TSTP Solution File: NUM581+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM581+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:27:45 EDT 2022
% Result : Theorem 1.65s 1.89s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 35 ( 14 unt; 2 nHn; 35 RR)
% Number of literals : 70 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
aSet0(xS),
file('NUM581+3.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM581+3.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM581+3.p',unknown),
[] ).
cnf(16,axiom,
~ aElementOf0(skc1,xS),
file('NUM581+3.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM581+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(sz00,u) ),
file('NUM581+3.p',unknown),
[] ).
cnf(47,axiom,
aElementOf0(skc1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
file('NUM581+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ aElementOf0(u,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,u)) ),
file('NUM581+3.p',unknown),
[] ).
cnf(58,axiom,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
file('NUM581+3.p',unknown),
[] ).
cnf(71,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0) ),
file('NUM581+3.p',unknown),
[] ).
cnf(109,axiom,
( ~ isCountable0(sdtlpdtrp0(xN,u))
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| skP6(u) ),
file('NUM581+3.p',unknown),
[] ).
cnf(112,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM581+3.p',unknown),
[] ).
cnf(121,axiom,
( ~ aElementOf0(u,xQ)
| aElementOf0(u,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
file('NUM581+3.p',unknown),
[] ).
cnf(163,axiom,
( ~ aElementOf0(u,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(u,xQ)
| equal(u,szmzizndt0(sdtlpdtrp0(xN,xi))) ),
file('NUM581+3.p',unknown),
[] ).
cnf(172,axiom,
( ~ sdtlseqdt0(u,v)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,v),sdtlpdtrp0(xN,u)) ),
file('NUM581+3.p',unknown),
[] ).
cnf(207,axiom,
( ~ skP6(u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,sdtmndt0(sdtlpdtrp0(xN,u),szmzizndt0(sdtlpdtrp0(xN,u))))
| aElementOf0(v,sdtlpdtrp0(xN,u)) ),
file('NUM581+3.p',unknown),
[] ).
cnf(272,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xS)
| ~ aElementOf0(skc1,u) ),
inference(res,[status(thm),theory(equality)],[112,16]),
[iquote('0:Res:112.3,16.0')] ).
cnf(278,plain,
( aElementOf0(skc1,xQ)
| equal(szmzizndt0(sdtlpdtrp0(xN,xi)),skc1) ),
inference(res,[status(thm),theory(equality)],[47,163]),
[iquote('0:Res:47.0,163.0')] ).
cnf(313,plain,
( ~ aSubsetOf0(u,xS)
| ~ aElementOf0(skc1,u) ),
inference(mrr,[status(thm)],[272,6]),
[iquote('0:MRR:272.0,6.0')] ).
cnf(326,plain,
equal(szmzizndt0(sdtlpdtrp0(xN,xi)),skc1),
inference(spt,[spt(split,[position(s1)])],[278]),
[iquote('1:Spt:278.1')] ).
cnf(360,plain,
aElementOf0(skc1,sdtlpdtrp0(xN,xi)),
inference(rew,[status(thm),theory(equality)],[326,58]),
[iquote('1:Rew:326.0,58.0')] ).
cnf(991,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,u))
| skP6(u) ),
inference(res,[status(thm),theory(equality)],[71,109]),
[iquote('0:Res:71.1,109.1')] ).
cnf(994,plain,
( ~ aElementOf0(u,szNzAzT0)
| skP6(u) ),
inference(mrr,[status(thm)],[991,56]),
[iquote('0:MRR:991.1,56.1')] ).
cnf(1002,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,sdtmndt0(sdtlpdtrp0(xN,u),szmzizndt0(sdtlpdtrp0(xN,u))))
| aElementOf0(v,sdtlpdtrp0(xN,u)) ),
inference(mrr,[status(thm)],[207,994]),
[iquote('0:MRR:207.0,994.1')] ).
cnf(6041,plain,
( ~ sdtlseqdt0(sz00,u)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(spr,[status(thm),theory(equality)],[30,172]),
[iquote('0:SpR:30.0,172.3')] ).
cnf(6047,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),xS) ),
inference(mrr,[status(thm)],[6041,41,11]),
[iquote('0:MRR:6041.0,6041.1,41.1,11.0')] ).
cnf(6459,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skc1,sdtlpdtrp0(xN,u)) ),
inference(res,[status(thm),theory(equality)],[6047,313]),
[iquote('0:Res:6047.1,313.0')] ).
cnf(6990,plain,
~ aElementOf0(xi,szNzAzT0),
inference(res,[status(thm),theory(equality)],[360,6459]),
[iquote('1:Res:360.0,6459.1')] ).
cnf(6991,plain,
$false,
inference(mrr,[status(thm)],[6990,15]),
[iquote('1:MRR:6990.0,15.0')] ).
cnf(6992,plain,
~ equal(szmzizndt0(sdtlpdtrp0(xN,xi)),skc1),
inference(spt,[spt(split,[position(sa)])],[6991,326]),
[iquote('1:Spt:6991.0,278.1,326.0')] ).
cnf(6993,plain,
aElementOf0(skc1,xQ),
inference(spt,[spt(split,[position(s2)])],[278]),
[iquote('1:Spt:6991.0,278.0')] ).
cnf(7682,plain,
( ~ aElementOf0(u,xQ)
| ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(u,sdtlpdtrp0(xN,xi)) ),
inference(res,[status(thm),theory(equality)],[121,1002]),
[iquote('0:Res:121.1,1002.1')] ).
cnf(7686,plain,
( ~ aElementOf0(u,xQ)
| aElementOf0(u,sdtlpdtrp0(xN,xi)) ),
inference(mrr,[status(thm)],[7682,15]),
[iquote('0:MRR:7682.1,15.0')] ).
cnf(7707,plain,
( ~ aElementOf0(skc1,xQ)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[7686,6459]),
[iquote('0:Res:7686.1,6459.1')] ).
cnf(7709,plain,
$false,
inference(mrr,[status(thm)],[7707,6993,15]),
[iquote('1:MRR:7707.0,7707.1,6993.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM581+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 08:47:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.65/1.89
% 1.65/1.89 SPASS V 3.9
% 1.65/1.89 SPASS beiseite: Proof found.
% 1.65/1.89 % SZS status Theorem
% 1.65/1.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.89 SPASS derived 5907 clauses, backtracked 1382 clauses, performed 27 splits and kept 3698 clauses.
% 1.65/1.89 SPASS allocated 102984 KBytes.
% 1.65/1.89 SPASS spent 0:00:01.50 on the problem.
% 1.65/1.89 0:00:00.04 for the input.
% 1.65/1.89 0:00:00.44 for the FLOTTER CNF translation.
% 1.65/1.89 0:00:00.08 for inferences.
% 1.65/1.89 0:00:00.02 for the backtracking.
% 1.65/1.89 0:00:00.85 for the reduction.
% 1.65/1.89
% 1.65/1.89
% 1.65/1.89 Here is a proof with depth 3, length 35 :
% 1.65/1.89 % SZS output start Refutation
% See solution above
% 1.65/1.89 Formulae used in the proof : m__3435 mZeroNum m__3989 m__ m__3623 mZeroLess m__3671 m__4007 mDefSub m__3989_02 m__3754
% 1.65/1.89
%------------------------------------------------------------------------------