TSTP Solution File: NUM582+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM582+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:27:45 EDT 2022
% Result : Theorem 0.72s 0.90s
% Output : Refutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 9 unt; 0 nHn; 23 RR)
% Number of literals : 52 ( 0 equ; 36 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM582+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM582+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM582+1.p',unknown),
[] ).
cnf(11,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM582+1.p',unknown),
[] ).
cnf(13,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM582+1.p',unknown),
[] ).
cnf(23,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM582+1.p',unknown),
[] ).
cnf(24,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('NUM582+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(sz00,u) ),
file('NUM582+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM582+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ sdtlseqdt0(u,v)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,v),sdtlpdtrp0(xN,u)) ),
file('NUM582+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| ~ aSubsetOf0(u,v)
| ~ aSubsetOf0(v,w)
| aSubsetOf0(u,w) ),
file('NUM582+1.p',unknown),
[] ).
cnf(172,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aSubsetOf0(w,v)
| aSubsetOf0(w,u) ),
inference(mrr,[status(thm)],[121,45]),
[iquote('0:MRR:121.0,121.1,45.2,45.2')] ).
cnf(179,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),u) ),
inference(res,[status(thm),theory(equality)],[172,24]),
[iquote('0:Res:172.3,24.0')] ).
cnf(254,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[11,45]),
[iquote('0:Res:11.0,45.1')] ).
cnf(258,plain,
aSet0(xS),
inference(ssi,[status(thm)],[254,3,2]),
[iquote('0:SSi:254.0,3.0,2.0')] ).
cnf(259,plain,
( ~ aSubsetOf0(u,xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),u) ),
inference(mrr,[status(thm)],[179,258]),
[iquote('0:MRR:179.0,258.0')] ).
cnf(2069,plain,
( ~ sdtlseqdt0(sz00,u)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(spr,[status(thm),theory(equality)],[23,108]),
[iquote('0:SpR:23.0,108.3')] ).
cnf(2075,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(res,[status(thm),theory(equality)],[108,259]),
[iquote('0:Res:108.3,259.1')] ).
cnf(2076,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(mrr,[status(thm)],[2069,34,9]),
[iquote('0:MRR:2069.0,2069.1,34.1,9.0')] ).
cnf(2078,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(mrr,[status(thm)],[2075,13]),
[iquote('0:MRR:2075.2,13.0')] ).
cnf(2079,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0) ),
inference(mrr,[status(thm)],[2078,2076]),
[iquote('0:MRR:2078.2,2076.1')] ).
cnf(2083,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[34,2079]),
[iquote('0:Res:34.1,2079.0')] ).
cnf(2090,plain,
$false,
inference(mrr,[status(thm)],[2083,13,9]),
[iquote('0:MRR:2083.0,2083.1,13.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM582+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 23:53:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/0.90
% 0.72/0.90 SPASS V 3.9
% 0.72/0.90 SPASS beiseite: Proof found.
% 0.72/0.90 % SZS status Theorem
% 0.72/0.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.72/0.90 SPASS derived 1416 clauses, backtracked 119 clauses, performed 9 splits and kept 874 clauses.
% 0.72/0.90 SPASS allocated 101012 KBytes.
% 0.72/0.90 SPASS spent 0:00:00.54 on the problem.
% 0.72/0.90 0:00:00.04 for the input.
% 0.72/0.90 0:00:00.24 for the FLOTTER CNF translation.
% 0.72/0.90 0:00:00.02 for inferences.
% 0.72/0.90 0:00:00.00 for the backtracking.
% 0.72/0.90 0:00:00.19 for the reduction.
% 0.72/0.90
% 0.72/0.90
% 0.72/0.90 Here is a proof with depth 3, length 23 :
% 0.72/0.90 % SZS output start Refutation
% See solution above
% 0.72/0.90 Formulae used in the proof : mNATSet mZeroNum m__3435 m__3989 m__3623 m__ mZeroLess mDefSub m__3754 mSubTrans
% 0.72/0.90
%------------------------------------------------------------------------------