TSTP Solution File: NUM545+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM545+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:27:20 EDT 2022
% Result : Theorem 133.75s 133.96s
% Output : Refutation 133.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 34 ( 19 unt; 4 nHn; 34 RR)
% Number of literals : 66 ( 0 equ; 37 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM545+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM545+1.p',unknown),
[] ).
cnf(4,axiom,
isFinite0(xS),
file('NUM545+1.p',unknown),
[] ).
cnf(5,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM545+1.p',unknown),
[] ).
cnf(6,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM545+1.p',unknown),
[] ).
cnf(8,axiom,
equal(slbdtrb0(sz00),slcrc0),
file('NUM545+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,slcrc0)
| aSet0(u) ),
file('NUM545+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ aSet0(u)
| aSubsetOf0(u,u) ),
file('NUM545+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
file('NUM545+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(u)) ),
file('NUM545+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM545+1.p',unknown),
[] ).
cnf(31,axiom,
( equal(slcrc0,xS)
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('NUM545+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM545+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ isFinite0(u)
| ~ aSubsetOf0(u,szNzAzT0)
| ~ equal(v,szmzazxdt0(u))
| aElementOf0(v,u)
| equal(u,slcrc0) ),
file('NUM545+1.p',unknown),
[] ).
cnf(106,plain,
~ aSubsetOf0(xS,slbdtrb0(sz00)),
inference(res,[status(thm),theory(equality)],[5,23]),
[iquote('0:Res:5.0,23.0')] ).
cnf(108,plain,
~ aSubsetOf0(xS,slcrc0),
inference(rew,[status(thm),theory(equality)],[8,106]),
[iquote('0:Rew:8.0,106.0')] ).
cnf(109,plain,
equal(slcrc0,xS),
inference(spt,[spt(split,[position(s1)])],[31]),
[iquote('1:Spt:31.0')] ).
cnf(115,plain,
( ~ equal(u,xS)
| aSet0(u) ),
inference(rew,[status(thm),theory(equality)],[109,9]),
[iquote('1:Rew:109.0,9.0')] ).
cnf(118,plain,
~ aSubsetOf0(xS,xS),
inference(rew,[status(thm),theory(equality)],[109,108]),
[iquote('1:Rew:109.0,108.0')] ).
cnf(124,plain,
~ aSet0(xS),
inference(res,[status(thm),theory(equality)],[11,118]),
[iquote('1:Res:11.1,118.0')] ).
cnf(125,plain,
~ equal(xS,xS),
inference(sor,[status(thm)],[124,115]),
[iquote('1:SoR:124.0,115.1')] ).
cnf(126,plain,
$false,
inference(obv,[status(thm),theory(equality)],[125]),
[iquote('1:Obv:125.0')] ).
cnf(127,plain,
~ equal(slcrc0,xS),
inference(spt,[spt(split,[position(sa)])],[126,109]),
[iquote('1:Spt:126.0,31.0,109.0')] ).
cnf(128,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(spt,[spt(split,[position(s2)])],[31]),
[iquote('1:Spt:126.0,31.1')] ).
cnf(142,plain,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(res,[status(thm),theory(equality)],[128,23]),
[iquote('1:Res:128.0,23.1')] ).
cnf(143,plain,
~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(res,[status(thm),theory(equality)],[20,142]),
[iquote('1:Res:20.1,142.0')] ).
cnf(152,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[6,26]),
[iquote('0:Res:6.0,26.1')] ).
cnf(155,plain,
aSet0(xS),
inference(ssi,[status(thm)],[152,3,2]),
[iquote('0:SSi:152.0,3.0,2.0')] ).
cnf(1052,plain,
( ~ isFinite0(u)
| ~ aSubsetOf0(u,szNzAzT0)
| aElementOf0(szmzazxdt0(u),u)
| equal(u,slcrc0) ),
inference(eqr,[status(thm),theory(equality)],[68]),
[iquote('0:EqR:68.2')] ).
cnf(1941,plain,
( ~ isFinite0(u)
| ~ aSet0(v)
| ~ aSubsetOf0(u,szNzAzT0)
| ~ aSubsetOf0(u,v)
| equal(u,slcrc0)
| aElementOf0(szmzazxdt0(u),v) ),
inference(res,[status(thm),theory(equality)],[1052,47]),
[iquote('0:Res:1052.2,47.1')] ).
cnf(74987,plain,
( ~ isFinite0(xS)
| ~ aSet0(szNzAzT0)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ aSubsetOf0(xS,szNzAzT0)
| equal(slcrc0,xS) ),
inference(res,[status(thm),theory(equality)],[1941,143]),
[iquote('1:Res:1941.5,143.0')] ).
cnf(75032,plain,
( ~ isFinite0(xS)
| ~ aSet0(szNzAzT0)
| ~ aSubsetOf0(xS,szNzAzT0)
| equal(slcrc0,xS) ),
inference(obv,[status(thm),theory(equality)],[74987]),
[iquote('1:Obv:74987.2')] ).
cnf(75033,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| equal(slcrc0,xS) ),
inference(ssi,[status(thm)],[75032,3,2,4,155]),
[iquote('1:SSi:75032.1,75032.0,3.0,2.0,4.0,155.0')] ).
cnf(75034,plain,
$false,
inference(mrr,[status(thm)],[75033,6,127]),
[iquote('1:MRR:75033.0,75033.1,6.0,127.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM545+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.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 : Thu Jul 7 00:09:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 133.75/133.96
% 133.75/133.96 SPASS V 3.9
% 133.75/133.96 SPASS beiseite: Proof found.
% 133.75/133.96 % SZS status Theorem
% 133.75/133.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 133.75/133.96 SPASS derived 55223 clauses, backtracked 5640 clauses, performed 31 splits and kept 19008 clauses.
% 133.75/133.96 SPASS allocated 156066 KBytes.
% 133.75/133.96 SPASS spent 0:02:01.42 on the problem.
% 133.75/133.96 0:00:00.04 for the input.
% 133.75/133.96 0:00:00.13 for the FLOTTER CNF translation.
% 133.75/133.96 0:00:00.97 for inferences.
% 133.75/133.96 0:00:03.98 for the backtracking.
% 133.75/133.96 0:1:55.81 for the reduction.
% 133.75/133.96
% 133.75/133.96
% 133.75/133.96 Here is a proof with depth 4, length 34 :
% 133.75/133.96 % SZS output start Refutation
% See solution above
% 133.75/133.96 Formulae used in the proof : mNATSet m__1986 mZeroNum mSegZero mDefEmp mSubRefl mSuccNum m__ mDefSub m__2035 mDefMax
% 133.75/133.96
%------------------------------------------------------------------------------