TSTP Solution File: NUM441+6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.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 : 300s
% DateTime : Thu Aug 31 12:08:21 EDT 2023
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 1198 ( 99 equ)
% Maximal formula atoms : 74 ( 27 avg)
% Number of connectives : 1554 ( 400 ~; 309 |; 739 &)
% ( 53 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 14 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 296 (; 229 !; 67 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1361,plain,
$false,
inference(subsumption_resolution,[],[f1360,f260]) ).
fof(f260,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( ( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(X0,stldt0(xB))
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0) )
& ( ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) )
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(xB))
| aElementOf0(X1,xB)
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,xB)
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(xB)) ) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(xA))
| aElementOf0(X2,xA)
| ~ aInteger0(X2) )
& ( ( ~ aElementOf0(X2,xA)
& aInteger0(X2) )
| ~ aElementOf0(X2,stldt0(xA)) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X3,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X3) )
& ( ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) )
| ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X4] :
( ( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X4,xB)
& ~ aElementOf0(X4,xA) )
| ~ aInteger0(X4) )
& ( ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) )
| ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,cS1395)
| ~ aInteger0(X6) )
& ( aInteger0(X6)
| ~ aElementOf0(X6,cS1395) ) )
& aSet0(cS1395)
& ! [X7] :
( ( aElementOf0(X7,stldt0(xB))
| aElementOf0(X7,xB)
| ~ aInteger0(X7) )
& ( ( ~ aElementOf0(X7,xB)
& aInteger0(X7) )
| ~ aElementOf0(X7,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,stldt0(xA)) )
& ! [X9] :
( ( aElementOf0(X9,cS1395)
| ~ aInteger0(X9) )
& ( aInteger0(X9)
| ~ aElementOf0(X9,cS1395) ) )
& aSet0(cS1395)
& ! [X10] :
( ( aElementOf0(X10,stldt0(xA))
| aElementOf0(X10,xA)
| ~ aInteger0(X10) )
& ( ( ~ aElementOf0(X10,xA)
& aInteger0(X10) )
| ~ aElementOf0(X10,stldt0(xA)) ) )
& aSet0(stldt0(xA)) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( ( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(X0,stldt0(xB))
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0) )
& ( ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) )
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(xB))
| aElementOf0(X1,xB)
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,xB)
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(xB)) ) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(xA))
| aElementOf0(X2,xA)
| ~ aInteger0(X2) )
& ( ( ~ aElementOf0(X2,xA)
& aInteger0(X2) )
| ~ aElementOf0(X2,stldt0(xA)) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X3,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X3) )
& ( ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) )
| ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X4] :
( ( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X4,xB)
& ~ aElementOf0(X4,xA) )
| ~ aInteger0(X4) )
& ( ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) )
| ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,cS1395)
| ~ aInteger0(X6) )
& ( aInteger0(X6)
| ~ aElementOf0(X6,cS1395) ) )
& aSet0(cS1395)
& ! [X7] :
( ( aElementOf0(X7,stldt0(xB))
| aElementOf0(X7,xB)
| ~ aInteger0(X7) )
& ( ( ~ aElementOf0(X7,xB)
& aInteger0(X7) )
| ~ aElementOf0(X7,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,stldt0(xA)) )
& ! [X9] :
( ( aElementOf0(X9,cS1395)
| ~ aInteger0(X9) )
& ( aInteger0(X9)
| ~ aElementOf0(X9,cS1395) ) )
& aSet0(cS1395)
& ! [X10] :
( ( aElementOf0(X10,stldt0(xA))
| aElementOf0(X10,xA)
| ~ aInteger0(X10) )
& ( ( ~ aElementOf0(X10,xA)
& aInteger0(X10) )
| ~ aElementOf0(X10,stldt0(xA)) ) )
& aSet0(stldt0(xA)) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( ~ aElementOf0(X1,xB)
& aInteger0(X1) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X4] :
( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395)
& ! [X7] :
( aElementOf0(X7,stldt0(xB))
<=> ( ~ aElementOf0(X7,xB)
& aInteger0(X7) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,stldt0(xA)) )
& ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395)
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
<=> ( ~ aElementOf0(X10,xA)
& aInteger0(X10) ) )
& aSet0(stldt0(xA)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( ~ aElementOf0(X1,xB)
& aInteger0(X1) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB))
& aInteger0(X3) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X4] :
( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X4,xB)
| aElementOf0(X4,xA) )
& aInteger0(X4) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X5] :
( aElementOf0(X5,stldt0(xB))
=> aElementOf0(X5,cS1395) )
& ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395)
& ! [X7] :
( aElementOf0(X7,stldt0(xB))
<=> ( ~ aElementOf0(X7,xB)
& aInteger0(X7) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
=> aElementOf0(X8,cS1395) )
& ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395)
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
<=> ( ~ aElementOf0(X10,xA)
& aInteger0(X10) ) )
& aSet0(stldt0(xA)) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) ),
file('/export/starexec/sandbox/tmp/tmp.QuxAOopCgj/Vampire---4.8_24854',m__1883) ).
fof(f1360,plain,
~ aSubsetOf0(stldt0(xA),cS1395),
inference(subsumption_resolution,[],[f1359,f269]) ).
fof(f269,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf_transformation,[],[f124]) ).
fof(f1359,plain,
( ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(subsumption_resolution,[],[f1358,f231]) ).
fof(f231,plain,
isOpen0(stldt0(xA)),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0))) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,sK4(X0))
& ~ aDivisorOf0(sK4(X0),sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(sK4(X0),X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,sK4(X0))
& aDivisorOf0(sK4(X0),sdtpldt0(X3,smndt0(X0)))
& sdtpldt0(X3,smndt0(X0)) = sdtasdt0(sK4(X0),sK5(X0,X3))
& aInteger0(sK5(X0,X3))
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)))
& sz00 != sK4(X0)
& aInteger0(sK4(X0)) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(xB))
| aElementOf0(X6,xB)
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,xB)
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7))) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,sK6(X7))
& ~ aDivisorOf0(sK6(X7),sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(sK6(X7),X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,sK6(X7))
& aDivisorOf0(sK6(X7),sdtpldt0(X10,smndt0(X7)))
& sdtpldt0(X10,smndt0(X7)) = sdtasdt0(sK6(X7),sK7(X7,X10))
& aInteger0(sK7(X7,X10))
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)))
& sz00 != sK6(X7)
& aInteger0(sK6(X7)) )
| ~ aElementOf0(X7,stldt0(xA)) )
& ! [X13] :
( ( aElementOf0(X13,stldt0(xA))
| aElementOf0(X13,xA)
| ~ aInteger0(X13) )
& ( ( ~ aElementOf0(X13,xA)
& aInteger0(X13) )
| ~ aElementOf0(X13,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,cS1395)
| ~ aElementOf0(X14,xB) )
& aSet0(xB)
& ! [X15] :
( ( aElementOf0(X15,cS1395)
| ~ aInteger0(X15) )
& ( aInteger0(X15)
| ~ aElementOf0(X15,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,cS1395)
| ~ aElementOf0(X16,xA) )
& aSet0(xA)
& ! [X17] :
( ( aElementOf0(X17,cS1395)
| ~ aInteger0(X17) )
& ( aInteger0(X17)
| ~ aElementOf0(X17,cS1395) ) )
& aSet0(cS1395) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f117,f121,f120,f119,f118]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0))) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,sK4(X0))
& ~ aDivisorOf0(sK4(X0),sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(sK4(X0),X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,sK4(X0))
& aDivisorOf0(sK4(X0),sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(sK4(X0),X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK4(X0)))
& sz00 != sK4(X0)
& aInteger0(sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X3] :
( ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(sK4(X0),X5)
& aInteger0(X5) )
=> ( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(sK4(X0),sK5(X0,X3))
& aInteger0(sK5(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X7] :
( ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,X8)
& ~ aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(X8,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7))) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,sK6(X7))
& ~ aDivisorOf0(sK6(X7),sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(sK6(X7),X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,sK6(X7))
& aDivisorOf0(sK6(X7),sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(sK6(X7),X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,sK6(X7)))
& sz00 != sK6(X7)
& aInteger0(sK6(X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X7,X10] :
( ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(sK6(X7),X12)
& aInteger0(X12) )
=> ( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(sK6(X7),sK7(X7,X10))
& aInteger0(sK7(X7,X10)) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(xB))
| aElementOf0(X6,xB)
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,xB)
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,X8)
& ~ aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(X8,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) )
| ~ aElementOf0(X7,stldt0(xA)) )
& ! [X13] :
( ( aElementOf0(X13,stldt0(xA))
| aElementOf0(X13,xA)
| ~ aInteger0(X13) )
& ( ( ~ aElementOf0(X13,xA)
& aInteger0(X13) )
| ~ aElementOf0(X13,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,cS1395)
| ~ aElementOf0(X14,xB) )
& aSet0(xB)
& ! [X15] :
( ( aElementOf0(X15,cS1395)
| ~ aInteger0(X15) )
& ( aInteger0(X15)
| ~ aElementOf0(X15,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,cS1395)
| ~ aElementOf0(X16,xA) )
& aSet0(xA)
& ! [X17] :
( ( aElementOf0(X17,cS1395)
| ~ aInteger0(X17) )
& ( aInteger0(X17)
| ~ aElementOf0(X17,cS1395) ) )
& aSet0(cS1395) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(xB))
| aElementOf0(X6,xB)
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,xB)
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,X8)
& ~ aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(X8,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) )
| ~ aElementOf0(X7,stldt0(xA)) )
& ! [X13] :
( ( aElementOf0(X13,stldt0(xA))
| aElementOf0(X13,xA)
| ~ aInteger0(X13) )
& ( ( ~ aElementOf0(X13,xA)
& aInteger0(X13) )
| ~ aElementOf0(X13,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,cS1395)
| ~ aElementOf0(X14,xB) )
& aSet0(xB)
& ! [X15] :
( ( aElementOf0(X15,cS1395)
| ~ aInteger0(X15) )
& ( aInteger0(X15)
| ~ aElementOf0(X15,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,cS1395)
| ~ aElementOf0(X16,xA) )
& aSet0(xA)
& ! [X17] :
( ( aElementOf0(X17,cS1395)
| ~ aInteger0(X17) )
& ( aInteger0(X17)
| ~ aElementOf0(X17,cS1395) ) )
& aSet0(cS1395) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,stldt0(xB))
<=> ( ~ aElementOf0(X6,xB)
& aInteger0(X6) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,X8)
& ~ aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(X8,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) )
| ~ aElementOf0(X7,stldt0(xA)) )
& ! [X13] :
( aElementOf0(X13,stldt0(xA))
<=> ( ~ aElementOf0(X13,xA)
& aInteger0(X13) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,cS1395)
| ~ aElementOf0(X14,xB) )
& aSet0(xB)
& ! [X15] :
( aElementOf0(X15,cS1395)
<=> aInteger0(X15) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,cS1395)
| ~ aElementOf0(X16,xA) )
& aSet0(xA)
& ! [X17] :
( aElementOf0(X17,cS1395)
<=> aInteger0(X17) )
& aSet0(cS1395) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,stldt0(xB))
<=> ( ~ aElementOf0(X6,xB)
& aInteger0(X6) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,stldt0(xA))
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ! [X10] :
( ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
| ( ~ sdteqdtlpzmzozddtrp0(X10,X7,X8)
& ~ aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ! [X11] :
( sdtpldt0(X10,smndt0(X7)) != sdtasdt0(X8,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X10) )
& ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) )
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) )
| ~ aElementOf0(X7,stldt0(xA)) )
& ! [X13] :
( aElementOf0(X13,stldt0(xA))
<=> ( ~ aElementOf0(X13,xA)
& aInteger0(X13) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,cS1395)
| ~ aElementOf0(X14,xB) )
& aSet0(xB)
& ! [X15] :
( aElementOf0(X15,cS1395)
<=> aInteger0(X15) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,cS1395)
| ~ aElementOf0(X16,xA) )
& aSet0(xA)
& ! [X17] :
( aElementOf0(X17,cS1395)
<=> aInteger0(X17) )
& aSet0(cS1395) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xB)) )
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
| ? [X4] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X4)
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(xB))
<=> ( ~ aElementOf0(X6,xB)
& aInteger0(X6) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X7] :
( aElementOf0(X7,stldt0(xA))
=> ? [X8] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),stldt0(xA))
& ! [X9] :
( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8))
=> aElementOf0(X9,stldt0(xA)) )
& ! [X10] :
( ( ( ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
| aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
| ? [X11] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X11)
& aInteger0(X11) ) )
& aInteger0(X10) )
=> aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& ( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X7,X8))
=> ( sdteqdtlpzmzozddtrp0(X10,X7,X8)
& aDivisorOf0(X8,sdtpldt0(X10,smndt0(X7)))
& ? [X12] :
( sdtpldt0(X10,smndt0(X7)) = sdtasdt0(X8,X12)
& aInteger0(X12) )
& aInteger0(X10) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sz00 != X8
& aInteger0(X8) ) )
& ! [X13] :
( aElementOf0(X13,stldt0(xA))
<=> ( ~ aElementOf0(X13,xA)
& aInteger0(X13) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X14] :
( aElementOf0(X14,xB)
=> aElementOf0(X14,cS1395) )
& aSet0(xB)
& ! [X15] :
( aElementOf0(X15,cS1395)
<=> aInteger0(X15) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X16] :
( aElementOf0(X16,xA)
=> aElementOf0(X16,cS1395) )
& aSet0(xA)
& ! [X17] :
( aElementOf0(X17,cS1395)
<=> aInteger0(X17) )
& aSet0(cS1395) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xB)) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xA))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xA)) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,cS1395) )
& aSet0(xB)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,cS1395) )
& aSet0(xA)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) ),
file('/export/starexec/sandbox/tmp/tmp.QuxAOopCgj/Vampire---4.8_24854',m__1826) ).
fof(f1358,plain,
( ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(subsumption_resolution,[],[f1357,f250]) ).
fof(f250,plain,
isOpen0(stldt0(xB)),
inference(cnf_transformation,[],[f122]) ).
fof(f1357,plain,
( ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(subsumption_resolution,[],[f1356,f200]) ).
fof(f200,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK1,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& ~ aElementOf0(sK2(X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK2(X1),szAzrzSzezqlpdtcmdtrp0(sK1,X1))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(sK1))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& sdtpldt0(X3,smndt0(sK1)) = sdtasdt0(X1,sK3(X1,X3))
& aInteger0(sK3(X1,X3))
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK1,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X6] :
( ( aElementOf0(X6,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB))
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( ( aElementOf0(X7,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X7,xB)
& ~ aElementOf0(X7,xA) )
| ~ aInteger0(X7) )
& ( ( ( aElementOf0(X7,xB)
| aElementOf0(X7,xA) )
& aInteger0(X7) )
| ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f111,f114,f113,f112]) ).
fof(f112,plain,
( ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK1,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(sK1))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ? [X5] :
( sdtasdt0(X1,X5) = sdtpldt0(X3,smndt0(sK1))
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK1,stldt0(sdtbsmnsldt0(xA,xB))) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X1] :
( ? [X2] :
( ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
=> ( ~ aElementOf0(sK2(X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK2(X1),szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X1,X3] :
( ? [X5] :
( sdtasdt0(X1,X5) = sdtpldt0(X3,smndt0(sK1))
& aInteger0(X5) )
=> ( sdtpldt0(X3,smndt0(sK1)) = sdtasdt0(X1,sK3(X1,X3))
& aInteger0(sK3(X1,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X3,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB))
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( ( aElementOf0(X7,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X7,xB)
& ~ aElementOf0(X7,xA) )
| ~ aInteger0(X7) )
& ( ( ( aElementOf0(X7,xB)
| aElementOf0(X7,xA) )
& aInteger0(X7) )
| ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ! [X3] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X5] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X5)
| ~ aInteger0(X5) ) )
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) )
& aInteger0(X4) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
| sz00 = X3
| ~ aInteger0(X3) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X1,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( ( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X0,xB)
& ~ aElementOf0(X0,xA) )
| ~ aInteger0(X0) )
& ( ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) )
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ! [X3] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X5] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X5)
| ~ aInteger0(X5) ) )
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) )
& aInteger0(X4) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
| sz00 = X3
| ~ aInteger0(X3) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [X1] :
( ( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X1,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X1) )
& ( ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) )
| ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( ( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ( ~ aElementOf0(X0,xB)
& ~ aElementOf0(X0,xA) )
| ~ aInteger0(X0) )
& ( ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) )
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ! [X3] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X5] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X5)
| ~ aInteger0(X5) ) )
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) )
& aInteger0(X4) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
| sz00 = X3
| ~ aInteger0(X3) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X2] :
( ! [X3] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ( ~ sdteqdtlpzmzozddtrp0(X4,X2,X3)
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ! [X5] :
( sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X5)
| ~ aInteger0(X5) ) )
| ~ aInteger0(X4) )
& ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) )
& aInteger0(X4) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
| sz00 = X3
| ~ aInteger0(X3) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X2] :
( aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X3] :
( ( ( ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| ? [X5] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X5)
& aInteger0(X5) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X4,X2,X3)
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ? [X6] :
( sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6)
& aInteger0(X6) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& sz00 != X3
& aInteger0(X3) ) ) ) ) ) ),
inference(rectify,[],[f42]) ).
fof(f42,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& sz00 != X1
& aInteger0(X1) ) ) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& sz00 != X1
& aInteger0(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QuxAOopCgj/Vampire---4.8_24854',m__) ).
fof(f1356,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(superposition,[],[f356,f289]) ).
fof(f289,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(cnf_transformation,[],[f124]) ).
fof(f356,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( ( isOpen0(X1)
& isOpen0(X0)
& aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> isOpen0(sdtslmnbsdt0(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.QuxAOopCgj/Vampire---4.8_24854',mInterOpen) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 15:15:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.20/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.QuxAOopCgj/Vampire---4.8_24854
% 0.20/0.35 % (25056)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (25063)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.20/0.42 % (25062)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.20/0.42 % (25059)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.20/0.42 % (25066)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.20/0.42 % (25065)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.20/0.42 % (25058)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.20/0.42 % (25068)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.20/0.44 % (25068)First to succeed.
% 0.20/0.44 % (25068)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for Vampire---4
% 0.20/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.45 % (25068)------------------------------
% 0.20/0.45 % (25068)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.45 % (25068)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.45 % (25068)Termination reason: Refutation
% 0.20/0.45
% 0.20/0.45 % (25068)Memory used [KB]: 6396
% 0.20/0.45 % (25068)Time elapsed: 0.027 s
% 0.20/0.45 % (25068)------------------------------
% 0.20/0.45 % (25068)------------------------------
% 0.20/0.45 % (25056)Success in time 0.089 s
% 0.20/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------