TSTP Solution File: NUM540+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM540+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:27:17 EDT 2022
% Result : Theorem 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 13 unt; 10 nHn; 29 RR)
% Number of literals : 60 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM540+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM540+1.p',unknown),
[] ).
cnf(4,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM540+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(slbdtrb0(sz00),slcrc0),
file('NUM540+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,slcrc0)
| aSet0(u) ),
file('NUM540+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aElementOf0(u,v)
| ~ equal(v,slcrc0) ),
file('NUM540+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM540+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(u),sz00) ),
file('NUM540+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| equal(u,slbdtrb0(v))
| aElementOf0(skf17(v,u),u)
| aElementOf0(skf17(v,u),szNzAzT0) ),
file('NUM540+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| equal(u,slbdtrb0(v))
| sdtlseqdt0(szszuzczcdt0(skf17(v,u)),v)
| aElementOf0(skf17(v,u),u) ),
file('NUM540+1.p',unknown),
[] ).
cnf(109,plain,
( ~ aSet0(slcrc0)
| ~ aElementOf0(sz00,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(skf17(sz00,slcrc0)),sz00)
| aElementOf0(skf17(sz00,slcrc0),slcrc0) ),
inference(res,[status(thm),theory(equality)],[76,6]),
[iquote('0:Res:76.4,6.0')] ).
cnf(110,plain,
( ~ aSet0(slcrc0)
| ~ aElementOf0(sz00,szNzAzT0)
| aElementOf0(skf17(sz00,slcrc0),szNzAzT0)
| aElementOf0(skf17(sz00,slcrc0),slcrc0) ),
inference(res,[status(thm),theory(equality)],[72,6]),
[iquote('0:Res:72.4,6.0')] ).
cnf(114,plain,
( ~ aSet0(slcrc0)
| aElementOf0(skf17(sz00,slcrc0),slcrc0)
| aElementOf0(skf17(sz00,slcrc0),szNzAzT0) ),
inference(mrr,[status(thm)],[110,4]),
[iquote('0:MRR:110.1,4.0')] ).
cnf(115,plain,
( ~ aSet0(slcrc0)
| sdtlseqdt0(szszuzczcdt0(skf17(sz00,slcrc0)),sz00)
| aElementOf0(skf17(sz00,slcrc0),slcrc0) ),
inference(mrr,[status(thm)],[109,4]),
[iquote('0:MRR:109.1,4.0')] ).
cnf(221,plain,
( ~ equal(slcrc0,slcrc0)
| aElementOf0(skf17(sz00,slcrc0),slcrc0)
| aElementOf0(skf17(sz00,slcrc0),szNzAzT0) ),
inference(sor,[status(thm)],[114,7]),
[iquote('0:SoR:114.0,7.1')] ).
cnf(222,plain,
( aElementOf0(skf17(sz00,slcrc0),slcrc0)
| aElementOf0(skf17(sz00,slcrc0),szNzAzT0) ),
inference(obv,[status(thm),theory(equality)],[221]),
[iquote('0:Obv:221.0')] ).
cnf(230,plain,
( ~ aSet0(szNzAzT0)
| aElementOf0(skf17(sz00,slcrc0),slcrc0)
| aElement0(skf17(sz00,slcrc0)) ),
inference(res,[status(thm),theory(equality)],[222,21]),
[iquote('0:Res:222.1,21.1')] ).
cnf(231,plain,
( aElementOf0(skf17(sz00,slcrc0),slcrc0)
| aElement0(skf17(sz00,slcrc0)) ),
inference(ssi,[status(thm)],[230,3,2]),
[iquote('0:SSi:230.0,3.0,2.0')] ).
cnf(235,plain,
aElementOf0(skf17(sz00,slcrc0),slcrc0),
inference(spt,[spt(split,[position(s1)])],[231]),
[iquote('1:Spt:231.0')] ).
cnf(236,plain,
~ equal(slcrc0,slcrc0),
inference(res,[status(thm),theory(equality)],[235,16]),
[iquote('1:Res:235.0,16.0')] ).
cnf(238,plain,
$false,
inference(obv,[status(thm),theory(equality)],[236]),
[iquote('1:Obv:236.0')] ).
cnf(239,plain,
~ aElementOf0(skf17(sz00,slcrc0),slcrc0),
inference(spt,[spt(split,[position(sa)])],[238,235]),
[iquote('1:Spt:238.0,231.0,235.0')] ).
cnf(240,plain,
aElement0(skf17(sz00,slcrc0)),
inference(spt,[spt(split,[position(s2)])],[231]),
[iquote('1:Spt:238.0,231.1')] ).
cnf(241,plain,
aElementOf0(skf17(sz00,slcrc0),szNzAzT0),
inference(mrr,[status(thm)],[222,239]),
[iquote('1:MRR:222.0,239.0')] ).
cnf(245,plain,
( ~ aSet0(slcrc0)
| sdtlseqdt0(szszuzczcdt0(skf17(sz00,slcrc0)),sz00) ),
inference(mrr,[status(thm)],[115,239]),
[iquote('1:MRR:115.2,239.0')] ).
cnf(257,plain,
( ~ equal(slcrc0,slcrc0)
| sdtlseqdt0(szszuzczcdt0(skf17(sz00,slcrc0)),sz00) ),
inference(sor,[status(thm)],[245,7]),
[iquote('1:SoR:245.0,7.1')] ).
cnf(258,plain,
sdtlseqdt0(szszuzczcdt0(skf17(sz00,slcrc0)),sz00),
inference(obv,[status(thm),theory(equality)],[257]),
[iquote('1:Obv:257.0')] ).
cnf(259,plain,
~ aElementOf0(skf17(sz00,slcrc0),szNzAzT0),
inference(res,[status(thm),theory(equality)],[258,27]),
[iquote('1:Res:258.0,27.1')] ).
cnf(261,plain,
$false,
inference(mrr,[status(thm)],[259,241]),
[iquote('1:MRR:259.0,241.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM540+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 : Tue Jul 5 21:50:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.54
% 0.18/0.54 SPASS V 3.9
% 0.18/0.54 SPASS beiseite: Proof found.
% 0.18/0.54 % SZS status Theorem
% 0.18/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54 SPASS derived 121 clauses, backtracked 9 clauses, performed 1 splits and kept 156 clauses.
% 0.18/0.54 SPASS allocated 98974 KBytes.
% 0.18/0.54 SPASS spent 0:00:00.20 on the problem.
% 0.18/0.54 0:00:00.04 for the input.
% 0.18/0.54 0:00:00.12 for the FLOTTER CNF translation.
% 0.18/0.54 0:00:00.00 for inferences.
% 0.18/0.54 0:00:00.00 for the backtracking.
% 0.18/0.54 0:00:00.01 for the reduction.
% 0.18/0.54
% 0.18/0.54
% 0.18/0.54 Here is a proof with depth 5, length 29 :
% 0.18/0.54 % SZS output start Refutation
% See solution above
% 0.18/0.54 Formulae used in the proof : mNATSet mZeroNum m__ mDefEmp mEOfElem mNoScLessZr mDefSeg
% 0.18/0.54
%------------------------------------------------------------------------------