TSTP Solution File: SWC117+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC117+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:01:50 EDT 2022
% Result : Theorem 101.94s 102.11s
% Output : Refutation 101.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 38
% Syntax : Number of clauses : 87 ( 25 unt; 10 nHn; 87 RR)
% Number of literals : 218 ( 0 equ; 137 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC117+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC117+1.p',unknown),
[] ).
cnf(3,axiom,
equalelemsP(skc4),
file('SWC117+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(7,axiom,
cyclefreeP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(8,axiom,
totalorderP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(9,axiom,
strictorderP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(11,axiom,
strictorderedP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(12,axiom,
duplicatefreeP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(13,axiom,
equalelemsP(nil),
file('SWC117+1.p',unknown),
[] ).
cnf(14,axiom,
segmentP(skc5,skc4),
file('SWC117+1.p',unknown),
[] ).
cnf(56,axiom,
ssList(skf46(u,v)),
file('SWC117+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC117+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ equal(skc4,nil)
| ~ equal(skc5,nil) ),
file('SWC117+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ neq(skc4,nil)
| ~ segmentP(skc5,skc4) ),
file('SWC117+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(hd(u))
| equal(nil,u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssList(u)
| ssList(tl(u))
| equal(nil,u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,v),nil) ),
file('SWC117+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(hd(u),tl(u)),u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(app(cons(u,nil),v),cons(u,v)) ),
file('SWC117+1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ frontsegP(v,u)
| equal(app(u,skf46(v,u)),v) ),
file('SWC117+1.p',unknown),
[] ).
cnf(140,axiom,
( ~ equalelemsP(u)
| ~ ssList(u)
| ~ segmentP(u,skc4)
| ~ neq(skc4,u)
| ~ segmentP(skc5,u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(u,w),v)
| frontsegP(v,u) ),
file('SWC117+1.p',unknown),
[] ).
cnf(157,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC117+1.p',unknown),
[] ).
cnf(183,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(app(u,x),v),w)
| segmentP(w,x) ),
file('SWC117+1.p',unknown),
[] ).
cnf(194,plain,
~ neq(skc4,nil),
inference(mrr,[status(thm)],[78,14]),
[iquote('0:MRR:78.1,14.0')] ).
cnf(199,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(x,app(u,w)),v)
| segmentP(v,u) ),
inference(rew,[status(thm),theory(equality)],[157,183]),
[iquote('0:Rew:157.3,183.4')] ).
cnf(253,plain,
( ~ ssList(u)
| neq(skc4,u)
| equal(skc4,u) ),
inference(res,[status(thm),theory(equality)],[2,105]),
[iquote('0:Res:2.0,105.0')] ).
cnf(255,plain,
( ~ ssItem(u)
| ~ equal(cons(u,skc4),nil) ),
inference(res,[status(thm),theory(equality)],[2,107]),
[iquote('0:Res:2.0,107.0')] ).
cnf(268,plain,
( ~ ssItem(u)
| ssList(cons(u,skc4)) ),
inference(res,[status(thm),theory(equality)],[2,88]),
[iquote('0:Res:2.0,88.0')] ).
cnf(412,plain,
( ~ ssList(u)
| ~ frontsegP(skc5,u)
| equal(app(u,skf46(skc5,u)),skc5) ),
inference(res,[status(thm),theory(equality)],[1,133]),
[iquote('0:Res:1.0,133.0')] ).
cnf(423,plain,
( equal(skc5,nil)
| equal(cons(hd(skc5),tl(skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[1,115]),
[iquote('0:Res:1.0,115.0')] ).
cnf(448,plain,
( ssItem(hd(skc5))
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,83]),
[iquote('0:Res:1.0,83.0')] ).
cnf(449,plain,
( ssList(tl(skc5))
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,84]),
[iquote('0:Res:1.0,84.0')] ).
cnf(2250,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[118]),
[iquote('0:EqR:118.2')] ).
cnf(2511,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[2250,88,13,12,9,8,7,11,10,6,75,74,71,70,69,73,72]),
[iquote('0:SSi:2250.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,75.0,74.0,71.0,70.0,69.0,73.0,72.2')] ).
cnf(2835,plain,
( ~ ssList(nil)
| ~ ssList(skc4)
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[105,194]),
[iquote('0:Res:105.2,194.0')] ).
cnf(2866,plain,
equal(skc4,nil),
inference(ssi,[status(thm)],[2835,2,3,13,12,9,8,7,11,10,6]),
[iquote('0:SSi:2835.1,2835.0,2.0,3.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).
cnf(2900,plain,
( ~ ssItem(u)
| ssList(cons(u,nil)) ),
inference(rew,[status(thm),theory(equality)],[2866,268]),
[iquote('0:Rew:2866.0,268.1')] ).
cnf(2901,plain,
( ~ ssItem(u)
| ~ equal(cons(u,nil),nil) ),
inference(rew,[status(thm),theory(equality)],[2866,255]),
[iquote('0:Rew:2866.0,255.1')] ).
cnf(2919,plain,
( ~ equalelemsP(u)
| ~ ssList(u)
| ~ segmentP(u,skc4)
| ~ neq(nil,u)
| ~ segmentP(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[2866,140]),
[iquote('0:Rew:2866.0,140.3')] ).
cnf(2921,plain,
( ~ ssList(u)
| neq(nil,u)
| equal(skc4,u) ),
inference(rew,[status(thm),theory(equality)],[2866,253]),
[iquote('0:Rew:2866.0,253.1')] ).
cnf(3020,plain,
( ~ equal(nil,nil)
| ~ equal(skc5,nil) ),
inference(rew,[status(thm),theory(equality)],[2866,77]),
[iquote('0:Rew:2866.0,77.0')] ).
cnf(3021,plain,
~ equal(skc5,nil),
inference(obv,[status(thm),theory(equality)],[3020]),
[iquote('0:Obv:3020.0')] ).
cnf(3022,plain,
ssItem(hd(skc5)),
inference(mrr,[status(thm)],[448,3021]),
[iquote('0:MRR:448.1,3021.0')] ).
cnf(3023,plain,
ssList(tl(skc5)),
inference(mrr,[status(thm)],[449,3021]),
[iquote('0:MRR:449.1,3021.0')] ).
cnf(3032,plain,
( ~ ssList(u)
| neq(nil,u)
| equal(nil,u) ),
inference(rew,[status(thm),theory(equality)],[2866,2921]),
[iquote('0:Rew:2866.0,2921.2')] ).
cnf(3034,plain,
equal(cons(hd(skc5),tl(skc5)),skc5),
inference(mrr,[status(thm)],[423,3021]),
[iquote('0:MRR:423.0,3021.0')] ).
cnf(3118,plain,
( ~ equalelemsP(u)
| ~ ssList(u)
| ~ segmentP(u,nil)
| ~ neq(nil,u)
| ~ segmentP(skc5,u) ),
inference(rew,[status(thm),theory(equality)],[2866,2919]),
[iquote('0:Rew:2866.0,2919.2')] ).
cnf(3119,plain,
( ~ equalelemsP(u)
| ~ ssList(u)
| ~ neq(nil,u)
| ~ segmentP(skc5,u) ),
inference(mrr,[status(thm)],[3118,66]),
[iquote('0:MRR:3118.2,66.1')] ).
cnf(4487,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(4501,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[4487,89]),
[iquote('0:SSi:4487.1,89.2')] ).
cnf(5665,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(cons(u,nil))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(spr,[status(thm),theory(equality)],[125,4501]),
[iquote('0:SpR:125.2,4501.2')] ).
cnf(5684,plain,
( ~ ssItem(u)
| ~ ssList(cons(u,nil))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(obv,[status(thm),theory(equality)],[5665]),
[iquote('0:Obv:5665.1')] ).
cnf(5685,plain,
( ~ ssItem(u)
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,nil)) ),
inference(ssi,[status(thm)],[5684,75,74,71,70,69,73,72,2511,2900]),
[iquote('0:SSi:5684.1,75.1,74.1,71.1,70.1,69.1,73.1,72.1,2511.1,2900.1')] ).
cnf(6418,plain,
( ~ ssList(u)
| ~ ssList(app(v,app(u,w)))
| ~ ssList(w)
| ~ ssList(v)
| segmentP(app(v,app(u,w)),u) ),
inference(eqr,[status(thm),theory(equality)],[199]),
[iquote('0:EqR:199.4')] ).
cnf(6454,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| segmentP(app(w,app(u,v)),u) ),
inference(ssi,[status(thm)],[6418,89]),
[iquote('0:SSi:6418.1,89.2,89.2')] ).
cnf(11004,plain,
( ~ ssItem(hd(skc5))
| ~ ssList(tl(skc5))
| frontsegP(skc5,cons(hd(skc5),nil)) ),
inference(spr,[status(thm),theory(equality)],[3034,5685]),
[iquote('0:SpR:3034.0,5685.2')] ).
cnf(15672,plain,
( ~ ssList(app(u,v))
| ~ ssList(u)
| ~ ssList(v)
| ~ ssList(nil)
| segmentP(app(u,v),u) ),
inference(spr,[status(thm),theory(equality)],[79,6454]),
[iquote('0:SpR:79.1,6454.3')] ).
cnf(15685,plain,
( ~ ssList(u)
| ~ ssList(v)
| segmentP(app(u,v),u) ),
inference(ssi,[status(thm)],[15672,13,12,9,8,7,11,10,6,89]),
[iquote('0:SSi:15672.3,15672.0,13.2,12.0,9.0,8.0,7.0,11.0,10.0,6.0,89.0')] ).
cnf(17979,plain,
( ~ ssList(u)
| ~ ssList(u)
| ~ ssList(skf46(skc5,u))
| ~ frontsegP(skc5,u)
| segmentP(skc5,u) ),
inference(spr,[status(thm),theory(equality)],[412,15685]),
[iquote('0:SpR:412.2,15685.2')] ).
cnf(18007,plain,
( ~ ssList(u)
| ~ ssList(skf46(skc5,u))
| ~ frontsegP(skc5,u)
| segmentP(skc5,u) ),
inference(obv,[status(thm),theory(equality)],[17979]),
[iquote('0:Obv:17979.0')] ).
cnf(28174,plain,
( ~ ssItem(hd(skc5))
| frontsegP(skc5,cons(hd(skc5),nil)) ),
inference(ssi,[status(thm)],[11004,3023]),
[iquote('0:SSi:11004.1,3023.0')] ).
cnf(28175,plain,
frontsegP(skc5,cons(hd(skc5),nil)),
inference(mrr,[status(thm)],[28174,3022]),
[iquote('0:MRR:28174.0,3022.0')] ).
cnf(47520,plain,
( ~ ssList(u)
| ~ frontsegP(skc5,u)
| segmentP(skc5,u) ),
inference(ssi,[status(thm)],[18007,56,1]),
[iquote('0:SSi:18007.1,56.0,1.0')] ).
cnf(52625,plain,
( ~ ssList(cons(hd(skc5),nil))
| segmentP(skc5,cons(hd(skc5),nil)) ),
inference(res,[status(thm),theory(equality)],[28175,47520]),
[iquote('0:Res:28175.0,47520.1')] ).
cnf(52633,plain,
segmentP(skc5,cons(hd(skc5),nil)),
inference(ssi,[status(thm)],[52625,75,3022,74,71,70,69,73,72,2511,2900]),
[iquote('0:SSi:52625.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).
cnf(52702,plain,
( ~ equalelemsP(cons(hd(skc5),nil))
| ~ ssList(cons(hd(skc5),nil))
| ~ neq(nil,cons(hd(skc5),nil)) ),
inference(res,[status(thm),theory(equality)],[52633,3119]),
[iquote('0:Res:52633.0,3119.3')] ).
cnf(52707,plain,
~ neq(nil,cons(hd(skc5),nil)),
inference(ssi,[status(thm)],[52702,75,3022,74,71,70,69,73,72,2511,2900]),
[iquote('0:SSi:52702.1,52702.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).
cnf(52714,plain,
( ~ ssList(cons(hd(skc5),nil))
| equal(cons(hd(skc5),nil),nil) ),
inference(res,[status(thm),theory(equality)],[3032,52707]),
[iquote('0:Res:3032.1,52707.0')] ).
cnf(52715,plain,
equal(cons(hd(skc5),nil),nil),
inference(ssi,[status(thm)],[52714,75,3022,74,71,70,69,73,72,2511,2900]),
[iquote('0:SSi:52714.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).
cnf(52775,plain,
( ~ ssItem(hd(skc5))
| ~ equal(nil,nil) ),
inference(spl,[status(thm),theory(equality)],[52715,2901]),
[iquote('0:SpL:52715.0,2901.1')] ).
cnf(52844,plain,
~ ssItem(hd(skc5)),
inference(obv,[status(thm),theory(equality)],[52775]),
[iquote('0:Obv:52775.1')] ).
cnf(52845,plain,
$false,
inference(ssi,[status(thm)],[52844,3022]),
[iquote('0:SSi:52844.0,3022.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC117+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 05:15:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 101.94/102.11
% 101.94/102.11 SPASS V 3.9
% 101.94/102.11 SPASS beiseite: Proof found.
% 101.94/102.11 % SZS status Theorem
% 101.94/102.11 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.94/102.11 SPASS derived 30968 clauses, backtracked 10333 clauses, performed 107 splits and kept 17040 clauses.
% 101.94/102.11 SPASS allocated 144416 KBytes.
% 101.94/102.11 SPASS spent 0:1:27.89 on the problem.
% 101.94/102.11 0:00:00.04 for the input.
% 101.94/102.11 0:00:00.06 for the FLOTTER CNF translation.
% 101.94/102.11 0:00:00.61 for inferences.
% 101.94/102.11 0:00:02.41 for the backtracking.
% 101.94/102.11 0:1:24.19 for the reduction.
% 101.94/102.11
% 101.94/102.11
% 101.94/102.11 Here is a proof with depth 7, length 87 :
% 101.94/102.11 % SZS output start Refutation
% See solution above
% 101.94/102.11 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax5 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax15 ax21 ax78 ax4 ax2 ax81 ax82 ax7
% 101.94/102.11
%------------------------------------------------------------------------------