TSTP Solution File: NUM440+6 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM440+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Fri May 3 02:49:17 EDT 2024
% Result : Theorem 7.63s 1.70s
% Output : CNFRefutation 7.63s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',m__1826) ).
fof(f40,conjecture,
( ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
=> ( 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) ) )
& aSet0(stldt0(xB)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xB),cS1395)
| ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xA),cS1395)
| ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
~ ( ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
=> ( 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) ) )
& aSet0(stldt0(xB)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xB),cS1395)
| ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xA),cS1395)
| ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) ) ) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f48,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(f49,plain,
~ ( ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
=> ( ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
=> ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
| ! [X4] :
( aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) ) ) ) ) ) ) )
& ( ( ! [X5] :
( aElementOf0(X5,stldt0(xB))
<=> ( ~ aElementOf0(X5,xB)
& aInteger0(X5) ) )
& aSet0(stldt0(xB)) )
=> ( ( ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xB),cS1395)
| ! [X7] :
( aElementOf0(X7,stldt0(xB))
=> aElementOf0(X7,cS1395) ) ) ) )
& ( ( ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& aSet0(stldt0(xA)) )
=> ( ( ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xA),cS1395)
| ! [X10] :
( aElementOf0(X10,stldt0(xA))
=> aElementOf0(X10,cS1395) ) ) ) ) ),
inference(rectify,[],[f41]) ).
fof(f100,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,[],[f48]) ).
fof(f101,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,[],[f100]) ).
fof(f102,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [X4] :
( aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB)))
<~> ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
& ! [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)) )
| ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [X7] :
( ~ aElementOf0(X7,cS1395)
& aElementOf0(X7,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395)
& ! [X5] :
( aElementOf0(X5,stldt0(xB))
<=> ( ~ aElementOf0(X5,xB)
& aInteger0(X5) ) )
& aSet0(stldt0(xB)) )
| ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [X10] :
( ~ aElementOf0(X10,cS1395)
& aElementOf0(X10,stldt0(xA)) )
& ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395)
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& aSet0(stldt0(xA)) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f103,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [X4] :
( aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB)))
<~> ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
& ! [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)) )
| ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [X7] :
( ~ aElementOf0(X7,cS1395)
& aElementOf0(X7,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395)
& ! [X5] :
( aElementOf0(X5,stldt0(xB))
<=> ( ~ aElementOf0(X5,xB)
& aInteger0(X5) ) )
& aSet0(stldt0(xB)) )
| ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [X10] :
( ~ aElementOf0(X10,cS1395)
& aElementOf0(X10,stldt0(xA)) )
& ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395)
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
& aSet0(stldt0(xA)) ) ),
inference(flattening,[],[f102]) ).
fof(f113,plain,
! [X8,X7] :
( ! [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)) ) )
| ~ sP6(X8,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f114,plain,
! [X1,X0] :
( ! [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)) ) )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f115,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP7(X1,X0)
& 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)) )
& sP6(X8,X7)
& 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(definition_folding,[],[f101,f114,f113]) ).
fof(f116,plain,
( ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( ~ aElementOf0(X8,xA)
& aInteger0(X8) ) )
| ~ sP8 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f117,plain,
( ! [X5] :
( aElementOf0(X5,stldt0(xB))
<=> ( ~ aElementOf0(X5,xB)
& aInteger0(X5) ) )
| ~ sP9 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f118,plain,
( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
| ~ sP10 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f119,plain,
( ? [X4] :
( aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB)))
<~> ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) ) )
| ~ sP11 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f120,plain,
( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB))
& aInteger0(X1) ) )
| ~ sP12 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f121,plain,
( ! [X2] :
( aElementOf0(X2,stldt0(xA))
<=> ( ~ aElementOf0(X2,xA)
& aInteger0(X2) ) )
| ~ sP13 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f122,plain,
( ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( ~ aElementOf0(X3,xB)
& aInteger0(X3) ) )
| ~ sP14 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f123,plain,
( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [X10] :
( ~ aElementOf0(X10,cS1395)
& aElementOf0(X10,stldt0(xA)) )
& ! [X9] :
( aElementOf0(X9,cS1395)
<=> aInteger0(X9) )
& aSet0(cS1395)
& sP8
& aSet0(stldt0(xA)) )
| ~ sP15 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f124,plain,
( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [X7] :
( ~ aElementOf0(X7,cS1395)
& aElementOf0(X7,stldt0(xB)) )
& ! [X6] :
( aElementOf0(X6,cS1395)
<=> aInteger0(X6) )
& aSet0(cS1395)
& sP9
& aSet0(stldt0(xB)) )
| ~ sP16 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f125,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& sP11
& sP14
& sP13
& sP12
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& sP10
& aSet0(sdtbsmnsldt0(xA,xB)) )
| sP16
| sP15 ),
inference(definition_folding,[],[f103,f124,f123,f122,f121,f120,f119,f118,f117,f116]) ).
fof(f191,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP7(X1,X0)
& 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)) )
& sP6(X8,X7)
& 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,[],[f115]) ).
fof(f192,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP7(X1,X0)
& 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)) )
& sP6(X8,X7)
& 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,[],[f191]) ).
fof(f193,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP7(X1,X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(xB))
| aElementOf0(X3,xB)
| ~ aInteger0(X3) )
& ( ( ~ aElementOf0(X3,xB)
& aInteger0(X3) )
| ~ aElementOf0(X3,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X4] :
( ? [X5] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),stldt0(xA))
& ! [X6] :
( aElementOf0(X6,stldt0(xA))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& sP6(X5,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X4,stldt0(xA)) )
& ! [X7] :
( ( aElementOf0(X7,stldt0(xA))
| aElementOf0(X7,xA)
| ~ aInteger0(X7) )
& ( ( ~ aElementOf0(X7,xA)
& aInteger0(X7) )
| ~ aElementOf0(X7,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,xB) )
& aSet0(xB)
& ! [X9] :
( ( aElementOf0(X9,cS1395)
| ~ aInteger0(X9) )
& ( aInteger0(X9)
| ~ aElementOf0(X9,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X10] :
( aElementOf0(X10,cS1395)
| ~ aElementOf0(X10,xA) )
& aSet0(xA)
& ! [X11] :
( ( aElementOf0(X11,cS1395)
| ~ aInteger0(X11) )
& ( aInteger0(X11)
| ~ aElementOf0(X11,cS1395) ) )
& aSet0(cS1395) ),
inference(rectify,[],[f192]) ).
fof(f194,plain,
! [X0] :
( ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP7(X1,X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sz00 != X1
& aInteger0(X1) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0)),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0))) )
& sP7(sK33(X0),X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0)))
& sz00 != sK33(X0)
& aInteger0(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f195,plain,
! [X4] :
( ? [X5] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),stldt0(xA))
& ! [X6] :
( aElementOf0(X6,stldt0(xA))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& sP6(X5,X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sz00 != X5
& aInteger0(X5) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4)),stldt0(xA))
& ! [X6] :
( aElementOf0(X6,stldt0(xA))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4))) )
& sP6(sK34(X4),X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4)))
& sz00 != sK34(X4)
& aInteger0(sK34(X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f196,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0)),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,stldt0(xB))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0))) )
& sP7(sK33(X0),X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,sK33(X0)))
& sz00 != sK33(X0)
& aInteger0(sK33(X0)) )
| ~ aElementOf0(X0,stldt0(xB)) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(xB))
| aElementOf0(X3,xB)
| ~ aInteger0(X3) )
& ( ( ~ aElementOf0(X3,xB)
& aInteger0(X3) )
| ~ aElementOf0(X3,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X4] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4)),stldt0(xA))
& ! [X6] :
( aElementOf0(X6,stldt0(xA))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4))) )
& sP6(sK34(X4),X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK34(X4)))
& sz00 != sK34(X4)
& aInteger0(sK34(X4)) )
| ~ aElementOf0(X4,stldt0(xA)) )
& ! [X7] :
( ( aElementOf0(X7,stldt0(xA))
| aElementOf0(X7,xA)
| ~ aInteger0(X7) )
& ( ( ~ aElementOf0(X7,xA)
& aInteger0(X7) )
| ~ aElementOf0(X7,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,xB) )
& aSet0(xB)
& ! [X9] :
( ( aElementOf0(X9,cS1395)
| ~ aInteger0(X9) )
& ( aInteger0(X9)
| ~ aElementOf0(X9,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X10] :
( aElementOf0(X10,cS1395)
| ~ aElementOf0(X10,xA) )
& aSet0(xA)
& ! [X11] :
( ( aElementOf0(X11,cS1395)
| ~ aInteger0(X11) )
& ( aInteger0(X11)
| ~ aElementOf0(X11,cS1395) ) )
& aSet0(cS1395) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f193,f195,f194]) ).
fof(f197,plain,
( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [X7] :
( ~ aElementOf0(X7,cS1395)
& aElementOf0(X7,stldt0(xB)) )
& ! [X6] :
( ( aElementOf0(X6,cS1395)
| ~ aInteger0(X6) )
& ( aInteger0(X6)
| ~ aElementOf0(X6,cS1395) ) )
& aSet0(cS1395)
& sP9
& aSet0(stldt0(xB)) )
| ~ sP16 ),
inference(nnf_transformation,[],[f124]) ).
fof(f198,plain,
( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,stldt0(xB)) )
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP9
& aSet0(stldt0(xB)) )
| ~ sP16 ),
inference(rectify,[],[f197]) ).
fof(f199,plain,
( ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,stldt0(xB)) )
=> ( ~ aElementOf0(sK35,cS1395)
& aElementOf0(sK35,stldt0(xB)) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ~ aElementOf0(sK35,cS1395)
& aElementOf0(sK35,stldt0(xB))
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP9
& aSet0(stldt0(xB)) )
| ~ sP16 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f198,f199]) ).
fof(f201,plain,
( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [X10] :
( ~ aElementOf0(X10,cS1395)
& aElementOf0(X10,stldt0(xA)) )
& ! [X9] :
( ( aElementOf0(X9,cS1395)
| ~ aInteger0(X9) )
& ( aInteger0(X9)
| ~ aElementOf0(X9,cS1395) ) )
& aSet0(cS1395)
& sP8
& aSet0(stldt0(xA)) )
| ~ sP15 ),
inference(nnf_transformation,[],[f123]) ).
fof(f202,plain,
( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,stldt0(xA)) )
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP8
& aSet0(stldt0(xA)) )
| ~ sP15 ),
inference(rectify,[],[f201]) ).
fof(f203,plain,
( ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,stldt0(xA)) )
=> ( ~ aElementOf0(sK36,cS1395)
& aElementOf0(sK36,stldt0(xA)) ) ),
introduced(choice_axiom,[]) ).
fof(f204,plain,
( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ~ aElementOf0(sK36,cS1395)
& aElementOf0(sK36,stldt0(xA))
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP8
& aSet0(stldt0(xA)) )
| ~ sP15 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f202,f203]) ).
fof(f211,plain,
( ! [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))) ) )
| ~ sP12 ),
inference(nnf_transformation,[],[f120]) ).
fof(f212,plain,
( ! [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))) ) )
| ~ sP12 ),
inference(flattening,[],[f211]) ).
fof(f213,plain,
( ! [X0] :
( ( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0) )
& ( ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) )
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| ~ sP12 ),
inference(rectify,[],[f212]) ).
fof(f214,plain,
( ? [X4] :
( ( ~ aElementOf0(X4,stldt0(xB))
| ~ aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| ~ aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) )
| aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| ~ sP11 ),
inference(nnf_transformation,[],[f119]) ).
fof(f215,plain,
( ? [X4] :
( ( ~ aElementOf0(X4,stldt0(xB))
| ~ aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| ~ aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(X4,stldt0(xB))
& aElementOf0(X4,stldt0(xA))
& aInteger0(X4) )
| aElementOf0(X4,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| ~ sP11 ),
inference(flattening,[],[f214]) ).
fof(f216,plain,
( ? [X0] :
( ( ~ aElementOf0(X0,stldt0(xB))
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) )
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| ~ sP11 ),
inference(rectify,[],[f215]) ).
fof(f217,plain,
( ? [X0] :
( ( ~ aElementOf0(X0,stldt0(xB))
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) )
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
=> ( ( ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| ~ aInteger0(sK37)
| ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(sK37,stldt0(xB))
& aElementOf0(sK37,stldt0(xA))
& aInteger0(sK37) )
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f218,plain,
( ( ( ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| ~ aInteger0(sK37)
| ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(sK37,stldt0(xB))
& aElementOf0(sK37,stldt0(xA))
& aInteger0(sK37) )
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB))) ) )
| ~ sP11 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f216,f217]) ).
fof(f219,plain,
( ! [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)) ) )
| ~ sP10 ),
inference(nnf_transformation,[],[f118]) ).
fof(f220,plain,
( ! [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)) ) )
| ~ sP10 ),
inference(flattening,[],[f219]) ).
fof(f347,plain,
! [X11] :
( aInteger0(X11)
| ~ aElementOf0(X11,cS1395) ),
inference(cnf_transformation,[],[f196]) ).
fof(f348,plain,
! [X11] :
( aElementOf0(X11,cS1395)
| ~ aInteger0(X11) ),
inference(cnf_transformation,[],[f196]) ).
fof(f350,plain,
! [X10] :
( aElementOf0(X10,cS1395)
| ~ aElementOf0(X10,xA) ),
inference(cnf_transformation,[],[f196]) ).
fof(f356,plain,
! [X8] :
( aElementOf0(X8,cS1395)
| ~ aElementOf0(X8,xB) ),
inference(cnf_transformation,[],[f196]) ).
fof(f359,plain,
! [X7] :
( aInteger0(X7)
| ~ aElementOf0(X7,stldt0(xA)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f360,plain,
! [X7] :
( ~ aElementOf0(X7,xA)
| ~ aElementOf0(X7,stldt0(xA)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f361,plain,
! [X7] :
( aElementOf0(X7,stldt0(xA))
| aElementOf0(X7,xA)
| ~ aInteger0(X7) ),
inference(cnf_transformation,[],[f196]) ).
fof(f371,plain,
! [X3] :
( aInteger0(X3)
| ~ aElementOf0(X3,stldt0(xB)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f372,plain,
! [X3] :
( ~ aElementOf0(X3,xB)
| ~ aElementOf0(X3,stldt0(xB)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f373,plain,
! [X3] :
( aElementOf0(X3,stldt0(xB))
| aElementOf0(X3,xB)
| ~ aInteger0(X3) ),
inference(cnf_transformation,[],[f196]) ).
fof(f387,plain,
( aElementOf0(sK35,stldt0(xB))
| ~ sP16 ),
inference(cnf_transformation,[],[f200]) ).
fof(f388,plain,
( ~ aElementOf0(sK35,cS1395)
| ~ sP16 ),
inference(cnf_transformation,[],[f200]) ).
fof(f395,plain,
( aElementOf0(sK36,stldt0(xA))
| ~ sP15 ),
inference(cnf_transformation,[],[f204]) ).
fof(f396,plain,
( ~ aElementOf0(sK36,cS1395)
| ~ sP15 ),
inference(cnf_transformation,[],[f204]) ).
fof(f397,plain,
( ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ sP15 ),
inference(cnf_transformation,[],[f204]) ).
fof(f404,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP12 ),
inference(cnf_transformation,[],[f213]) ).
fof(f405,plain,
! [X0] :
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP12 ),
inference(cnf_transformation,[],[f213]) ).
fof(f406,plain,
! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| ~ sP12 ),
inference(cnf_transformation,[],[f213]) ).
fof(f407,plain,
( aInteger0(sK37)
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP11 ),
inference(cnf_transformation,[],[f218]) ).
fof(f408,plain,
( aElementOf0(sK37,stldt0(xA))
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP11 ),
inference(cnf_transformation,[],[f218]) ).
fof(f409,plain,
( aElementOf0(sK37,stldt0(xB))
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP11 ),
inference(cnf_transformation,[],[f218]) ).
fof(f410,plain,
( ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| ~ aInteger0(sK37)
| ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP11 ),
inference(cnf_transformation,[],[f218]) ).
fof(f412,plain,
! [X0] :
( aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ sP10 ),
inference(cnf_transformation,[],[f220]) ).
fof(f413,plain,
! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ sP10 ),
inference(cnf_transformation,[],[f220]) ).
fof(f414,plain,
! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ sP10 ),
inference(cnf_transformation,[],[f220]) ).
fof(f422,plain,
( sP10
| sP16
| sP15 ),
inference(cnf_transformation,[],[f125]) ).
fof(f424,plain,
( sP12
| sP16
| sP15 ),
inference(cnf_transformation,[],[f125]) ).
fof(f427,plain,
( sP11
| sP16
| sP15 ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_176,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xB))
| aElementOf0(X0,xB) ),
inference(cnf_transformation,[],[f373]) ).
cnf(c_177,plain,
( ~ aElementOf0(X0,stldt0(xB))
| ~ aElementOf0(X0,xB) ),
inference(cnf_transformation,[],[f372]) ).
cnf(c_178,plain,
( ~ aElementOf0(X0,stldt0(xB))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f371]) ).
cnf(c_188,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA))
| aElementOf0(X0,xA) ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_189,plain,
( ~ aElementOf0(X0,stldt0(xA))
| ~ aElementOf0(X0,xA) ),
inference(cnf_transformation,[],[f360]) ).
cnf(c_190,plain,
( ~ aElementOf0(X0,stldt0(xA))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f359]) ).
cnf(c_193,plain,
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f356]) ).
cnf(c_199,plain,
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f350]) ).
cnf(c_201,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f348]) ).
cnf(c_202,plain,
( ~ aElementOf0(X0,cS1395)
| aInteger0(X0) ),
inference(cnf_transformation,[],[f347]) ).
cnf(c_205,plain,
( ~ aElementOf0(sK35,cS1395)
| ~ sP16 ),
inference(cnf_transformation,[],[f388]) ).
cnf(c_206,plain,
( ~ sP16
| aElementOf0(sK35,stldt0(xB)) ),
inference(cnf_transformation,[],[f387]) ).
cnf(c_212,plain,
( ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ sP15 ),
inference(cnf_transformation,[],[f397]) ).
cnf(c_213,plain,
( ~ aElementOf0(sK36,cS1395)
| ~ sP15 ),
inference(cnf_transformation,[],[f396]) ).
cnf(c_214,plain,
( ~ sP15
| aElementOf0(sK36,stldt0(xA)) ),
inference(cnf_transformation,[],[f395]) ).
cnf(c_226,plain,
( ~ aInteger0(X0)
| ~ sP12
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(cnf_transformation,[],[f406]) ).
cnf(c_227,plain,
( ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ sP12 ),
inference(cnf_transformation,[],[f405]) ).
cnf(c_228,plain,
( ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP12
| aInteger0(X0) ),
inference(cnf_transformation,[],[f404]) ).
cnf(c_229,plain,
( ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| ~ aInteger0(sK37)
| ~ sP11 ),
inference(cnf_transformation,[],[f410]) ).
cnf(c_230,plain,
( ~ sP11
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(sK37,stldt0(xB)) ),
inference(cnf_transformation,[],[f409]) ).
cnf(c_231,plain,
( ~ sP11
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(sK37,stldt0(xA)) ),
inference(cnf_transformation,[],[f408]) ).
cnf(c_232,plain,
( ~ sP11
| aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aInteger0(sK37) ),
inference(cnf_transformation,[],[f407]) ).
cnf(c_233,plain,
( ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ sP10
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(cnf_transformation,[],[f414]) ).
cnf(c_234,plain,
( ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ sP10
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(cnf_transformation,[],[f413]) ).
cnf(c_235,plain,
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ sP10
| aElementOf0(X0,xB)
| aElementOf0(X0,xA) ),
inference(cnf_transformation,[],[f412]) ).
cnf(c_244,negated_conjecture,
( sP16
| sP15
| sP11 ),
inference(cnf_transformation,[],[f427]) ).
cnf(c_247,negated_conjecture,
( sP16
| sP15
| sP12 ),
inference(cnf_transformation,[],[f424]) ).
cnf(c_249,negated_conjecture,
( sP16
| sP15
| sP10 ),
inference(cnf_transformation,[],[f422]) ).
cnf(c_409,plain,
( ~ aElementOf0(X0,xA)
| ~ sP10
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(global_subsumption_just,[status(thm)],[c_234,c_202,c_199,c_234]) ).
cnf(c_412,plain,
( ~ aElementOf0(X0,xB)
| ~ sP10
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(global_subsumption_just,[status(thm)],[c_233,c_202,c_193,c_233]) ).
cnf(c_446,plain,
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xB)) ),
inference(prop_impl_just,[status(thm)],[c_178]) ).
cnf(c_447,plain,
( ~ aElementOf0(X0,stldt0(xB))
| aInteger0(X0) ),
inference(renaming,[status(thm)],[c_446]) ).
cnf(c_934,plain,
( ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| ~ sP11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_229,c_447]) ).
cnf(c_3268,plain,
( ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| aInteger0(X0)
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_247,c_228]) ).
cnf(c_3282,plain,
( ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_247,c_227]) ).
cnf(c_3296,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_247,c_226]) ).
cnf(c_3394,plain,
( ~ aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aElementOf0(sK37,stldt0(xB))
| ~ aElementOf0(sK37,stldt0(xA))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_244,c_934]) ).
cnf(c_3410,plain,
( aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aInteger0(sK37)
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_244,c_232]) ).
cnf(c_3419,plain,
( aInteger0(sK37)
| sP16
| sP15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_3410,c_3268]) ).
cnf(c_3423,plain,
( aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(sK37,stldt0(xA))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_244,c_231]) ).
cnf(c_3436,plain,
( aElementOf0(sK37,stldt0(sdtbsmnsldt0(xA,xB)))
| aElementOf0(sK37,stldt0(xB))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_244,c_230]) ).
cnf(c_3465,plain,
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_249,c_412]) ).
cnf(c_3479,plain,
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_249,c_409]) ).
cnf(c_3507,plain,
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| sP16
| sP15 ),
inference(resolution,[status(thm)],[c_249,c_235]) ).
cnf(c_14964,plain,
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| aElementOf0(X0,xA)
| aElementOf0(X0,xB)
| ~ sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_3507]) ).
cnf(c_14965,plain,
( sP16
| sP15
| sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3507]) ).
cnf(c_14968,plain,
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,xA)
| ~ sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_3479]) ).
cnf(c_14969,plain,
( sP16
| sP15
| sP2_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3479]) ).
cnf(c_14970,plain,
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,xB)
| ~ sP3_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP3_iProver_def])],[c_3465]) ).
cnf(c_14971,plain,
( sP16
| sP15
| sP3_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3465]) ).
cnf(c_14972,plain,
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X0)
| ~ sP4_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP4_iProver_def])],[c_3296]) ).
cnf(c_14973,plain,
( sP16
| sP15
| sP4_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3296]) ).
cnf(c_14974,plain,
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ sP5_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP5_iProver_def])],[c_3282]) ).
cnf(c_14975,plain,
( sP16
| sP15
| sP5_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3282]) ).
cnf(c_14978,plain,
sdtbsmnsldt0(xA,xB) = sP7_iProver_def,
definition ).
cnf(c_14979,plain,
stldt0(sP7_iProver_def) = sP8_iProver_def,
definition ).
cnf(c_14980,plain,
stldt0(xA) = sP9_iProver_def,
definition ).
cnf(c_14981,plain,
stldt0(xB) = sP10_iProver_def,
definition ).
cnf(c_18551,plain,
( ~ aElementOf0(X0,xA)
| ~ sP2_iProver_def
| aElementOf0(X0,sP7_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_14968,c_14978]) ).
cnf(c_18558,plain,
( ~ aElementOf0(X0,xB)
| ~ sP3_iProver_def
| aElementOf0(X0,sP7_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_14970,c_14978]) ).
cnf(c_18572,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP9_iProver_def)
| sP16
| sP15 ),
inference(light_normalisation,[status(thm)],[c_3423,c_14978,c_14979,c_14980]) ).
cnf(c_18581,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP10_iProver_def)
| sP16
| sP15 ),
inference(light_normalisation,[status(thm)],[c_3436,c_14978,c_14979,c_14981]) ).
cnf(c_18605,plain,
( ~ aElementOf0(X0,sP7_iProver_def)
| ~ sP0_iProver_def
| aElementOf0(X0,xB)
| aElementOf0(X0,xA) ),
inference(light_normalisation,[status(thm)],[c_14964,c_14978]) ).
cnf(c_18614,plain,
( ~ aElementOf0(X0,sP7_iProver_def)
| ~ aElementOf0(X0,sP8_iProver_def)
| ~ sP5_iProver_def ),
inference(light_normalisation,[status(thm)],[c_14974,c_14978,c_14979]) ).
cnf(c_18621,plain,
( ~ aInteger0(X0)
| ~ sP4_iProver_def
| aElementOf0(X0,sP7_iProver_def)
| aElementOf0(X0,sP8_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_14972,c_14978,c_14979]) ).
cnf(c_18631,plain,
( ~ aElementOf0(sK37,sP8_iProver_def)
| ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP10_iProver_def)
| sP16
| sP15 ),
inference(light_normalisation,[status(thm)],[c_3394,c_14978,c_14979,c_14980,c_14981]) ).
cnf(c_18693,plain,
( ~ aInteger0(sK35)
| ~ sP16 ),
inference(superposition,[status(thm)],[c_201,c_205]) ).
cnf(c_18696,plain,
( ~ sP16
| aElementOf0(sK35,sP10_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_206,c_14981]) ).
cnf(c_18705,plain,
( ~ aInteger0(sK36)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_201,c_213]) ).
cnf(c_18708,plain,
( ~ sP15
| aElementOf0(sK36,sP9_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_214,c_14980]) ).
cnf(c_18758,plain,
( ~ aElementOf0(X0,sP10_iProver_def)
| aInteger0(X0) ),
inference(light_normalisation,[status(thm)],[c_178,c_14981]) ).
cnf(c_18764,plain,
( ~ sP16
| aInteger0(sK35) ),
inference(superposition,[status(thm)],[c_18696,c_18758]) ).
cnf(c_18767,plain,
~ sP16,
inference(global_subsumption_just,[status(thm)],[c_18764,c_18693,c_18764]) ).
cnf(c_18771,plain,
( ~ aElementOf0(sK37,sP8_iProver_def)
| ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP10_iProver_def)
| sP15 ),
inference(backward_subsumption_resolution,[status(thm)],[c_18631,c_18767]) ).
cnf(c_18772,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP10_iProver_def)
| sP15 ),
inference(backward_subsumption_resolution,[status(thm)],[c_18581,c_18767]) ).
cnf(c_18773,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP9_iProver_def)
| sP15 ),
inference(backward_subsumption_resolution,[status(thm)],[c_18572,c_18767]) ).
cnf(c_18778,plain,
( sP15
| sP5_iProver_def ),
inference(backward_subsumption_resolution,[status(thm)],[c_14975,c_18767]) ).
cnf(c_18779,plain,
( sP15
| sP4_iProver_def ),
inference(backward_subsumption_resolution,[status(thm)],[c_14973,c_18767]) ).
cnf(c_18780,plain,
( sP15
| sP3_iProver_def ),
inference(backward_subsumption_resolution,[status(thm)],[c_14971,c_18767]) ).
cnf(c_18781,plain,
( sP15
| sP2_iProver_def ),
inference(backward_subsumption_resolution,[status(thm)],[c_14969,c_18767]) ).
cnf(c_18783,plain,
( sP15
| sP0_iProver_def ),
inference(backward_subsumption_resolution,[status(thm)],[c_14965,c_18767]) ).
cnf(c_18784,plain,
( aInteger0(sK37)
| sP15 ),
inference(backward_subsumption_resolution,[status(thm)],[c_3419,c_18767]) ).
cnf(c_18828,plain,
( ~ aElementOf0(X0,sP9_iProver_def)
| aInteger0(X0) ),
inference(light_normalisation,[status(thm)],[c_190,c_14980]) ).
cnf(c_18833,plain,
( ~ sP15
| aInteger0(sK36) ),
inference(superposition,[status(thm)],[c_18708,c_18828]) ).
cnf(c_18838,plain,
~ sP15,
inference(global_subsumption_just,[status(thm)],[c_212,c_18705,c_18833]) ).
cnf(c_18852,plain,
sP5_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_18778,c_14975,c_18693,c_18705,c_18764,c_18833]) ).
cnf(c_18854,plain,
( ~ aElementOf0(X0,sP7_iProver_def)
| ~ aElementOf0(X0,sP8_iProver_def) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18614,c_18852]) ).
cnf(c_18858,plain,
sP4_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_18779,c_14973,c_18693,c_18705,c_18764,c_18833]) ).
cnf(c_18860,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,sP7_iProver_def)
| aElementOf0(X0,sP8_iProver_def) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18621,c_18858]) ).
cnf(c_18865,plain,
sP3_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_18780,c_14971,c_18767,c_18838]) ).
cnf(c_18867,plain,
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,sP7_iProver_def) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18558,c_18865]) ).
cnf(c_18875,plain,
sP2_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_18781,c_14969,c_18693,c_18705,c_18764,c_18833]) ).
cnf(c_18877,plain,
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,sP7_iProver_def) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18551,c_18875]) ).
cnf(c_18887,plain,
sP0_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_18783,c_14965,c_18693,c_18705,c_18764,c_18833]) ).
cnf(c_18889,plain,
( ~ aElementOf0(X0,sP7_iProver_def)
| aElementOf0(X0,xB)
| aElementOf0(X0,xA) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18605,c_18887]) ).
cnf(c_18894,plain,
aInteger0(sK37),
inference(global_subsumption_just,[status(thm)],[c_18784,c_3419,c_18693,c_18705,c_18764,c_18833]) ).
cnf(c_18958,plain,
( aElementOf0(sK37,sP10_iProver_def)
| aElementOf0(sK37,sP8_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_18772,c_18705,c_18772,c_18833]) ).
cnf(c_18959,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP10_iProver_def) ),
inference(renaming,[status(thm)],[c_18958]) ).
cnf(c_18968,plain,
( aElementOf0(sK37,sP9_iProver_def)
| aElementOf0(sK37,sP8_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_18773,c_18705,c_18773,c_18833]) ).
cnf(c_18969,plain,
( aElementOf0(sK37,sP8_iProver_def)
| aElementOf0(sK37,sP9_iProver_def) ),
inference(renaming,[status(thm)],[c_18968]) ).
cnf(c_19010,plain,
( ~ aElementOf0(sK37,sP10_iProver_def)
| ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP8_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_18771,c_18705,c_18771,c_18833]) ).
cnf(c_19011,plain,
( ~ aElementOf0(sK37,sP8_iProver_def)
| ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP10_iProver_def) ),
inference(renaming,[status(thm)],[c_19010]) ).
cnf(c_19018,plain,
( ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP10_iProver_def)
| ~ aInteger0(sK37)
| aElementOf0(sK37,sP7_iProver_def) ),
inference(superposition,[status(thm)],[c_18860,c_19011]) ).
cnf(c_19019,plain,
( ~ aElementOf0(sK37,sP9_iProver_def)
| ~ aElementOf0(sK37,sP10_iProver_def)
| aElementOf0(sK37,sP7_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19018,c_18894]) ).
cnf(c_19188,plain,
( ~ aElementOf0(X0,xB)
| ~ aElementOf0(X0,sP10_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_177,c_14981]) ).
cnf(c_19197,plain,
( ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,sP9_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_189,c_14980]) ).
cnf(c_20033,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,xB)
| aElementOf0(X0,sP10_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_176,c_14981]) ).
cnf(c_20043,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,sP7_iProver_def)
| aElementOf0(X0,sP10_iProver_def) ),
inference(superposition,[status(thm)],[c_20033,c_18867]) ).
cnf(c_20060,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,xA)
| aElementOf0(X0,sP9_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_188,c_14980]) ).
cnf(c_20070,plain,
( ~ aInteger0(X0)
| aElementOf0(X0,sP7_iProver_def)
| aElementOf0(X0,sP9_iProver_def) ),
inference(superposition,[status(thm)],[c_20060,c_18877]) ).
cnf(c_20183,plain,
( ~ aElementOf0(sK37,sP10_iProver_def)
| ~ aInteger0(sK37)
| aElementOf0(sK37,sP7_iProver_def) ),
inference(superposition,[status(thm)],[c_20070,c_19019]) ).
cnf(c_20191,plain,
( ~ aElementOf0(sK37,sP10_iProver_def)
| aElementOf0(sK37,sP7_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20183,c_18894]) ).
cnf(c_20474,plain,
( ~ aInteger0(sK37)
| aElementOf0(sK37,sP7_iProver_def) ),
inference(superposition,[status(thm)],[c_20043,c_20191]) ).
cnf(c_20475,plain,
aElementOf0(sK37,sP7_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_20474,c_18894]) ).
cnf(c_20477,plain,
( aElementOf0(sK37,xB)
| aElementOf0(sK37,xA) ),
inference(superposition,[status(thm)],[c_20475,c_18889]) ).
cnf(c_20478,plain,
~ aElementOf0(sK37,sP8_iProver_def),
inference(superposition,[status(thm)],[c_20475,c_18854]) ).
cnf(c_20483,plain,
aElementOf0(sK37,sP9_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_18969,c_20478]) ).
cnf(c_20485,plain,
aElementOf0(sK37,sP10_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_18959,c_20478]) ).
cnf(c_20498,plain,
( ~ aElementOf0(sK37,sP9_iProver_def)
| aElementOf0(sK37,xB) ),
inference(superposition,[status(thm)],[c_20477,c_19197]) ).
cnf(c_20501,plain,
aElementOf0(sK37,xB),
inference(forward_subsumption_resolution,[status(thm)],[c_20498,c_20483]) ).
cnf(c_20571,plain,
~ aElementOf0(sK37,sP10_iProver_def),
inference(superposition,[status(thm)],[c_20501,c_19188]) ).
cnf(c_20574,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20571,c_20485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM440+6 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n026.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 : 300
% 0.13/0.34 % DateTime : Thu May 2 19:57:51 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.63/1.70 % SZS status Started for theBenchmark.p
% 7.63/1.70 % SZS status Theorem for theBenchmark.p
% 7.63/1.70
% 7.63/1.70 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.63/1.70
% 7.63/1.70 ------ iProver source info
% 7.63/1.70
% 7.63/1.70 git: date: 2024-05-02 19:28:25 +0000
% 7.63/1.70 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.63/1.70 git: non_committed_changes: false
% 7.63/1.70
% 7.63/1.70 ------ Parsing...
% 7.63/1.70 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.63/1.70
% 7.63/1.70 ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 7.63/1.70
% 7.63/1.70 ------ Preprocessing... gs_s sp: 7 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.63/1.70
% 7.63/1.70 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.63/1.70 ------ Proving...
% 7.63/1.70 ------ Problem Properties
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70 clauses 176
% 7.63/1.70 conjectures 3
% 7.63/1.70 EPR 45
% 7.63/1.70 Horn 122
% 7.63/1.70 unary 16
% 7.63/1.70 binary 40
% 7.63/1.70 lits 572
% 7.63/1.70 lits eq 64
% 7.63/1.70 fd_pure 0
% 7.63/1.70 fd_pseudo 0
% 7.63/1.70 fd_cond 16
% 7.63/1.70 fd_pseudo_cond 9
% 7.63/1.70 AC symbols 0
% 7.63/1.70
% 7.63/1.70 ------ Schedule dynamic 5 is on
% 7.63/1.70
% 7.63/1.70 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70 ------
% 7.63/1.70 Current options:
% 7.63/1.70 ------
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70 ------ Proving...
% 7.63/1.70
% 7.63/1.70
% 7.63/1.70 % SZS status Theorem for theBenchmark.p
% 7.63/1.70
% 7.63/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.63/1.70
% 7.63/1.70
%------------------------------------------------------------------------------