TSTP Solution File: SWC090+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC090+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 22:01:38 EDT 2022
% Result : Theorem 30.86s 31.09s
% Output : Refutation 30.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of clauses : 80 ( 42 unt; 7 nHn; 80 RR)
% Number of literals : 172 ( 0 equ; 96 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc9),
file('SWC090+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc8),
file('SWC090+1.p',unknown),
[] ).
cnf(3,axiom,
ssList(skc7),
file('SWC090+1.p',unknown),
[] ).
cnf(4,axiom,
ssList(skc6),
file('SWC090+1.p',unknown),
[] ).
cnf(7,axiom,
ssList(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(8,axiom,
cyclefreeP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(11,axiom,
totalorderedP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(12,axiom,
strictorderedP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(13,axiom,
duplicatefreeP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC090+1.p',unknown),
[] ).
cnf(15,axiom,
neq(skc7,nil),
file('SWC090+1.p',unknown),
[] ).
cnf(61,axiom,
equal(app(skc8,skc9),skc7),
file('SWC090+1.p',unknown),
[] ).
cnf(62,axiom,
equal(app(skc9,skc8),skc6),
file('SWC090+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ ssList(u)
| segmentP(u,u) ),
file('SWC090+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC090+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC090+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC090+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC090+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC090+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ segmentP(skc6,u)
| ~ segmentP(skc7,u) ),
file('SWC090+1.p',unknown),
[] ).
cnf(132,axiom,
( ~ ssList(u)
| ~ ssList(v)
| equal(nil,v)
| equal(hd(app(v,u)),hd(v)) ),
file('SWC090+1.p',unknown),
[] ).
cnf(158,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC090+1.p',unknown),
[] ).
cnf(184,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(app(u,x),v),w)
| segmentP(w,x) ),
file('SWC090+1.p',unknown),
[] ).
cnf(186,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(tl(u),tl(v))
| ~ equal(hd(u),hd(v))
| equal(u,v)
| equal(nil,v)
| equal(nil,u) ),
file('SWC090+1.p',unknown),
[] ).
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)],[158,184]),
[iquote('0:Rew:158.3,184.4')] ).
cnf(243,plain,
( ~ neq(skc6,nil)
| ~ segmentP(skc7,skc6)
| ~ segmentP(skc6,skc6) ),
inference(res,[status(thm),theory(equality)],[4,126]),
[iquote('0:Res:4.0,126.0')] ).
cnf(276,plain,
equal(app(nil,skc6),skc6),
inference(res,[status(thm),theory(equality)],[4,80]),
[iquote('0:Res:4.0,80.0')] ).
cnf(277,plain,
equal(app(skc6,nil),skc6),
inference(res,[status(thm),theory(equality)],[4,81]),
[iquote('0:Res:4.0,81.0')] ).
cnf(282,plain,
segmentP(skc6,skc6),
inference(res,[status(thm),theory(equality)],[4,68]),
[iquote('0:Res:4.0,68.0')] ).
cnf(283,plain,
segmentP(skc6,nil),
inference(res,[status(thm),theory(equality)],[4,69]),
[iquote('0:Res:4.0,69.0')] ).
cnf(324,plain,
( ~ ssList(u)
| ssList(app(u,skc6)) ),
inference(res,[status(thm),theory(equality)],[4,90]),
[iquote('0:Res:4.0,90.1')] ).
cnf(415,plain,
( ~ neq(skc7,nil)
| ~ segmentP(skc7,skc7)
| ~ segmentP(skc6,skc7) ),
inference(res,[status(thm),theory(equality)],[3,126]),
[iquote('0:Res:3.0,126.0')] ).
cnf(449,plain,
equal(app(skc7,nil),skc7),
inference(res,[status(thm),theory(equality)],[3,81]),
[iquote('0:Res:3.0,81.0')] ).
cnf(454,plain,
segmentP(skc7,skc7),
inference(res,[status(thm),theory(equality)],[3,68]),
[iquote('0:Res:3.0,68.0')] ).
cnf(456,plain,
( ~ ssList(u)
| ~ equal(tl(skc7),tl(u))
| ~ equal(hd(skc7),hd(u))
| equal(nil,u)
| equal(skc7,u)
| equal(skc7,nil) ),
inference(res,[status(thm),theory(equality)],[3,186]),
[iquote('0:Res:3.0,186.1')] ).
cnf(544,plain,
( ~ segmentP(skc7,skc6)
| ~ neq(skc6,nil) ),
inference(mrr,[status(thm)],[243,282]),
[iquote('0:MRR:243.2,282.0')] ).
cnf(545,plain,
~ segmentP(skc6,skc7),
inference(mrr,[status(thm)],[415,15,454]),
[iquote('0:MRR:415.0,415.1,15.0,454.0')] ).
cnf(554,plain,
equal(skc7,nil),
inference(spt,[spt(split,[position(s1)])],[456]),
[iquote('1:Spt:456.5')] ).
cnf(666,plain,
~ segmentP(skc6,nil),
inference(rew,[status(thm),theory(equality)],[554,545]),
[iquote('1:Rew:554.0,545.0')] ).
cnf(710,plain,
$false,
inference(mrr,[status(thm)],[666,283]),
[iquote('1:MRR:666.0,283.0')] ).
cnf(830,plain,
~ equal(skc7,nil),
inference(spt,[spt(split,[position(sa)])],[710,554]),
[iquote('1:Spt:710.0,456.5,554.0')] ).
cnf(831,plain,
( ~ ssList(u)
| ~ equal(tl(skc7),tl(u))
| ~ equal(hd(skc7),hd(u))
| equal(nil,u)
| equal(skc7,u) ),
inference(spt,[spt(split,[position(s2)])],[456]),
[iquote('1:Spt:710.0,456.0,456.1,456.2,456.3,456.4')] ).
cnf(2796,plain,
( ~ ssList(skc8)
| ~ ssList(skc9)
| equal(skc9,nil)
| equal(hd(skc9),hd(skc6)) ),
inference(spr,[status(thm),theory(equality)],[62,132]),
[iquote('0:SpR:62.0,132.3')] ).
cnf(2801,plain,
( equal(skc9,nil)
| equal(hd(skc9),hd(skc6)) ),
inference(ssi,[status(thm)],[2796,1,2]),
[iquote('0:SSi:2796.1,2796.0,1.0,2.0')] ).
cnf(4802,plain,
( ~ ssList(u)
| ~ ssList(skc9)
| ~ ssList(skc8)
| equal(app(skc8,app(skc9,u)),app(skc7,u)) ),
inference(spr,[status(thm),theory(equality)],[61,158]),
[iquote('0:SpR:61.0,158.3')] ).
cnf(4816,plain,
( ~ ssList(u)
| equal(app(skc8,app(skc9,u)),app(skc7,u)) ),
inference(ssi,[status(thm)],[4802,2,1]),
[iquote('0:SSi:4802.2,4802.1,2.0,1.0')] ).
cnf(5922,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(5937,plain,
( ~ ssList(skc9)
| ~ ssList(u)
| ~ ssList(skc8)
| ~ ssList(v)
| ~ equal(app(v,skc6),u)
| segmentP(u,skc9) ),
inference(spl,[status(thm),theory(equality)],[62,199]),
[iquote('0:SpL:62.0,199.4')] ).
cnf(5955,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,skc6),u)
| segmentP(u,skc9) ),
inference(ssi,[status(thm)],[5937,2,1]),
[iquote('0:SSi:5937.2,5937.0,2.0,1.0')] ).
cnf(5959,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| segmentP(app(w,app(u,v)),u) ),
inference(ssi,[status(thm)],[5922,90]),
[iquote('0:SSi:5922.1,90.2,90.2')] ).
cnf(8324,plain,
equal(skc9,nil),
inference(spt,[spt(split,[position(s2s1)])],[2801]),
[iquote('2:Spt:2801.0')] ).
cnf(8328,plain,
equal(app(nil,skc8),skc6),
inference(rew,[status(thm),theory(equality)],[8324,62]),
[iquote('2:Rew:8324.0,62.0')] ).
cnf(8329,plain,
equal(app(skc8,nil),skc7),
inference(rew,[status(thm),theory(equality)],[8324,61]),
[iquote('2:Rew:8324.0,61.0')] ).
cnf(8384,plain,
( ~ ssList(skc8)
| equal(skc8,skc6) ),
inference(spr,[status(thm),theory(equality)],[8328,80]),
[iquote('2:SpR:8328.0,80.1')] ).
cnf(8407,plain,
equal(skc8,skc6),
inference(ssi,[status(thm)],[8384,2]),
[iquote('2:SSi:8384.0,2.0')] ).
cnf(8428,plain,
equal(app(skc6,nil),skc7),
inference(rew,[status(thm),theory(equality)],[8407,8329]),
[iquote('2:Rew:8407.0,8329.0')] ).
cnf(8434,plain,
equal(skc7,skc6),
inference(rew,[status(thm),theory(equality)],[277,8428]),
[iquote('2:Rew:277.0,8428.0')] ).
cnf(8451,plain,
neq(skc6,nil),
inference(rew,[status(thm),theory(equality)],[8434,15]),
[iquote('2:Rew:8434.0,15.0')] ).
cnf(8473,plain,
( ~ segmentP(skc6,skc6)
| ~ neq(skc6,nil) ),
inference(rew,[status(thm),theory(equality)],[8434,544]),
[iquote('2:Rew:8434.0,544.0')] ).
cnf(8661,plain,
~ neq(skc6,nil),
inference(mrr,[status(thm)],[8473,282]),
[iquote('2:MRR:8473.0,282.0')] ).
cnf(8662,plain,
$false,
inference(mrr,[status(thm)],[8661,8451]),
[iquote('2:MRR:8661.0,8451.0')] ).
cnf(8783,plain,
~ equal(skc9,nil),
inference(spt,[spt(split,[position(s2sa)])],[8662,8324]),
[iquote('2:Spt:8662.0,2801.0,8324.0')] ).
cnf(8784,plain,
equal(hd(skc9),hd(skc6)),
inference(spt,[spt(split,[position(s2s2)])],[2801]),
[iquote('2:Spt:8662.0,2801.1')] ).
cnf(20924,plain,
( ~ ssList(app(u,skc6))
| ~ ssList(u)
| segmentP(app(u,skc6),skc9) ),
inference(eqr,[status(thm),theory(equality)],[5955]),
[iquote('0:EqR:5955.2')] ).
cnf(20939,plain,
( ~ ssList(u)
| segmentP(app(u,skc6),skc9) ),
inference(ssi,[status(thm)],[20924,324]),
[iquote('0:SSi:20924.0,324.1')] ).
cnf(20956,plain,
( ~ ssList(nil)
| segmentP(skc6,skc9) ),
inference(spr,[status(thm),theory(equality)],[276,20939]),
[iquote('0:SpR:276.0,20939.1')] ).
cnf(20965,plain,
segmentP(skc6,skc9),
inference(ssi,[status(thm)],[20956,14,13,10,9,8,12,11,7]),
[iquote('0:SSi:20956.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(25186,plain,
( ~ ssList(u)
| ~ ssList(skc9)
| ~ ssList(u)
| ~ ssList(skc8)
| segmentP(app(skc7,u),skc9) ),
inference(spr,[status(thm),theory(equality)],[4816,5959]),
[iquote('0:SpR:4816.1,5959.3')] ).
cnf(25223,plain,
( ~ ssList(skc9)
| ~ ssList(u)
| ~ ssList(skc8)
| segmentP(app(skc7,u),skc9) ),
inference(obv,[status(thm),theory(equality)],[25186]),
[iquote('0:Obv:25186.0')] ).
cnf(28675,plain,
( ~ ssList(u)
| segmentP(app(skc7,u),skc9) ),
inference(ssi,[status(thm)],[25223,2,1]),
[iquote('0:SSi:25223.2,25223.0,2.0,1.0')] ).
cnf(31984,plain,
( ~ ssList(nil)
| segmentP(skc7,skc9) ),
inference(spr,[status(thm),theory(equality)],[449,28675]),
[iquote('0:SpR:449.0,28675.1')] ).
cnf(31996,plain,
segmentP(skc7,skc9),
inference(ssi,[status(thm)],[31984,14,13,10,9,8,12,11,7]),
[iquote('0:SSi:31984.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(32006,plain,
( ~ ssList(skc9)
| ~ neq(skc9,nil)
| ~ segmentP(skc6,skc9) ),
inference(res,[status(thm),theory(equality)],[31996,126]),
[iquote('0:Res:31996.0,126.3')] ).
cnf(32150,plain,
( ~ neq(skc9,nil)
| ~ segmentP(skc6,skc9) ),
inference(ssi,[status(thm)],[32006,1]),
[iquote('0:SSi:32006.0,1.0')] ).
cnf(32151,plain,
~ neq(skc9,nil),
inference(mrr,[status(thm)],[32150,20965]),
[iquote('0:MRR:32150.1,20965.0')] ).
cnf(32394,plain,
( ~ ssList(nil)
| ~ ssList(skc9)
| equal(skc9,nil) ),
inference(res,[status(thm),theory(equality)],[106,32151]),
[iquote('0:Res:106.2,32151.0')] ).
cnf(32396,plain,
equal(skc9,nil),
inference(ssi,[status(thm)],[32394,1,14,13,10,9,8,12,11,7]),
[iquote('0:SSi:32394.1,32394.0,1.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(32397,plain,
$false,
inference(mrr,[status(thm)],[32396,8783]),
[iquote('2:MRR:32396.0,8783.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC090+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Sat Jun 11 22:25:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 30.86/31.09
% 30.86/31.09 SPASS V 3.9
% 30.86/31.09 SPASS beiseite: Proof found.
% 30.86/31.09 % SZS status Theorem
% 30.86/31.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.86/31.09 SPASS derived 20149 clauses, backtracked 4856 clauses, performed 46 splits and kept 10853 clauses.
% 30.86/31.09 SPASS allocated 127790 KBytes.
% 30.86/31.09 SPASS spent 0:0:26.68 on the problem.
% 30.86/31.09 0:00:00.04 for the input.
% 30.86/31.09 0:00:00.07 for the FLOTTER CNF translation.
% 30.86/31.09 0:00:00.33 for inferences.
% 30.86/31.09 0:00:00.98 for the backtracking.
% 30.86/31.09 0:0:24.91 for the reduction.
% 30.86/31.09
% 30.86/31.09
% 30.86/31.09 Here is a proof with depth 5, length 80 :
% 30.86/31.09 % SZS output start Refutation
% See solution above
% 30.86/31.09 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax57 ax28 ax84 ax26 ax15 ax85 ax82 ax7 ax77
% 30.86/31.09
%------------------------------------------------------------------------------