TSTP Solution File: NUM574+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM574+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 14:27:40 EDT 2022
% Result : Theorem 0.56s 0.76s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 35 ( 20 unt; 1 nHn; 35 RR)
% Number of literals : 60 ( 0 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(6,axiom,
isCountable0(xS),
file('NUM574+1.p',unknown),
[] ).
cnf(9,axiom,
sdtlseqdt0(xj,xi),
file('NUM574+1.p',unknown),
[] ).
cnf(12,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(14,axiom,
aElementOf0(xj,szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(16,axiom,
aElementOf0(skf25(u),szNzAzT0),
file('NUM574+1.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM574+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aSet0(u)
| aSubsetOf0(u,u) ),
file('NUM574+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(sz00,u) ),
file('NUM574+1.p',unknown),
[] ).
cnf(38,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
file('NUM574+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM574+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(u,sz00)
| equal(szszuzczcdt0(skf25(u)),u) ),
file('NUM574+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ sdtlseqdt0(u,v)
| ~ sdtlseqdt0(v,u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| equal(v,u) ),
file('NUM574+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('NUM574+1.p',unknown),
[] ).
cnf(170,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),xi) ),
inference(mrr,[status(thm)],[108,9,38]),
[iquote('0:MRR:108.0,108.3,9.0,38.0')] ).
cnf(181,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xj,szNzAzT0)
| equal(xi,xj) ),
inference(res,[status(thm),theory(equality)],[9,106]),
[iquote('0:Res:9.0,106.2')] ).
cnf(203,plain,
( ~ sdtlseqdt0(xi,xj)
| equal(xi,xj) ),
inference(mrr,[status(thm)],[181,15,14]),
[iquote('0:MRR:181.0,181.2,15.0,14.0')] ).
cnf(250,plain,
~ equal(szszuzczcdt0(skf25(u)),xi),
inference(res,[status(thm),theory(equality)],[16,170]),
[iquote('0:Res:16.0,170.0')] ).
cnf(287,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[12,47]),
[iquote('0:Res:12.0,47.1')] ).
cnf(292,plain,
aSet0(xS),
inference(ssi,[status(thm)],[287,3,2]),
[iquote('0:SSi:287.0,3.0,2.0')] ).
cnf(435,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(u,xi)
| equal(u,sz00) ),
inference(spl,[status(thm),theory(equality)],[64,250]),
[iquote('0:SpL:64.2,250.0')] ).
cnf(442,plain,
( ~ equal(xi,xi)
| equal(xi,sz00) ),
inference(res,[status(thm),theory(equality)],[15,435]),
[iquote('0:Res:15.0,435.0')] ).
cnf(452,plain,
equal(xi,sz00),
inference(obv,[status(thm),theory(equality)],[442]),
[iquote('0:Obv:442.0')] ).
cnf(467,plain,
( ~ sdtlseqdt0(sz00,xj)
| equal(xi,xj) ),
inference(rew,[status(thm),theory(equality)],[452,203]),
[iquote('0:Rew:452.0,203.0')] ).
cnf(468,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,sz00),sdtlpdtrp0(xN,xj)),
inference(rew,[status(thm),theory(equality)],[452,38]),
[iquote('0:Rew:452.0,38.0')] ).
cnf(486,plain,
( ~ sdtlseqdt0(sz00,xj)
| equal(xj,sz00) ),
inference(rew,[status(thm),theory(equality)],[452,467]),
[iquote('0:Rew:452.0,467.1')] ).
cnf(487,plain,
~ aSubsetOf0(xS,sdtlpdtrp0(xN,xj)),
inference(rew,[status(thm),theory(equality)],[25,468]),
[iquote('0:Rew:25.0,468.0')] ).
cnf(498,plain,
( ~ aElementOf0(xj,szNzAzT0)
| equal(xj,sz00) ),
inference(res,[status(thm),theory(equality)],[35,486]),
[iquote('0:Res:35.1,486.0')] ).
cnf(499,plain,
equal(xj,sz00),
inference(mrr,[status(thm)],[498,14]),
[iquote('0:MRR:498.0,14.0')] ).
cnf(509,plain,
~ aSubsetOf0(xS,sdtlpdtrp0(xN,sz00)),
inference(rew,[status(thm),theory(equality)],[499,487]),
[iquote('0:Rew:499.0,487.0')] ).
cnf(515,plain,
~ aSubsetOf0(xS,xS),
inference(rew,[status(thm),theory(equality)],[25,509]),
[iquote('0:Rew:25.0,509.0')] ).
cnf(519,plain,
~ aSet0(xS),
inference(res,[status(thm),theory(equality)],[28,515]),
[iquote('0:Res:28.1,515.0')] ).
cnf(520,plain,
$false,
inference(ssi,[status(thm)],[519,6,292]),
[iquote('0:SSi:519.0,6.0,292.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM574+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.15 % Command : run_spass %d %s
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Thu Jul 7 07:23:59 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.56/0.76
% 0.56/0.76 SPASS V 3.9
% 0.56/0.76 SPASS beiseite: Proof found.
% 0.56/0.76 % SZS status Theorem
% 0.56/0.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.76 SPASS derived 256 clauses, backtracked 0 clauses, performed 0 splits and kept 279 clauses.
% 0.56/0.76 SPASS allocated 100975 KBytes.
% 0.56/0.76 SPASS spent 0:00:00.37 on the problem.
% 0.56/0.76 0:00:00.04 for the input.
% 0.56/0.76 0:00:00.27 for the FLOTTER CNF translation.
% 0.56/0.76 0:00:00.00 for inferences.
% 0.56/0.76 0:00:00.00 for the backtracking.
% 0.56/0.76 0:00:00.03 for the reduction.
% 0.56/0.76
% 0.56/0.76
% 0.56/0.76 Here is a proof with depth 3, length 35 :
% 0.56/0.76 % SZS output start Refutation
% See solution above
% 0.56/0.76 Formulae used in the proof : mNATSet m__3435 m__ m__3786 mNatExtra m__3623 mSubRefl mZeroLess mDefSub mLessASymm m__3786_02
% 0.56/0.76
%------------------------------------------------------------------------------