TSTP Solution File: NUM537+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 : Mon Jul 18 14:27:15 EDT 2022
% Result : Theorem 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of clauses : 44 ( 16 unt; 11 nHn; 44 RR)
% Number of literals : 99 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aSet0(xS),
file('NUM537+2.p',unknown),
[] ).
cnf(4,axiom,
~ aElementOf0(skc2,xS),
file('NUM537+2.p',unknown),
[] ).
cnf(5,axiom,
( skC0
| aElementOf0(skc3,xS) ),
file('NUM537+2.p',unknown),
[] ).
cnf(6,axiom,
~ aElementOf0(xx,xS),
file('NUM537+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ skC0
| aElementOf0(skc2,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
file('NUM537+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| aElement0(u)
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ aElementOf0(skc3,sdtmndt0(sdtpldt0(xS,xx),xx))
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM537+2.p',unknown),
[] ).
cnf(26,axiom,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| ~ skC0
| aElement0(u) ),
file('NUM537+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| aElementOf0(u,xS)
| equal(u,xx)
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,xS)
| aElementOf0(u,sdtpldt0(xS,xx))
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(38,axiom,
( ~ equal(u,xx)
| ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(39,axiom,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| ~ skC0
| aElementOf0(u,xS)
| equal(u,xx) ),
file('NUM537+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,xS)
| ~ skC0
| aElementOf0(u,sdtpldt0(xS,xx)) ),
file('NUM537+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ equal(u,xx)
| ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(u,sdtpldt0(xS,xx))
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(50,axiom,
( ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ skC0
| aElementOf0(u,sdtpldt0(xS,xx)) ),
file('NUM537+2.p',unknown),
[] ).
cnf(58,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,sdtpldt0(xS,xx))
| equal(u,xx)
| aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| skC0 ),
file('NUM537+2.p',unknown),
[] ).
cnf(59,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,sdtpldt0(xS,xx))
| ~ skC0
| equal(u,xx)
| aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
file('NUM537+2.p',unknown),
[] ).
cnf(66,plain,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| aElement0(u) ),
inference(mrr,[status(thm)],[26,19]),
[iquote('0:MRR:26.1,19.2')] ).
cnf(68,plain,
( ~ equal(u,xx)
| ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(mrr,[status(thm)],[42,38]),
[iquote('0:MRR:42.2,38.2')] ).
cnf(70,plain,
( ~ aElement0(u)
| ~ aElementOf0(u,xS)
| aElementOf0(u,sdtpldt0(xS,xx)) ),
inference(mrr,[status(thm)],[40,36]),
[iquote('0:MRR:40.2,36.3')] ).
cnf(71,plain,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| equal(u,xx)
| aElementOf0(u,xS) ),
inference(mrr,[status(thm)],[39,35]),
[iquote('0:MRR:39.1,35.3')] ).
cnf(72,plain,
( ~ aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(u,sdtpldt0(xS,xx)) ),
inference(mrr,[status(thm)],[50,43]),
[iquote('0:MRR:50.1,43.2')] ).
cnf(75,plain,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| equal(u,xx)
| aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx))
| skC0 ),
inference(mrr,[status(thm)],[58,66]),
[iquote('0:MRR:58.0,66.1')] ).
cnf(76,plain,
( ~ aElementOf0(u,sdtpldt0(xS,xx))
| equal(u,xx)
| aElementOf0(u,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(mrr,[status(thm)],[59,66,75]),
[iquote('0:MRR:59.0,59.2,66.1,75.3')] ).
cnf(77,plain,
( ~ aElementOf0(skc2,sdtpldt0(xS,xx))
| equal(skc2,xx) ),
inference(res,[status(thm),theory(equality)],[71,4]),
[iquote('0:Res:71.1,4.0')] ).
cnf(146,plain,
skC0,
inference(spt,[spt(split,[position(s1)])],[5]),
[iquote('1:Spt:5.0')] ).
cnf(147,plain,
aElementOf0(skc2,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(mrr,[status(thm)],[18,146]),
[iquote('1:MRR:18.0,146.0')] ).
cnf(177,plain,
~ equal(skc2,xx),
inference(res,[status(thm),theory(equality)],[147,68]),
[iquote('1:Res:147.0,68.1')] ).
cnf(179,plain,
~ aElementOf0(skc2,sdtpldt0(xS,xx)),
inference(mrr,[status(thm)],[77,177]),
[iquote('1:MRR:77.1,177.0')] ).
cnf(210,plain,
aElementOf0(skc2,sdtpldt0(xS,xx)),
inference(res,[status(thm),theory(equality)],[147,72]),
[iquote('1:Res:147.0,72.0')] ).
cnf(212,plain,
$false,
inference(mrr,[status(thm)],[210,179]),
[iquote('1:MRR:210.0,179.0')] ).
cnf(215,plain,
~ skC0,
inference(spt,[spt(split,[position(sa)])],[212,146]),
[iquote('1:Spt:212.0,5.0,146.0')] ).
cnf(216,plain,
aElementOf0(skc3,xS),
inference(spt,[spt(split,[position(s2)])],[5]),
[iquote('1:Spt:212.0,5.1')] ).
cnf(218,plain,
~ aElementOf0(skc3,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(mrr,[status(thm)],[20,215]),
[iquote('1:MRR:20.1,215.0')] ).
cnf(220,plain,
( ~ aSet0(xS)
| aElement0(skc3) ),
inference(res,[status(thm),theory(equality)],[216,22]),
[iquote('1:Res:216.0,22.1')] ).
cnf(221,plain,
aElement0(skc3),
inference(ssi,[status(thm)],[220,3]),
[iquote('1:SSi:220.0,3.0')] ).
cnf(564,plain,
( ~ aElementOf0(skc3,sdtpldt0(xS,xx))
| equal(skc3,xx) ),
inference(res,[status(thm),theory(equality)],[76,218]),
[iquote('1:Res:76.2,218.0')] ).
cnf(568,plain,
( ~ aElement0(skc3)
| ~ aElementOf0(skc3,xS)
| equal(skc3,xx) ),
inference(res,[status(thm),theory(equality)],[70,564]),
[iquote('1:Res:70.2,564.0')] ).
cnf(570,plain,
( ~ aElementOf0(skc3,xS)
| equal(skc3,xx) ),
inference(ssi,[status(thm)],[568,221]),
[iquote('1:SSi:568.0,221.0')] ).
cnf(571,plain,
equal(skc3,xx),
inference(mrr,[status(thm)],[570,216]),
[iquote('1:MRR:570.0,216.0')] ).
cnf(572,plain,
aElementOf0(xx,xS),
inference(rew,[status(thm),theory(equality)],[571,216]),
[iquote('1:Rew:571.0,216.0')] ).
cnf(576,plain,
$false,
inference(mrr,[status(thm)],[572,6]),
[iquote('1:MRR:572.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jul 6 00:18:22 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.22/0.55
% 0.22/0.55 SPASS V 3.9
% 0.22/0.55 SPASS beiseite: Proof found.
% 0.22/0.55 % SZS status Theorem
% 0.22/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.55 SPASS derived 339 clauses, backtracked 39 clauses, performed 3 splits and kept 215 clauses.
% 0.22/0.55 SPASS allocated 98543 KBytes.
% 0.22/0.55 SPASS spent 0:00:00.17 on the problem.
% 0.22/0.55 0:00:00.04 for the input.
% 0.22/0.55 0:00:00.09 for the FLOTTER CNF translation.
% 0.22/0.55 0:00:00.00 for inferences.
% 0.22/0.55 0:00:00.00 for the backtracking.
% 0.22/0.55 0:00:00.02 for the reduction.
% 0.22/0.55
% 0.22/0.55
% 0.22/0.55 Here is a proof with depth 2, length 44 :
% 0.22/0.55 % SZS output start Refutation
% See solution above
% 0.22/0.55 Formulae used in the proof : m__679 m__ m__679_02 mEOfElem
% 0.22/0.55
%------------------------------------------------------------------------------