TSTP Solution File: NUM534+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM534+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 14:27:12 EDT 2022
% Result : Theorem 0.55s 0.73s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of clauses : 76 ( 27 unt; 18 nHn; 76 RR)
% Number of literals : 191 ( 0 equ; 116 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(xS),
file('NUM534+1.p',unknown),
[] ).
cnf(3,axiom,
aElementOf0(xx,xS),
file('NUM534+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(u,slcrc0)
| aSet0(u) ),
file('NUM534+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
file('NUM534+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aElementOf0(u,v)
| ~ equal(v,slcrc0) ),
file('NUM534+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ skP1(u,v,w)
| aElementOf0(w,v) ),
file('NUM534+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM534+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ skP0(u,v,w)
| equal(w,u)
| aElementOf0(w,v) ),
file('NUM534+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,v)
| skP0(w,v,u) ),
file('NUM534+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aElement0(u)
| ~ equal(u,v)
| skP0(v,w,u) ),
file('NUM534+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM534+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| aSubsetOf0(v,u)
| aElementOf0(skf5(v,w),v) ),
file('NUM534+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtmndt0(v,u))
| aSet0(w) ),
file('NUM534+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aElement0(u)
| ~ aElementOf0(u,v)
| equal(u,w)
| skP1(w,v,u) ),
file('NUM534+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtmndt0(v,u))
| ~ skP1(u,v,x)
| aElementOf0(x,w) ),
file('NUM534+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,x)
| ~ equal(x,sdtmndt0(v,u))
| skP1(u,v,w) ),
file('NUM534+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| equal(w,sdtpldt0(v,u))
| aElementOf0(skf6(v,u,w),w)
| skP0(u,v,skf6(v,u,w)) ),
file('NUM534+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| ~ aElementOf0(skf6(v,u,w),w)
| ~ skP0(u,v,skf6(v,u,w))
| equal(w,sdtpldt0(v,u)) ),
file('NUM534+1.p',unknown),
[] ).
cnf(43,plain,
( ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS))
| ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS) ),
inference(res,[status(thm),theory(equality)],[36,9]),
[iquote('0:Res:36.5,9.0')] ).
cnf(44,plain,
( ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(xx)
| aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(res,[status(thm),theory(equality)],[34,9]),
[iquote('0:Res:34.5,9.0')] ).
cnf(48,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(mrr,[status(thm)],[44,2]),
[iquote('0:MRR:44.0,2.0')] ).
cnf(49,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| ~ skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(mrr,[status(thm)],[43,2]),
[iquote('0:MRR:43.0,2.0')] ).
cnf(53,plain,
( ~ aSet0(xS)
| aElement0(xx) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.1')] ).
cnf(54,plain,
aElement0(xx),
inference(ssi,[status(thm)],[53,2]),
[iquote('0:SSi:53.0,2.0')] ).
cnf(55,plain,
( ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(mrr,[status(thm)],[48,54]),
[iquote('0:MRR:48.0,54.0')] ).
cnf(56,plain,
( ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| ~ skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(mrr,[status(thm)],[49,54]),
[iquote('0:MRR:49.0,54.0')] ).
cnf(68,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| aSet0(sdtmndt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[24]),
[iquote('0:EqR:24.2')] ).
cnf(75,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aSet0(v)
| aSubsetOf0(v,u)
| aElement0(skf5(v,w)) ),
inference(res,[status(thm),theory(equality)],[22,12]),
[iquote('0:Res:22.3,12.1')] ).
cnf(77,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| aSubsetOf0(v,u)
| aElement0(skf5(v,w)) ),
inference(obv,[status(thm),theory(equality)],[75]),
[iquote('0:Obv:75.1')] ).
cnf(115,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(xS,u)
| aElementOf0(xx,u) ),
inference(res,[status(thm),theory(equality)],[3,21]),
[iquote('0:Res:3.0,21.1')] ).
cnf(121,plain,
( ~ aSet0(u)
| ~ aSet0(xS)
| ~ aSet0(u)
| aElement0(skf5(xS,v))
| aElementOf0(xx,u) ),
inference(res,[status(thm),theory(equality)],[77,115]),
[iquote('0:Res:77.2,115.1')] ).
cnf(123,plain,
( ~ aSet0(u)
| ~ aSet0(xS)
| ~ aSet0(u)
| aElementOf0(skf5(xS,v),xS)
| aElementOf0(xx,u) ),
inference(res,[status(thm),theory(equality)],[22,115]),
[iquote('0:Res:22.2,115.1')] ).
cnf(126,plain,
( ~ aSet0(xS)
| ~ aSet0(u)
| aElement0(skf5(xS,v))
| aElementOf0(xx,u) ),
inference(obv,[status(thm),theory(equality)],[121]),
[iquote('0:Obv:121.0')] ).
cnf(127,plain,
( ~ aSet0(u)
| aElement0(skf5(xS,v))
| aElementOf0(xx,u) ),
inference(ssi,[status(thm)],[126,2]),
[iquote('0:SSi:126.0,2.0')] ).
cnf(128,plain,
( ~ aSet0(xS)
| ~ aSet0(u)
| aElementOf0(skf5(xS,v),xS)
| aElementOf0(xx,u) ),
inference(obv,[status(thm),theory(equality)],[123]),
[iquote('0:Obv:123.0')] ).
cnf(129,plain,
( ~ aSet0(u)
| aElementOf0(skf5(xS,v),xS)
| aElementOf0(xx,u) ),
inference(ssi,[status(thm)],[128,2]),
[iquote('0:SSi:128.0,2.0')] ).
cnf(130,plain,
( ~ aSet0(u)
| aElementOf0(xx,u) ),
inference(spt,[spt(split,[position(s1)])],[127]),
[iquote('1:Spt:127.0,127.2')] ).
cnf(131,plain,
( ~ aSet0(u)
| ~ equal(u,slcrc0) ),
inference(res,[status(thm),theory(equality)],[130,10]),
[iquote('1:Res:130.1,10.0')] ).
cnf(134,plain,
~ equal(u,slcrc0),
inference(mrr,[status(thm)],[131,4]),
[iquote('1:MRR:131.0,4.1')] ).
cnf(139,plain,
$false,
inference(eqr,[status(thm),theory(equality)],[134]),
[iquote('1:EqR:134.0')] ).
cnf(140,plain,
aElement0(skf5(xS,u)),
inference(spt,[spt(split,[position(s2)])],[127]),
[iquote('1:Spt:139.0,127.1')] ).
cnf(199,plain,
( ~ aSet0(u)
| aElementOf0(xx,u) ),
inference(spt,[spt(split,[position(s2s1)])],[129]),
[iquote('2:Spt:129.0,129.2')] ).
cnf(200,plain,
( ~ aSet0(u)
| ~ equal(u,slcrc0) ),
inference(res,[status(thm),theory(equality)],[199,10]),
[iquote('2:Res:199.1,10.0')] ).
cnf(203,plain,
~ equal(u,slcrc0),
inference(mrr,[status(thm)],[200,4]),
[iquote('2:MRR:200.0,4.1')] ).
cnf(208,plain,
$false,
inference(eqr,[status(thm),theory(equality)],[203]),
[iquote('2:EqR:203.0')] ).
cnf(209,plain,
aElementOf0(skf5(xS,u),xS),
inference(spt,[spt(split,[position(s2s2)])],[129]),
[iquote('2:Spt:208.0,129.1')] ).
cnf(252,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,sdtmndt0(v,u))
| skP1(u,v,w) ),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.3')] ).
cnf(294,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ skP1(u,v,w)
| aElementOf0(w,sdtmndt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[28]),
[iquote('0:EqR:28.2')] ).
cnf(932,plain,
( ~ aSet0(xS)
| ~ aElement0(xx)
| aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(sor,[status(thm)],[55,68]),
[iquote('0:SoR:55.0,68.2')] ).
cnf(936,plain,
( aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(ssi,[status(thm)],[932,54,2]),
[iquote('0:SSi:932.1,932.0,54.0,2.0')] ).
cnf(1126,plain,
aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS),
inference(spt,[spt(split,[position(s2s2s1)])],[936]),
[iquote('3:Spt:936.0')] ).
cnf(1127,plain,
( ~ aSet0(sdtmndt0(xS,xx))
| ~ skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(mrr,[status(thm)],[56,1126]),
[iquote('3:MRR:56.1,1126.0')] ).
cnf(1128,plain,
~ skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)),
inference(ssi,[status(thm)],[1127,68,2,54]),
[iquote('3:SSi:1127.0,68.0,2.0,54.2')] ).
cnf(1135,plain,
( ~ aSet0(xS)
| aElement0(skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(res,[status(thm),theory(equality)],[1126,12]),
[iquote('3:Res:1126.0,12.1')] ).
cnf(1137,plain,
aElement0(skf6(sdtmndt0(xS,xx),xx,xS)),
inference(ssi,[status(thm)],[1135,2]),
[iquote('3:SSi:1135.0,2.0')] ).
cnf(1151,plain,
( ~ aElement0(skf6(sdtmndt0(xS,xx),xx,xS))
| ~ equal(skf6(sdtmndt0(xS,xx),xx,xS),xx) ),
inference(res,[status(thm),theory(equality)],[19,1128]),
[iquote('3:Res:19.2,1128.0')] ).
cnf(1152,plain,
( ~ aElement0(skf6(sdtmndt0(xS,xx),xx,xS))
| ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),sdtmndt0(xS,xx)) ),
inference(res,[status(thm),theory(equality)],[18,1128]),
[iquote('3:Res:18.2,1128.0')] ).
cnf(1153,plain,
~ equal(skf6(sdtmndt0(xS,xx),xx,xS),xx),
inference(ssi,[status(thm)],[1151,1137]),
[iquote('3:SSi:1151.0,1137.0')] ).
cnf(1154,plain,
~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),sdtmndt0(xS,xx)),
inference(ssi,[status(thm)],[1152,1137]),
[iquote('3:SSi:1152.0,1137.0')] ).
cnf(1166,plain,
( ~ aElement0(xx)
| ~ aSet0(xS)
| ~ skP1(xx,xS,skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(res,[status(thm),theory(equality)],[294,1154]),
[iquote('3:Res:294.3,1154.0')] ).
cnf(1167,plain,
~ skP1(xx,xS,skf6(sdtmndt0(xS,xx),xx,xS)),
inference(ssi,[status(thm)],[1166,2,54]),
[iquote('3:SSi:1166.1,1166.0,2.0,54.0')] ).
cnf(1173,plain,
( ~ aElement0(skf6(sdtmndt0(xS,xx),xx,xS))
| ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| equal(skf6(sdtmndt0(xS,xx),xx,xS),xx) ),
inference(res,[status(thm),theory(equality)],[25,1167]),
[iquote('3:Res:25.3,1167.0')] ).
cnf(1174,plain,
( ~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS)
| equal(skf6(sdtmndt0(xS,xx),xx,xS),xx) ),
inference(ssi,[status(thm)],[1173,1137]),
[iquote('3:SSi:1173.0,1137.0')] ).
cnf(1175,plain,
$false,
inference(mrr,[status(thm)],[1174,1126,1153]),
[iquote('3:MRR:1174.0,1174.1,1126.0,1153.0')] ).
cnf(1176,plain,
~ aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS),
inference(spt,[spt(split,[position(s2s2sa)])],[1175,1126]),
[iquote('3:Spt:1175.0,936.0,1126.0')] ).
cnf(1177,plain,
skP0(xx,sdtmndt0(xS,xx),skf6(sdtmndt0(xS,xx),xx,xS)),
inference(spt,[spt(split,[position(s2s2s2)])],[936]),
[iquote('3:Spt:1175.0,936.1')] ).
cnf(1185,plain,
( equal(skf6(sdtmndt0(xS,xx),xx,xS),xx)
| aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),sdtmndt0(xS,xx)) ),
inference(res,[status(thm),theory(equality)],[1177,17]),
[iquote('3:Res:1177.0,17.0')] ).
cnf(1224,plain,
equal(skf6(sdtmndt0(xS,xx),xx,xS),xx),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1185]),
[iquote('4:Spt:1185.0')] ).
cnf(1227,plain,
~ aElementOf0(xx,xS),
inference(rew,[status(thm),theory(equality)],[1224,1176]),
[iquote('4:Rew:1224.0,1176.0')] ).
cnf(1237,plain,
$false,
inference(mrr,[status(thm)],[1227,3]),
[iquote('4:MRR:1227.0,3.0')] ).
cnf(1238,plain,
~ equal(skf6(sdtmndt0(xS,xx),xx,xS),xx),
inference(spt,[spt(split,[position(s2s2s2sa)])],[1237,1224]),
[iquote('4:Spt:1237.0,1185.0,1224.0')] ).
cnf(1239,plain,
aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),sdtmndt0(xS,xx)),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1185]),
[iquote('4:Spt:1237.0,1185.1')] ).
cnf(1249,plain,
( ~ aElement0(xx)
| ~ aSet0(xS)
| skP1(xx,xS,skf6(sdtmndt0(xS,xx),xx,xS)) ),
inference(res,[status(thm),theory(equality)],[1239,252]),
[iquote('4:Res:1239.0,252.2')] ).
cnf(1250,plain,
skP1(xx,xS,skf6(sdtmndt0(xS,xx),xx,xS)),
inference(ssi,[status(thm)],[1249,2,54]),
[iquote('4:SSi:1249.1,1249.0,2.0,54.0')] ).
cnf(1275,plain,
aElementOf0(skf6(sdtmndt0(xS,xx),xx,xS),xS),
inference(res,[status(thm),theory(equality)],[1250,11]),
[iquote('4:Res:1250.0,11.0')] ).
cnf(1278,plain,
$false,
inference(mrr,[status(thm)],[1275,1176]),
[iquote('4:MRR:1275.0,1176.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM534+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 12:55:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.73
% 0.55/0.73 SPASS V 3.9
% 0.55/0.73 SPASS beiseite: Proof found.
% 0.55/0.73 % SZS status Theorem
% 0.55/0.73 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.73 SPASS derived 871 clauses, backtracked 49 clauses, performed 4 splits and kept 479 clauses.
% 0.55/0.73 SPASS allocated 98900 KBytes.
% 0.55/0.73 SPASS spent 0:00:00.37 on the problem.
% 0.55/0.73 0:00:00.03 for the input.
% 0.55/0.73 0:00:00.07 for the FLOTTER CNF translation.
% 0.55/0.73 0:00:00.02 for inferences.
% 0.55/0.73 0:00:00.00 for the backtracking.
% 0.55/0.73 0:00:00.22 for the reduction.
% 0.55/0.73
% 0.55/0.73
% 0.55/0.73 Here is a proof with depth 7, length 76 :
% 0.55/0.73 % SZS output start Refutation
% See solution above
% 0.55/0.73 Formulae used in the proof : m__617 m__617_02 mDefEmp m__ mDefDiff mEOfElem mDefCons mDefSub
% 0.55/0.73
%------------------------------------------------------------------------------