TSTP Solution File: NUM603+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM603+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:27:59 EDT 2022
% Result : Theorem 0.84s 1.03s
% Output : Refutation 0.84s
% 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('NUM603+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM603+1.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM603+1.p',unknown),
[] ).
cnf(17,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM603+1.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM603+1.p',unknown),
[] ).
cnf(38,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM603+1.p',unknown),
[] ).
cnf(41,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('NUM603+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(sz00,u) ),
file('NUM603+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM603+1.p',unknown),
[] ).
cnf(132,axiom,
( ~ sdtlseqdt0(u,v)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,v),sdtlpdtrp0(xN,u)) ),
file('NUM603+1.p',unknown),
[] ).
cnf(146,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| ~ aSubsetOf0(u,v)
| ~ aSubsetOf0(v,w)
| aSubsetOf0(u,w) ),
file('NUM603+1.p',unknown),
[] ).
cnf(205,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aSubsetOf0(w,v)
| aSubsetOf0(w,u) ),
inference(mrr,[status(thm)],[146,66]),
[iquote('0:MRR:146.0,146.1,66.2,66.2')] ).
cnf(218,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),u) ),
inference(res,[status(thm),theory(equality)],[205,41]),
[iquote('0:Res:205.3,41.0')] ).
cnf(317,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[17,66]),
[iquote('0:Res:17.0,66.1')] ).
cnf(322,plain,
aSet0(xS),
inference(ssi,[status(thm)],[317,3,2]),
[iquote('0:SSi:317.0,3.0,2.0')] ).
cnf(323,plain,
( ~ aSubsetOf0(u,xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),u) ),
inference(mrr,[status(thm)],[218,322]),
[iquote('0:MRR:218.0,322.0')] ).
cnf(2314,plain,
( ~ sdtlseqdt0(sz00,u)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(spr,[status(thm),theory(equality)],[38,132]),
[iquote('0:SpR:38.0,132.3')] ).
cnf(2320,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(res,[status(thm),theory(equality)],[132,323]),
[iquote('0:Res:132.3,323.1')] ).
cnf(2321,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(mrr,[status(thm)],[2314,53,15]),
[iquote('0:MRR:2314.0,2314.1,53.1,15.0')] ).
cnf(2323,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(mrr,[status(thm)],[2320,21]),
[iquote('0:MRR:2320.2,21.0')] ).
cnf(2324,plain,
( ~ sdtlseqdt0(u,xi)
| ~ aElementOf0(u,szNzAzT0) ),
inference(mrr,[status(thm)],[2323,2321]),
[iquote('0:MRR:2323.2,2321.1')] ).
cnf(2328,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[53,2324]),
[iquote('0:Res:53.1,2324.0')] ).
cnf(2335,plain,
$false,
inference(mrr,[status(thm)],[2328,21,15]),
[iquote('0:MRR:2328.0,2328.1,21.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : NUM603+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 : Tue Jul 5 17:22:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.84/1.03
% 0.84/1.03 SPASS V 3.9
% 0.84/1.03 SPASS beiseite: Proof found.
% 0.84/1.03 % SZS status Theorem
% 0.84/1.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.03 SPASS derived 1542 clauses, backtracked 132 clauses, performed 10 splits and kept 981 clauses.
% 0.84/1.03 SPASS allocated 101075 KBytes.
% 0.84/1.03 SPASS spent 0:00:00.67 on the problem.
% 0.84/1.03 0:00:00.04 for the input.
% 0.84/1.03 0:00:00.30 for the FLOTTER CNF translation.
% 0.84/1.03 0:00:00.03 for inferences.
% 0.84/1.03 0:00:00.00 for the backtracking.
% 0.84/1.03 0:00:00.26 for the reduction.
% 0.84/1.03
% 0.84/1.03
% 0.84/1.03 Here is a proof with depth 3, length 23 :
% 0.84/1.03 % SZS output start Refutation
% See solution above
% 0.84/1.03 Formulae used in the proof : mNATSet mZeroNum m__3435 m__5034 m__3623 m__ mZeroLess mDefSub m__3754 mSubTrans
% 0.84/1.03
%------------------------------------------------------------------------------