TSTP Solution File: ITP004+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 00:37:28 EDT 2022
% Result : Theorem 6.34s 6.52s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 36 ( 8 unt; 6 nHn; 36 RR)
% Number of literals : 118 ( 0 equ; 84 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ne(skc2),
file('ITP004+2.p',unknown),
[] ).
cnf(4,axiom,
mem(skc3,arr(skc2,bool)),
file('ITP004+2.p',unknown),
[] ).
cnf(11,axiom,
~ p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(c_2Epred__set_2EREST(skc2),skc3)),skc3)),
file('ITP004+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ ne(u)
| mem(c_2Epred__set_2ECHOICE(u),arr(arr(u,bool),u)) ),
file('ITP004+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ ne(u)
| mem(c_2Epred__set_2EREST(u),arr(arr(u,bool),arr(u,bool))) ),
file('ITP004+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ ne(u)
| mem(c_2Epred__set_2EDELETE(u),arr(arr(u,bool),arr(u,arr(u,bool)))) ),
file('ITP004+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ mem(u,v)
| ~ mem(w,arr(v,x))
| mem(ap(w,u),x) ),
file('ITP004+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| equal(ap(ap(c_2Epred__set_2EDELETE(u),v),ap(c_2Epred__set_2ECHOICE(u),v)),ap(c_2Epred__set_2EREST(u),v)) ),
file('ITP004+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),w),v))
| mem(skf4(u,x,y),u) ),
file('ITP004+2.p',unknown),
[] ).
cnf(39,axiom,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),w),v))
| p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,w)),w)) ),
file('ITP004+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ ne(u)
| ~ p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,w)),v))
| ~ mem(v,arr(u,bool))
| ~ mem(x,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),x),v)) ),
file('ITP004+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ ne(u)
| ~ p(ap(ap(c_2Ebool_2EIN(u),v),ap(ap(c_2Epred__set_2EDELETE(u),w),x)))
| ~ mem(x,u)
| ~ mem(v,u)
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Ebool_2EIN(u),v),w)) ),
file('ITP004+2.p',unknown),
[] ).
cnf(61,plain,
mem(c_2Epred__set_2EREST(skc2),arr(arr(skc2,bool),arr(skc2,bool))),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(70,plain,
( ~ ne(skc2)
| equal(ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),ap(c_2Epred__set_2ECHOICE(skc2),skc3)),ap(c_2Epred__set_2EREST(skc2),skc3)) ),
inference(res,[status(thm),theory(equality)],[4,35]),
[iquote('0:Res:4.0,35.1')] ).
cnf(106,plain,
( ~ ne(skc2)
| ~ p(ap(ap(c_2Ebool_2EIN(skc2),skf4(skc2,skc3,u)),skc3))
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| ~ mem(skc3,arr(skc2,bool)) ),
inference(res,[status(thm),theory(equality)],[40,11]),
[iquote('0:Res:40.4,11.0')] ).
cnf(115,plain,
equal(ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),ap(c_2Epred__set_2ECHOICE(skc2),skc3)),ap(c_2Epred__set_2EREST(skc2),skc3)),
inference(mrr,[status(thm)],[70,1]),
[iquote('0:MRR:70.0,1.0')] ).
cnf(125,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(skc2),skf4(skc2,skc3,u)),skc3))
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool)) ),
inference(mrr,[status(thm)],[106,1,4]),
[iquote('0:MRR:106.0,106.3,1.0,4.0')] ).
cnf(154,plain,
( ~ mem(u,arr(skc2,bool))
| mem(ap(c_2Epred__set_2EREST(skc2),u),arr(skc2,bool)) ),
inference(res,[status(thm),theory(equality)],[61,21]),
[iquote('0:Res:61.0,21.1')] ).
cnf(160,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| mem(ap(c_2Epred__set_2ECHOICE(u),v),u) ),
inference(res,[status(thm),theory(equality)],[12,21]),
[iquote('0:Res:12.1,21.1')] ).
cnf(164,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| mem(ap(c_2Epred__set_2EDELETE(u),v),arr(u,arr(u,bool))) ),
inference(res,[status(thm),theory(equality)],[20,21]),
[iquote('0:Res:20.1,21.1')] ).
cnf(1056,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(w,u)
| mem(ap(ap(c_2Epred__set_2EDELETE(u),v),w),arr(u,bool)) ),
inference(res,[status(thm),theory(equality)],[164,21]),
[iquote('0:Res:164.2,21.1')] ).
cnf(4378,plain,
( ~ ne(u)
| ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(u),w),x),arr(u,bool))
| ~ mem(x,u)
| ~ mem(skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),w),x)),u)
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),ap(ap(c_2Epred__set_2EDELETE(u),w),x)),v))
| p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),w),x))),w)) ),
inference(res,[status(thm),theory(equality)],[39,42]),
[iquote('0:Res:39.4,42.1')] ).
cnf(4386,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(u),w),x),arr(u,bool))
| ~ mem(x,u)
| ~ mem(skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),w),x)),u)
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),ap(ap(c_2Epred__set_2EDELETE(u),w),x)),v))
| p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),w),x))),w)) ),
inference(obv,[status(thm),theory(equality)],[4378]),
[iquote('0:Obv:4378.0')] ).
cnf(4387,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(u),w),x),arr(u,bool))
| ~ mem(x,u)
| ~ mem(w,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),ap(ap(c_2Epred__set_2EDELETE(u),w),x)),v))
| p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),w),x))),w)) ),
inference(mrr,[status(thm)],[4386,37]),
[iquote('0:MRR:4386.4,37.4')] ).
cnf(4388,plain,
( ~ ne(u)
| ~ mem(v,arr(u,bool))
| ~ mem(w,u)
| ~ mem(x,arr(u,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(u),ap(ap(c_2Epred__set_2EDELETE(u),x),w)),v))
| p(ap(ap(c_2Ebool_2EIN(u),skf4(u,v,ap(ap(c_2Epred__set_2EDELETE(u),x),w))),x)) ),
inference(mrr,[status(thm)],[4387,1056]),
[iquote('0:MRR:4387.2,1056.3')] ).
cnf(17615,plain,
( ~ ne(skc2)
| ~ mem(skc3,arr(skc2,bool))
| ~ mem(u,skc2)
| ~ mem(skc3,arr(skc2,bool))
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),u)),skc3)) ),
inference(res,[status(thm),theory(equality)],[4388,125]),
[iquote('0:Res:4388.5,125.0')] ).
cnf(17629,plain,
( ~ ne(skc2)
| ~ mem(u,skc2)
| ~ mem(skc3,arr(skc2,bool))
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),u)),skc3)) ),
inference(obv,[status(thm),theory(equality)],[17615]),
[iquote('0:Obv:17615.1')] ).
cnf(17630,plain,
( ~ mem(u,skc2)
| ~ mem(skc3,arr(skc2,bool))
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),u)),skc3)) ),
inference(ssi,[status(thm)],[17629,1]),
[iquote('0:SSi:17629.0,1.0')] ).
cnf(17631,plain,
( ~ mem(u,skc2)
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(ap(c_2Epred__set_2EDELETE(skc2),skc3),u)),skc3)) ),
inference(mrr,[status(thm)],[17630,4]),
[iquote('0:MRR:17630.1,4.0')] ).
cnf(18069,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(skc2),skc3),skc2)
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(skc2),ap(c_2Epred__set_2EREST(skc2),skc3)),skc3)) ),
inference(spr,[status(thm),theory(equality)],[115,17631]),
[iquote('0:SpR:115.0,17631.2')] ).
cnf(18783,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(skc2),skc3),skc2)
| ~ mem(ap(c_2Epred__set_2EREST(skc2),skc3),arr(skc2,bool)) ),
inference(mrr,[status(thm)],[18069,11]),
[iquote('0:MRR:18069.2,11.0')] ).
cnf(19307,plain,
( ~ mem(skc3,arr(skc2,bool))
| ~ mem(ap(c_2Epred__set_2ECHOICE(skc2),skc3),skc2) ),
inference(res,[status(thm),theory(equality)],[154,18783]),
[iquote('0:Res:154.1,18783.1')] ).
cnf(19309,plain,
~ mem(ap(c_2Epred__set_2ECHOICE(skc2),skc3),skc2),
inference(mrr,[status(thm)],[19307,4]),
[iquote('0:MRR:19307.0,4.0')] ).
cnf(19310,plain,
( ~ ne(skc2)
| ~ mem(skc3,arr(skc2,bool)) ),
inference(res,[status(thm),theory(equality)],[160,19309]),
[iquote('0:Res:160.2,19309.0')] ).
cnf(19313,plain,
~ mem(skc3,arr(skc2,bool)),
inference(ssi,[status(thm)],[19310,1]),
[iquote('0:SSi:19310.0,1.0')] ).
cnf(19314,plain,
$false,
inference(mrr,[status(thm)],[19313,4]),
[iquote('0:MRR:19313.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP004+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jun 3 02:16:31 EDT 2022
% 0.11/0.33 % CPUTime :
% 6.34/6.52
% 6.34/6.52 SPASS V 3.9
% 6.34/6.52 SPASS beiseite: Proof found.
% 6.34/6.52 % SZS status Theorem
% 6.34/6.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.34/6.52 SPASS derived 13613 clauses, backtracked 3833 clauses, performed 56 splits and kept 6365 clauses.
% 6.34/6.52 SPASS allocated 114888 KBytes.
% 6.34/6.52 SPASS spent 0:00:04.65 on the problem.
% 6.34/6.52 0:00:00.03 for the input.
% 6.34/6.52 0:00:00.06 for the FLOTTER CNF translation.
% 6.34/6.52 0:00:00.23 for inferences.
% 6.34/6.52 0:00:00.14 for the backtracking.
% 6.34/6.52 0:00:04.10 for the reduction.
% 6.34/6.52
% 6.34/6.52
% 6.34/6.52 Here is a proof with depth 5, length 36 :
% 6.34/6.52 % SZS output start Refutation
% See solution above
% 6.34/6.52 Formulae used in the proof : conj_thm_2Epred__set_2EREST__SUBSET mem_c_2Epred__set_2ECHOICE mem_c_2Epred__set_2EREST mem_c_2Epred__set_2EDELETE ap_tp ax_thm_2Epred__set_2EREST__DEF ax_thm_2Epred__set_2ESUBSET__DEF conj_thm_2Epred__set_2EIN__DELETE
% 6.34/6.52
%------------------------------------------------------------------------------