TSTP Solution File: SWC190-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC190-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:02:21 EDT 2022
% Result : Unsatisfiable 27.71s 27.88s
% Output : Refutation 27.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of clauses : 76 ( 34 unt; 1 nHn; 76 RR)
% Number of literals : 174 ( 0 equ; 105 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(sk1,sk3),
file('SWC190-1.p',unknown),
[] ).
cnf(9,axiom,
ssList(sk7),
file('SWC190-1.p',unknown),
[] ).
cnf(10,axiom,
ssList(sk8),
file('SWC190-1.p',unknown),
[] ).
cnf(11,axiom,
equal(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),sk1),
file('SWC190-1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(sk6,sk5),
file('SWC190-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ ssItem(u)
| ~ memberP(sk3,u)
| equal(sk9,u) ),
file('SWC190-1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(17,axiom,
strictorderedP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(18,axiom,
totalorderedP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(19,axiom,
strictorderP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(20,axiom,
totalorderP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(21,axiom,
cyclefreeP(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(22,axiom,
ssList(nil),
file('SWC190-1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skaf44(u)),
file('SWC190-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC190-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC190-1.p',unknown),
[] ).
cnf(134,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC190-1.p',unknown),
[] ).
cnf(163,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(u,v),w),app(u,app(v,w))) ),
file('SWC190-1.p',unknown),
[] ).
cnf(171,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC190-1.p',unknown),
[] ).
cnf(189,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(w,cons(v,x)),u)
| memberP(u,v) ),
file('SWC190-1.p',unknown),
[] ).
cnf(193,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('SWC190-1.p',unknown),
[] ).
cnf(202,plain,
equal(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),sk3),
inference(rew,[status(thm),theory(equality)],[6,11]),
[iquote('0:Rew:6.0,11.0')] ).
cnf(447,plain,
( ~ ssItem(u)
| ssList(cons(u,sk8)) ),
inference(res,[status(thm),theory(equality)],[10,100]),
[iquote('0:Res:10.0,100.1')] ).
cnf(483,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[86]),
[iquote('1:Spt:86.1')] ).
cnf(486,plain,
ssList(cons(u,sk8)),
inference(mrr,[status(thm)],[447,483]),
[iquote('1:MRR:447.0,483.0')] ).
cnf(488,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,483]),
[iquote('1:MRR:84.0,483.0')] ).
cnf(489,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,483]),
[iquote('1:MRR:83.0,483.0')] ).
cnf(490,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,483]),
[iquote('1:MRR:82.0,483.0')] ).
cnf(491,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,483]),
[iquote('1:MRR:81.0,483.0')] ).
cnf(492,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,483]),
[iquote('1:MRR:80.0,483.0')] ).
cnf(493,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[79,483]),
[iquote('1:MRR:79.0,483.0')] ).
cnf(494,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[78,483]),
[iquote('1:MRR:78.0,483.0')] ).
cnf(512,plain,
( ~ memberP(sk3,u)
| equal(sk9,u) ),
inference(mrr,[status(thm)],[14,483]),
[iquote('1:MRR:14.0,483.0')] ).
cnf(619,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[100,483]),
[iquote('1:MRR:100.1,483.0')] ).
cnf(624,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[130,483]),
[iquote('1:MRR:130.1,483.0')] ).
cnf(625,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[134,483]),
[iquote('1:MRR:134.1,483.0')] ).
cnf(633,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,cons(x,w)),u)
| memberP(u,x) ),
inference(mrr,[status(thm)],[189,483]),
[iquote('1:MRR:189.1,483.0')] ).
cnf(1319,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[624]),
[iquote('1:EqR:624.1')] ).
cnf(1320,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1319,619,15,16,17,18,19,20,21,22,494,493,492,491,490,489,488]),
[iquote('1:SSi:1319.0,619.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,494.0,493.0,492.0,491.0,490.0,489.0,488.1')] ).
cnf(3098,plain,
( ~ ssList(app(u,cons(v,w)))
| ~ ssList(u)
| ~ ssList(w)
| memberP(app(u,cons(v,w)),v) ),
inference(eqr,[status(thm),theory(equality)],[633]),
[iquote('1:EqR:633.3')] ).
cnf(3112,plain,
( ~ ssList(u)
| ~ ssList(v)
| memberP(app(u,cons(w,v)),w) ),
inference(ssi,[status(thm)],[3098,99,619]),
[iquote('1:SSi:3098.0,99.1,619.2')] ).
cnf(16415,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| equal(app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),sk3) ),
inference(spr,[status(thm),theory(equality)],[202,163]),
[iquote('0:SpR:202.0,163.3')] ).
cnf(16434,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| equal(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8)),sk3) ),
inference(rew,[status(thm),theory(equality)],[625,16415]),
[iquote('1:Rew:625.1,16415.3')] ).
cnf(24044,plain,
equal(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8)),sk3),
inference(ssi,[status(thm)],[16434,10,619,22,21,20,19,18,17,16,15,1320,488,489,490,491,492,493,494,99,9]),
[iquote('1:SSi:16434.2,16434.1,16434.0,10.0,619.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,1320.0,488.0,489.0,490.0,491.0,492.0,493.1,494.0,99.2,9.0,619.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,1320.0,488.0,489.0,490.0,491.0,492.0,493.1,494.0')] ).
cnf(24552,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk8)
| memberP(sk3,sk6) ),
inference(spr,[status(thm),theory(equality)],[24044,3112]),
[iquote('1:SpR:24044.0,3112.2')] ).
cnf(24553,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,sk8))
| equal(app(sk7,app(cons(sk5,nil),cons(sk6,sk8))),sk3) ),
inference(spr,[status(thm),theory(equality)],[24044,163]),
[iquote('1:SpR:24044.0,163.3')] ).
cnf(24588,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,sk8))
| equal(app(sk7,cons(sk5,cons(sk6,sk8))),sk3) ),
inference(rew,[status(thm),theory(equality)],[625,24553]),
[iquote('1:Rew:625.1,24553.3')] ).
cnf(24589,plain,
equal(app(sk7,cons(sk5,cons(sk6,sk8))),sk3),
inference(ssi,[status(thm)],[24588,486,619,22,21,20,19,18,17,16,15,1320,488,489,490,491,492,493,494,9]),
[iquote('1:SSi:24588.2,24588.1,24588.0,486.0,619.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,1320.0,488.0,489.0,490.0,491.0,492.0,493.0,494.1,9.0')] ).
cnf(25254,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk6,sk8))
| memberP(sk3,sk5) ),
inference(spr,[status(thm),theory(equality)],[24589,3112]),
[iquote('1:SpR:24589.0,3112.2')] ).
cnf(25275,plain,
memberP(sk3,sk5),
inference(ssi,[status(thm)],[25254,486,9]),
[iquote('1:SSi:25254.1,25254.0,486.0,9.0')] ).
cnf(25459,plain,
equal(sk9,sk5),
inference(res,[status(thm),theory(equality)],[25275,512]),
[iquote('1:Res:25275.0,512.0')] ).
cnf(25463,plain,
( ~ memberP(sk3,u)
| equal(sk5,u) ),
inference(rew,[status(thm),theory(equality)],[25459,512]),
[iquote('1:Rew:25459.0,512.1')] ).
cnf(25855,plain,
memberP(sk3,sk6),
inference(ssi,[status(thm)],[24552,10,99,9,619,22,21,20,19,18,17,16,15,1320,488,489,490,491,492,493,494]),
[iquote('1:SSi:24552.1,24552.0,10.0,99.0,9.0,619.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,1320.0,488.0,489.0,490.0,491.1,492.0,493.2,494.0')] ).
cnf(25993,plain,
equal(sk6,sk5),
inference(res,[status(thm),theory(equality)],[25855,25463]),
[iquote('1:Res:25855.0,25463.0')] ).
cnf(25996,plain,
$false,
inference(mrr,[status(thm)],[25993,12]),
[iquote('1:MRR:25993.0,12.0')] ).
cnf(26000,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[86]),
[iquote('1:Spt:25996.0,86.0,86.2')] ).
cnf(26027,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)],[193,26000]),
[iquote('1:MRR:193.1,26000.1')] ).
cnf(35684,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)],[171,99]),
[iquote('0:SpR:171.3,99.2')] ).
cnf(35721,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[35684]),
[iquote('0:Obv:35684.0')] ).
cnf(35722,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[35721,100]),
[iquote('0:SSi:35721.2,100.2')] ).
cnf(37234,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)],[26027]),
[iquote('1:EqR:26027.5')] ).
cnf(37263,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[37234,99,100]),
[iquote('1:SSi:37234.0,99.2,99.2,100.2,100.2')] ).
cnf(37264,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[35722,37263]),
[iquote('1:MRR:35722.3,37263.1')] ).
cnf(37273,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[37264]),
[iquote('1:Con:37264.2')] ).
cnf(37274,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[447,37273]),
[iquote('1:MRR:447.1,37273.0')] ).
cnf(37280,plain,
$false,
inference(unc,[status(thm)],[37274,61]),
[iquote('1:UnC:37274.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC190-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 13:55:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.71/27.88
% 27.71/27.88 SPASS V 3.9
% 27.71/27.88 SPASS beiseite: Proof found.
% 27.71/27.88 % SZS status Theorem
% 27.71/27.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.71/27.88 SPASS derived 25824 clauses, backtracked 7653 clauses, performed 55 splits and kept 17971 clauses.
% 27.71/27.88 SPASS allocated 103115 KBytes.
% 27.71/27.88 SPASS spent 0:0:22.66 on the problem.
% 27.71/27.88 0:00:00.04 for the input.
% 27.71/27.88 0:00:00.00 for the FLOTTER CNF translation.
% 27.71/27.88 0:00:00.28 for inferences.
% 27.71/27.88 0:00:00.95 for the backtracking.
% 27.71/27.88 0:0:21.08 for the reduction.
% 27.71/27.88
% 27.71/27.88
% 27.71/27.88 Here is a proof with depth 4, length 76 :
% 27.71/27.88 % SZS output start Refutation
% See solution above
% 27.71/27.88 Formulae used in the proof : co1_6 co1_9 co1_10 co1_11 co1_12 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause85 clause86 clause116 clause120 clause149 clause157 clause175 clause179
% 27.71/27.88
%------------------------------------------------------------------------------