,69,73,72,2142,3002]),
[iquote('0:SSi:5055.1,75.1,74.1,71.1,70.1,69.1,73.1,72.1,2142.1,3002.1')] ).
cnf(5910,plain,
( ~ ssItem(hd(skc5))
| ~ ssList(tl(skc5))
| frontsegP(skc5,cons(hd(skc5),nil)) ),
inference(spr,[status(thm),theory(equality)],[2282,5056]),
[iquote('0:SpR:2282.0,5056.2')] ).
cnf(6105,plain,
( ~ ssItem(hd(skc5))
| frontsegP(skc5,cons(hd(skc5),nil)) ),
inference(ssi,[status(thm)],[5910,2272]),
[iquote('0:SSi:5910.1,2272.0')] ).
cnf(6106,plain,
frontsegP(skc5,cons(hd(skc5),nil)),
inference(mrr,[status(thm)],[6105,2273]),
[iquote('0:MRR:6105.0,2273.0')] ).
cnf(6263,plain,
( ~ strictorderedP(cons(hd(skc5),nil))
| ~ ssList(cons(hd(skc5),nil))
| ~ neq(nil,cons(hd(skc5),nil)) ),
inference(res,[status(thm),theory(equality)],[6106,2371]),
[iquote('0:Res:6106.0,2371.3')] ).
cnf(6266,plain,
~ neq(nil,cons(hd(skc5),nil)),
inference(ssi,[status(thm)],[6263,75,2273,74,71,70,69,73,72,2142,3002]),
[iquote('0:SSi:6263.1,6263.0,75.0,2273.1,74.0,2273.1,71.0,2273.1,70.0,2273.1,69.0,2273.1,73.0,2273.1,72.0,2273.1,2142.0,2273.1,3002.0,2273.1,75.0,2273.1,74.0,2273.1,71.0,2273.1,70.0,2273.1,69.0,2273.1,73.0,2273.1,72.0,2273.1,2142.0,2273.1,3002.0,2273.1')] ).
cnf(6421,plain,
( ~ ssList(cons(hd(skc5),nil))
| equal(cons(hd(skc5),nil),nil) ),
inference(res,[status(thm),theory(equality)],[2280,6266]),
[iquote('0:Res:2280.1,6266.0')] ).
cnf(6422,plain,
equal(cons(hd(skc5),nil),nil),
inference(ssi,[status(thm)],[6421,75,2273,74,71,70,69,73,72,2142,3002]),
[iquote('0:SSi:6421.0,75.0,2273.1,74.0,2273.1,71.0,2273.1,70.0,2273.1,69.0,2273.1,73.0,2273.1,72.0,2273.1,2142.0,2273.1,3002.0,2273.1')] ).
cnf(6462,plain,
( ~ ssItem(hd(skc5))
| ~ equal(nil,nil) ),
inference(spl,[status(thm),theory(equality)],[6422,2143]),
[iquote('0:SpL:6422.0,2143.1')] ).
cnf(6475,plain,
~ ssItem(hd(skc5)),
inference(obv,[status(thm),theory(equality)],[6462]),
[iquote('0:Obv:6462.1')] ).
cnf(6476,plain,
$false,
inference(ssi,[status(thm)],[6475,2273]),
[iquote('0:SSi:6475.0,2273.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC021+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 11:44:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.01/2.26
% 2.01/2.26 SPASS V 3.9
% 2.01/2.26 SPASS beiseite: Proof found.
% 2.01/2.26 % SZS status Theorem
% 2.01/2.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.01/2.26 SPASS derived 4181 clauses, backtracked 1028 clauses, performed 38 splits and kept 2857 clauses.
% 2.01/2.26 SPASS allocated 103441 KBytes.
% 2.01/2.26 SPASS spent 0:00:01.78 on the problem.
% 2.01/2.26 0:00:00.04 for the input.
% 2.01/2.26 0:00:00.07 for the FLOTTER CNF translation.
% 2.01/2.26 0:00:00.04 for inferences.
% 2.01/2.26 0:00:00.03 for the backtracking.
% 2.01/2.26 0:00:01.42 for the reduction.
% 2.01/2.26
% 2.01/2.26
% 2.01/2.26 Here is a proof with depth 6, length 73 :
% 2.01/2.26 % SZS output start Refutation
% See solution above
% 2.09/2.26 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax42 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax75 ax76 ax16 ax26 ax15 ax21 ax78 ax4 ax2 ax81 ax5
% 2.09/2.26
%------------------------------------------------------------------------------