TSTP Solution File: NUM558+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM558+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:27:29 EDT 2022
% Result : Theorem 2.60s 2.83s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of clauses : 47 ( 19 unt; 0 nHn; 47 RR)
% Number of literals : 105 ( 0 equ; 64 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aSet0(xS),
file('NUM558+1.p',unknown),
[] ).
cnf(5,axiom,
aSet0(xT),
file('NUM558+1.p',unknown),
[] ).
cnf(6,axiom,
aSet0(xQ),
file('NUM558+1.p',unknown),
[] ).
cnf(7,axiom,
isFinite0(xQ),
file('NUM558+1.p',unknown),
[] ).
cnf(8,axiom,
aElement0(xy),
file('NUM558+1.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM558+1.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(xx,xS),
file('NUM558+1.p',unknown),
[] ).
cnf(13,axiom,
~ aElementOf0(xx,xT),
file('NUM558+1.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('NUM558+1.p',unknown),
[] ).
cnf(22,axiom,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('NUM558+1.p',unknown),
[] ).
cnf(33,axiom,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
file('NUM558+1.p',unknown),
[] ).
cnf(34,axiom,
equal(sdtpldt0(sdtmndt0(xQ,xy),xx),xP),
file('NUM558+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM558+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElement0(u)
| ~ equal(u,v)
| skP0(v,w,u) ),
file('NUM558+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElement0(v)
| isFinite0(sdtmndt0(u,v)) ),
file('NUM558+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM558+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtmndt0(v,u))
| aSet0(w) ),
file('NUM558+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ equal(w,slbdtsldtrb0(u,v))
| aSet0(w) ),
file('NUM558+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aElementOf0(x,szNzAzT0)
| ~ equal(w,slbdtsldtrb0(u,x))
| aSubsetOf0(v,u) ),
file('NUM558+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtpldt0(v,u))
| ~ skP0(u,v,x)
| aElementOf0(x,w) ),
file('NUM558+1.p',unknown),
[] ).
cnf(139,plain,
( ~ aSet0(xT)
| ~ aSubsetOf0(u,xT)
| ~ aElementOf0(xx,u) ),
inference(res,[status(thm),theory(equality)],[64,13]),
[iquote('0:Res:64.3,13.0')] ).
cnf(144,plain,
( ~ aSubsetOf0(u,xT)
| ~ aElementOf0(xx,u) ),
inference(mrr,[status(thm)],[139,5]),
[iquote('0:MRR:139.0,5.0')] ).
cnf(188,plain,
( ~ aSet0(xS)
| aElement0(xx) ),
inference(res,[status(thm),theory(equality)],[11,40]),
[iquote('0:Res:11.0,40.1')] ).
cnf(195,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[21,40]),
[iquote('0:Res:21.0,40.1')] ).
cnf(196,plain,
aElement0(xx),
inference(ssi,[status(thm)],[188,4]),
[iquote('0:SSi:188.0,4.0')] ).
cnf(458,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| aSet0(sdtmndt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[67]),
[iquote('0:EqR:67.2')] ).
cnf(717,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),u)
| aElementOf0(xP,u) ),
inference(res,[status(thm),theory(equality)],[22,64]),
[iquote('0:Res:22.0,64.1')] ).
cnf(923,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| aSet0(slbdtsldtrb0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[75]),
[iquote('0:EqR:75.2')] ).
cnf(1121,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0)
| aElement0(xQ) ),
inference(sor,[status(thm)],[195,923]),
[iquote('0:SoR:195.0,923.2')] ).
cnf(1126,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aElement0(xQ) ),
inference(ssi,[status(thm)],[1121,4]),
[iquote('0:SSi:1121.0,4.0')] ).
cnf(1127,plain,
aElement0(xQ),
inference(mrr,[status(thm)],[1126,10]),
[iquote('0:MRR:1126.0,10.0')] ).
cnf(1335,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(res,[status(thm),theory(equality)],[33,717]),
[iquote('0:Res:33.0,717.1')] ).
cnf(1351,plain,
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(sor,[status(thm)],[1335,923]),
[iquote('0:SoR:1335.0,923.2')] ).
cnf(1356,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(ssi,[status(thm)],[1351,5]),
[iquote('0:SSi:1351.0,5.0')] ).
cnf(1357,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(mrr,[status(thm)],[1356,10]),
[iquote('0:MRR:1356.0,10.0')] ).
cnf(1820,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,slbdtsldtrb0(u,w))
| ~ aElementOf0(w,szNzAzT0)
| aSubsetOf0(v,u) ),
inference(eqr,[status(thm),theory(equality)],[93]),
[iquote('0:EqR:93.3')] ).
cnf(1896,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ skP0(u,v,w)
| aElementOf0(w,sdtpldt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[99]),
[iquote('0:EqR:99.2')] ).
cnf(5299,plain,
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| aSubsetOf0(xP,xT) ),
inference(res,[status(thm),theory(equality)],[1357,1820]),
[iquote('0:Res:1357.0,1820.1')] ).
cnf(5332,plain,
( ~ aElementOf0(xk,szNzAzT0)
| aSubsetOf0(xP,xT) ),
inference(ssi,[status(thm)],[5299,5]),
[iquote('0:SSi:5299.0,5.0')] ).
cnf(5333,plain,
aSubsetOf0(xP,xT),
inference(mrr,[status(thm)],[5332,10]),
[iquote('0:MRR:5332.0,10.0')] ).
cnf(5729,plain,
~ aElementOf0(xx,xP),
inference(res,[status(thm),theory(equality)],[5333,144]),
[iquote('0:Res:5333.0,144.0')] ).
cnf(7958,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ skP0(xx,sdtmndt0(xQ,xy),u)
| aElementOf0(u,xP) ),
inference(spr,[status(thm),theory(equality)],[34,1896]),
[iquote('0:SpR:34.0,1896.3')] ).
cnf(7963,plain,
( ~ skP0(xx,sdtmndt0(xQ,xy),u)
| aElementOf0(u,xP) ),
inference(ssi,[status(thm)],[7958,458,1127,6,7,8,63,196]),
[iquote('0:SSi:7958.1,7958.0,458.0,1127.0,6.0,7.0,8.0,63.3,1127.0,6.0,7.0,8.0,196.2')] ).
cnf(8929,plain,
( ~ aElement0(u)
| ~ equal(u,xx)
| aElementOf0(u,xP) ),
inference(res,[status(thm),theory(equality)],[53,7963]),
[iquote('0:Res:53.2,7963.0')] ).
cnf(9164,plain,
( ~ aElement0(xx)
| ~ equal(xx,xx) ),
inference(res,[status(thm),theory(equality)],[8929,5729]),
[iquote('0:Res:8929.2,5729.0')] ).
cnf(9165,plain,
~ aElement0(xx),
inference(obv,[status(thm),theory(equality)],[9164]),
[iquote('0:Obv:9164.1')] ).
cnf(9166,plain,
$false,
inference(ssi,[status(thm)],[9165,196]),
[iquote('0:SSi:9165.0,196.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM558+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 12:13:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.60/2.83
% 2.60/2.83 SPASS V 3.9
% 2.60/2.83 SPASS beiseite: Proof found.
% 2.60/2.83 % SZS status Theorem
% 2.60/2.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/2.83 SPASS derived 6877 clauses, backtracked 1195 clauses, performed 16 splits and kept 3965 clauses.
% 2.60/2.83 SPASS allocated 105022 KBytes.
% 2.60/2.83 SPASS spent 0:00:02.40 on the problem.
% 2.60/2.83 0:00:00.04 for the input.
% 2.60/2.83 0:00:00.13 for the FLOTTER CNF translation.
% 2.60/2.83 0:00:00.11 for inferences.
% 2.60/2.83 0:00:00.04 for the backtracking.
% 2.60/2.83 0:00:02.01 for the reduction.
% 2.60/2.83
% 2.60/2.83
% 2.60/2.83 Here is a proof with depth 6, length 47 :
% 2.60/2.83 % SZS output start Refutation
% See solution above
% 2.60/2.83 Formulae used in the proof : m__2202_02 m__2291 m__2304 m__2202 m__2256 m__ m__2270 m__2378 m__2227 m__2357 mEOfElem mDefCons mFDiffSet mDefSub mDefDiff mDefSel
% 2.60/2.83
%------------------------------------------------------------------------------