TSTP Solution File: NUM629+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM629+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 14:28:18 EDT 2022
% Result : Theorem 43.93s 44.15s
% Output : Refutation 43.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of clauses : 54 ( 19 unt; 0 nHn; 54 RR)
% Number of literals : 125 ( 0 equ; 76 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM629+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM629+1.p',unknown),
[] ).
cnf(13,axiom,
aSet0(xO),
file('NUM629+1.p',unknown),
[] ).
cnf(14,axiom,
isCountable0(xO),
file('NUM629+1.p',unknown),
[] ).
cnf(19,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM629+1.p',unknown),
[] ).
cnf(25,axiom,
aElementOf0(xp,xO),
file('NUM629+1.p',unknown),
[] ).
cnf(28,axiom,
aElementOf0(xn,szNzAzT0),
file('NUM629+1.p',unknown),
[] ).
cnf(46,axiom,
equal(sbrdtbr0(xP),xk),
file('NUM629+1.p',unknown),
[] ).
cnf(53,axiom,
equal(sdtlpdtrp0(xe,xn),xp),
file('NUM629+1.p',unknown),
[] ).
cnf(54,axiom,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('NUM629+1.p',unknown),
[] ).
cnf(67,axiom,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('NUM629+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ aElementOf0(u,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,u)) ),
file('NUM629+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM629+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM629+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0) ),
file('NUM629+1.p',unknown),
[] ).
cnf(94,axiom,
equal(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xD),
file('NUM629+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(szmzizndt0(sdtlpdtrp0(xN,u)),sdtlpdtrp0(xe,u)) ),
file('NUM629+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ isCountable0(u)
| ~ aSet0(u)
| ~ aElement0(v)
| isCountable0(sdtmndt0(u,v)) ),
file('NUM629+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtmndt0(v,u))
| aSet0(w) ),
file('NUM629+1.p',unknown),
[] ).
cnf(164,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| ~ aSubsetOf0(u,v)
| ~ aSubsetOf0(v,w)
| aSubsetOf0(u,w) ),
file('NUM629+1.p',unknown),
[] ).
cnf(187,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aElementOf0(w,szNzAzT0)
| ~ equal(x,slbdtsldtrb0(u,w))
| ~ equal(sbrdtbr0(v),w)
| aElementOf0(v,x) ),
file('NUM629+1.p',unknown),
[] ).
cnf(196,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,u))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(u)),sdtmndt0(sdtlpdtrp0(xN,u),szmzizndt0(sdtlpdtrp0(xN,u)))) ),
file('NUM629+1.p',unknown),
[] ).
cnf(224,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aSubsetOf0(w,v)
| aSubsetOf0(w,u) ),
inference(mrr,[status(thm)],[164,83]),
[iquote('0:MRR:164.0,164.1,83.2,83.2')] ).
cnf(231,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,u))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(u)),sdtmndt0(sdtlpdtrp0(xN,u),sdtlpdtrp0(xe,u))) ),
inference(rew,[status(thm),theory(equality)],[107,196]),
[iquote('0:Rew:107.1,196.3')] ).
cnf(232,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(u)),sdtmndt0(sdtlpdtrp0(xN,u),sdtlpdtrp0(xe,u))) ),
inference(mrr,[status(thm)],[231,89,78]),
[iquote('0:MRR:231.1,231.2,89.1,78.1')] ).
cnf(340,plain,
( ~ aSet0(xO)
| aElement0(xp) ),
inference(res,[status(thm),theory(equality)],[25,81]),
[iquote('0:Res:25.0,81.1')] ).
cnf(352,plain,
aElement0(xp),
inference(ssi,[status(thm)],[340,14,13]),
[iquote('0:SSi:340.0,14.0,13.0')] ).
cnf(369,plain,
( ~ aSet0(szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
inference(res,[status(thm),theory(equality)],[89,83]),
[iquote('0:Res:89.1,83.1')] ).
cnf(377,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
inference(ssi,[status(thm)],[369,3,2]),
[iquote('0:SSi:369.0,3.0,2.0')] ).
cnf(515,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(sdtmndt0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xe,xn)),xD) ),
inference(spr,[status(thm),theory(equality)],[107,94]),
[iquote('0:SpR:107.1,94.0')] ).
cnf(519,plain,
( ~ aElementOf0(xn,szNzAzT0)
| equal(sdtmndt0(sdtlpdtrp0(xN,xn),xp),xD) ),
inference(rew,[status(thm),theory(equality)],[53,515]),
[iquote('0:Rew:53.0,515.1')] ).
cnf(520,plain,
equal(sdtmndt0(sdtlpdtrp0(xN,xn),xp),xD),
inference(mrr,[status(thm)],[519,28]),
[iquote('0:MRR:519.0,28.0')] ).
cnf(650,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aElement0(xp)
| isCountable0(xD) ),
inference(spr,[status(thm),theory(equality)],[520,109]),
[iquote('0:SpR:520.0,109.3')] ).
cnf(652,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtlpdtrp0(xN,xn))
| isCountable0(xD) ),
inference(ssi,[status(thm)],[650,352]),
[iquote('0:SSi:650.2,352.0')] ).
cnf(679,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| isCountable0(xD) ),
inference(sor,[status(thm)],[652,78,377]),
[iquote('0:SoR:652.0,652.1,78.1,377.1')] ).
cnf(682,plain,
( ~ aElementOf0(xn,szNzAzT0)
| isCountable0(xD) ),
inference(obv,[status(thm),theory(equality)],[679]),
[iquote('0:Obv:679.0')] ).
cnf(683,plain,
isCountable0(xD),
inference(mrr,[status(thm)],[682,28]),
[iquote('0:MRR:682.0,28.0')] ).
cnf(770,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| aSet0(sdtmndt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[115]),
[iquote('0:EqR:115.2')] ).
cnf(1146,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),xp)) ),
inference(spr,[status(thm),theory(equality)],[53,232]),
[iquote('0:SpR:53.0,232.1')] ).
cnf(1156,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD) ),
inference(rew,[status(thm),theory(equality)],[520,1146]),
[iquote('0:Rew:520.0,1146.1')] ).
cnf(1157,plain,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
inference(mrr,[status(thm)],[1156,28]),
[iquote('0:MRR:1156.0,28.0')] ).
cnf(1164,plain,
( ~ aSet0(xD)
| ~ aSubsetOf0(u,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aSubsetOf0(u,xD) ),
inference(res,[status(thm),theory(equality)],[1157,224]),
[iquote('0:Res:1157.0,224.1')] ).
cnf(2885,plain,
( ~ aElement0(xp)
| ~ aSet0(sdtlpdtrp0(xN,xn))
| aSet0(xD) ),
inference(spr,[status(thm),theory(equality)],[520,770]),
[iquote('0:SpR:520.0,770.2')] ).
cnf(2889,plain,
( ~ aSet0(sdtlpdtrp0(xN,xn))
| aSet0(xD) ),
inference(ssi,[status(thm)],[2885,352]),
[iquote('0:SSi:2885.0,352.0')] ).
cnf(2901,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aSet0(xD) ),
inference(sor,[status(thm)],[2889,377]),
[iquote('0:SoR:2889.0,377.1')] ).
cnf(2906,plain,
aSet0(xD),
inference(mrr,[status(thm)],[2901,28]),
[iquote('0:MRR:2901.0,28.0')] ).
cnf(2913,plain,
( ~ aSubsetOf0(u,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aSubsetOf0(u,xD) ),
inference(mrr,[status(thm)],[1164,2906]),
[iquote('0:MRR:1164.0,2906.0')] ).
cnf(2963,plain,
aSubsetOf0(xP,xD),
inference(res,[status(thm),theory(equality)],[67,2913]),
[iquote('0:Res:67.0,2913.0')] ).
cnf(5233,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aElementOf0(w,szNzAzT0)
| ~ equal(sbrdtbr0(v),w)
| aElementOf0(v,slbdtsldtrb0(u,w)) ),
inference(eqr,[status(thm),theory(equality)],[187]),
[iquote('0:EqR:187.3')] ).
cnf(58774,plain,
( ~ aSet0(xD)
| ~ aSubsetOf0(xP,xD)
| ~ aElementOf0(xk,szNzAzT0)
| ~ equal(sbrdtbr0(xP),xk) ),
inference(res,[status(thm),theory(equality)],[5233,54]),
[iquote('0:Res:5233.4,54.0')] ).
cnf(58793,plain,
( ~ aSet0(xD)
| ~ aSubsetOf0(xP,xD)
| ~ aElementOf0(xk,szNzAzT0)
| ~ equal(xk,xk) ),
inference(rew,[status(thm),theory(equality)],[46,58774]),
[iquote('0:Rew:46.0,58774.3')] ).
cnf(58794,plain,
( ~ aSet0(xD)
| ~ aSubsetOf0(xP,xD)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(obv,[status(thm),theory(equality)],[58793]),
[iquote('0:Obv:58793.3')] ).
cnf(58795,plain,
( ~ aSubsetOf0(xP,xD)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(ssi,[status(thm)],[58794,683,2906]),
[iquote('0:SSi:58794.0,683.0,2906.0')] ).
cnf(58796,plain,
$false,
inference(mrr,[status(thm)],[58795,2963,19]),
[iquote('0:MRR:58795.0,58795.1,2963.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM629+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 23:17:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 43.93/44.15
% 43.93/44.15 SPASS V 3.9
% 43.93/44.15 SPASS beiseite: Proof found.
% 43.93/44.15 % SZS status Theorem
% 43.93/44.15 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.93/44.15 SPASS derived 46552 clauses, backtracked 13181 clauses, performed 99 splits and kept 27736 clauses.
% 43.93/44.15 SPASS allocated 138168 KBytes.
% 43.93/44.15 SPASS spent 0:0:40.78 on the problem.
% 43.93/44.15 0:00:00.04 for the input.
% 43.93/44.15 0:00:00.25 for the FLOTTER CNF translation.
% 43.93/44.15 0:00:00.81 for inferences.
% 43.93/44.15 0:00:01.42 for the backtracking.
% 43.93/44.15 0:0:37.64 for the reduction.
% 43.93/44.15
% 43.93/44.15
% 43.93/44.15 Here is a proof with depth 3, length 54 :
% 43.93/44.15 % SZS output start Refutation
% See solution above
% 43.93/44.15 Formulae used in the proof : mNATSet m__4908 m__3533 m__5182 m__5309 m__5217 m__ m__5334 m__3671 mEOfElem mDefSub m__5585 m__4660 mCDiffSet mDefDiff mSubTrans mDefSel m__3623
% 43.93/44.15
%------------------------------------------------------------------------------