TSTP Solution File: NUM611+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM611+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:28:05 EDT 2022
% Result : Theorem 32.64s 32.86s
% Output : Refutation 32.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of clauses : 63 ( 26 unt; 0 nHn; 63 RR)
% Number of literals : 134 ( 0 equ; 77 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
aFunction0(xc),
file('NUM611+3.p',unknown),
[] ).
cnf(16,axiom,
aSet0(xQ),
file('NUM611+3.p',unknown),
[] ).
cnf(17,axiom,
aSet0(xP),
file('NUM611+3.p',unknown),
[] ).
cnf(19,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM611+3.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM611+3.p',unknown),
[] ).
cnf(29,axiom,
aElementOf0(xp,xQ),
file('NUM611+3.p',unknown),
[] ).
cnf(30,axiom,
aSubsetOf0(xP,xQ),
file('NUM611+3.p',unknown),
[] ).
cnf(37,axiom,
equal(szszuzczcdt0(xk),xK),
file('NUM611+3.p',unknown),
[] ).
cnf(46,axiom,
equal(sbrdtbr0(xQ),xK),
file('NUM611+3.p',unknown),
[] ).
cnf(48,axiom,
aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM611+3.p',unknown),
[] ).
cnf(49,axiom,
equal(szmzizndt0(xQ),xp),
file('NUM611+3.p',unknown),
[] ).
cnf(50,axiom,
~ equal(sbrdtbr0(xP),xk),
file('NUM611+3.p',unknown),
[] ).
cnf(52,axiom,
aElementOf0(skf68(u),szDzozmdt0(xc)),
file('NUM611+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ aSet0(u)
| aSubsetOf0(u,u) ),
file('NUM611+3.p',unknown),
[] ).
cnf(67,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM611+3.p',unknown),
[] ).
cnf(74,axiom,
equal(sdtmndt0(xQ,szmzizndt0(xQ)),xP),
file('NUM611+3.p',unknown),
[] ).
cnf(82,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| aSet0(u) ),
file('NUM611+3.p',unknown),
[] ).
cnf(105,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM611+3.p',unknown),
[] ).
cnf(113,axiom,
( ~ aElementOf0(u,szDzozmdt0(xc))
| equal(sbrdtbr0(u),xK) ),
file('NUM611+3.p',unknown),
[] ).
cnf(120,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM611+3.p',unknown),
[] ).
cnf(121,axiom,
( ~ aSet0(u)
| ~ isFinite0(u)
| aElementOf0(sbrdtbr0(u),szNzAzT0) ),
file('NUM611+3.p',unknown),
[] ).
cnf(137,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| isFinite0(v) ),
file('NUM611+3.p',unknown),
[] ).
cnf(183,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| sdtlseqdt0(sbrdtbr0(v),sbrdtbr0(u)) ),
file('NUM611+3.p',unknown),
[] ).
cnf(216,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(v),szszuzczcdt0(u))
| sdtlseqdt0(v,u) ),
file('NUM611+3.p',unknown),
[] ).
cnf(233,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElementOf0(v,u)
| equal(szszuzczcdt0(sbrdtbr0(sdtmndt0(u,v))),sbrdtbr0(u)) ),
file('NUM611+3.p',unknown),
[] ).
cnf(247,axiom,
( ~ sdtlseqdt0(u,v)
| ~ sdtlseqdt0(v,u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| equal(v,u) ),
file('NUM611+3.p',unknown),
[] ).
cnf(402,plain,
equal(sdtmndt0(xQ,xp),xP),
inference(rew,[status(thm),theory(equality)],[49,74]),
[iquote('0:Rew:49.0,74.0')] ).
cnf(492,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ sdtlseqdt0(sbrdtbr0(xP),xk)
| ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ aElementOf0(xk,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[247,50]),
[iquote('0:Res:247.4,50.0')] ).
cnf(508,plain,
( ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ sdtlseqdt0(sbrdtbr0(xP),xk)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(mrr,[status(thm)],[492,21]),
[iquote('0:MRR:492.3,21.0')] ).
cnf(543,plain,
aSet0(skf68(u)),
inference(res,[status(thm),theory(equality)],[52,82]),
[iquote('0:Res:52.0,82.0')] ).
cnf(587,plain,
equal(sbrdtbr0(skf68(u)),xK),
inference(res,[status(thm),theory(equality)],[52,113]),
[iquote('0:Res:52.0,113.0')] ).
cnf(649,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[48,105]),
[iquote('0:Res:48.0,105.1')] ).
cnf(651,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(skf68(u)) ),
inference(res,[status(thm),theory(equality)],[52,105]),
[iquote('0:Res:52.0,105.1')] ).
cnf(669,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[649,67,8]),
[iquote('0:SSi:649.0,67.0,8.1')] ).
cnf(670,plain,
aElement0(skf68(u)),
inference(ssi,[status(thm)],[651,67,8]),
[iquote('0:SSi:651.0,67.0,8.1')] ).
cnf(726,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(spl,[status(thm),theory(equality)],[46,120]),
[iquote('0:SpL:46.0,120.1')] ).
cnf(728,plain,
( ~ aSet0(skf68(u))
| ~ aElementOf0(xK,szNzAzT0)
| isFinite0(skf68(u)) ),
inference(spl,[status(thm),theory(equality)],[587,120]),
[iquote('0:SpL:587.0,120.1')] ).
cnf(732,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(ssi,[status(thm)],[726,16,669]),
[iquote('0:SSi:726.0,16.0,669.0')] ).
cnf(733,plain,
isFinite0(xQ),
inference(mrr,[status(thm)],[732,19]),
[iquote('0:MRR:732.0,19.0')] ).
cnf(734,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(skf68(u)) ),
inference(ssi,[status(thm)],[728,543,670]),
[iquote('0:SSi:728.0,543.0,670.0')] ).
cnf(735,plain,
isFinite0(skf68(u)),
inference(mrr,[status(thm)],[734,19]),
[iquote('0:MRR:734.0,19.0')] ).
cnf(1284,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| isFinite0(xP) ),
inference(res,[status(thm),theory(equality)],[30,137]),
[iquote('0:Res:30.0,137.2')] ).
cnf(2350,plain,
( ~ isFinite0(skf68(u))
| ~ aSet0(skf68(u))
| ~ aSubsetOf0(v,skf68(u))
| sdtlseqdt0(sbrdtbr0(v),xK) ),
inference(spr,[status(thm),theory(equality)],[587,183]),
[iquote('0:SpR:587.0,183.3')] ).
cnf(2359,plain,
( ~ aSubsetOf0(u,skf68(v))
| sdtlseqdt0(sbrdtbr0(u),xK) ),
inference(ssi,[status(thm)],[2350,735,670,543]),
[iquote('0:SSi:2350.1,2350.0,735.0,670.0,543.0,735.0,670.0,543.0')] ).
cnf(3825,plain,
( ~ aSet0(skf68(u))
| sdtlseqdt0(sbrdtbr0(skf68(u)),xK) ),
inference(res,[status(thm),theory(equality)],[65,2359]),
[iquote('0:Res:65.1,2359.0')] ).
cnf(3827,plain,
( ~ aSet0(skf68(u))
| sdtlseqdt0(xK,xK) ),
inference(rew,[status(thm),theory(equality)],[587,3825]),
[iquote('0:Rew:587.0,3825.1')] ).
cnf(3828,plain,
sdtlseqdt0(xK,xK),
inference(ssi,[status(thm)],[3827,543,670,735]),
[iquote('0:SSi:3827.0,543.0,670.0,735.0')] ).
cnf(3936,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(u),xK)
| sdtlseqdt0(u,xk) ),
inference(spl,[status(thm),theory(equality)],[37,216]),
[iquote('0:SpL:37.0,216.2')] ).
cnf(3938,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ sdtlseqdt0(xK,szszuzczcdt0(u))
| sdtlseqdt0(xk,u) ),
inference(spl,[status(thm),theory(equality)],[37,216]),
[iquote('0:SpL:37.0,216.2')] ).
cnf(3944,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(u),xK)
| sdtlseqdt0(u,xk) ),
inference(mrr,[status(thm)],[3936,21]),
[iquote('0:MRR:3936.0,21.0')] ).
cnf(3945,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ sdtlseqdt0(xK,szszuzczcdt0(u))
| sdtlseqdt0(xk,u) ),
inference(mrr,[status(thm)],[3938,21]),
[iquote('0:MRR:3938.1,21.0')] ).
cnf(4862,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),sbrdtbr0(xQ)) ),
inference(spr,[status(thm),theory(equality)],[402,233]),
[iquote('0:SpR:402.0,233.3')] ).
cnf(4961,plain,
isFinite0(xP),
inference(ssi,[status(thm)],[1284,16,733,669]),
[iquote('0:SSi:1284.1,1284.0,16.0,733.0,669.0,16.0,733.0,669.0')] ).
cnf(5022,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(rew,[status(thm),theory(equality)],[46,4862]),
[iquote('0:Rew:46.0,4862.3')] ).
cnf(5023,plain,
( ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(ssi,[status(thm)],[5022,16,733,669]),
[iquote('0:SSi:5022.1,5022.0,16.0,733.0,669.0,16.0,733.0,669.0')] ).
cnf(5024,plain,
equal(szszuzczcdt0(sbrdtbr0(xP)),xK),
inference(mrr,[status(thm)],[5023,29]),
[iquote('0:MRR:5023.0,29.0')] ).
cnf(47661,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ sdtlseqdt0(xK,xK)
| sdtlseqdt0(xk,sbrdtbr0(xP)) ),
inference(spl,[status(thm),theory(equality)],[5024,3945]),
[iquote('0:SpL:5024.0,3945.1')] ).
cnf(47667,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| sdtlseqdt0(xk,sbrdtbr0(xP)) ),
inference(mrr,[status(thm)],[47661,3828]),
[iquote('0:MRR:47661.1,3828.0')] ).
cnf(47668,plain,
( ~ sdtlseqdt0(sbrdtbr0(xP),xk)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(mrr,[status(thm)],[508,47667]),
[iquote('0:MRR:508.0,47667.1')] ).
cnf(47783,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ sdtlseqdt0(xK,xK)
| sdtlseqdt0(sbrdtbr0(xP),xk) ),
inference(spl,[status(thm),theory(equality)],[5024,3944]),
[iquote('0:SpL:5024.0,3944.1')] ).
cnf(47788,plain,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(mrr,[status(thm)],[47783,3828,47668]),
[iquote('0:MRR:47783.1,47783.2,3828.0,47668.0')] ).
cnf(47792,plain,
( ~ aSet0(xP)
| ~ isFinite0(xP) ),
inference(res,[status(thm),theory(equality)],[121,47788]),
[iquote('0:Res:121.2,47788.0')] ).
cnf(47795,plain,
$false,
inference(ssi,[status(thm)],[47792,17,4961]),
[iquote('0:SSi:47792.1,47792.0,17.0,4961.0,17.0,4961.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM611+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 : Wed Jul 6 19:25:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 32.64/32.86
% 32.64/32.86 SPASS V 3.9
% 32.64/32.86 SPASS beiseite: Proof found.
% 32.64/32.86 % SZS status Theorem
% 32.64/32.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.64/32.86 SPASS derived 37578 clauses, backtracked 9725 clauses, performed 61 splits and kept 20838 clauses.
% 32.64/32.86 SPASS allocated 130292 KBytes.
% 32.64/32.86 SPASS spent 0:0:31.43 on the problem.
% 32.64/32.86 0:00:00.04 for the input.
% 32.64/32.86 0:00:00.77 for the FLOTTER CNF translation.
% 32.64/32.86 0:00:00.69 for inferences.
% 32.64/32.86 0:00:00.89 for the backtracking.
% 32.64/32.86 0:0:28.32 for the reduction.
% 32.64/32.86
% 32.64/32.86
% 32.64/32.86 Here is a proof with depth 3, length 63 :
% 32.64/32.86 % SZS output start Refutation
% See solution above
% 32.64/32.86 Formulae used in the proof : m__3453 m__5116 m__5078 m__5164 m__3418 m__3533 m__5173 m__5195 m__5147 m__ mSubRefl mDomSet mEOfElem mCardNum mSubFSet mCardSub mSuccLess mCardDiff mLessASymm
% 32.64/32.86
%------------------------------------------------------------------------------