TSTP Solution File: SWC031-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC031-1 : 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 22:01:13 EDT 2022
% Result : Unsatisfiable 4.52s 4.74s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of clauses : 93 ( 27 unt; 8 nHn; 93 RR)
% Number of literals : 215 ( 0 equ; 134 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 : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
ssList(sk3),
file('SWC031-1.p',unknown),
[] ).
cnf(4,axiom,
ssList(sk4),
file('SWC031-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk2,sk4),
file('SWC031-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk1,sk3),
file('SWC031-1.p',unknown),
[] ).
cnf(7,axiom,
frontsegP(sk4,sk3),
file('SWC031-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssList(u)
| ~ totalorderedP(u)
| ~ frontsegP(sk4,u)
| ~ segmentP(u,sk3)
| ~ neq(sk3,u) ),
file('SWC031-1.p',unknown),
[] ).
cnf(10,axiom,
( equal(nil,sk2)
| equal(nil,sk1) ),
file('SWC031-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(nil,sk1)
| ~ equal(nil,sk2) ),
file('SWC031-1.p',unknown),
[] ).
cnf(25,axiom,
ssItem(skaf83(u)),
file('SWC031-1.p',unknown),
[] ).
cnf(26,axiom,
ssList(skaf82(u)),
file('SWC031-1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC031-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC031-1.p',unknown),
[] ).
cnf(97,axiom,
( ~ ssList(u)
| ~ frontsegP(nil,u)
| equal(nil,u) ),
file('SWC031-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(111,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,v),nil) ),
file('SWC031-1.p',unknown),
[] ).
cnf(115,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| equal(u,v)
| neq(u,v) ),
file('SWC031-1.p',unknown),
[] ).
cnf(122,axiom,
( ~ ssList(u)
| equal(cons(skaf83(u),skaf82(u)),u)
| equal(nil,u) ),
file('SWC031-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,nil),v)
| singletonP(v) ),
file('SWC031-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(app(cons(u,nil),v),cons(u,v)) ),
file('SWC031-1.p',unknown),
[] ).
cnf(157,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,w),u)
| frontsegP(u,v) ),
file('SWC031-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC031-1.p',unknown),
[] ).
cnf(192,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('SWC031-1.p',unknown),
[] ).
cnf(201,plain,
( equal(nil,sk4)
| equal(nil,sk3) ),
inference(rew,[status(thm),theory(equality)],[6,10,5]),
[iquote('0:Rew:6.0,10.1,5.0,10.0')] ).
cnf(202,plain,
( ~ equal(nil,sk3)
| ~ equal(nil,sk4) ),
inference(rew,[status(thm),theory(equality)],[5,13,6]),
[iquote('0:Rew:5.0,13.1,6.0,13.0')] ).
cnf(269,plain,
( equal(cons(skaf83(sk4),skaf82(sk4)),sk4)
| equal(nil,sk4) ),
inference(res,[status(thm),theory(equality)],[4,122]),
[iquote('0:Res:4.0,122.0')] ).
cnf(348,plain,
( ~ ssItem(u)
| ssList(cons(u,sk4)) ),
inference(res,[status(thm),theory(equality)],[4,99]),
[iquote('0:Res:4.0,99.1')] ).
cnf(456,plain,
( ~ frontsegP(nil,sk3)
| equal(nil,sk3) ),
inference(res,[status(thm),theory(equality)],[3,97]),
[iquote('0:Res:3.0,97.0')] ).
cnf(516,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk3),nil) ),
inference(res,[status(thm),theory(equality)],[3,111]),
[iquote('0:Res:3.0,111.1')] ).
cnf(520,plain,
( ~ ssItem(u)
| ssList(cons(u,sk3)) ),
inference(res,[status(thm),theory(equality)],[3,99]),
[iquote('0:Res:3.0,99.1')] ).
cnf(559,plain,
( ~ frontsegP(sk4,sk3)
| equal(nil,sk3) ),
inference(rew,[status(thm),theory(equality)],[201,456]),
[iquote('0:Rew:201.0,456.0')] ).
cnf(560,plain,
equal(nil,sk3),
inference(mrr,[status(thm)],[559,7]),
[iquote('0:MRR:559.0,7.0')] ).
cnf(572,plain,
( ~ ssList(u)
| segmentP(u,sk3) ),
inference(rew,[status(thm),theory(equality)],[560,69]),
[iquote('0:Rew:560.0,69.1')] ).
cnf(581,plain,
( ~ equal(nil,sk3)
| ~ equal(sk4,sk3) ),
inference(rew,[status(thm),theory(equality)],[560,202]),
[iquote('0:Rew:560.0,202.1')] ).
cnf(586,plain,
( ~ ssItem(u)
| cyclefreeP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,83]),
[iquote('0:Rew:560.0,83.1')] ).
cnf(587,plain,
( ~ ssItem(u)
| totalorderP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,82]),
[iquote('0:Rew:560.0,82.1')] ).
cnf(588,plain,
( ~ ssItem(u)
| strictorderP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,81]),
[iquote('0:Rew:560.0,81.1')] ).
cnf(589,plain,
( ~ ssItem(u)
| totalorderedP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,80]),
[iquote('0:Rew:560.0,80.1')] ).
cnf(590,plain,
( ~ ssItem(u)
| strictorderedP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,79]),
[iquote('0:Rew:560.0,79.1')] ).
cnf(591,plain,
( ~ ssItem(u)
| duplicatefreeP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,78]),
[iquote('0:Rew:560.0,78.1')] ).
cnf(592,plain,
( ~ ssItem(u)
| equalelemsP(cons(u,sk3)) ),
inference(rew,[status(thm),theory(equality)],[560,77]),
[iquote('0:Rew:560.0,77.1')] ).
cnf(593,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,sk3),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[560,129]),
[iquote('0:Rew:560.0,129.2')] ).
cnf(594,plain,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,sk3),u),cons(v,u)) ),
inference(rew,[status(thm),theory(equality)],[560,133]),
[iquote('0:Rew:560.0,133.2')] ).
cnf(631,plain,
( ~ totalorderedP(u)
| ~ ssList(u)
| ~ neq(sk3,u)
| ~ frontsegP(sk4,u) ),
inference(mrr,[status(thm)],[9,572]),
[iquote('0:MRR:9.3,572.1')] ).
cnf(641,plain,
( ~ equal(sk3,sk3)
| ~ equal(sk4,sk3) ),
inference(rew,[status(thm),theory(equality)],[560,581]),
[iquote('0:Rew:560.0,581.0')] ).
cnf(642,plain,
~ equal(sk4,sk3),
inference(obv,[status(thm),theory(equality)],[641]),
[iquote('0:Obv:641.0')] ).
cnf(653,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk3),sk3) ),
inference(rew,[status(thm),theory(equality)],[560,516]),
[iquote('0:Rew:560.0,516.1')] ).
cnf(656,plain,
( equal(cons(skaf83(sk4),skaf82(sk4)),sk4)
| equal(sk4,sk3) ),
inference(rew,[status(thm),theory(equality)],[560,269]),
[iquote('0:Rew:560.0,269.1')] ).
cnf(657,plain,
equal(cons(skaf83(sk4),skaf82(sk4)),sk4),
inference(mrr,[status(thm)],[656,642]),
[iquote('0:MRR:656.1,642.0')] ).
cnf(750,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(753,plain,
equalelemsP(cons(u,sk3)),
inference(mrr,[status(thm)],[592,750]),
[iquote('1:MRR:592.0,750.0')] ).
cnf(754,plain,
duplicatefreeP(cons(u,sk3)),
inference(mrr,[status(thm)],[591,750]),
[iquote('1:MRR:591.0,750.0')] ).
cnf(755,plain,
strictorderedP(cons(u,sk3)),
inference(mrr,[status(thm)],[590,750]),
[iquote('1:MRR:590.0,750.0')] ).
cnf(756,plain,
totalorderedP(cons(u,sk3)),
inference(mrr,[status(thm)],[589,750]),
[iquote('1:MRR:589.0,750.0')] ).
cnf(757,plain,
strictorderP(cons(u,sk3)),
inference(mrr,[status(thm)],[588,750]),
[iquote('1:MRR:588.0,750.0')] ).
cnf(758,plain,
totalorderP(cons(u,sk3)),
inference(mrr,[status(thm)],[587,750]),
[iquote('1:MRR:587.0,750.0')] ).
cnf(759,plain,
cyclefreeP(cons(u,sk3)),
inference(mrr,[status(thm)],[586,750]),
[iquote('1:MRR:586.0,750.0')] ).
cnf(761,plain,
ssList(cons(u,sk3)),
inference(mrr,[status(thm)],[520,750]),
[iquote('1:MRR:520.0,750.0')] ).
cnf(764,plain,
~ equal(cons(u,sk3),sk3),
inference(mrr,[status(thm)],[653,750]),
[iquote('1:MRR:653.0,750.0')] ).
cnf(778,plain,
( equal(u,v)
| neq(u,v) ),
inference(mrr,[status(thm)],[115,750]),
[iquote('1:MRR:115.1,115.0,750.0')] ).
cnf(857,plain,
( ~ ssList(u)
| ~ equal(cons(v,sk3),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[593,750]),
[iquote('1:MRR:593.1,750.0')] ).
cnf(859,plain,
( ~ ssList(u)
| equal(app(cons(v,sk3),u),cons(v,u)) ),
inference(mrr,[status(thm)],[594,750]),
[iquote('1:MRR:594.1,750.0')] ).
cnf(1175,plain,
( ~ ssList(cons(u,sk3))
| singletonP(cons(u,sk3)) ),
inference(eqr,[status(thm),theory(equality)],[857]),
[iquote('1:EqR:857.1')] ).
cnf(1176,plain,
singletonP(cons(u,sk3)),
inference(ssi,[status(thm)],[1175,753,754,755,756,757,758,759,761]),
[iquote('1:SSi:1175.0,753.0,754.0,755.0,756.0,757.0,758.0,759.0,761.0')] ).
cnf(2928,plain,
( ~ ssList(app(u,v))
| ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[157]),
[iquote('0:EqR:157.3')] ).
cnf(2944,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[2928,98]),
[iquote('0:SSi:2928.0,98.2')] ).
cnf(3443,plain,
( ~ ssList(u)
| ~ ssList(cons(v,sk3))
| ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk3)) ),
inference(spr,[status(thm),theory(equality)],[859,2944]),
[iquote('1:SpR:859.1,2944.2')] ).
cnf(3460,plain,
( ~ ssList(cons(u,sk3))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,sk3)) ),
inference(obv,[status(thm),theory(equality)],[3443]),
[iquote('1:Obv:3443.0')] ).
cnf(3461,plain,
( ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk3)) ),
inference(ssi,[status(thm)],[3460,753,754,755,756,757,758,759,761,1176]),
[iquote('1:SSi:3460.0,753.0,754.0,755.0,756.0,757.0,758.0,759.0,761.0,1176.0')] ).
cnf(3737,plain,
( ~ ssList(skaf82(sk4))
| frontsegP(sk4,cons(skaf83(sk4),sk3)) ),
inference(spr,[status(thm),theory(equality)],[657,3461]),
[iquote('1:SpR:657.0,3461.1')] ).
cnf(4831,plain,
frontsegP(sk4,cons(skaf83(sk4),sk3)),
inference(ssi,[status(thm)],[3737,26,4]),
[iquote('1:SSi:3737.0,26.0,4.0')] ).
cnf(5117,plain,
( ~ totalorderedP(cons(skaf83(sk4),sk3))
| ~ ssList(cons(skaf83(sk4),sk3))
| ~ neq(sk3,cons(skaf83(sk4),sk3)) ),
inference(res,[status(thm),theory(equality)],[4831,631]),
[iquote('1:Res:4831.0,631.3')] ).
cnf(5120,plain,
~ neq(sk3,cons(skaf83(sk4),sk3)),
inference(ssi,[status(thm)],[5117,753,754,755,756,757,758,759,761,1176]),
[iquote('1:SSi:5117.1,5117.0,753.0,754.0,755.0,756.0,757.0,758.0,759.0,761.0,1176.0,753.0,754.0,755.0,756.0,757.0,758.0,759.0,761.0,1176.0')] ).
cnf(5205,plain,
equal(cons(skaf83(sk4),sk3),sk3),
inference(res,[status(thm),theory(equality)],[778,5120]),
[iquote('1:Res:778.1,5120.0')] ).
cnf(5206,plain,
$false,
inference(mrr,[status(thm)],[5205,764]),
[iquote('1:MRR:5205.0,764.0')] ).
cnf(5207,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:5206.0,85.0,85.2')] ).
cnf(5219,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)],[192,5207]),
[iquote('1:MRR:192.1,5207.1')] ).
cnf(10249,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)],[170,98]),
[iquote('0:SpR:170.3,98.2')] ).
cnf(10285,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[10249]),
[iquote('0:Obv:10249.0')] ).
cnf(10286,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[10285,99]),
[iquote('0:SSi:10285.2,99.2')] ).
cnf(10876,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)],[5219]),
[iquote('1:EqR:5219.5')] ).
cnf(10905,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[10876,98,99]),
[iquote('1:SSi:10876.0,98.2,98.2,99.2,99.2')] ).
cnf(10906,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[10286,10905]),
[iquote('1:MRR:10286.3,10905.1')] ).
cnf(10909,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[10906]),
[iquote('1:Con:10906.2')] ).
cnf(10911,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[348,10909]),
[iquote('1:MRR:348.1,10909.0')] ).
cnf(10913,plain,
$false,
inference(unc,[status(thm)],[10911,25]),
[iquote('1:UnC:10911.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC031-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 09:47:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.52/4.74
% 4.52/4.74 SPASS V 3.9
% 4.52/4.74 SPASS beiseite: Proof found.
% 4.52/4.74 % SZS status Theorem
% 4.52/4.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.52/4.74 SPASS derived 6742 clauses, backtracked 1549 clauses, performed 44 splits and kept 4714 clauses.
% 4.52/4.74 SPASS allocated 85026 KBytes.
% 4.52/4.74 SPASS spent 0:00:04.00 on the problem.
% 4.52/4.74 0:00:00.04 for the input.
% 4.52/4.74 0:00:00.00 for the FLOTTER CNF translation.
% 4.52/4.74 0:00:00.09 for inferences.
% 4.52/4.74 0:00:00.12 for the backtracking.
% 4.52/4.74 0:00:03.55 for the reduction.
% 4.52/4.74
% 4.52/4.74
% 4.52/4.74 Here is a proof with depth 5, length 93 :
% 4.52/4.74 % SZS output start Refutation
% See solution above
% 4.52/4.74 Formulae used in the proof : co1_3 co1_4 co1_5 co1_6 co1_7 co1_9 co1_10 co1_13 clause12 clause13 clause56 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause84 clause85 clause86 clause98 clause102 clause109 clause116 clause120 clause144 clause157 clause179
% 4.52/4.74
%------------------------------------------------------------------------------