TSTP Solution File: SWC404+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 22:03:51 EDT 2022
% Result : Theorem 29.50s 29.68s
% Output : Refutation 29.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of clauses : 53 ( 28 unt; 4 nHn; 53 RR)
% Number of literals : 125 ( 0 equ; 79 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssItem(skc11),
file('SWC404+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc10),
file('SWC404+1.p',unknown),
[] ).
cnf(3,axiom,
ssList(skc9),
file('SWC404+1.p',unknown),
[] ).
cnf(5,axiom,
ssList(skc7),
file('SWC404+1.p',unknown),
[] ).
cnf(6,axiom,
strictorderedP(skc7),
file('SWC404+1.p',unknown),
[] ).
cnf(17,axiom,
memberP(skc7,skc11),
file('SWC404+1.p',unknown),
[] ).
cnf(34,axiom,
ssList(skf69(u)),
file('SWC404+1.p',unknown),
[] ).
cnf(35,axiom,
ssList(skf68(u)),
file('SWC404+1.p',unknown),
[] ).
cnf(36,axiom,
ssList(skf67(u)),
file('SWC404+1.p',unknown),
[] ).
cnf(37,axiom,
ssItem(skf66(u)),
file('SWC404+1.p',unknown),
[] ).
cnf(38,axiom,
ssItem(skf65(u)),
file('SWC404+1.p',unknown),
[] ).
cnf(56,axiom,
~ memberP(skc8,skc11),
file('SWC404+1.p',unknown),
[] ).
cnf(72,axiom,
equal(app(app(skc9,skc7),skc10),skc8),
file('SWC404+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ equal(skc7,nil)
| equal(skc8,nil) ),
file('SWC404+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC404+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ leq(skf65(u),skf66(u))
| totalorderedP(u) ),
file('SWC404+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ lt(v,u)
| leq(v,u) ),
file('SWC404+1.p',unknown),
[] ).
cnf(147,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ memberP(v,w)
| memberP(app(v,u),w) ),
file('SWC404+1.p',unknown),
[] ).
cnf(148,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ memberP(u,w)
| memberP(app(v,u),w) ),
file('SWC404+1.p',unknown),
[] ).
cnf(153,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ totalorderedP(cons(v,u))
| leq(v,hd(u))
| equal(nil,u) ),
file('SWC404+1.p',unknown),
[] ).
cnf(175,axiom,
( ~ ssList(u)
| totalorderedP(u)
| equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u) ),
file('SWC404+1.p',unknown),
[] ).
cnf(193,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssItem(y)
| ~ ssItem(z)
| ~ strictorderedP(u)
| ~ equal(app(app(x,cons(z,w)),cons(y,v)),u)
| lt(z,y) ),
file('SWC404+1.p',unknown),
[] ).
cnf(226,plain,
( totalorderedP(skc7)
| equal(app(app(skf67(skc7),cons(skf65(skc7),skf68(skc7))),cons(skf66(skc7),skf69(skc7))),skc7) ),
inference(res,[status(thm),theory(equality)],[5,175]),
[iquote('0:Res:5.0,175.0')] ).
cnf(267,plain,
( ~ leq(skf65(skc7),skf66(skc7))
| totalorderedP(skc7) ),
inference(res,[status(thm),theory(equality)],[5,104]),
[iquote('0:Res:5.0,104.0')] ).
cnf(315,plain,
( ~ ssItem(u)
| ~ totalorderedP(cons(u,skc7))
| leq(u,hd(skc7))
| equal(skc7,nil) ),
inference(res,[status(thm),theory(equality)],[5,153]),
[iquote('0:Res:5.0,153.1')] ).
cnf(333,plain,
( ~ ssList(u)
| ssList(app(u,skc7)) ),
inference(res,[status(thm),theory(equality)],[5,93]),
[iquote('0:Res:5.0,93.1')] ).
cnf(568,plain,
equal(skc7,nil),
inference(spt,[spt(split,[position(s1)])],[315]),
[iquote('1:Spt:315.3')] ).
cnf(575,plain,
( ~ equal(nil,nil)
| equal(skc8,nil) ),
inference(rew,[status(thm),theory(equality)],[568,73]),
[iquote('1:Rew:568.0,73.0')] ).
cnf(680,plain,
memberP(nil,skc11),
inference(rew,[status(thm),theory(equality)],[568,17]),
[iquote('1:Rew:568.0,17.0')] ).
cnf(729,plain,
equal(skc8,nil),
inference(obv,[status(thm),theory(equality)],[575]),
[iquote('1:Obv:575.0')] ).
cnf(839,plain,
~ memberP(nil,skc11),
inference(rew,[status(thm),theory(equality)],[729,56]),
[iquote('1:Rew:729.0,56.0')] ).
cnf(881,plain,
$false,
inference(mrr,[status(thm)],[839,680]),
[iquote('1:MRR:839.0,680.0')] ).
cnf(1081,plain,
~ equal(skc7,nil),
inference(spt,[spt(split,[position(sa)])],[881,568]),
[iquote('1:Spt:881.0,315.3,568.0')] ).
cnf(1082,plain,
( ~ ssItem(u)
| ~ totalorderedP(cons(u,skc7))
| leq(u,hd(skc7)) ),
inference(spt,[spt(split,[position(s2)])],[315]),
[iquote('1:Spt:881.0,315.0,315.1,315.2')] ).
cnf(1904,plain,
totalorderedP(skc7),
inference(spt,[spt(split,[position(s2s1)])],[226]),
[iquote('2:Spt:226.0')] ).
cnf(3650,plain,
( ~ ssList(skc10)
| ~ ssList(app(skc9,skc7))
| ~ ssItem(u)
| ~ memberP(app(skc9,skc7),u)
| memberP(skc8,u) ),
inference(spr,[status(thm),theory(equality)],[72,147]),
[iquote('0:SpR:72.0,147.4')] ).
cnf(3657,plain,
( ~ ssItem(u)
| ~ memberP(app(skc9,skc7),u)
| memberP(skc8,u) ),
inference(ssi,[status(thm)],[3650,333,3,2]),
[iquote('0:SSi:3650.1,3650.0,333.0,3.0,2.1')] ).
cnf(12157,plain,
( ~ ssList(skc7)
| ~ ssList(skc9)
| ~ ssItem(u)
| ~ ssItem(u)
| ~ memberP(skc7,u)
| memberP(skc8,u) ),
inference(res,[status(thm),theory(equality)],[148,3657]),
[iquote('0:Res:148.4,3657.1')] ).
cnf(12159,plain,
( ~ ssList(skc7)
| ~ ssList(skc9)
| ~ ssItem(u)
| ~ memberP(skc7,u)
| memberP(skc8,u) ),
inference(obv,[status(thm),theory(equality)],[12157]),
[iquote('0:Obv:12157.2')] ).
cnf(21177,plain,
( ~ ssItem(u)
| ~ memberP(skc7,u)
| memberP(skc8,u) ),
inference(ssi,[status(thm)],[12159,3,5,6,1904]),
[iquote('2:SSi:12159.1,12159.0,3.0,5.0,6.0,1904.0')] ).
cnf(25421,plain,
( ~ ssItem(skc11)
| ~ memberP(skc7,skc11) ),
inference(res,[status(thm),theory(equality)],[21177,56]),
[iquote('2:Res:21177.2,56.0')] ).
cnf(25422,plain,
~ memberP(skc7,skc11),
inference(ssi,[status(thm)],[25421,1]),
[iquote('2:SSi:25421.0,1.0')] ).
cnf(25423,plain,
$false,
inference(mrr,[status(thm)],[25422,17]),
[iquote('2:MRR:25422.0,17.0')] ).
cnf(25424,plain,
~ totalorderedP(skc7),
inference(spt,[spt(split,[position(s2sa)])],[25423,1904]),
[iquote('2:Spt:25423.0,226.0,1904.0')] ).
cnf(25425,plain,
equal(app(app(skf67(skc7),cons(skf65(skc7),skf68(skc7))),cons(skf66(skc7),skf69(skc7))),skc7),
inference(spt,[spt(split,[position(s2s2)])],[226]),
[iquote('2:Spt:25423.0,226.1')] ).
cnf(25426,plain,
~ leq(skf65(skc7),skf66(skc7)),
inference(mrr,[status(thm)],[267,25424]),
[iquote('2:MRR:267.1,25424.0')] ).
cnf(25547,plain,
( ~ ssList(u)
| ~ ssList(skf69(skc7))
| ~ ssList(skf68(skc7))
| ~ ssList(skf67(skc7))
| ~ ssItem(skf66(skc7))
| ~ ssItem(skf65(skc7))
| ~ strictorderedP(u)
| ~ equal(skc7,u)
| lt(skf65(skc7),skf66(skc7)) ),
inference(spl,[status(thm),theory(equality)],[25425,193]),
[iquote('2:SpL:25425.0,193.7')] ).
cnf(25568,plain,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ equal(skc7,u)
| lt(skf65(skc7),skf66(skc7)) ),
inference(ssi,[status(thm)],[25547,38,5,6,37,36,35,34]),
[iquote('2:SSi:25547.5,25547.4,25547.3,25547.2,25547.1,38.0,5.0,6.0,37.0,5.0,6.0,36.0,5.0,6.0,35.0,5.0,6.0,34.0,5.0,6.0')] ).
cnf(25621,plain,
( ~ ssItem(skf66(skc7))
| ~ ssItem(skf65(skc7))
| ~ lt(skf65(skc7),skf66(skc7)) ),
inference(res,[status(thm),theory(equality)],[120,25426]),
[iquote('2:Res:120.3,25426.0')] ).
cnf(32565,plain,
~ lt(skf65(skc7),skf66(skc7)),
inference(ssi,[status(thm)],[25621,38,5,6,37]),
[iquote('2:SSi:25621.1,25621.0,38.0,5.0,6.0,37.0,5.0,6.0')] ).
cnf(32566,plain,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ equal(skc7,u) ),
inference(mrr,[status(thm)],[25568,32565]),
[iquote('2:MRR:25568.3,32565.0')] ).
cnf(35578,plain,
~ equal(skc7,skc7),
inference(ems,[status(thm)],[32566,5,6]),
[iquote('2:EmS:32566.0,32566.1,5.0,6.0')] ).
cnf(35580,plain,
$false,
inference(obv,[status(thm),theory(equality)],[35578]),
[iquote('2:Obv:35578.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 13:42:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.50/29.68
% 29.50/29.68 SPASS V 3.9
% 29.50/29.68 SPASS beiseite: Proof found.
% 29.50/29.68 % SZS status Theorem
% 29.50/29.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.50/29.68 SPASS derived 24692 clauses, backtracked 6250 clauses, performed 84 splits and kept 13032 clauses.
% 29.50/29.68 SPASS allocated 126238 KBytes.
% 29.50/29.68 SPASS spent 0:0:24.66 on the problem.
% 29.50/29.68 0:00:00.04 for the input.
% 29.50/29.68 0:00:00.06 for the FLOTTER CNF translation.
% 29.50/29.68 0:00:00.30 for inferences.
% 29.50/29.68 0:00:00.52 for the backtracking.
% 29.50/29.68 0:0:23.36 for the reduction.
% 29.50/29.68
% 29.50/29.68
% 29.50/29.68 Here is a proof with depth 4, length 53 :
% 29.50/29.68 % SZS output start Refutation
% See solution above
% 29.50/29.68 Formulae used in the proof : co1 ax11 ax2 ax17 ax26 ax93 ax36 ax67 ax12
% 29.50/29.68
%------------------------------------------------------------------------------