TSTP Solution File: SWC355-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC355-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 22:03:31 EDT 2022
% Result : Unsatisfiable 56.08s 56.27s
% Output : Refutation 73.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 49
% Syntax : Number of clauses : 142 ( 41 unt; 16 nHn; 142 RR)
% Number of literals : 361 ( 0 equ; 225 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC355-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC355-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC355-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC355-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC355-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ neq(sk4,nil)
| equal(app(sk3,cons(sk5,nil)),sk4) ),
file('SWC355-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('SWC355-1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(17,axiom,
strictorderedP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(18,axiom,
totalorderedP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(19,axiom,
strictorderP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(20,axiom,
totalorderP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(21,axiom,
cyclefreeP(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(22,axiom,
ssList(nil),
file('SWC355-1.p',unknown),
[] ).
cnf(26,axiom,
ssItem(skaf83(u)),
file('SWC355-1.p',unknown),
[] ).
cnf(27,axiom,
ssList(skaf82(u)),
file('SWC355-1.p',unknown),
[] ).
cnf(62,axiom,
ssList(skaf48(u,v)),
file('SWC355-1.p',unknown),
[] ).
cnf(63,axiom,
ssList(skaf47(u,v)),
file('SWC355-1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC355-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ frontsegP(nil,u)
| equal(nil,u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(111,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(hd(cons(v,u)),v) ),
file('SWC355-1.p',unknown),
[] ).
cnf(112,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),nil) ),
file('SWC355-1.p',unknown),
[] ).
cnf(113,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssList(u)
| ~ singletonP(u)
| equal(cons(skaf44(u),nil),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(123,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(134,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(137,axiom,
( ~ ssList(u)
| ~ ssList(v)
| equal(nil,u)
| equal(hd(app(u,v)),hd(u)) ),
file('SWC355-1.p',unknown),
[] ).
cnf(142,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ rearsegP(u,v)
| ~ rearsegP(v,u)
| equal(u,v) ),
file('SWC355-1.p',unknown),
[] ).
cnf(157,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(w,v),u)
| rearsegP(u,v) ),
file('SWC355-1.p',unknown),
[] ).
cnf(158,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,w),u)
| frontsegP(u,v) ),
file('SWC355-1.p',unknown),
[] ).
cnf(163,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(u,v),w),app(u,app(v,w))) ),
file('SWC355-1.p',unknown),
[] ).
cnf(171,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC355-1.p',unknown),
[] ).
cnf(182,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ segmentP(u,v)
| equal(app(app(skaf47(u,v),v),skaf48(v,u)),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(187,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(app(v,w),u),x)
| segmentP(x,w) ),
file('SWC355-1.p',unknown),
[] ).
cnf(193,axiom,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
file('SWC355-1.p',unknown),
[] ).
cnf(204,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(205,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.1')] ).
cnf(206,plain,
~ segmentP(sk2,sk1),
inference(mrr,[status(thm)],[205,204]),
[iquote('0:MRR:205.1,204.0')] ).
cnf(207,plain,
( ~ neq(sk2,nil)
| equal(app(sk1,cons(sk5,nil)),sk2) ),
inference(rew,[status(thm),theory(equality)],[6,13,5]),
[iquote('0:Rew:6.0,13.1,5.0,13.1,5.0,13.0')] ).
cnf(208,plain,
equal(app(sk1,cons(sk5,nil)),sk2),
inference(mrr,[status(thm)],[207,204]),
[iquote('0:MRR:207.0,204.0')] ).
cnf(212,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(w,app(v,x)),u)
| segmentP(u,v) ),
inference(rew,[status(thm),theory(equality)],[163,187]),
[iquote('0:Rew:163.3,187.4')] ).
cnf(293,plain,
equal(app(nil,sk2),sk2),
inference(res,[status(thm),theory(equality)],[2,88]),
[iquote('0:Res:2.0,88.0')] ).
cnf(350,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,100]),
[iquote('0:Res:2.0,100.1')] ).
cnf(559,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[86]),
[iquote('1:Spt:86.1')] ).
cnf(565,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,559]),
[iquote('1:MRR:84.0,559.0')] ).
cnf(566,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,559]),
[iquote('1:MRR:83.0,559.0')] ).
cnf(567,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,559]),
[iquote('1:MRR:82.0,559.0')] ).
cnf(568,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,559]),
[iquote('1:MRR:81.0,559.0')] ).
cnf(569,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,559]),
[iquote('1:MRR:80.0,559.0')] ).
cnf(570,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[79,559]),
[iquote('1:MRR:79.0,559.0')] ).
cnf(571,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[78,559]),
[iquote('1:MRR:78.0,559.0')] ).
cnf(684,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[100,559]),
[iquote('1:MRR:100.1,559.0')] ).
cnf(685,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),u) ),
inference(mrr,[status(thm)],[113,559]),
[iquote('1:MRR:113.1,559.0')] ).
cnf(686,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),nil) ),
inference(mrr,[status(thm)],[112,559]),
[iquote('1:MRR:112.1,559.0')] ).
cnf(687,plain,
( ~ ssList(u)
| equal(hd(cons(v,u)),v) ),
inference(mrr,[status(thm)],[111,559]),
[iquote('1:MRR:111.1,559.0')] ).
cnf(689,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[130,559]),
[iquote('1:MRR:130.1,559.0')] ).
cnf(690,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[134,559]),
[iquote('1:MRR:134.1,559.0')] ).
cnf(2056,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[689]),
[iquote('1:EqR:689.1')] ).
cnf(2057,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[2056,684,22,21,20,19,18,17,16,15,565,566,567,568,569,570,571]),
[iquote('1:SSi:2056.0,684.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,565.0,566.0,567.0,568.0,569.0,570.0,571.1')] ).
cnf(2204,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| equal(nil,u)
| equal(hd(u),skaf83(u)) ),
inference(spr,[status(thm),theory(equality)],[123,687]),
[iquote('1:SpR:123.2,687.1')] ).
cnf(2214,plain,
( ~ ssList(u)
| equal(nil,u)
| equal(hd(u),skaf83(u)) ),
inference(ssi,[status(thm)],[2204,27]),
[iquote('1:SSi:2204.1,27.0')] ).
cnf(2221,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(nil,u)
| equal(hd(app(u,v)),skaf83(u)) ),
inference(rew,[status(thm),theory(equality)],[2214,137]),
[iquote('1:Rew:2214.2,137.3')] ).
cnf(2892,plain,
( ~ ssList(u)
| ~ ssList(cons(v,nil))
| ~ ssList(u)
| equal(cons(v,nil),nil)
| equal(hd(cons(v,u)),skaf83(cons(v,nil))) ),
inference(spr,[status(thm),theory(equality)],[690,2221]),
[iquote('1:SpR:690.1,2221.3')] ).
cnf(2898,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| equal(cons(u,nil),nil)
| equal(hd(cons(u,v)),skaf83(cons(u,nil))) ),
inference(obv,[status(thm),theory(equality)],[2892]),
[iquote('1:Obv:2892.0')] ).
cnf(2899,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| equal(cons(u,nil),nil)
| equal(skaf83(cons(u,nil)),u) ),
inference(rew,[status(thm),theory(equality)],[687,2898]),
[iquote('1:Rew:687.1,2898.3')] ).
cnf(2900,plain,
( ~ ssList(cons(u,nil))
| equal(cons(u,nil),nil)
| equal(skaf83(cons(u,nil)),u) ),
inference(con,[status(thm)],[2899]),
[iquote('1:Con:2899.1')] ).
cnf(3604,plain,
( ~ ssList(app(u,v))
| ~ ssList(v)
| ~ ssList(u)
| rearsegP(app(u,v),v) ),
inference(eqr,[status(thm),theory(equality)],[157]),
[iquote('0:EqR:157.3')] ).
cnf(3622,plain,
( ~ ssList(u)
| ~ ssList(v)
| rearsegP(app(v,u),u) ),
inference(ssi,[status(thm)],[3604,99]),
[iquote('0:SSi:3604.0,99.2')] ).
cnf(3662,plain,
( ~ ssList(app(u,v))
| ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[158]),
[iquote('0:EqR:158.3')] ).
cnf(3680,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[3662,99]),
[iquote('0:SSi:3662.0,99.2')] ).
cnf(5060,plain,
( ~ ssList(skaf47(u,nil))
| ~ ssList(u)
| ~ ssList(nil)
| ~ segmentP(u,nil)
| equal(app(skaf47(u,nil),skaf48(nil,u)),u) ),
inference(spr,[status(thm),theory(equality)],[87,182]),
[iquote('0:SpR:87.1,182.3')] ).
cnf(5071,plain,
( ~ ssList(u)
| ~ segmentP(u,nil)
| equal(app(skaf47(u,nil),skaf48(nil,u)),u) ),
inference(ssi,[status(thm)],[5060,22,21,20,19,18,17,16,15,63]),
[iquote('0:SSi:5060.2,5060.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,63.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(5072,plain,
( ~ ssList(u)
| equal(app(skaf47(u,nil),skaf48(nil,u)),u) ),
inference(mrr,[status(thm)],[5071,70]),
[iquote('0:MRR:5071.1,70.1')] ).
cnf(6269,plain,
( ~ ssList(cons(u,v))
| ~ ssList(v)
| equal(cons(u,v),nil)
| equal(skaf83(cons(u,v)),u) ),
inference(spr,[status(thm),theory(equality)],[2214,687]),
[iquote('1:SpR:2214.2,687.1')] ).
cnf(6291,plain,
( ~ ssList(u)
| equal(cons(v,u),nil)
| equal(skaf83(cons(v,u)),v) ),
inference(ssi,[status(thm)],[6269,684]),
[iquote('1:SSi:6269.0,684.1')] ).
cnf(6292,plain,
( ~ ssList(u)
| equal(skaf83(cons(v,u)),v) ),
inference(mrr,[status(thm)],[6291,686]),
[iquote('1:MRR:6291.1,686.1')] ).
cnf(6514,plain,
( ~ ssList(u)
| ~ singletonP(u)
| ~ ssList(nil)
| equal(skaf44(u),skaf83(u)) ),
inference(spr,[status(thm),theory(equality)],[115,6292]),
[iquote('1:SpR:115.2,6292.1')] ).
cnf(6517,plain,
( ~ ssList(u)
| ~ singletonP(u)
| equal(skaf44(u),skaf83(u)) ),
inference(ssi,[status(thm)],[6514,22,21,20,19,18,17,16,15]),
[iquote('1:SSi:6514.2,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(6518,plain,
( ~ ssList(u)
| ~ singletonP(u)
| equal(cons(skaf83(u),nil),u) ),
inference(rew,[status(thm),theory(equality)],[6517,115]),
[iquote('1:Rew:6517.2,115.2')] ).
cnf(6926,plain,
( ~ ssList(u)
| ~ ssList(u)
| ~ ssList(cons(v,nil))
| rearsegP(cons(v,u),u) ),
inference(spr,[status(thm),theory(equality)],[690,3622]),
[iquote('1:SpR:690.1,3622.2')] ).
cnf(6951,plain,
( ~ ssList(u)
| ~ ssList(cons(v,nil))
| rearsegP(cons(v,u),u) ),
inference(obv,[status(thm),theory(equality)],[6926]),
[iquote('1:Obv:6926.0')] ).
cnf(6952,plain,
( ~ ssList(u)
| rearsegP(cons(v,u),u) ),
inference(ssi,[status(thm)],[6951,684,22,21,20,19,18,17,16,15,565,566,567,568,569,570,571,2057]),
[iquote('1:SSi:6951.1,684.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,565.0,566.0,567.0,568.0,569.0,570.0,571.0,2057.1')] ).
cnf(7295,plain,
( ~ ssList(u)
| ~ ssList(cons(v,u))
| ~ ssList(u)
| ~ rearsegP(u,cons(v,u))
| equal(cons(v,u),u) ),
inference(res,[status(thm),theory(equality)],[6952,142]),
[iquote('1:Res:6952.1,142.2')] ).
cnf(7298,plain,
( ~ ssList(cons(u,v))
| ~ ssList(v)
| ~ rearsegP(v,cons(u,v))
| equal(cons(u,v),v) ),
inference(obv,[status(thm),theory(equality)],[7295]),
[iquote('1:Obv:7295.0')] ).
cnf(7299,plain,
( ~ ssList(u)
| ~ rearsegP(u,cons(v,u))
| equal(cons(v,u),u) ),
inference(ssi,[status(thm)],[7298,684]),
[iquote('1:SSi:7298.0,684.1')] ).
cnf(7300,plain,
( ~ ssList(u)
| ~ rearsegP(u,cons(v,u)) ),
inference(mrr,[status(thm)],[7299,685]),
[iquote('1:MRR:7299.2,685.1')] ).
cnf(7327,plain,
( ~ ssList(u)
| ~ singletonP(u)
| ~ ssList(nil)
| ~ rearsegP(nil,u) ),
inference(spl,[status(thm),theory(equality)],[6518,7300]),
[iquote('1:SpL:6518.2,7300.1')] ).
cnf(7334,plain,
( ~ ssList(u)
| ~ singletonP(u)
| ~ rearsegP(nil,u) ),
inference(ssi,[status(thm)],[7327,22,21,20,19,18,17,16,15]),
[iquote('1:SSi:7327.2,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7405,plain,
( ~ ssList(u)
| ~ ssList(skaf47(u,nil))
| ~ ssList(skaf48(nil,u))
| frontsegP(u,skaf47(u,nil)) ),
inference(spr,[status(thm),theory(equality)],[5072,3680]),
[iquote('0:SpR:5072.1,3680.2')] ).
cnf(7408,plain,
( ~ ssList(u)
| ~ ssList(skaf48(nil,u))
| ~ ssList(skaf47(u,nil))
| rearsegP(u,skaf48(nil,u)) ),
inference(spr,[status(thm),theory(equality)],[5072,3622]),
[iquote('0:SpR:5072.1,3622.2')] ).
cnf(7421,plain,
( ~ ssList(u)
| frontsegP(u,skaf47(u,nil)) ),
inference(ssi,[status(thm)],[7405,62,22,21,20,19,18,17,16,15,63]),
[iquote('0:SSi:7405.2,7405.1,62.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,63.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7422,plain,
( ~ ssList(u)
| rearsegP(u,skaf48(nil,u)) ),
inference(ssi,[status(thm)],[7408,63,22,21,20,19,18,17,16,15,62]),
[iquote('0:SSi:7408.2,7408.1,63.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,62.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7553,plain,
( ~ ssList(nil)
| ~ ssList(skaf47(nil,nil))
| equal(skaf47(nil,nil),nil) ),
inference(res,[status(thm),theory(equality)],[7421,98]),
[iquote('0:Res:7421.1,98.1')] ).
cnf(7556,plain,
equal(skaf47(nil,nil),nil),
inference(ssi,[status(thm)],[7553,63,22,21,20,19,18,17,16,15]),
[iquote('0:SSi:7553.1,7553.0,63.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7564,plain,
( ~ ssList(nil)
| equal(app(nil,skaf48(nil,nil)),nil) ),
inference(spr,[status(thm),theory(equality)],[7556,5072]),
[iquote('0:SpR:7556.0,5072.1')] ).
cnf(7567,plain,
equal(app(nil,skaf48(nil,nil)),nil),
inference(ssi,[status(thm)],[7564,22,21,20,19,18,17,16,15]),
[iquote('0:SSi:7564.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7570,plain,
( ~ ssList(skaf48(nil,nil))
| equal(skaf48(nil,nil),nil) ),
inference(spr,[status(thm),theory(equality)],[7567,88]),
[iquote('0:SpR:7567.0,88.1')] ).
cnf(7593,plain,
equal(skaf48(nil,nil),nil),
inference(ssi,[status(thm)],[7570,62,22,21,20,19,18,17,16,15]),
[iquote('0:SSi:7570.0,62.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7901,plain,
( ~ ssList(nil)
| ~ ssList(skaf48(nil,nil))
| ~ singletonP(skaf48(nil,nil)) ),
inference(res,[status(thm),theory(equality)],[7422,7334]),
[iquote('1:Res:7422.1,7334.2')] ).
cnf(7906,plain,
~ singletonP(skaf48(nil,nil)),
inference(ssi,[status(thm)],[7901,62,22,21,20,19,18,17,16,15]),
[iquote('1:SSi:7901.1,7901.0,62.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(7940,plain,
( ~ ssList(skaf48(nil,nil))
| ~ equal(cons(u,nil),skaf48(nil,nil)) ),
inference(sor,[status(thm)],[7906,689]),
[iquote('1:SoR:7906.0,689.2')] ).
cnf(7945,plain,
( ~ ssList(skaf48(nil,nil))
| ~ equal(cons(u,nil),nil) ),
inference(rew,[status(thm),theory(equality)],[7593,7940]),
[iquote('1:Rew:7593.0,7940.1')] ).
cnf(7946,plain,
~ equal(cons(u,nil),nil),
inference(ssi,[status(thm)],[7945,62,22,21,20,19,18,17,16,15]),
[iquote('1:SSi:7945.0,62.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(14740,plain,
( equal(cons(u,nil),nil)
| equal(skaf83(cons(u,nil)),u) ),
inference(ssi,[status(thm)],[2900,684,22,21,20,19,18,17,16,15,565,566,567,568,569,570,571,2057]),
[iquote('1:SSi:2900.0,684.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,565.0,566.0,567.0,568.0,569.0,570.0,571.0,2057.1')] ).
cnf(14741,plain,
equal(skaf83(cons(u,nil)),u),
inference(mrr,[status(thm)],[14740,7946]),
[iquote('1:MRR:14740.0,7946.0')] ).
cnf(15150,plain,
( ~ ssList(cons(u,nil))
| equal(cons(u,nil),nil)
| equal(cons(u,skaf82(cons(u,nil))),cons(u,nil)) ),
inference(spr,[status(thm),theory(equality)],[14741,123]),
[iquote('1:SpR:14741.0,123.2')] ).
cnf(15164,plain,
( equal(cons(u,nil),nil)
| equal(cons(u,skaf82(cons(u,nil))),cons(u,nil)) ),
inference(ssi,[status(thm)],[15150,684,22,21,20,19,18,17,16,15,565,566,567,568,569,570,571,2057]),
[iquote('1:SSi:15150.0,684.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,565.0,566.0,567.0,568.0,569.0,570.0,571.0,2057.1')] ).
cnf(15165,plain,
equal(cons(u,skaf82(cons(u,nil))),cons(u,nil)),
inference(mrr,[status(thm)],[15164,7946]),
[iquote('1:MRR:15164.0,7946.0')] ).
cnf(18373,plain,
( ~ ssList(skaf82(cons(u,nil)))
| ssList(cons(u,nil)) ),
inference(spr,[status(thm),theory(equality)],[15165,684]),
[iquote('1:SpR:15165.0,684.1')] ).
cnf(18432,plain,
ssList(cons(u,nil)),
inference(ssi,[status(thm)],[18373,27,684,22,21,20,19,18,17,16,15,565,566,567,568,569,570,571,2057]),
[iquote('1:SSi:18373.0,27.0,684.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,565.0,566.0,567.0,568.0,569.0,570.0,571.1,2057.0')] ).
cnf(34782,plain,
( ~ ssList(u)
| ~ ssList(sk1)
| ~ ssList(v)
| ~ ssList(cons(sk5,nil))
| ~ equal(app(v,sk2),u)
| segmentP(u,sk1) ),
inference(spl,[status(thm),theory(equality)],[208,212]),
[iquote('0:SpL:208.0,212.4')] ).
cnf(39708,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,sk2),u)
| segmentP(u,sk1) ),
inference(ssi,[status(thm)],[34782,565,566,567,568,569,570,571,2057,18432,1]),
[iquote('1:SSi:34782.3,34782.1,565.0,566.0,567.0,568.0,569.0,570.0,571.0,2057.0,18432.0,1.0')] ).
cnf(41236,plain,
( ~ ssList(app(u,sk2))
| ~ ssList(u)
| segmentP(app(u,sk2),sk1) ),
inference(eqr,[status(thm),theory(equality)],[39708]),
[iquote('1:EqR:39708.2')] ).
cnf(45347,plain,
( ~ ssList(u)
| segmentP(app(u,sk2),sk1) ),
inference(ssi,[status(thm)],[41236,99,2]),
[iquote('1:SSi:41236.0,99.0,2.2')] ).
cnf(47544,plain,
( ~ ssList(nil)
| segmentP(sk2,sk1) ),
inference(spr,[status(thm),theory(equality)],[293,45347]),
[iquote('1:SpR:293.0,45347.1')] ).
cnf(47562,plain,
segmentP(sk2,sk1),
inference(ssi,[status(thm)],[47544,22,21,20,19,18,17,16,15]),
[iquote('1:SSi:47544.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0')] ).
cnf(47563,plain,
$false,
inference(mrr,[status(thm)],[47562,206]),
[iquote('1:MRR:47562.0,206.0')] ).
cnf(47577,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[86]),
[iquote('1:Spt:47563.0,86.0,86.2')] ).
cnf(47647,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
inference(mrr,[status(thm)],[193,47577]),
[iquote('1:MRR:193.1,47577.1')] ).
cnf(64956,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssList(cons(w,v))
| ~ ssList(u)
| ssList(cons(w,app(v,u))) ),
inference(spr,[status(thm),theory(equality)],[171,99]),
[iquote('0:SpR:171.3,99.2')] ).
cnf(65004,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[64956]),
[iquote('0:Obv:64956.0')] ).
cnf(65005,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[65004,100]),
[iquote('0:SSi:65004.2,100.2')] ).
cnf(65659,plain,
( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
| ~ ssItem(v)
| ~ ssList(u)
| ~ ssList(w)
| ~ ssList(x) ),
inference(eqr,[status(thm),theory(equality)],[47647]),
[iquote('1:EqR:47647.5')] ).
cnf(65687,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[65659,99,100]),
[iquote('1:SSi:65659.0,99.2,99.2,100.2,100.2')] ).
cnf(65688,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[65005,65687]),
[iquote('1:MRR:65005.3,65687.1')] ).
cnf(65691,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[65688]),
[iquote('1:Con:65688.2')] ).
cnf(65693,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[350,65691]),
[iquote('1:MRR:350.1,65691.0')] ).
cnf(65695,plain,
$false,
inference(unc,[status(thm)],[65693,26]),
[iquote('1:UnC:65693.0,26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC355-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 11 22:55:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 56.08/56.27
% 56.08/56.27 SPASS V 3.9
% 56.08/56.27 SPASS beiseite: Proof found.
% 56.08/56.27 % SZS status Theorem
% 56.08/56.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.08/56.27 SPASS derived 42578 clauses, backtracked 21076 clauses, performed 178 splits and kept 28351 clauses.
% 56.08/56.27 SPASS allocated 120641 KBytes.
% 56.08/56.27 SPASS spent 0:0:55.84 on the problem.
% 56.08/56.27 0:00:00.04 for the input.
% 56.08/56.27 0:00:00.00 for the FLOTTER CNF translation.
% 56.08/56.27 0:00:00.66 for inferences.
% 56.08/56.27 0:00:02.27 for the backtracking.
% 56.08/56.27 0:0:52.20 for the reduction.
% 56.08/56.27
% 56.08/56.27
% 56.08/56.27 Here is a proof with depth 6, length 142 :
% 56.08/56.27 % SZS output start Refutation
% See solution above
% 73.66/73.85 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_13 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause48 clause49 clause56 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause84 clause85 clause86 clause97 clause98 clause99 clause101 clause109 clause116 clause120 clause123 clause128 clause143 clause144 clause149 clause157 clause168 clause173 clause179
% 73.66/73.85
%------------------------------------------------------------------------------