TSTP Solution File: ITP023+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ITP023+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 : Sun Jul 17 00:37:53 EDT 2022
% Result : Theorem 230.31s 230.50s
% Output : Refutation 230.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 42 ( 12 unt; 1 nHn; 42 RR)
% Number of literals : 116 ( 0 equ; 84 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
p(c_2Ebool_2ET),
file('ITP023+2.p',unknown),
[] ).
cnf(2,axiom,
ne(ty_2Erealax_2Ereal),
file('ITP023+2.p',unknown),
[] ).
cnf(5,axiom,
mem(skc3,ty_2Erealax_2Ereal),
file('ITP023+2.p',unknown),
[] ).
cnf(6,axiom,
mem(skc2,ty_2Erealax_2Ereal),
file('ITP023+2.p',unknown),
[] ).
cnf(7,axiom,
mem(c_2Ebool_2ET,bool),
file('ITP023+2.p',unknown),
[] ).
cnf(21,axiom,
mem(c_2Ereal__topology_2Ebounded__def,arr(arr(ty_2Erealax_2Ereal,bool),bool)),
file('ITP023+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ p(u)
| p(v)
| skP11(v,u) ),
file('ITP023+2.p',unknown),
[] ).
cnf(37,axiom,
mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('ITP023+2.p',unknown),
[] ).
cnf(38,axiom,
mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('ITP023+2.p',unknown),
[] ).
cnf(57,axiom,
( ~ p(u)
| ~ p(v)
| ~ skP11(u,v) ),
file('ITP023+2.p',unknown),
[] ).
cnf(71,axiom,
~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3)))),
file('ITP023+2.p',unknown),
[] ).
cnf(78,axiom,
( ~ mem(u,v)
| ~ mem(w,arr(v,x))
| mem(ap(w,u),x) ),
file('ITP023+2.p',unknown),
[] ).
cnf(81,axiom,
( ~ ne(u)
| ~ ne(v)
| mem(c_2Epair_2E_2C(v,u),arr(v,arr(u,ty_2Epair_2Eprod(v,u)))) ),
file('ITP023+2.p',unknown),
[] ).
cnf(87,axiom,
( ~ p(u)
| ~ p(v)
| ~ mem(u,bool)
| ~ mem(v,bool)
| equal(v,u) ),
file('ITP023+2.p',unknown),
[] ).
cnf(94,axiom,
( ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)))) ),
file('ITP023+2.p',unknown),
[] ).
cnf(123,axiom,
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,u))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),v),u))
| ~ mem(u,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(v,arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,v)) ),
file('ITP023+2.p',unknown),
[] ).
cnf(124,axiom,
( ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)))) ),
file('ITP023+2.p',unknown),
[] ).
cnf(207,plain,
( ~ p(u)
| skP11(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3))),u) ),
inference(res,[status(thm),theory(equality)],[36,71]),
[iquote('0:Res:36.1,71.0')] ).
cnf(396,plain,
( ~ mem(u,arr(ty_2Erealax_2Ereal,bool))
| mem(ap(c_2Ereal__topology_2Ebounded__def,u),bool) ),
inference(res,[status(thm),theory(equality)],[21,78]),
[iquote('0:Res:21.0,78.1')] ).
cnf(402,plain,
( ~ mem(u,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| mem(ap(c_2Ereal__topology_2Ecball,u),arr(ty_2Erealax_2Ereal,bool)) ),
inference(res,[status(thm),theory(equality)],[38,78]),
[iquote('0:Res:38.0,78.1')] ).
cnf(403,plain,
( ~ mem(u,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| mem(ap(c_2Ereal__topology_2Eball,u),arr(ty_2Erealax_2Ereal,bool)) ),
inference(res,[status(thm),theory(equality)],[37,78]),
[iquote('0:Res:37.0,78.1')] ).
cnf(487,plain,
( ~ p(c_2Ebool_2ET)
| ~ p(u)
| ~ mem(u,bool)
| equal(u,c_2Ebool_2ET) ),
inference(res,[status(thm),theory(equality)],[7,87]),
[iquote('0:Res:7.0,87.2')] ).
cnf(495,plain,
( ~ p(u)
| ~ mem(u,bool)
| equal(u,c_2Ebool_2ET) ),
inference(ssi,[status(thm)],[487,1]),
[iquote('0:SSi:487.0,1.0')] ).
cnf(499,plain,
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,u))
| ~ mem(u,arr(ty_2Erealax_2Ereal,bool))
| equal(ap(c_2Ereal__topology_2Ebounded__def,u),c_2Ebool_2ET) ),
inference(res,[status(thm),theory(equality)],[396,495]),
[iquote('0:Res:396.1,495.1')] ).
cnf(543,plain,
( ~ ne(u)
| ~ ne(v)
| ~ mem(w,v)
| mem(ap(c_2Epair_2E_2C(v,u),w),arr(u,ty_2Epair_2Eprod(v,u))) ),
inference(res,[status(thm),theory(equality)],[81,78]),
[iquote('0:Res:81.2,78.1')] ).
cnf(721,plain,
( ~ p(u)
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3))))
| ~ p(u) ),
inference(res,[status(thm),theory(equality)],[207,57]),
[iquote('0:Res:207.1,57.2')] ).
cnf(723,plain,
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3))))
| ~ p(u) ),
inference(obv,[status(thm),theory(equality)],[721]),
[iquote('0:Obv:721.0')] ).
cnf(724,plain,
~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3)))),
inference(con,[status(thm)],[723]),
[iquote('0:Con:723.1')] ).
cnf(787,plain,
( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| equal(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v))),c_2Ebool_2ET) ),
inference(sor,[status(thm)],[499,94]),
[iquote('0:SoR:499.0,94.2')] ).
cnf(11641,plain,
( ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u))))
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)))) ),
inference(res,[status(thm),theory(equality)],[124,123]),
[iquote('0:Res:124.2,123.1')] ).
cnf(11642,plain,
( ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| ~ p(c_2Ebool_2ET)
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)))) ),
inference(rew,[status(thm),theory(equality)],[787,11641]),
[iquote('0:Rew:787.3,11641.2')] ).
cnf(11643,plain,
( ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(v,ty_2Erealax_2Ereal)
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)),arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),v),u)))) ),
inference(mrr,[status(thm)],[11642,1]),
[iquote('0:MRR:11642.2,1.0')] ).
cnf(12693,plain,
( ~ ne(u)
| ~ ne(v)
| ~ mem(w,v)
| ~ mem(x,u)
| mem(ap(ap(c_2Epair_2E_2C(v,u),w),x),ty_2Epair_2Eprod(v,u)) ),
inference(res,[status(thm),theory(equality)],[543,78]),
[iquote('0:Res:543.3,78.1')] ).
cnf(42728,plain,
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ~ mem(v,ty_2Erealax_2Ereal)
| ~ mem(u,ty_2Erealax_2Ereal)
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v)),arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v)))) ),
inference(res,[status(thm),theory(equality)],[402,11643]),
[iquote('0:Res:402.1,11643.2')] ).
cnf(42729,plain,
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ~ mem(v,ty_2Erealax_2Ereal)
| ~ mem(u,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),u),v)))) ),
inference(mrr,[status(thm)],[42728,403]),
[iquote('0:MRR:42728.3,403.1')] ).
cnf(187056,plain,
( ~ mem(skc2,ty_2Erealax_2Ereal)
| ~ mem(skc3,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(sor,[status(thm)],[724,42729]),
[iquote('0:SoR:724.0,42729.3')] ).
cnf(187142,plain,
( ~ mem(skc3,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(mrr,[status(thm)],[187056,6]),
[iquote('0:MRR:187056.0,6.0')] ).
cnf(187143,plain,
~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),skc2),skc3),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(mrr,[status(thm)],[187142,5]),
[iquote('0:MRR:187142.0,5.0')] ).
cnf(195275,plain,
( ~ ne(ty_2Erealax_2Ereal)
| ~ ne(ty_2Erealax_2Ereal)
| ~ mem(skc2,ty_2Erealax_2Ereal)
| ~ mem(skc3,ty_2Erealax_2Ereal) ),
inference(res,[status(thm),theory(equality)],[12693,187143]),
[iquote('0:Res:12693.4,187143.0')] ).
cnf(195278,plain,
( ~ ne(ty_2Erealax_2Ereal)
| ~ mem(skc2,ty_2Erealax_2Ereal)
| ~ mem(skc3,ty_2Erealax_2Ereal) ),
inference(obv,[status(thm),theory(equality)],[195275]),
[iquote('0:Obv:195275.0')] ).
cnf(195279,plain,
( ~ mem(skc2,ty_2Erealax_2Ereal)
| ~ mem(skc3,ty_2Erealax_2Ereal) ),
inference(ssi,[status(thm)],[195278,2]),
[iquote('0:SSi:195278.0,2.0')] ).
cnf(195280,plain,
$false,
inference(mrr,[status(thm)],[195279,6,5]),
[iquote('0:MRR:195279.0,195279.1,6.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP023+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.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 : Thu Jun 2 16:16:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 230.31/230.50
% 230.31/230.50 SPASS V 3.9
% 230.31/230.50 SPASS beiseite: Proof found.
% 230.31/230.50 % SZS status Theorem
% 230.31/230.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 230.31/230.50 SPASS derived 133983 clauses, backtracked 60041 clauses, performed 359 splits and kept 80926 clauses.
% 230.31/230.50 SPASS allocated 244057 KBytes.
% 230.31/230.50 SPASS spent 0:3:49.90 on the problem.
% 230.31/230.50 0:00:00.04 for the input.
% 230.31/230.50 0:00:00.08 for the FLOTTER CNF translation.
% 230.31/230.50 0:00:02.72 for inferences.
% 230.31/230.50 0:00:04.71 for the backtracking.
% 230.31/230.50 0:3:40.46 for the reduction.
% 230.31/230.50
% 230.31/230.50
% 230.31/230.50 Here is a proof with depth 4, length 42 :
% 230.31/230.50 % SZS output start Refutation
% See solution above
% 230.31/230.50 Formulae used in the proof : ax_true_p ne_ty_2Erealax_2Ereal conj_thm_2Ereal__topology_2EBOUNDED__BALL mem_c_2Ebool_2ET mem_c_2Ereal__topology_2Ebounded__def conj_thm_2Esat_2Edc__neg mem_c_2Ereal__topology_2Eball mem_c_2Ereal__topology_2Ecball ap_tp mem_c_2Epair_2E_2C boolext conj_thm_2Ereal__topology_2EBOUNDED__CBALL cCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------