TSTP Solution File: NUM574+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM574+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.78s 0.94s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 44 ( 19 unt; 2 nHn; 44 RR)
% Number of literals : 82 ( 0 equ; 42 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
sdtlseqdt0(xj,xi),
file('NUM574+3.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(xj,szNzAzT0),
file('NUM574+3.p',unknown),
[] ).
cnf(16,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM574+3.p',unknown),
[] ).
cnf(17,axiom,
aElementOf0(skf35(u),szNzAzT0),
file('NUM574+3.p',unknown),
[] ).
cnf(24,axiom,
aElementOf0(skc1,sdtlpdtrp0(xN,xi)),
file('NUM574+3.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM574+3.p',unknown),
[] ).
cnf(30,axiom,
~ aElementOf0(skc1,sdtlpdtrp0(xN,xj)),
file('NUM574+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(sz00,u) ),
file('NUM574+3.p',unknown),
[] ).
cnf(45,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
file('NUM574+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
file('NUM574+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM574+3.p',unknown),
[] ).
cnf(59,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),u) ),
file('NUM574+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ skP0(u,v,w)
| equal(w,u)
| aElementOf0(w,v) ),
file('NUM574+3.p',unknown),
[] ).
cnf(71,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,v)
| skP0(w,v,u) ),
file('NUM574+3.p',unknown),
[] ).
cnf(78,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(u,sz00)
| equal(szszuzczcdt0(skf35(u)),u) ),
file('NUM574+3.p',unknown),
[] ).
cnf(95,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,sdtlpdtrp0(xN,u))
| aElementOf0(v,szNzAzT0) ),
file('NUM574+3.p',unknown),
[] ).
cnf(141,axiom,
( ~ sdtlseqdt0(u,v)
| ~ sdtlseqdt0(v,u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| equal(v,u) ),
file('NUM574+3.p',unknown),
[] ).
cnf(148,axiom,
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('NUM574+3.p',unknown),
[] ).
cnf(227,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),xi) ),
inference(mrr,[status(thm)],[148,10,45]),
[iquote('0:MRR:148.0,148.3,10.0,45.0')] ).
cnf(236,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xj,szNzAzT0)
| equal(xi,xj) ),
inference(res,[status(thm),theory(equality)],[10,141]),
[iquote('0:Res:10.0,141.2')] ).
cnf(250,plain,
( ~ aElement0(skc1)
| skP0(u,sdtlpdtrp0(xN,xi),skc1) ),
inference(res,[status(thm),theory(equality)],[24,71]),
[iquote('0:Res:24.0,71.1')] ).
cnf(254,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(skc1,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[24,95]),
[iquote('0:Res:24.0,95.0')] ).
cnf(265,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| aElement0(skc1) ),
inference(res,[status(thm),theory(equality)],[24,54]),
[iquote('0:Res:24.0,54.1')] ).
cnf(280,plain,
( ~ skP0(u,sdtlpdtrp0(xN,xj),skc1)
| equal(skc1,u) ),
inference(res,[status(thm),theory(equality)],[70,30]),
[iquote('0:Res:70.1,30.0')] ).
cnf(305,plain,
aElementOf0(skc1,szNzAzT0),
inference(mrr,[status(thm)],[254,16]),
[iquote('0:MRR:254.0,16.0')] ).
cnf(309,plain,
( ~ sdtlseqdt0(xi,xj)
| equal(xi,xj) ),
inference(mrr,[status(thm)],[236,16,15]),
[iquote('0:MRR:236.0,236.2,16.0,15.0')] ).
cnf(336,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElement0(skc1) ),
inference(sor,[status(thm)],[265,52]),
[iquote('0:SoR:265.0,52.1')] ).
cnf(338,plain,
aElement0(skc1),
inference(mrr,[status(thm)],[336,16]),
[iquote('0:MRR:336.0,16.0')] ).
cnf(339,plain,
skP0(u,sdtlpdtrp0(xN,xi),skc1),
inference(mrr,[status(thm)],[250,338]),
[iquote('0:MRR:250.0,338.0')] ).
cnf(375,plain,
~ equal(szszuzczcdt0(skf35(u)),xi),
inference(res,[status(thm),theory(equality)],[17,227]),
[iquote('0:Res:17.0,227.0')] ).
cnf(404,plain,
~ equal(szszuzczcdt0(skc1),skc1),
inference(res,[status(thm),theory(equality)],[305,59]),
[iquote('0:Res:305.0,59.0')] ).
cnf(746,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(u,xi)
| equal(u,sz00) ),
inference(spl,[status(thm),theory(equality)],[78,375]),
[iquote('0:SpL:78.2,375.0')] ).
cnf(1031,plain,
( ~ equal(xi,xi)
| equal(xi,sz00) ),
inference(res,[status(thm),theory(equality)],[16,746]),
[iquote('0:Res:16.0,746.0')] ).
cnf(1048,plain,
equal(xi,sz00),
inference(obv,[status(thm),theory(equality)],[1031]),
[iquote('0:Obv:1031.0')] ).
cnf(1056,plain,
skP0(u,sdtlpdtrp0(xN,sz00),skc1),
inference(rew,[status(thm),theory(equality)],[1048,339]),
[iquote('0:Rew:1048.0,339.0')] ).
cnf(1070,plain,
( ~ sdtlseqdt0(sz00,xj)
| equal(xi,xj) ),
inference(rew,[status(thm),theory(equality)],[1048,309]),
[iquote('0:Rew:1048.0,309.0')] ).
cnf(1107,plain,
skP0(u,xS,skc1),
inference(rew,[status(thm),theory(equality)],[29,1056]),
[iquote('0:Rew:29.0,1056.0')] ).
cnf(1113,plain,
( ~ sdtlseqdt0(sz00,xj)
| equal(xj,sz00) ),
inference(rew,[status(thm),theory(equality)],[1048,1070]),
[iquote('0:Rew:1048.0,1070.1')] ).
cnf(1156,plain,
( ~ aElementOf0(xj,szNzAzT0)
| equal(xj,sz00) ),
inference(res,[status(thm),theory(equality)],[40,1113]),
[iquote('0:Res:40.1,1113.0')] ).
cnf(1157,plain,
equal(xj,sz00),
inference(mrr,[status(thm)],[1156,15]),
[iquote('0:MRR:1156.0,15.0')] ).
cnf(1167,plain,
( ~ skP0(u,sdtlpdtrp0(xN,sz00),skc1)
| equal(skc1,u) ),
inference(rew,[status(thm),theory(equality)],[1157,280]),
[iquote('0:Rew:1157.0,280.0')] ).
cnf(1193,plain,
( ~ skP0(u,xS,skc1)
| equal(skc1,u) ),
inference(rew,[status(thm),theory(equality)],[29,1167]),
[iquote('0:Rew:29.0,1167.0')] ).
cnf(1194,plain,
equal(skc1,u),
inference(mrr,[status(thm)],[1193,1107]),
[iquote('0:MRR:1193.0,1107.0')] ).
cnf(1195,plain,
$false,
inference(unc,[status(thm)],[1194,404]),
[iquote('0:UnC:1194.0,404.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM574+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jul 6 06:29:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.78/0.94
% 0.78/0.94 SPASS V 3.9
% 0.78/0.94 SPASS beiseite: Proof found.
% 0.78/0.94 % SZS status Theorem
% 0.78/0.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.94 SPASS derived 737 clauses, backtracked 0 clauses, performed 2 splits and kept 588 clauses.
% 0.78/0.94 SPASS allocated 102490 KBytes.
% 0.78/0.94 SPASS spent 0:00:00.59 on the problem.
% 0.78/0.94 0:00:00.04 for the input.
% 0.78/0.94 0:00:00.43 for the FLOTTER CNF translation.
% 0.78/0.94 0:00:00.01 for inferences.
% 0.78/0.94 0:00:00.00 for the backtracking.
% 0.78/0.94 0:00:00.07 for the reduction.
% 0.78/0.94
% 0.78/0.94
% 0.78/0.94 Here is a proof with depth 3, length 44 :
% 0.78/0.94 % SZS output start Refutation
% See solution above
% 0.78/0.94 Formulae used in the proof : m__ m__3786 mNatExtra m__3623 mZeroLess m__3671 mEOfElem mNatNSucc mDefCons mLessASymm m__3786_02
% 0.78/0.94
%------------------------------------------------------------------------------