TSTP Solution File: NUM625+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM625+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:28:15 EDT 2022
% Result : Theorem 2.22s 2.43s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of clauses : 48 ( 29 unt; 0 nHn; 48 RR)
% Number of literals : 84 ( 0 equ; 38 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM625+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM625+1.p',unknown),
[] ).
cnf(7,axiom,
aFunction0(xc),
file('NUM625+1.p',unknown),
[] ).
cnf(13,axiom,
aSet0(xO),
file('NUM625+1.p',unknown),
[] ).
cnf(14,axiom,
isCountable0(xO),
file('NUM625+1.p',unknown),
[] ).
cnf(15,axiom,
aSet0(xP),
file('NUM625+1.p',unknown),
[] ).
cnf(19,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM625+1.p',unknown),
[] ).
cnf(23,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('NUM625+1.p',unknown),
[] ).
cnf(29,axiom,
aElementOf0(xx,xP),
file('NUM625+1.p',unknown),
[] ).
cnf(31,axiom,
aElementOf0(xx,xO),
file('NUM625+1.p',unknown),
[] ).
cnf(33,axiom,
aElementOf0(xx,xQ),
file('NUM625+1.p',unknown),
[] ).
cnf(34,axiom,
equal(xx,xp),
file('NUM625+1.p',unknown),
[] ).
cnf(50,axiom,
aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM625+1.p',unknown),
[] ).
cnf(51,axiom,
equal(szmzizndt0(xQ),xp),
file('NUM625+1.p',unknown),
[] ).
cnf(52,axiom,
equal(sbrdtbr0(xP),xk),
file('NUM625+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM625+1.p',unknown),
[] ).
cnf(71,axiom,
equal(sdtmndt0(xQ,szmzizndt0(xQ)),xP),
file('NUM625+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM625+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM625+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ equal(u,v)
| ~ skP1(v,w,u) ),
file('NUM625+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM625+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElement0(v)
| isFinite0(sdtpldt0(u,v)) ),
file('NUM625+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| equal(sdtpldt0(sdtmndt0(u,v),v),u) ),
file('NUM625+1.p',unknown),
[] ).
cnf(169,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,x)
| ~ equal(x,sdtmndt0(v,u))
| skP1(u,v,w) ),
file('NUM625+1.p',unknown),
[] ).
cnf(223,plain,
aElementOf0(xp,xQ),
inference(rew,[status(thm),theory(equality)],[34,33]),
[iquote('0:Rew:34.0,33.0')] ).
cnf(224,plain,
aElementOf0(xp,xO),
inference(rew,[status(thm),theory(equality)],[34,31]),
[iquote('0:Rew:34.0,31.0')] ).
cnf(226,plain,
aElementOf0(xp,xP),
inference(rew,[status(thm),theory(equality)],[34,29]),
[iquote('0:Rew:34.0,29.0')] ).
cnf(229,plain,
equal(sdtmndt0(xQ,xp),xP),
inference(rew,[status(thm),theory(equality)],[51,71]),
[iquote('0:Rew:51.0,71.0')] ).
cnf(344,plain,
( ~ aSet0(xO)
| aElement0(xp) ),
inference(res,[status(thm),theory(equality)],[224,89]),
[iquote('0:Res:224.0,89.1')] ).
cnf(361,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[50,89]),
[iquote('0:Res:50.0,89.1')] ).
cnf(365,plain,
aElement0(xp),
inference(ssi,[status(thm)],[344,14,13]),
[iquote('0:SSi:344.0,14.0,13.0')] ).
cnf(375,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[361,66,7]),
[iquote('0:SSi:361.0,66.0,7.1')] ).
cnf(380,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xQ) ),
inference(res,[status(thm),theory(equality)],[23,91]),
[iquote('0:Res:23.0,91.1')] ).
cnf(389,plain,
aSet0(xQ),
inference(ssi,[status(thm)],[380,3,2]),
[iquote('0:SSi:380.0,3.0,2.0')] ).
cnf(403,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xP) ),
inference(spl,[status(thm),theory(equality)],[52,100]),
[iquote('0:SpL:52.0,100.1')] ).
cnf(408,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xP) ),
inference(ssi,[status(thm)],[403,15]),
[iquote('0:SSi:403.0,15.0')] ).
cnf(409,plain,
isFinite0(xP),
inference(mrr,[status(thm)],[408,19]),
[iquote('0:MRR:408.0,19.0')] ).
cnf(809,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(sdtpldt0(xP,xp),xQ) ),
inference(spr,[status(thm),theory(equality)],[229,125]),
[iquote('0:SpR:229.0,125.2')] ).
cnf(811,plain,
( ~ aElementOf0(xp,xQ)
| equal(sdtpldt0(xP,xp),xQ) ),
inference(ssi,[status(thm)],[809,375,389]),
[iquote('0:SSi:809.0,375.0,389.0')] ).
cnf(812,plain,
equal(sdtpldt0(xP,xp),xQ),
inference(mrr,[status(thm)],[811,223]),
[iquote('0:MRR:811.0,223.0')] ).
cnf(819,plain,
( ~ isFinite0(xP)
| ~ aSet0(xP)
| ~ aElement0(xp)
| isFinite0(xQ) ),
inference(spr,[status(thm),theory(equality)],[812,118]),
[iquote('0:SpR:812.0,118.3')] ).
cnf(823,plain,
isFinite0(xQ),
inference(ssi,[status(thm)],[819,365,15,409]),
[iquote('0:SSi:819.2,819.1,819.0,365.0,15.0,409.0,15.0,409.0')] ).
cnf(7641,plain,
( ~ aElement0(xp)
| ~ aSet0(xQ)
| ~ aElementOf0(u,v)
| ~ equal(v,xP)
| skP1(xp,xQ,u) ),
inference(spl,[status(thm),theory(equality)],[229,169]),
[iquote('0:SpL:229.0,169.3')] ).
cnf(7644,plain,
( ~ aElementOf0(u,v)
| ~ equal(v,xP)
| skP1(xp,xQ,u) ),
inference(ssi,[status(thm)],[7641,375,389,823,365]),
[iquote('0:SSi:7641.1,7641.0,375.0,389.0,823.0,365.0')] ).
cnf(8421,plain,
( ~ equal(xP,xP)
| skP1(xp,xQ,xp) ),
inference(res,[status(thm),theory(equality)],[226,7644]),
[iquote('0:Res:226.0,7644.0')] ).
cnf(8431,plain,
skP1(xp,xQ,xp),
inference(obv,[status(thm),theory(equality)],[8421]),
[iquote('0:Obv:8421.0')] ).
cnf(8450,plain,
~ equal(xp,xp),
inference(res,[status(thm),theory(equality)],[8431,92]),
[iquote('0:Res:8431.0,92.1')] ).
cnf(8452,plain,
$false,
inference(obv,[status(thm),theory(equality)],[8450]),
[iquote('0:Obv:8450.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM625+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jul 6 00:34:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.22/2.43
% 2.22/2.43 SPASS V 3.9
% 2.22/2.43 SPASS beiseite: Proof found.
% 2.22/2.43 % SZS status Theorem
% 2.22/2.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.22/2.43 SPASS derived 6117 clauses, backtracked 908 clauses, performed 28 splits and kept 3488 clauses.
% 2.22/2.43 SPASS allocated 104507 KBytes.
% 2.22/2.43 SPASS spent 0:00:01.99 on the problem.
% 2.22/2.43 0:00:00.04 for the input.
% 2.22/2.43 0:00:00.24 for the FLOTTER CNF translation.
% 2.22/2.43 0:00:00.10 for inferences.
% 2.22/2.43 0:00:00.02 for the backtracking.
% 2.22/2.43 0:00:01.52 for the reduction.
% 2.22/2.43
% 2.22/2.43
% 2.22/2.43 Here is a proof with depth 3, length 48 :
% 2.22/2.43 % SZS output start Refutation
% See solution above
% 2.22/2.43 Formulae used in the proof : mNATSet m__3453 m__4908 m__5164 m__3533 m__5106 m__5348 m__5365 m__5481 m__5496 m__5116 m__5147 m__5217 mDomSet mEOfElem mDefSub mDefDiff mCardNum mFConsSet mConsDiff
% 2.22/2.43
%------------------------------------------------------------------------------