TSTP Solution File: SWC021-1 by SPASS---3.9
View Problem
- 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 : n013.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 22:01:08 EDT 2022
% Result : Unsatisfiable 8.56s 8.73s
% Output : Refutation 8.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of clauses : 92 ( 38 unt; 6 nHn; 92 RR)
% Number of literals : 205 ( 0 equ; 128 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC021-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC021-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC021-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC021-1.p',unknown),
[] ).
cnf(7,axiom,
frontsegP(sk4,sk3),
file('SWC021-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ frontsegP(sk1,u)
| ~ frontsegP(sk2,u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ frontsegP(sk4,u)
| ~ segmentP(u,sk3)
| ~ neq(sk3,u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(nil,sk1)
| ~ equal(nil,sk2) ),
file('SWC021-1.p',unknown),
[] ).
cnf(24,axiom,
ssList(skaf82(u)),
file('SWC021-1.p',unknown),
[] ).
cnf(58,axiom,
ssItem(skaf44(u)),
file('SWC021-1.p',unknown),
[] ).
cnf(67,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC021-1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssList(u)
| frontsegP(u,u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(96,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(97,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(110,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(113,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| equal(u,v)
| neq(u,v) ),
file('SWC021-1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(127,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC021-1.p',unknown),
[] ).
cnf(131,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC021-1.p',unknown),
[] ).
cnf(155,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,w),u)
| frontsegP(u,v) ),
file('SWC021-1.p',unknown),
[] ).
cnf(168,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC021-1.p',unknown),
[] ).
cnf(190,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('SWC021-1.p',unknown),
[] ).
cnf(199,plain,
frontsegP(sk4,sk1),
inference(rew,[status(thm),theory(equality)],[6,7]),
[iquote('0:Rew:6.0,7.0')] ).
cnf(201,plain,
frontsegP(sk2,sk1),
inference(rew,[status(thm),theory(equality)],[5,199]),
[iquote('0:Rew:5.0,199.0')] ).
cnf(202,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ segmentP(u,sk1)
| ~ neq(sk1,u)
| ~ frontsegP(sk2,u) ),
inference(rew,[status(thm),theory(equality)],[6,10,5]),
[iquote('0:Rew:6.0,10.4,6.0,10.3,5.0,10.2')] ).
cnf(267,plain,
( equal(nil,sk2)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(res,[status(thm),theory(equality)],[2,120]),
[iquote('0:Res:2.0,120.0')] ).
cnf(433,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1)
| ~ frontsegP(sk1,sk1) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(469,plain,
frontsegP(sk1,sk1),
inference(res,[status(thm),theory(equality)],[1,72]),
[iquote('0:Res:1.0,72.0')] ).
cnf(516,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk1),sk1) ),
inference(res,[status(thm),theory(equality)],[1,110]),
[iquote('0:Res:1.0,110.1')] ).
cnf(519,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,97]),
[iquote('0:Res:1.0,97.1')] ).
cnf(556,plain,
~ neq(sk1,nil),
inference(mrr,[status(thm)],[433,201,469]),
[iquote('0:MRR:433.1,433.2,201.0,469.0')] ).
cnf(563,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[83]),
[iquote('1:Spt:83.1')] ).
cnf(566,plain,
ssList(cons(u,sk1)),
inference(mrr,[status(thm)],[519,563]),
[iquote('1:MRR:519.0,563.0')] ).
cnf(569,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[81,563]),
[iquote('1:MRR:81.0,563.0')] ).
cnf(570,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[80,563]),
[iquote('1:MRR:80.0,563.0')] ).
cnf(571,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[79,563]),
[iquote('1:MRR:79.0,563.0')] ).
cnf(572,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[78,563]),
[iquote('1:MRR:78.0,563.0')] ).
cnf(573,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[77,563]),
[iquote('1:MRR:77.0,563.0')] ).
cnf(574,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[76,563]),
[iquote('1:MRR:76.0,563.0')] ).
cnf(575,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[75,563]),
[iquote('1:MRR:75.0,563.0')] ).
cnf(577,plain,
~ equal(cons(u,sk1),sk1),
inference(mrr,[status(thm)],[516,563]),
[iquote('1:MRR:516.0,563.0')] ).
cnf(594,plain,
( equal(u,v)
| neq(u,v) ),
inference(mrr,[status(thm)],[113,563]),
[iquote('1:MRR:113.1,113.0,563.0')] ).
cnf(691,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[127,563]),
[iquote('1:MRR:127.1,563.0')] ).
cnf(692,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[131,563]),
[iquote('1:MRR:131.1,563.0')] ).
cnf(1992,plain,
equal(nil,sk1),
inference(res,[status(thm),theory(equality)],[594,556]),
[iquote('1:Res:594.1,556.0')] ).
cnf(2012,plain,
cyclefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,569]),
[iquote('1:Rew:1992.0,569.0')] ).
cnf(2013,plain,
totalorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,570]),
[iquote('1:Rew:1992.0,570.0')] ).
cnf(2014,plain,
strictorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,571]),
[iquote('1:Rew:1992.0,571.0')] ).
cnf(2015,plain,
totalorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,572]),
[iquote('1:Rew:1992.0,572.0')] ).
cnf(2016,plain,
strictorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,573]),
[iquote('1:Rew:1992.0,573.0')] ).
cnf(2017,plain,
duplicatefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,574]),
[iquote('1:Rew:1992.0,574.0')] ).
cnf(2018,plain,
equalelemsP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1992,575]),
[iquote('1:Rew:1992.0,575.0')] ).
cnf(2029,plain,
( ~ ssList(u)
| segmentP(u,sk1) ),
inference(rew,[status(thm),theory(equality)],[1992,67]),
[iquote('1:Rew:1992.0,67.1')] ).
cnf(2062,plain,
( ~ ssList(u)
| ~ equal(cons(v,sk1),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[1992,691]),
[iquote('1:Rew:1992.0,691.1')] ).
cnf(2063,plain,
( ~ ssList(u)
| equal(app(cons(v,sk1),u),cons(v,u)) ),
inference(rew,[status(thm),theory(equality)],[1992,692]),
[iquote('1:Rew:1992.0,692.1')] ).
cnf(2086,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ neq(sk1,u)
| ~ frontsegP(sk2,u) ),
inference(mrr,[status(thm)],[202,2029]),
[iquote('1:MRR:202.2,2029.1')] ).
cnf(2100,plain,
( ~ equal(sk1,sk1)
| ~ equal(sk2,sk1) ),
inference(rew,[status(thm),theory(equality)],[1992,11]),
[iquote('1:Rew:1992.0,11.1,1992.0,11.0')] ).
cnf(2101,plain,
~ equal(sk2,sk1),
inference(obv,[status(thm),theory(equality)],[2100]),
[iquote('1:Obv:2100.0')] ).
cnf(2131,plain,
( equal(sk2,sk1)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(rew,[status(thm),theory(equality)],[1992,267]),
[iquote('1:Rew:1992.0,267.0')] ).
cnf(2132,plain,
equal(cons(skaf83(sk2),skaf82(sk2)),sk2),
inference(mrr,[status(thm)],[2131,2101]),
[iquote('1:MRR:2131.0,2101.0')] ).
cnf(2400,plain,
( ~ ssList(cons(u,sk1))
| singletonP(cons(u,sk1)) ),
inference(eqr,[status(thm),theory(equality)],[2062]),
[iquote('1:EqR:2062.1')] ).
cnf(2401,plain,
singletonP(cons(u,sk1)),
inference(ssi,[status(thm)],[2400,566,2012,2013,2014,2015,2016,2017,2018]),
[iquote('1:SSi:2400.0,566.0,2012.0,2013.0,2014.0,2015.0,2016.0,2017.0,2018.0')] ).
cnf(4297,plain,
( ~ ssList(app(u,v))
| ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[155]),
[iquote('0:EqR:155.3')] ).
cnf(4313,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[4297,96]),
[iquote('0:SSi:4297.0,96.2')] ).
cnf(4628,plain,
( ~ ssList(u)
| ~ ssList(cons(v,sk1))
| ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk1)) ),
inference(spr,[status(thm),theory(equality)],[2063,4313]),
[iquote('1:SpR:2063.1,4313.2')] ).
cnf(4643,plain,
( ~ ssList(cons(u,sk1))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,sk1)) ),
inference(obv,[status(thm),theory(equality)],[4628]),
[iquote('1:Obv:4628.0')] ).
cnf(4644,plain,
( ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk1)) ),
inference(ssi,[status(thm)],[4643,566,2012,2013,2014,2015,2016,2017,2018,2401]),
[iquote('1:SSi:4643.0,566.0,2012.0,2013.0,2014.0,2015.0,2016.0,2017.0,2018.0,2401.0')] ).
cnf(4756,plain,
( ~ ssList(skaf82(sk2))
| frontsegP(sk2,cons(skaf83(sk2),sk1)) ),
inference(spr,[status(thm),theory(equality)],[2132,4644]),
[iquote('1:SpR:2132.0,4644.1')] ).
cnf(5890,plain,
frontsegP(sk2,cons(skaf83(sk2),sk1)),
inference(ssi,[status(thm)],[4756,24,2]),
[iquote('1:SSi:4756.0,24.0,2.0')] ).
cnf(6199,plain,
( ~ strictorderedP(cons(skaf83(sk2),sk1))
| ~ ssList(cons(skaf83(sk2),sk1))
| ~ neq(sk1,cons(skaf83(sk2),sk1)) ),
inference(res,[status(thm),theory(equality)],[5890,2086]),
[iquote('1:Res:5890.0,2086.3')] ).
cnf(6202,plain,
~ neq(sk1,cons(skaf83(sk2),sk1)),
inference(ssi,[status(thm)],[6199,566,2012,2013,2014,2015,2016,2017,2018,2401]),
[iquote('1:SSi:6199.1,6199.0,566.0,2012.0,2013.0,2014.0,2015.0,2016.0,2017.0,2018.0,2401.0,566.0,2012.0,2013.0,2014.0,2015.0,2016.0,2017.0,2018.0,2401.0')] ).
cnf(6238,plain,
equal(cons(skaf83(sk2),sk1),sk1),
inference(res,[status(thm),theory(equality)],[594,6202]),
[iquote('1:Res:594.1,6202.0')] ).
cnf(6239,plain,
$false,
inference(mrr,[status(thm)],[6238,577]),
[iquote('1:MRR:6238.0,577.0')] ).
cnf(6240,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[83]),
[iquote('1:Spt:6239.0,83.0,83.2')] ).
cnf(6255,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)],[190,6240]),
[iquote('1:MRR:190.1,6240.1')] ).
cnf(15627,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)],[168,96]),
[iquote('0:SpR:168.3,96.2')] ).
cnf(15670,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[15627]),
[iquote('0:Obv:15627.0')] ).
cnf(15671,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[15670,97]),
[iquote('0:SSi:15670.2,97.2')] ).
cnf(16999,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)],[6255]),
[iquote('1:EqR:6255.5')] ).
cnf(17028,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[16999,96,97]),
[iquote('1:SSi:16999.0,96.2,96.2,97.2,97.2')] ).
cnf(17029,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[15671,17028]),
[iquote('1:MRR:15671.3,17028.1')] ).
cnf(17032,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[17029]),
[iquote('1:Con:17029.2')] ).
cnf(17034,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[519,17032]),
[iquote('1:MRR:519.1,17032.0')] ).
cnf(17036,plain,
$false,
inference(unc,[status(thm)],[17034,58]),
[iquote('1:UnC:17034.0,58.0')] ).
%------------------------------------------------------------------------------
%----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 : n013.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 21:15:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 8.56/8.73
% 8.56/8.73 SPASS V 3.9
% 8.56/8.73 SPASS beiseite: Proof found.
% 8.56/8.73 % SZS status Theorem
% 8.56/8.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.56/8.73 SPASS derived 11089 clauses, backtracked 5042 clauses, performed 130 splits and kept 10315 clauses.
% 8.56/8.73 SPASS allocated 88652 KBytes.
% 8.56/8.73 SPASS spent 0:00:07.08 on the problem.
% 8.56/8.73 0:00:00.04 for the input.
% 8.56/8.73 0:00:00.00 for the FLOTTER CNF translation.
% 8.56/8.73 0:00:00.13 for inferences.
% 8.56/8.73 0:00:00.21 for the backtracking.
% 8.56/8.73 0:00:06.46 for the reduction.
% 8.56/8.73
% 8.56/8.73
% 8.56/8.73 Here is a proof with depth 5, length 92 :
% 8.56/8.73 % SZS output start Refutation
% See solution above
% 8.56/8.73 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_9 co1_10 co1_11 clause13 clause47 clause56 clause61 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause85 clause86 clause99 clause102 clause109 clause116 clause120 clause144 clause157 clause179
% 8.56/8.73
%------------------------------------------------------------------------------