TSTP Solution File: NUM566+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM566+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:27:35 EDT 2022
% Result : Theorem 0.72s 0.88s
% Output : Refutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of clauses : 78 ( 31 unt; 9 nHn; 78 RR)
% Number of literals : 149 ( 0 equ; 73 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
aSet0(xS),
file('NUM566+3.p',unknown),
[] ).
cnf(7,axiom,
isCountable0(xS),
file('NUM566+3.p',unknown),
[] ).
cnf(8,axiom,
aFunction0(xc),
file('NUM566+3.p',unknown),
[] ).
cnf(12,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM566+3.p',unknown),
[] ).
cnf(13,axiom,
equal(xK,sz00),
file('NUM566+3.p',unknown),
[] ).
cnf(15,axiom,
aSet0(skf33(u,v)),
file('NUM566+3.p',unknown),
[] ).
cnf(19,axiom,
~ aElementOf0(u,slcrc0),
file('NUM566+3.p',unknown),
[] ).
cnf(21,axiom,
aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))),
file('NUM566+3.p',unknown),
[] ).
cnf(24,axiom,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('NUM566+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ aSubsetOf0(u,xS)
| skP7(u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM566+3.p',unknown),
[] ).
cnf(32,axiom,
equal(slbdtsldtrb0(xS,xK),szDzozmdt0(xc)),
file('NUM566+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| aSet0(u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| aSubsetOf0(u,xS) ),
file('NUM566+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ aElementOf0(u,slbdtsldtrb0(xS,sz00))
| skP6(u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(49,axiom,
( ~ aSet0(u)
| skP7(u)
| aElementOf0(skf34(u),u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM566+3.p',unknown),
[] ).
cnf(58,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| equal(sbrdtbr0(u),xK) ),
file('NUM566+3.p',unknown),
[] ).
cnf(59,axiom,
( ~ isCountable0(u)
| ~ aSubsetOf0(u,szNzAzT0)
| skP2(u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(61,axiom,
( ~ aSet0(u)
| ~ aElementOf0(skf34(v),xS)
| skP7(u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(62,axiom,
( ~ aSet0(u)
| equal(u,slcrc0)
| aElementOf0(skf35(u),u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElementOf0(u,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(u,xT) ),
file('NUM566+3.p',unknown),
[] ).
cnf(66,axiom,
( ~ skP6(u)
| equal(sdtlpdtrp0(xc,u),sdtlpdtrp0(xc,slcrc0)) ),
file('NUM566+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ aSet0(u)
| ~ equal(sbrdtbr0(u),sz00)
| equal(u,slcrc0) ),
file('NUM566+3.p',unknown),
[] ).
cnf(81,axiom,
( ~ aElementOf0(u,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(skf56(v),szDzozmdt0(xc)) ),
file('NUM566+3.p',unknown),
[] ).
cnf(88,axiom,
( ~ aElementOf0(u,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| equal(sdtlpdtrp0(xc,skf56(u)),u) ),
file('NUM566+3.p',unknown),
[] ).
cnf(108,axiom,
( ~ skP7(u)
| ~ isCountable0(u)
| ~ aElementOf0(v,xT)
| equal(sbrdtbr0(skf33(v,u)),xK) ),
file('NUM566+3.p',unknown),
[] ).
cnf(127,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| ~ equal(sdtlpdtrp0(xc,u),v)
| aElementOf0(v,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
file('NUM566+3.p',unknown),
[] ).
cnf(130,axiom,
( ~ isCountable0(u)
| ~ skP7(u)
| ~ aElementOf0(v,xT)
| ~ equal(sdtlpdtrp0(xc,skf33(v,u)),v) ),
file('NUM566+3.p',unknown),
[] ).
cnf(211,plain,
equal(slbdtsldtrb0(xS,sz00),szDzozmdt0(xc)),
inference(rew,[status(thm),theory(equality)],[13,32]),
[iquote('0:Rew:13.0,32.0')] ).
cnf(212,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rew,[status(thm),theory(equality)],[211,24]),
[iquote('0:Rew:211.0,24.0')] ).
cnf(214,plain,
( ~ aElementOf0(u,szDzozmdt0(xc))
| skP6(u) ),
inference(rew,[status(thm),theory(equality)],[211,48]),
[iquote('0:Rew:211.0,48.0')] ).
cnf(215,plain,
( ~ aElementOf0(u,szDzozmdt0(xc))
| equal(sbrdtbr0(u),sz00) ),
inference(rew,[status(thm),theory(equality)],[13,58]),
[iquote('0:Rew:13.0,58.1')] ).
cnf(219,plain,
( ~ isCountable0(u)
| ~ skP7(u)
| ~ aElementOf0(v,xT)
| equal(sbrdtbr0(skf33(v,u)),sz00) ),
inference(rew,[status(thm),theory(equality)],[13,108]),
[iquote('0:Rew:13.0,108.3')] ).
cnf(321,plain,
( aElementOf0(skf34(xS),xS)
| skP7(xS) ),
inference(res,[status(thm),theory(equality)],[6,49]),
[iquote('0:Res:6.0,49.0')] ).
cnf(330,plain,
( ~ aElementOf0(skf34(u),xS)
| skP7(xS) ),
inference(res,[status(thm),theory(equality)],[6,61]),
[iquote('0:Res:6.0,61.0')] ).
cnf(339,plain,
( ~ skP7(xS)
| ~ aElementOf0(u,xT)
| equal(sbrdtbr0(skf33(u,xS)),sz00) ),
inference(res,[status(thm),theory(equality)],[7,219]),
[iquote('0:Res:7.0,219.1')] ).
cnf(343,plain,
( ~ skP7(xS)
| ~ equal(sdtlpdtrp0(xc,skf33(u,xS)),u)
| ~ aElementOf0(u,xT) ),
inference(res,[status(thm),theory(equality)],[7,130]),
[iquote('0:Res:7.0,130.1')] ).
cnf(348,plain,
skP7(xS),
inference(mrr,[status(thm)],[321,330]),
[iquote('0:MRR:321.0,330.0')] ).
cnf(350,plain,
( ~ aElementOf0(u,xT)
| equal(sbrdtbr0(skf33(u,xS)),sz00) ),
inference(mrr,[status(thm)],[339,348]),
[iquote('0:MRR:339.0,348.0')] ).
cnf(353,plain,
( ~ aElementOf0(u,xT)
| ~ equal(sdtlpdtrp0(xc,skf33(u,xS)),u) ),
inference(mrr,[status(thm)],[343,348]),
[iquote('0:MRR:343.0,348.0')] ).
cnf(408,plain,
( ~ isCountable0(xS)
| skP2(xS) ),
inference(res,[status(thm),theory(equality)],[12,59]),
[iquote('0:Res:12.0,59.1')] ).
cnf(411,plain,
skP2(xS),
inference(ssi,[status(thm)],[408,7,6,348]),
[iquote('0:SSi:408.0,7.0,6.0,348.0')] ).
cnf(494,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| aElementOf0(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),xT) ),
inference(res,[status(thm),theory(equality)],[62,65]),
[iquote('0:Res:62.2,65.0')] ).
cnf(513,plain,
( equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| aElementOf0(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),xT) ),
inference(ssi,[status(thm)],[494,21]),
[iquote('0:SSi:494.0,21.0')] ).
cnf(523,plain,
( ~ aSet0(skf33(u,xS))
| ~ aElementOf0(u,xT)
| ~ equal(sz00,sz00)
| equal(skf33(u,xS),slcrc0) ),
inference(spl,[status(thm),theory(equality)],[350,70]),
[iquote('0:SpL:350.1,70.1')] ).
cnf(525,plain,
( ~ aSet0(skf33(u,xS))
| ~ aElementOf0(u,xT)
| equal(skf33(u,xS),slcrc0) ),
inference(obv,[status(thm),theory(equality)],[523]),
[iquote('0:Obv:523.2')] ).
cnf(526,plain,
( ~ aElementOf0(u,xT)
| equal(skf33(u,xS),slcrc0) ),
inference(ssi,[status(thm)],[525,15,7,6,348,411]),
[iquote('0:SSi:525.0,15.0,7.0,6.0,348.0,411.0')] ).
cnf(534,plain,
( ~ aElementOf0(u,xT)
| ~ equal(sdtlpdtrp0(xc,slcrc0),u) ),
inference(rew,[status(thm),theory(equality)],[526,353]),
[iquote('0:Rew:526.1,353.1')] ).
cnf(705,plain,
~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(eqr,[status(thm),theory(equality)],[534]),
[iquote('0:EqR:534.1')] ).
cnf(765,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| aElementOf0(skf56(u),szDzozmdt0(xc)) ),
inference(res,[status(thm),theory(equality)],[62,81]),
[iquote('0:Res:62.2,81.0')] ).
cnf(766,plain,
( equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| aElementOf0(skf56(u),szDzozmdt0(xc)) ),
inference(ssi,[status(thm)],[765,21]),
[iquote('0:SSi:765.0,21.0')] ).
cnf(768,plain,
equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0),
inference(spt,[spt(split,[position(s1)])],[766]),
[iquote('1:Spt:766.0')] ).
cnf(774,plain,
( ~ aElementOf0(u,szDzozmdt0(xc))
| ~ equal(sdtlpdtrp0(xc,u),v)
| aElementOf0(v,slcrc0) ),
inference(rew,[status(thm),theory(equality)],[768,127]),
[iquote('1:Rew:768.0,127.2')] ).
cnf(775,plain,
( ~ aElementOf0(u,szDzozmdt0(xc))
| ~ equal(sdtlpdtrp0(xc,u),v) ),
inference(mrr,[status(thm)],[774,19]),
[iquote('1:MRR:774.2,19.0')] ).
cnf(780,plain,
( ~ skP6(u)
| ~ aElementOf0(u,szDzozmdt0(xc))
| ~ equal(sdtlpdtrp0(xc,slcrc0),v) ),
inference(spl,[status(thm),theory(equality)],[66,775]),
[iquote('1:SpL:66.1,775.1')] ).
cnf(785,plain,
( ~ skP6(u)
| ~ aElementOf0(u,szDzozmdt0(xc)) ),
inference(aed,[status(thm),theory(equality)],[780]),
[iquote('1:AED:780.2')] ).
cnf(786,plain,
~ aElementOf0(u,szDzozmdt0(xc)),
inference(mrr,[status(thm)],[785,214]),
[iquote('1:MRR:785.0,214.1')] ).
cnf(787,plain,
$false,
inference(unc,[status(thm)],[786,212]),
[iquote('1:UnC:786.0,212.0')] ).
cnf(788,plain,
~ equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0),
inference(spt,[spt(split,[position(sa)])],[787,768]),
[iquote('1:Spt:787.0,766.0,768.0')] ).
cnf(789,plain,
aElementOf0(skf56(u),szDzozmdt0(xc)),
inference(spt,[spt(split,[position(s2)])],[766]),
[iquote('1:Spt:787.0,766.1')] ).
cnf(790,plain,
aElementOf0(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),xT),
inference(mrr,[status(thm)],[513,788]),
[iquote('1:MRR:513.0,788.0')] ).
cnf(791,plain,
equal(sbrdtbr0(skf56(u)),sz00),
inference(res,[status(thm),theory(equality)],[789,215]),
[iquote('1:Res:789.0,215.0')] ).
cnf(792,plain,
aSubsetOf0(skf56(u),xS),
inference(res,[status(thm),theory(equality)],[789,47]),
[iquote('1:Res:789.0,47.0')] ).
cnf(793,plain,
aSet0(skf56(u)),
inference(res,[status(thm),theory(equality)],[789,40]),
[iquote('1:Res:789.0,40.0')] ).
cnf(794,plain,
skP6(skf56(u)),
inference(res,[status(thm),theory(equality)],[789,214]),
[iquote('1:Res:789.0,214.0')] ).
cnf(796,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(skf56(u)) ),
inference(res,[status(thm),theory(equality)],[789,50]),
[iquote('1:Res:789.0,50.1')] ).
cnf(797,plain,
aElement0(skf56(u)),
inference(ssi,[status(thm)],[796,31,8]),
[iquote('1:SSi:796.0,31.0,8.1')] ).
cnf(799,plain,
skP7(skf56(u)),
inference(res,[status(thm),theory(equality)],[792,26]),
[iquote('1:Res:792.0,26.0')] ).
cnf(807,plain,
( ~ aSet0(skf56(u))
| ~ equal(sz00,sz00)
| equal(skf56(u),slcrc0) ),
inference(spl,[status(thm),theory(equality)],[791,70]),
[iquote('1:SpL:791.0,70.1')] ).
cnf(812,plain,
( ~ aSet0(skf56(u))
| equal(skf56(u),slcrc0) ),
inference(obv,[status(thm),theory(equality)],[807]),
[iquote('1:Obv:807.1')] ).
cnf(813,plain,
equal(skf56(u),slcrc0),
inference(ssi,[status(thm)],[812,793,794,797,799]),
[iquote('1:SSi:812.0,793.0,794.0,797.0,799.0')] ).
cnf(821,plain,
( ~ aElementOf0(u,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| equal(sdtlpdtrp0(xc,slcrc0),u) ),
inference(rew,[status(thm),theory(equality)],[813,88]),
[iquote('1:Rew:813.0,88.1')] ).
cnf(829,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| equal(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),sdtlpdtrp0(xc,slcrc0)) ),
inference(res,[status(thm),theory(equality)],[62,821]),
[iquote('1:Res:62.2,821.0')] ).
cnf(830,plain,
( equal(sdtlcdtrc0(xc,szDzozmdt0(xc)),slcrc0)
| equal(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),sdtlpdtrp0(xc,slcrc0)) ),
inference(ssi,[status(thm)],[829,21]),
[iquote('1:SSi:829.0,21.0')] ).
cnf(831,plain,
equal(skf35(sdtlcdtrc0(xc,szDzozmdt0(xc))),sdtlpdtrp0(xc,slcrc0)),
inference(mrr,[status(thm)],[830,788]),
[iquote('1:MRR:830.0,788.0')] ).
cnf(832,plain,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(rew,[status(thm),theory(equality)],[831,790]),
[iquote('1:Rew:831.0,790.0')] ).
cnf(834,plain,
$false,
inference(mrr,[status(thm)],[832,705]),
[iquote('1:MRR:832.0,705.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM566+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n010.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Thu Jul 7 16:34:01 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.72/0.88
% 0.72/0.88 SPASS V 3.9
% 0.72/0.88 SPASS beiseite: Proof found.
% 0.72/0.88 % SZS status Theorem
% 0.72/0.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.72/0.88 SPASS derived 421 clauses, backtracked 71 clauses, performed 5 splits and kept 456 clauses.
% 0.72/0.88 SPASS allocated 102811 KBytes.
% 0.72/0.88 SPASS spent 0:00:00.56 on the problem.
% 0.72/0.88 0:00:00.02 for the input.
% 0.72/0.88 0:00:00.46 for the FLOTTER CNF translation.
% 0.72/0.88 0:00:00.00 for inferences.
% 0.72/0.88 0:00:00.00 for the backtracking.
% 0.72/0.88 0:00:00.04 for the reduction.
% 0.72/0.88
% 0.72/0.88
% 0.72/0.88 Here is a proof with depth 4, length 78 :
% 0.72/0.88 % SZS output start Refutation
% See solution above
% 0.72/0.88 Formulae used in the proof : m__3435 m__3453 m__3462 m__ m__3476 mDomSet m__3507 mEOfElem m__3398 mDefEmp mCardEmpty
% 0.72/0.88
%------------------------------------------------------------------------------