TSTP Solution File: SWC211-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC211-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:02:30 EDT 2022
% Result : Unsatisfiable 4.82s 5.02s
% Output : Refutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of clauses : 83 ( 34 unt; 6 nHn; 83 RR)
% Number of literals : 191 ( 0 equ; 119 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 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('SWC211-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC211-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC211-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC211-1.p',unknown),
[] ).
cnf(7,axiom,
neq(sk2,nil),
file('SWC211-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(app(cons(u,nil),v),sk4)
| equal(app(v,cons(u,nil)),sk3) ),
file('SWC211-1.p',unknown),
[] ).
cnf(9,axiom,
~ neq(sk1,nil),
file('SWC211-1.p',unknown),
[] ).
cnf(23,axiom,
ssList(skaf82(u)),
file('SWC211-1.p',unknown),
[] ).
cnf(57,axiom,
ssItem(skaf44(u)),
file('SWC211-1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC211-1.p',unknown),
[] ).
cnf(95,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(96,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(109,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),u) ),
file('SWC211-1.p',unknown),
[] ).
cnf(112,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| equal(u,v)
| neq(u,v) ),
file('SWC211-1.p',unknown),
[] ).
cnf(119,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC211-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC211-1.p',unknown),
[] ).
cnf(127,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ neq(u,v)
| ~ equal(u,v) ),
file('SWC211-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),nil)
| equal(nil,v) ),
file('SWC211-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC211-1.p',unknown),
[] ).
cnf(167,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC211-1.p',unknown),
[] ).
cnf(189,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('SWC211-1.p',unknown),
[] ).
cnf(199,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),sk2)
| equal(app(u,cons(v,nil)),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,8,130,5]),
[iquote('0:Rew:6.0,8.3,130.2,8.2,5.0,8.2')] ).
cnf(262,plain,
( equal(nil,sk2)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(res,[status(thm),theory(equality)],[2,119]),
[iquote('0:Res:2.0,119.0')] ).
cnf(342,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,96]),
[iquote('0:Res:2.0,96.1')] ).
cnf(511,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk1),sk1) ),
inference(res,[status(thm),theory(equality)],[1,109]),
[iquote('0:Res:1.0,109.1')] ).
cnf(514,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,96]),
[iquote('0:Res:1.0,96.1')] ).
cnf(557,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[82]),
[iquote('1:Spt:82.1')] ).
cnf(560,plain,
ssList(cons(u,sk1)),
inference(mrr,[status(thm)],[514,557]),
[iquote('1:MRR:514.0,557.0')] ).
cnf(563,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[80,557]),
[iquote('1:MRR:80.0,557.0')] ).
cnf(564,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[79,557]),
[iquote('1:MRR:79.0,557.0')] ).
cnf(565,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[78,557]),
[iquote('1:MRR:78.0,557.0')] ).
cnf(566,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[77,557]),
[iquote('1:MRR:77.0,557.0')] ).
cnf(567,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[76,557]),
[iquote('1:MRR:76.0,557.0')] ).
cnf(568,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[75,557]),
[iquote('1:MRR:75.0,557.0')] ).
cnf(569,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[74,557]),
[iquote('1:MRR:74.0,557.0')] ).
cnf(571,plain,
~ equal(cons(u,sk1),sk1),
inference(mrr,[status(thm)],[511,557]),
[iquote('1:MRR:511.0,557.0')] ).
cnf(587,plain,
( equal(u,v)
| neq(u,v) ),
inference(mrr,[status(thm)],[112,557]),
[iquote('1:MRR:112.1,112.0,557.0')] ).
cnf(597,plain,
( ~ neq(u,v)
| ~ equal(u,v) ),
inference(mrr,[status(thm)],[127,557]),
[iquote('1:MRR:127.1,127.0,557.0')] ).
cnf(688,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[126,557]),
[iquote('1:MRR:126.1,557.0')] ).
cnf(694,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk2)
| equal(app(u,cons(v,nil)),sk1) ),
inference(mrr,[status(thm)],[199,557]),
[iquote('1:MRR:199.1,557.0')] ).
cnf(1781,plain,
equal(nil,sk1),
inference(res,[status(thm),theory(equality)],[587,9]),
[iquote('1:Res:587.1,9.0')] ).
cnf(1792,plain,
neq(sk2,sk1),
inference(rew,[status(thm),theory(equality)],[1781,7]),
[iquote('1:Rew:1781.0,7.0')] ).
cnf(1801,plain,
equalelemsP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,569]),
[iquote('1:Rew:1781.0,569.0')] ).
cnf(1802,plain,
duplicatefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,568]),
[iquote('1:Rew:1781.0,568.0')] ).
cnf(1803,plain,
strictorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,567]),
[iquote('1:Rew:1781.0,567.0')] ).
cnf(1804,plain,
totalorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,566]),
[iquote('1:Rew:1781.0,566.0')] ).
cnf(1805,plain,
strictorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,565]),
[iquote('1:Rew:1781.0,565.0')] ).
cnf(1806,plain,
totalorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,564]),
[iquote('1:Rew:1781.0,564.0')] ).
cnf(1807,plain,
cyclefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1781,563]),
[iquote('1:Rew:1781.0,563.0')] ).
cnf(1852,plain,
( ~ ssList(u)
| ~ equal(cons(v,sk1),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[1781,688]),
[iquote('1:Rew:1781.0,688.1')] ).
cnf(1854,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk2)
| equal(app(u,cons(v,sk1)),sk1) ),
inference(rew,[status(thm),theory(equality)],[1781,694]),
[iquote('1:Rew:1781.0,694.2')] ).
cnf(1856,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),sk1)
| equal(nil,v) ),
inference(rew,[status(thm),theory(equality)],[1781,129]),
[iquote('1:Rew:1781.0,129.2')] ).
cnf(1914,plain,
( equal(sk2,sk1)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(rew,[status(thm),theory(equality)],[1781,262]),
[iquote('1:Rew:1781.0,262.0')] ).
cnf(1939,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(u,v),sk1)
| equal(sk1,v) ),
inference(rew,[status(thm),theory(equality)],[1781,1856]),
[iquote('1:Rew:1781.0,1856.3')] ).
cnf(2219,plain,
~ equal(sk2,sk1),
inference(res,[status(thm),theory(equality)],[1792,597]),
[iquote('1:Res:1792.0,597.0')] ).
cnf(2390,plain,
( ~ ssList(cons(u,sk1))
| singletonP(cons(u,sk1)) ),
inference(eqr,[status(thm),theory(equality)],[1852]),
[iquote('1:EqR:1852.1')] ).
cnf(2391,plain,
singletonP(cons(u,sk1)),
inference(ssi,[status(thm)],[2390,560,1801,1802,1803,1804,1805,1806,1807]),
[iquote('1:SSi:2390.0,560.0,1801.0,1802.0,1803.0,1804.0,1805.0,1806.0,1807.0')] ).
cnf(3036,plain,
( ~ ssList(u)
| ~ ssList(u)
| ~ ssList(cons(v,sk1))
| ~ equal(cons(v,u),sk2)
| ~ equal(sk1,sk1)
| equal(cons(v,sk1),sk1) ),
inference(spl,[status(thm),theory(equality)],[1854,1939]),
[iquote('1:SpL:1854.2,1939.2')] ).
cnf(3054,plain,
( ~ ssList(u)
| ~ ssList(cons(v,sk1))
| ~ equal(cons(v,u),sk2)
| equal(cons(v,sk1),sk1) ),
inference(obv,[status(thm),theory(equality)],[3036]),
[iquote('1:Obv:3036.4')] ).
cnf(3055,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk2)
| equal(cons(v,sk1),sk1) ),
inference(ssi,[status(thm)],[3054,560,1801,1802,1803,1804,1805,1806,1807,2391]),
[iquote('1:SSi:3054.1,560.0,1801.0,1802.0,1803.0,1804.0,1805.0,1806.0,1807.0,2391.0')] ).
cnf(3056,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk2) ),
inference(mrr,[status(thm)],[3055,571]),
[iquote('1:MRR:3055.2,571.0')] ).
cnf(3148,plain,
equal(cons(skaf83(sk2),skaf82(sk2)),sk2),
inference(mrr,[status(thm)],[1914,2219]),
[iquote('1:MRR:1914.0,2219.0')] ).
cnf(3276,plain,
( ~ ssList(skaf82(sk2))
| ~ equal(sk2,sk2) ),
inference(spl,[status(thm),theory(equality)],[3148,3056]),
[iquote('1:SpL:3148.0,3056.1')] ).
cnf(3410,plain,
~ ssList(skaf82(sk2)),
inference(obv,[status(thm),theory(equality)],[3276]),
[iquote('1:Obv:3276.1')] ).
cnf(3411,plain,
$false,
inference(ssi,[status(thm)],[3410,23,2]),
[iquote('1:SSi:3410.0,23.0,2.0')] ).
cnf(3437,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[82]),
[iquote('1:Spt:3411.0,82.0,82.2')] ).
cnf(3444,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)],[189,3437]),
[iquote('1:MRR:189.1,3437.1')] ).
cnf(12317,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)],[167,95]),
[iquote('0:SpR:167.3,95.2')] ).
cnf(12358,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[12317]),
[iquote('0:Obv:12317.0')] ).
cnf(12359,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[12358,96]),
[iquote('0:SSi:12358.2,96.2')] ).
cnf(14825,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)],[3444]),
[iquote('1:EqR:3444.5')] ).
cnf(14853,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[14825,95,96]),
[iquote('1:SSi:14825.0,95.2,95.2,96.2,96.2')] ).
cnf(14854,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[12359,14853]),
[iquote('1:MRR:12359.3,14853.1')] ).
cnf(14857,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[14854]),
[iquote('1:Con:14854.2')] ).
cnf(14859,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[342,14857]),
[iquote('1:MRR:342.1,14857.0')] ).
cnf(14861,plain,
$false,
inference(unc,[status(thm)],[14859,57]),
[iquote('1:UnC:14859.0,57.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC211-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 06:29:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.82/5.02
% 4.82/5.02 SPASS V 3.9
% 4.82/5.02 SPASS beiseite: Proof found.
% 4.82/5.02 % SZS status Theorem
% 4.82/5.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.82/5.02 SPASS derived 10031 clauses, backtracked 4666 clauses, performed 101 splits and kept 9079 clauses.
% 4.82/5.02 SPASS allocated 86480 KBytes.
% 4.82/5.02 SPASS spent 0:00:04.00 on the problem.
% 4.82/5.02 0:00:00.04 for the input.
% 4.82/5.02 0:00:00.00 for the FLOTTER CNF translation.
% 4.82/5.02 0:00:00.07 for inferences.
% 4.82/5.02 0:00:00.08 for the backtracking.
% 4.82/5.02 0:00:03.59 for the reduction.
% 4.82/5.02
% 4.82/5.02
% 4.82/5.02 Here is a proof with depth 2, length 83 :
% 4.82/5.02 % SZS output start Refutation
% See solution above
% 4.82/5.02 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 clause13 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause85 clause86 clause99 clause102 clause109 clause116 clause117 clause119 clause120 clause157 clause179
% 4.82/5.02
%------------------------------------------------------------------------------