TSTP Solution File: ITP015+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ITP015+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 00:37:43 EDT 2022
% Result : Theorem 92.24s 92.44s
% Output : Refutation 92.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 45 ( 14 unt; 4 nHn; 45 RR)
% Number of literals : 103 ( 0 equ; 61 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ne(skc1),
file('ITP015+2.p',unknown),
[] ).
cnf(5,axiom,
ne(bool),
file('ITP015+2.p',unknown),
[] ).
cnf(8,axiom,
mem(c_2Ebool_2EF,bool),
file('ITP015+2.p',unknown),
[] ).
cnf(9,axiom,
~ p(c_2Ebool_2EF),
file('ITP015+2.p',unknown),
[] ).
cnf(10,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
file('ITP015+2.p',unknown),
[] ).
cnf(13,axiom,
mem(c_2Einteger_2Eint__of__num,arr(ty_2Enum_2Enum,ty_2Einteger_2Eint)),
file('ITP015+2.p',unknown),
[] ).
cnf(22,axiom,
mem(c_2Einteger_2Eint__lt,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
file('ITP015+2.p',unknown),
[] ).
cnf(29,axiom,
equal(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),
file('ITP015+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ ne(u)
| ~ ne(v)
| ne(ty_2Efcp_2Ecart(v,u)) ),
file('ITP015+2.p',unknown),
[] ).
cnf(38,axiom,
( ~ ne(u)
| mem(c_2Ewords_2En2w(u),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,u))) ),
file('ITP015+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ mem(u,ty_2Enum_2Enum)
| equal(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,u)),u) ),
file('ITP015+2.p',unknown),
[] ).
cnf(43,axiom,
~ equal(ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),
file('ITP015+2.p',unknown),
[] ).
cnf(47,axiom,
( ~ ne(u)
| equal(ap(c_2Ewords_2Eword__2comp(u),ap(c_2Ewords_2En2w(u),c_2Enum_2E0)),ap(c_2Ewords_2En2w(u),c_2Enum_2E0)) ),
file('ITP015+2.p',unknown),
[] ).
cnf(48,axiom,
( ~ mem(u,v)
| ~ mem(w,arr(v,x))
| mem(ap(w,u),x) ),
file('ITP015+2.p',unknown),
[] ).
cnf(49,axiom,
( ~ mem(u,bool)
| ~ mem(v,bool)
| p(u)
| p(v)
| equal(v,u) ),
file('ITP015+2.p',unknown),
[] ).
cnf(63,axiom,
( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,u)),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,v))))
| ~ mem(v,ty_2Enum_2Enum)
| ~ mem(u,ty_2Enum_2Enum) ),
file('ITP015+2.p',unknown),
[] ).
cnf(64,axiom,
( ~ ne(u)
| ~ mem(v,u)
| ~ mem(w,u)
| equal(ap(ap(ap(c_2Ebool_2ECOND(u),c_2Ebool_2EF),v),w),w) ),
file('ITP015+2.p',unknown),
[] ).
cnf(81,axiom,
( ~ ne(u)
| ~ mem(v,ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,u)),ap(ap(c_2Einteger_2Eint__lt,v),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(u),ap(c_2Ewords_2En2w(u),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,v))))),ap(c_2Ewords_2En2w(u),ap(c_2Einteger_2ENum,v))),ap(c_2Einteger__word_2Ei2w(u),v)) ),
file('ITP015+2.p',unknown),
[] ).
cnf(86,plain,
( ~ mem(u,ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,skc1)),ap(ap(c_2Einteger_2Eint__lt,u),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(skc1),ap(c_2Ewords_2En2w(skc1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,u))))),ap(c_2Ewords_2En2w(skc1),ap(c_2Einteger_2ENum,u))),ap(c_2Einteger__word_2Ei2w(skc1),u)) ),
inference(res,[status(thm),theory(equality)],[1,81]),
[iquote('0:Res:1.0,81.0')] ).
cnf(97,plain,
equal(ap(c_2Ewords_2Eword__2comp(skc1),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),
inference(res,[status(thm),theory(equality)],[1,47]),
[iquote('0:Res:1.0,47.0')] ).
cnf(102,plain,
mem(c_2Ewords_2En2w(skc1),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,skc1))),
inference(res,[status(thm),theory(equality)],[1,38]),
[iquote('0:Res:1.0,38.0')] ).
cnf(110,plain,
( ~ ne(u)
| ne(ty_2Efcp_2Ecart(u,skc1)) ),
inference(res,[status(thm),theory(equality)],[1,30]),
[iquote('0:Res:1.0,30.1')] ).
cnf(140,plain,
( ~ mem(u,bool)
| p(c_2Ebool_2EF)
| p(u)
| equal(u,c_2Ebool_2EF) ),
inference(res,[status(thm),theory(equality)],[8,49]),
[iquote('0:Res:8.0,49.0')] ).
cnf(142,plain,
( ~ mem(u,bool)
| p(u)
| equal(u,c_2Ebool_2EF) ),
inference(mrr,[status(thm)],[140,9]),
[iquote('0:MRR:140.1,9.0')] ).
cnf(145,plain,
( ~ mem(u,ty_2Enum_2Enum)
| mem(ap(c_2Einteger_2Eint__of__num,u),ty_2Einteger_2Eint) ),
inference(res,[status(thm),theory(equality)],[13,48]),
[iquote('0:Res:13.0,48.1')] ).
cnf(148,plain,
( ~ mem(u,ty_2Enum_2Enum)
| mem(ap(c_2Ewords_2En2w(skc1),u),ty_2Efcp_2Ecart(bool,skc1)) ),
inference(res,[status(thm),theory(equality)],[102,48]),
[iquote('0:Res:102.0,48.1')] ).
cnf(152,plain,
( ~ mem(u,ty_2Einteger_2Eint)
| mem(ap(c_2Einteger_2Eint__lt,u),arr(ty_2Einteger_2Eint,bool)) ),
inference(res,[status(thm),theory(equality)],[22,48]),
[iquote('0:Res:22.0,48.1')] ).
cnf(176,plain,
( ~ mem(u,ty_2Einteger_2Eint)
| ~ mem(v,ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__lt,u),v),bool) ),
inference(res,[status(thm),theory(equality)],[152,48]),
[iquote('0:Res:152.1,48.1')] ).
cnf(199,plain,
( ~ mem(u,ty_2Einteger_2Eint)
| ~ mem(v,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__lt,u),v))
| equal(ap(ap(c_2Einteger_2Eint__lt,u),v),c_2Ebool_2EF) ),
inference(res,[status(thm),theory(equality)],[176,142]),
[iquote('0:Res:176.2,142.0')] ).
cnf(466,plain,
( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,u)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)))
| ~ mem(c_2Enum_2E0,ty_2Enum_2Enum)
| ~ mem(u,ty_2Enum_2Enum) ),
inference(spl,[status(thm),theory(equality)],[29,63]),
[iquote('0:SpL:29.0,63.0')] ).
cnf(467,plain,
( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,u)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)))
| ~ mem(u,ty_2Enum_2Enum) ),
inference(mrr,[status(thm)],[466,10]),
[iquote('0:MRR:466.1,10.0')] ).
cnf(4426,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,u),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(u,ty_2Enum_2Enum)
| equal(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,u)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),c_2Ebool_2EF) ),
inference(res,[status(thm),theory(equality)],[199,467]),
[iquote('0:Res:199.2,467.0')] ).
cnf(4429,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(u,ty_2Enum_2Enum)
| equal(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,u)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),c_2Ebool_2EF) ),
inference(mrr,[status(thm)],[4426,145]),
[iquote('0:MRR:4426.0,145.1')] ).
cnf(12595,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,skc1)),ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(skc1),ap(c_2Ewords_2En2w(skc1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))))),ap(c_2Ewords_2En2w(skc1),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)))),ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))) ),
inference(spr,[status(thm),theory(equality)],[29,86]),
[iquote('0:SpR:29.0,86.1')] ).
cnf(25652,plain,
( ~ mem(c_2Enum_2E0,ty_2Enum_2Enum)
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,skc1)),ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))),ap(c_2Ewords_2Eword__2comp(skc1),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0))),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))) ),
inference(spr,[status(thm),theory(equality)],[40,12595]),
[iquote('0:SpR:40.1,12595.1')] ).
cnf(25655,plain,
( ~ mem(c_2Enum_2E0,ty_2Enum_2Enum)
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,skc1)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))) ),
inference(rew,[status(thm),theory(equality)],[4429,25652,97]),
[iquote('0:Rew:4429.2,25652.2,97.0,25652.2')] ).
cnf(25656,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| equal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,skc1)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)),ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0))) ),
inference(mrr,[status(thm)],[25655,10]),
[iquote('0:MRR:25655.0,10.0')] ).
cnf(79976,plain,
( ~ ne(ty_2Efcp_2Ecart(bool,skc1))
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,skc1))
| ~ mem(ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,skc1))
| equal(ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)) ),
inference(spr,[status(thm),theory(equality)],[25656,64]),
[iquote('0:SpR:25656.1,64.3')] ).
cnf(79981,plain,
( ~ ne(ty_2Efcp_2Ecart(bool,skc1))
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,skc1))
| equal(ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)) ),
inference(obv,[status(thm),theory(equality)],[79976]),
[iquote('0:Obv:79976.2')] ).
cnf(79982,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,skc1))
| equal(ap(c_2Einteger__word_2Ei2w(skc1),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0)) ),
inference(ssi,[status(thm)],[79981,110,5]),
[iquote('0:SSi:79981.0,110.0,5.1')] ).
cnf(79983,plain,
( ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Ewords_2En2w(skc1),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,skc1)) ),
inference(mrr,[status(thm)],[79982,43]),
[iquote('0:MRR:79982.2,43.0')] ).
cnf(79987,plain,
( ~ mem(c_2Enum_2E0,ty_2Enum_2Enum)
| ~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint) ),
inference(res,[status(thm),theory(equality)],[148,79983]),
[iquote('0:Res:148.1,79983.1')] ).
cnf(79989,plain,
~ mem(ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),ty_2Einteger_2Eint),
inference(mrr,[status(thm)],[79987,10]),
[iquote('0:MRR:79987.0,10.0')] ).
cnf(79990,plain,
~ mem(c_2Enum_2E0,ty_2Enum_2Enum),
inference(res,[status(thm),theory(equality)],[145,79989]),
[iquote('0:Res:145.1,79989.0')] ).
cnf(79991,plain,
$false,
inference(mrr,[status(thm)],[79990,10]),
[iquote('0:MRR:79990.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP015+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 14:25:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 92.24/92.44
% 92.24/92.44 SPASS V 3.9
% 92.24/92.44 SPASS beiseite: Proof found.
% 92.24/92.44 % SZS status Theorem
% 92.24/92.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.24/92.44 SPASS derived 55780 clauses, backtracked 28553 clauses, performed 450 splits and kept 42979 clauses.
% 92.24/92.44 SPASS allocated 169570 KBytes.
% 92.24/92.44 SPASS spent 0:1:32.00 on the problem.
% 92.24/92.44 0:00:00.04 for the input.
% 92.24/92.44 0:00:00.08 for the FLOTTER CNF translation.
% 92.24/92.44 0:00:01.31 for inferences.
% 92.24/92.44 0:00:02.09 for the backtracking.
% 92.24/92.44 0:1:27.99 for the reduction.
% 92.24/92.44
% 92.24/92.44
% 92.24/92.44 Here is a proof with depth 6, length 45 :
% 92.24/92.44 % SZS output start Refutation
% See solution above
% 92.24/92.44 Formulae used in the proof : conj_thm_2Einteger__word_2Ei2w__0 bool_ne mem_c_2Ebool_2EF ax_false_p mem_c_2Enum_2E0 mem_c_2Einteger_2Eint__of__num mem_c_2Einteger_2Eint__lt conj_thm_2Einteger_2EINT__NEG__0 ne_ty_2Efcp_2Ecart mem_c_2Ewords_2En2w conj_thm_2Einteger_2ENUM__OF__INT conj_thm_2Ewords_2EWORD__NEG__0 ap_tp boolext conj_thm_2Einteger_2EINT__LT__CALCULATE conj_thm_2Ebool_2Ebool__case__thm ax_thm_2Einteger__word_2Ei2w__def
% 113.35/113.59
%------------------------------------------------------------------------------