TSTP Solution File: NUM609+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM609+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:28:03 EDT 2022
% Result : Theorem 1.69s 1.88s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of clauses : 38 ( 21 unt; 1 nHn; 38 RR)
% Number of literals : 70 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM609+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM609+1.p',unknown),
[] ).
cnf(7,axiom,
aFunction0(xc),
file('NUM609+1.p',unknown),
[] ).
cnf(13,axiom,
aSet0(xO),
file('NUM609+1.p',unknown),
[] ).
cnf(14,axiom,
isCountable0(xO),
file('NUM609+1.p',unknown),
[] ).
cnf(15,axiom,
aSet0(xP),
file('NUM609+1.p',unknown),
[] ).
cnf(23,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('NUM609+1.p',unknown),
[] ).
cnf(25,axiom,
aElementOf0(xp,xO),
file('NUM609+1.p',unknown),
[] ).
cnf(26,axiom,
~ aSubsetOf0(xP,xQ),
file('NUM609+1.p',unknown),
[] ).
cnf(42,axiom,
aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM609+1.p',unknown),
[] ).
cnf(43,axiom,
equal(szmzizndt0(xQ),xp),
file('NUM609+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM609+1.p',unknown),
[] ).
cnf(58,axiom,
equal(sdtmndt0(xQ,szmzizndt0(xQ)),xP),
file('NUM609+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ skP1(u,v,w)
| aElementOf0(w,v) ),
file('NUM609+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM609+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM609+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| aSubsetOf0(v,u)
| aElementOf0(skf26(v,w),v) ),
file('NUM609+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aElementOf0(skf26(v,u),u)
| aSubsetOf0(v,u) ),
file('NUM609+1.p',unknown),
[] ).
cnf(151,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,x)
| ~ equal(x,sdtmndt0(v,u))
| skP1(u,v,w) ),
file('NUM609+1.p',unknown),
[] ).
cnf(205,plain,
equal(sdtmndt0(xQ,xp),xP),
inference(rew,[status(thm),theory(equality)],[43,58]),
[iquote('0:Rew:43.0,58.0')] ).
cnf(230,plain,
( ~ aSet0(xP)
| ~ aSet0(xQ)
| ~ aElementOf0(skf26(xP,xQ),xQ) ),
inference(res,[status(thm),theory(equality)],[111,26]),
[iquote('0:Res:111.3,26.0')] ).
cnf(231,plain,
( ~ aSet0(xP)
| ~ aSet0(xQ)
| aElementOf0(skf26(xP,u),xP) ),
inference(res,[status(thm),theory(equality)],[103,26]),
[iquote('0:Res:103.3,26.0')] ).
cnf(232,plain,
( ~ aSet0(xQ)
| aElementOf0(skf26(xP,u),xP) ),
inference(mrr,[status(thm)],[231,15]),
[iquote('0:MRR:231.0,15.0')] ).
cnf(233,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(skf26(xP,xQ),xQ) ),
inference(mrr,[status(thm)],[230,15]),
[iquote('0:MRR:230.0,15.0')] ).
cnf(307,plain,
( ~ aSet0(xO)
| aElement0(xp) ),
inference(res,[status(thm),theory(equality)],[25,72]),
[iquote('0:Res:25.0,72.1')] ).
cnf(320,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[42,72]),
[iquote('0:Res:42.0,72.1')] ).
cnf(322,plain,
aElement0(xp),
inference(ssi,[status(thm)],[307,14,13]),
[iquote('0:SSi:307.0,14.0,13.0')] ).
cnf(331,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[320,53,7]),
[iquote('0:SSi:320.0,53.0,7.1')] ).
cnf(334,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xQ) ),
inference(res,[status(thm),theory(equality)],[23,74]),
[iquote('0:Res:23.0,74.1')] ).
cnf(342,plain,
aSet0(xQ),
inference(ssi,[status(thm)],[334,3,2]),
[iquote('0:SSi:334.0,3.0,2.0')] ).
cnf(343,plain,
aElementOf0(skf26(xP,u),xP),
inference(mrr,[status(thm)],[232,342]),
[iquote('0:MRR:232.0,342.0')] ).
cnf(344,plain,
~ aElementOf0(skf26(xP,xQ),xQ),
inference(mrr,[status(thm)],[233,342]),
[iquote('0:MRR:233.0,342.0')] ).
cnf(3435,plain,
( ~ aElement0(xp)
| ~ aSet0(xQ)
| ~ aElementOf0(u,v)
| ~ equal(v,xP)
| skP1(xp,xQ,u) ),
inference(spl,[status(thm),theory(equality)],[205,151]),
[iquote('0:SpL:205.0,151.3')] ).
cnf(3436,plain,
( ~ aElementOf0(u,v)
| ~ equal(v,xP)
| skP1(xp,xQ,u) ),
inference(ssi,[status(thm)],[3435,342,331,322]),
[iquote('0:SSi:3435.1,3435.0,342.0,331.0,322.0')] ).
cnf(6906,plain,
( ~ equal(xP,xP)
| skP1(xp,xQ,skf26(xP,u)) ),
inference(res,[status(thm),theory(equality)],[343,3436]),
[iquote('0:Res:343.0,3436.0')] ).
cnf(6945,plain,
skP1(xp,xQ,skf26(xP,u)),
inference(obv,[status(thm),theory(equality)],[6906]),
[iquote('0:Obv:6906.0')] ).
cnf(6962,plain,
aElementOf0(skf26(xP,u),xQ),
inference(res,[status(thm),theory(equality)],[6945,65]),
[iquote('0:Res:6945.0,65.0')] ).
cnf(6966,plain,
$false,
inference(unc,[status(thm)],[6962,344]),
[iquote('0:UnC:6962.0,344.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM609+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 : Fri Jul 8 01:17:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.88
% 1.69/1.88 SPASS V 3.9
% 1.69/1.88 SPASS beiseite: Proof found.
% 1.69/1.88 % SZS status Theorem
% 1.69/1.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.69/1.88 SPASS derived 5031 clauses, backtracked 565 clauses, performed 12 splits and kept 2705 clauses.
% 1.69/1.88 SPASS allocated 103632 KBytes.
% 1.69/1.88 SPASS spent 0:00:01.49 on the problem.
% 1.69/1.88 0:00:00.04 for the input.
% 1.69/1.88 0:00:00.24 for the FLOTTER CNF translation.
% 1.69/1.88 0:00:00.08 for inferences.
% 1.69/1.88 0:00:00.03 for the backtracking.
% 1.69/1.88 0:00:01.04 for the reduction.
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Here is a proof with depth 3, length 38 :
% 1.69/1.88 % SZS output start Refutation
% See solution above
% 1.69/1.88 Formulae used in the proof : mNATSet m__3453 m__4908 m__5164 m__5106 m__5182 m__ m__5116 m__5147 mDomSet mDefDiff mEOfElem mDefSub
% 1.69/1.88
%------------------------------------------------------------------------------