TSTP Solution File: NUM584+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM584+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 14:27:47 EDT 2022
% Result : Theorem 87.48s 87.68s
% Output : Refutation 87.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 31 ( 18 unt; 0 nHn; 31 RR)
% Number of literals : 61 ( 0 equ; 35 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(6,axiom,
isCountable0(xS),
file('NUM584+1.p',unknown),
[] ).
cnf(8,axiom,
aFunction0(xN),
file('NUM584+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(11,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(20,axiom,
equal(szDzozmdt0(xN),szNzAzT0),
file('NUM584+1.p',unknown),
[] ).
cnf(23,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM584+1.p',unknown),
[] ).
cnf(29,axiom,
equal(slbdtsldtrb0(xS,xK),szDzozmdt0(xc)),
file('NUM584+1.p',unknown),
[] ).
cnf(42,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('NUM584+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM584+1.p',unknown),
[] ).
cnf(52,axiom,
equal(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xK),
file('NUM584+1.p',unknown),
[] ).
cnf(56,axiom,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('NUM584+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aFunction0(u)
| ~ aElementOf0(v,szDzozmdt0(u))
| aElement0(sdtlpdtrp0(u,v)) ),
file('NUM584+1.p',unknown),
[] ).
cnf(142,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aElementOf0(w,szNzAzT0)
| ~ equal(x,slbdtsldtrb0(u,w))
| ~ equal(sbrdtbr0(v),w)
| aElementOf0(v,x) ),
file('NUM584+1.p',unknown),
[] ).
cnf(169,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(rew,[status(thm),theory(equality)],[29,56]),
[iquote('0:Rew:29.0,56.0')] ).
cnf(266,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[11,45]),
[iquote('0:Res:11.0,45.1')] ).
cnf(271,plain,
aSet0(xS),
inference(ssi,[status(thm)],[266,3,2]),
[iquote('0:SSi:266.0,3.0,2.0')] ).
cnf(442,plain,
( ~ aFunction0(xN)
| ~ aElementOf0(u,szNzAzT0)
| aElement0(sdtlpdtrp0(xN,u)) ),
inference(spl,[status(thm),theory(equality)],[20,66]),
[iquote('0:SpL:20.0,66.1')] ).
cnf(444,plain,
( ~ aElementOf0(u,szNzAzT0)
| aElement0(sdtlpdtrp0(xN,u)) ),
inference(ssi,[status(thm)],[442,8]),
[iquote('0:SSi:442.0,8.0')] ).
cnf(446,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| aElement0(xS) ),
inference(spr,[status(thm),theory(equality)],[23,444]),
[iquote('0:SpR:23.0,444.1')] ).
cnf(447,plain,
aElement0(xS),
inference(mrr,[status(thm)],[446,9]),
[iquote('0:MRR:446.0,9.0')] ).
cnf(3817,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ equal(v,szDzozmdt0(xc))
| ~ equal(sbrdtbr0(u),xK)
| aElementOf0(u,v) ),
inference(spl,[status(thm),theory(equality)],[29,142]),
[iquote('0:SpL:29.0,142.3')] ).
cnf(3818,plain,
( ~ aSubsetOf0(u,xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ equal(v,szDzozmdt0(xc))
| ~ equal(sbrdtbr0(u),xK)
| aElementOf0(u,v) ),
inference(ssi,[status(thm)],[3817,447,271,6]),
[iquote('0:SSi:3817.0,447.0,271.0,6.0')] ).
cnf(3819,plain,
( ~ aSubsetOf0(u,xS)
| ~ equal(v,szDzozmdt0(xc))
| ~ equal(sbrdtbr0(u),xK)
| aElementOf0(u,v) ),
inference(mrr,[status(thm)],[3818,10]),
[iquote('0:MRR:3818.1,10.0')] ).
cnf(11679,plain,
( ~ aSubsetOf0(u,xS)
| ~ equal(sbrdtbr0(u),xK)
| aElementOf0(u,szDzozmdt0(xc)) ),
inference(eqr,[status(thm),theory(equality)],[3819]),
[iquote('0:EqR:3819.1')] ).
cnf(69243,plain,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ~ equal(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xK) ),
inference(res,[status(thm),theory(equality)],[11679,169]),
[iquote('0:Res:11679.2,169.0')] ).
cnf(69245,plain,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ~ equal(xK,xK) ),
inference(rew,[status(thm),theory(equality)],[52,69243]),
[iquote('0:Rew:52.0,69243.1')] ).
cnf(69246,plain,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(obv,[status(thm),theory(equality)],[69245]),
[iquote('0:Obv:69245.1')] ).
cnf(69247,plain,
$false,
inference(mrr,[status(thm)],[69246,42]),
[iquote('0:MRR:69246.0,42.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM584+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 15:45:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 87.48/87.68
% 87.48/87.68 SPASS V 3.9
% 87.48/87.68 SPASS beiseite: Proof found.
% 87.48/87.68 % SZS status Theorem
% 87.48/87.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.48/87.68 SPASS derived 51551 clauses, backtracked 14306 clauses, performed 59 splits and kept 23770 clauses.
% 87.48/87.68 SPASS allocated 155501 KBytes.
% 87.48/87.68 SPASS spent 0:1:20.13 on the problem.
% 87.48/87.68 0:00:00.04 for the input.
% 87.48/87.68 0:00:00.24 for the FLOTTER CNF translation.
% 87.48/87.68 0:00:00.92 for inferences.
% 87.48/87.68 0:00:03.25 for the backtracking.
% 87.48/87.68 0:1:15.07 for the reduction.
% 87.48/87.68
% 87.48/87.68
% 87.48/87.68 Here is a proof with depth 3, length 31 :
% 87.48/87.68 % SZS output start Refutation
% See solution above
% 87.48/87.68 Formulae used in the proof : mNATSet m__3435 m__3623 mZeroNum m__3418 m__3453 m__4024 mDefSub m__4007 m__ mImgElm mDefSel
% 87.48/87.68
%------------------------------------------------------------------------------