TSTP Solution File: NUM437+5 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM437+5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:26:11 EDT 2022
% Result : Theorem 3.29s 3.46s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 52 ( 17 unt; 12 nHn; 52 RR)
% Number of literals : 120 ( 0 equ; 62 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aSet0(sbsmnsldt0(xS)),
file('NUM437+5.p',unknown),
[] ).
cnf(6,axiom,
aElementOf0(skc1,sbsmnsldt0(xS)),
file('NUM437+5.p',unknown),
[] ).
cnf(7,axiom,
aElementOf0(skf17(u),xS),
file('NUM437+5.p',unknown),
[] ).
cnf(11,axiom,
aInteger0(skf33(u,v)),
file('NUM437+5.p',unknown),
[] ).
cnf(16,axiom,
( ~ aElementOf0(u,xS)
| aSet0(u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(17,axiom,
( ~ aElementOf0(u,xS)
| isOpen0(u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(18,axiom,
( ~ aElementOf0(u,sbsmnsldt0(xS))
| aInteger0(u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(30,axiom,
( ~ aElementOf0(u,sbsmnsldt0(xS))
| aElementOf0(u,skf17(u)) ),
file('NUM437+5.p',unknown),
[] ).
cnf(48,axiom,
( ~ aElementOf0(u,cS1395)
| ~ aElementOf0(v,xS)
| aInteger0(u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(55,axiom,
( ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS)
| aElementOf0(u,cS1395) ),
file('NUM437+5.p',unknown),
[] ).
cnf(56,axiom,
( ~ aInteger0(u)
| equal(u,sz00)
| aElementOf0(skf19(u),szAzrzSzezqlpdtcmdtrp0(skc1,u)) ),
file('NUM437+5.p',unknown),
[] ).
cnf(57,axiom,
( ~ aInteger0(u)
| ~ aElementOf0(skf19(v),sbsmnsldt0(xS))
| equal(u,sz00) ),
file('NUM437+5.p',unknown),
[] ).
cnf(67,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(68,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| aSubsetOf0(v,u)
| aElementOf0(skf22(v,w),v) ),
file('NUM437+5.p',unknown),
[] ).
cnf(70,axiom,
( ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS)
| ~ equal(skf33(v,u),sz00) ),
file('NUM437+5.p',unknown),
[] ).
cnf(72,axiom,
( ~ aInteger0(u)
| ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS)
| aElementOf0(u,sbsmnsldt0(xS)) ),
file('NUM437+5.p',unknown),
[] ).
cnf(74,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aElementOf0(skf22(v,u),u)
| aSubsetOf0(v,u) ),
file('NUM437+5.p',unknown),
[] ).
cnf(93,axiom,
( ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS)
| ~ aElementOf0(w,szAzrzSzezqlpdtcmdtrp0(u,skf33(v,u)))
| aElementOf0(w,v) ),
file('NUM437+5.p',unknown),
[] ).
cnf(146,plain,
( ~ aElementOf0(u,v)
| ~ aSubsetOf0(v,sbsmnsldt0(xS))
| aElementOf0(u,sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[4,67]),
[iquote('0:Res:4.0,67.0')] ).
cnf(152,plain,
( ~ aSet0(u)
| aSubsetOf0(u,sbsmnsldt0(xS))
| aElementOf0(skf22(u,v),u) ),
inference(res,[status(thm),theory(equality)],[4,68]),
[iquote('0:Res:4.0,68.1')] ).
cnf(159,plain,
aSet0(skf17(u)),
inference(res,[status(thm),theory(equality)],[7,16]),
[iquote('0:Res:7.0,16.0')] ).
cnf(160,plain,
isOpen0(skf17(u)),
inference(res,[status(thm),theory(equality)],[7,17]),
[iquote('0:Res:7.0,17.0')] ).
cnf(162,plain,
( ~ aInteger0(u)
| ~ aElementOf0(u,skf17(v))
| aElementOf0(u,sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[7,72]),
[iquote('0:Res:7.0,72.1')] ).
cnf(165,plain,
( ~ aElementOf0(u,skf17(v))
| aElementOf0(u,cS1395) ),
inference(res,[status(thm),theory(equality)],[7,55]),
[iquote('0:Res:7.0,55.1')] ).
cnf(166,plain,
( ~ aElementOf0(u,cS1395)
| aInteger0(u) ),
inference(res,[status(thm),theory(equality)],[7,48]),
[iquote('0:Res:7.0,48.1')] ).
cnf(205,plain,
aElementOf0(skc1,skf17(skc1)),
inference(res,[status(thm),theory(equality)],[6,30]),
[iquote('0:Res:6.0,30.0')] ).
cnf(206,plain,
aInteger0(skc1),
inference(res,[status(thm),theory(equality)],[6,18]),
[iquote('0:Res:6.0,18.0')] ).
cnf(425,plain,
( ~ aInteger0(u)
| equal(u,sz00) ),
inference(spt,[spt(split,[position(s1)])],[57]),
[iquote('1:Spt:57.0,57.2')] ).
cnf(492,plain,
equal(skc1,sz00),
inference(ems,[status(thm)],[425,206]),
[iquote('1:EmS:425.0,206.0')] ).
cnf(507,plain,
aElementOf0(sz00,skf17(sz00)),
inference(rew,[status(thm),theory(equality)],[492,205]),
[iquote('1:Rew:492.0,205.0')] ).
cnf(530,plain,
equal(skf33(u,v),sz00),
inference(ems,[status(thm)],[425,11]),
[iquote('1:EmS:425.0,11.0')] ).
cnf(543,plain,
( ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS)
| ~ equal(sz00,sz00) ),
inference(rew,[status(thm),theory(equality)],[530,70]),
[iquote('1:Rew:530.0,70.2')] ).
cnf(548,plain,
( ~ aElementOf0(u,v)
| ~ aElementOf0(v,xS) ),
inference(obv,[status(thm),theory(equality)],[543]),
[iquote('1:Obv:543.2')] ).
cnf(629,plain,
~ aElementOf0(skf17(sz00),xS),
inference(res,[status(thm),theory(equality)],[507,548]),
[iquote('1:Res:507.0,548.0')] ).
cnf(633,plain,
$false,
inference(mrr,[status(thm)],[629,7]),
[iquote('1:MRR:629.0,7.0')] ).
cnf(634,plain,
~ aElementOf0(skf19(u),sbsmnsldt0(xS)),
inference(spt,[spt(split,[position(s2)])],[57]),
[iquote('1:Spt:633.0,57.1')] ).
cnf(2237,plain,
( ~ aSet0(skf17(u))
| ~ aInteger0(skf22(skf17(u),v))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aElementOf0(skf22(skf17(u),v),sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[152,162]),
[iquote('0:Res:152.2,162.1')] ).
cnf(2239,plain,
( ~ aSet0(skf17(u))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aElementOf0(skf22(skf17(u),v),cS1395) ),
inference(res,[status(thm),theory(equality)],[152,165]),
[iquote('0:Res:152.2,165.0')] ).
cnf(2246,plain,
( aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aElementOf0(skf22(skf17(u),v),cS1395) ),
inference(ssi,[status(thm)],[2239,159,160]),
[iquote('0:SSi:2239.0,159.0,160.0')] ).
cnf(2257,plain,
( ~ aInteger0(skf22(skf17(u),v))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aElementOf0(skf22(skf17(u),v),sbsmnsldt0(xS)) ),
inference(ssi,[status(thm)],[2237,159,160]),
[iquote('0:SSi:2237.0,159.0,160.0')] ).
cnf(2341,plain,
( aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aInteger0(skf22(skf17(u),v)) ),
inference(res,[status(thm),theory(equality)],[2246,166]),
[iquote('0:Res:2246.1,166.0')] ).
cnf(2345,plain,
( aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aElementOf0(skf22(skf17(u),v),sbsmnsldt0(xS)) ),
inference(mrr,[status(thm)],[2257,2341]),
[iquote('0:MRR:2257.0,2341.1')] ).
cnf(3007,plain,
( ~ aSet0(sbsmnsldt0(xS))
| ~ aSet0(skf17(u))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[2345,74]),
[iquote('0:Res:2345.1,74.2')] ).
cnf(3011,plain,
( ~ aSet0(sbsmnsldt0(xS))
| ~ aSet0(skf17(u))
| aSubsetOf0(skf17(u),sbsmnsldt0(xS)) ),
inference(obv,[status(thm),theory(equality)],[3007]),
[iquote('0:Obv:3007.2')] ).
cnf(3051,plain,
( ~ aInteger0(skf33(u,skc1))
| ~ aElementOf0(skc1,u)
| ~ aElementOf0(u,xS)
| equal(skf33(u,skc1),sz00)
| aElementOf0(skf19(skf33(u,skc1)),u) ),
inference(res,[status(thm),theory(equality)],[56,93]),
[iquote('0:Res:56.2,93.2')] ).
cnf(5664,plain,
( ~ aElementOf0(skc1,u)
| ~ aElementOf0(u,xS)
| equal(skf33(u,skc1),sz00)
| aElementOf0(skf19(skf33(u,skc1)),u) ),
inference(ssi,[status(thm)],[3051,11,206]),
[iquote('0:SSi:3051.0,11.0,206.0')] ).
cnf(5665,plain,
( ~ aElementOf0(skc1,u)
| ~ aElementOf0(u,xS)
| aElementOf0(skf19(skf33(u,skc1)),u) ),
inference(mrr,[status(thm)],[5664,70]),
[iquote('0:MRR:5664.2,70.2')] ).
cnf(9111,plain,
aSubsetOf0(skf17(u),sbsmnsldt0(xS)),
inference(ssi,[status(thm)],[3011,159,160,4]),
[iquote('0:SSi:3011.1,3011.0,159.0,160.0,4.0')] ).
cnf(9177,plain,
( ~ aElementOf0(u,skf17(v))
| aElementOf0(u,sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[9111,146]),
[iquote('0:Res:9111.0,146.1')] ).
cnf(9616,plain,
( ~ aElementOf0(skc1,skf17(u))
| ~ aElementOf0(skf17(u),xS)
| aElementOf0(skf19(skf33(skf17(u),skc1)),sbsmnsldt0(xS)) ),
inference(res,[status(thm),theory(equality)],[5665,9177]),
[iquote('0:Res:5665.2,9177.0')] ).
cnf(9625,plain,
~ aElementOf0(skc1,skf17(u)),
inference(mrr,[status(thm)],[9616,7,634]),
[iquote('1:MRR:9616.1,9616.2,7.0,634.0')] ).
cnf(9626,plain,
$false,
inference(unc,[status(thm)],[9625,205]),
[iquote('1:UnC:9625.0,205.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM437+5 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jul 6 02:52:28 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.29/3.46
% 3.29/3.46 SPASS V 3.9
% 3.29/3.46 SPASS beiseite: Proof found.
% 3.29/3.46 % SZS status Theorem
% 3.29/3.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.29/3.46 SPASS derived 6926 clauses, backtracked 2203 clauses, performed 52 splits and kept 4998 clauses.
% 3.29/3.46 SPASS allocated 105165 KBytes.
% 3.29/3.46 SPASS spent 0:00:02.94 on the problem.
% 3.29/3.46 0:00:00.03 for the input.
% 3.29/3.46 0:00:00.17 for the FLOTTER CNF translation.
% 3.29/3.46 0:00:00.09 for inferences.
% 3.29/3.46 0:00:00.05 for the backtracking.
% 3.29/3.46 0:00:02.50 for the reduction.
% 3.29/3.46
% 3.29/3.46
% 3.29/3.46 Here is a proof with depth 5, length 52 :
% 3.29/3.46 % SZS output start Refutation
% See solution above
% 3.29/3.46 Formulae used in the proof : m__ mIntOne m__1750 mSubset
% 3.29/3.46
%------------------------------------------------------------------------------