%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:12 PM UTC 2026
% Result : Theorem 2.04s 1.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 8 unt; 3 def)
% Number of atoms : 1114 ( 66 equ)
% Maximal formula atoms : 67 ( 25 avg)
% Number of connectives : 1414 ( 343 ~; 277 |; 689 &)
% ( 59 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 14 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 271 ( 217 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [X0,X1] :
( ( aSubsetOf0(X0,cS1395)
& aSubsetOf0(X1,cS1395)
& isOpen0(X0)
& isOpen0(X1) )
=> isOpen0(sdtslmnbsdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
fof(f39,axiom,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xB)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xA) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xB) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1826) ).
fof(f40,axiom,
( aSet0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xA) ) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xB) ) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xA) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xB) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X0)
& aElementOf0(X0,stldt0(xA))
& aElementOf0(X0,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f41,conjecture,
( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f43,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,xB)
=> aElementOf0(X3,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( aElementOf0(X4,stldt0(xA))
<=> ( aInteger0(X4)
& ~ aElementOf0(X4,xA) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(xA))
=> ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& ! [X7] :
( ( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6))
=> ( aInteger0(X7)
& ? [X8] :
( aInteger0(X8)
& sdtasdt0(X6,X8) = sdtpldt0(X7,smndt0(X5)) )
& aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& sdteqdtlpzmzozddtrp0(X7,X5,X6) ) )
& ( ( aInteger0(X7)
& ( ? [X9] :
( aInteger0(X9)
& sdtpldt0(X7,smndt0(X5)) = sdtasdt0(X6,X9) )
| aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
| sdteqdtlpzmzozddtrp0(X7,X5,X6) ) )
=> aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6)) ) )
& ! [X10] :
( aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6))
=> aElementOf0(X10,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,xB) ) )
& ! [X12] :
( aElementOf0(X12,stldt0(xB))
=> ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& ! [X14] :
( ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
=> ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12)) )
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& sdteqdtlpzmzozddtrp0(X14,X12,X13) ) )
& ( ( aInteger0(X14)
& ( ? [X16] :
( aInteger0(X16)
& sdtpldt0(X14,smndt0(X12)) = sdtasdt0(X13,X16) )
| aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
| sdteqdtlpzmzozddtrp0(X14,X12,X13) ) )
=> aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) ) )
& ! [X17] :
( aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13))
=> aElementOf0(X17,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(rectify,[],[f39]) ).
fof(f44,plain,
( aSet0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X2] :
( aElementOf0(X2,stldt0(xA))
=> aElementOf0(X2,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( aInteger0(X3)
& ~ aElementOf0(X3,xB) ) )
& aSet0(cS1395)
& ! [X4] :
( aElementOf0(X4,cS1395)
<=> aInteger0(X4) )
& ! [X5] :
( aElementOf0(X5,stldt0(xB))
=> aElementOf0(X5,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X6] :
( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X6)
& ( aElementOf0(X6,xA)
| aElementOf0(X6,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X7)
& ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( aInteger0(X8)
& ~ aElementOf0(X8,xA) ) )
& ! [X9] :
( aElementOf0(X9,stldt0(xB))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,xB) ) )
& ! [X10] :
( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X10)
& aElementOf0(X10,stldt0(xA))
& aElementOf0(X10,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(rectify,[],[f40]) ).
fof(f45,plain,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X3] :
( aInteger0(X3)
& sz00 != X3
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) ) )
& ( ( aInteger0(X4)
& ( ? [X6] :
( aInteger0(X6)
& sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6) )
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| sdteqdtlpzmzozddtrp0(X4,X2,X3) ) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) ) )
=> ( ! [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
inference(rectify,[],[f42]) ).
fof(f49,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( aElementOf0(X4,stldt0(xA))
<=> ( aInteger0(X4)
& ~ aElementOf0(X4,xA) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& ! [X7] :
( ( ( aInteger0(X7)
& ? [X8] :
( aInteger0(X8)
& sdtasdt0(X6,X8) = sdtpldt0(X7,smndt0(X5)) )
& aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& sdteqdtlpzmzozddtrp0(X7,X5,X6) )
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& ( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| ~ aInteger0(X7)
| ( ! [X9] :
( ~ aInteger0(X9)
| sdtpldt0(X7,smndt0(X5)) != sdtasdt0(X6,X9) )
& ~ aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& ~ sdteqdtlpzmzozddtrp0(X7,X5,X6) ) ) )
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,xB) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& ! [X14] :
( ( ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12)) )
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& sdteqdtlpzmzozddtrp0(X14,X12,X13) )
| ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ~ aInteger0(X14)
| ( ! [X16] :
( ~ aInteger0(X16)
| sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16) )
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ~ sdteqdtlpzmzozddtrp0(X14,X12,X13) ) ) )
& ! [X17] :
( aElementOf0(X17,stldt0(xB))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) )
| ~ aElementOf0(X12,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(ennf_transformation,[],[f43]) ).
fof(f50,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( aElementOf0(X4,stldt0(xA))
<=> ( aInteger0(X4)
& ~ aElementOf0(X4,xA) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& ! [X7] :
( ( ( aInteger0(X7)
& ? [X8] :
( aInteger0(X8)
& sdtasdt0(X6,X8) = sdtpldt0(X7,smndt0(X5)) )
& aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& sdteqdtlpzmzozddtrp0(X7,X5,X6) )
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& ( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| ~ aInteger0(X7)
| ( ! [X9] :
( ~ aInteger0(X9)
| sdtpldt0(X7,smndt0(X5)) != sdtasdt0(X6,X9) )
& ~ aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& ~ sdteqdtlpzmzozddtrp0(X7,X5,X6) ) ) )
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,xB) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& ! [X14] :
( ( ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12)) )
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& sdteqdtlpzmzozddtrp0(X14,X12,X13) )
| ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ~ aInteger0(X14)
| ( ! [X16] :
( ~ aInteger0(X16)
| sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16) )
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ~ sdteqdtlpzmzozddtrp0(X14,X12,X13) ) ) )
& ! [X17] :
( aElementOf0(X17,stldt0(xB))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) )
| ~ aElementOf0(X12,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( aSet0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,stldt0(xA)) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X3] :
( aElementOf0(X3,stldt0(xB))
<=> ( aInteger0(X3)
& ~ aElementOf0(X3,xB) ) )
& aSet0(cS1395)
& ! [X4] :
( aElementOf0(X4,cS1395)
<=> aInteger0(X4) )
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X6] :
( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X6)
& ( aElementOf0(X6,xA)
| aElementOf0(X6,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X7)
& ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(xA))
<=> ( aInteger0(X8)
& ~ aElementOf0(X8,xA) ) )
& ! [X9] :
( aElementOf0(X9,stldt0(xB))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,xB) ) )
& ! [X10] :
( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X10)
& aElementOf0(X10,stldt0(xA))
& aElementOf0(X10,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f52,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) ) ) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f53,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) ) ) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) ),
inference(flattening,[],[f52]) ).
fof(f93,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(X1,cS1395)
| ~ isOpen0(X0)
| ~ isOpen0(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f94,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(X1,cS1395)
| ~ isOpen0(X0)
| ~ isOpen0(X1) ),
inference(flattening,[],[f93]) ).
fof(f97,definition,
! [X12,X13] :
( ! [X14] :
( ( ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(X13,X15) = sdtpldt0(X14,smndt0(X12)) )
& aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& sdteqdtlpzmzozddtrp0(X14,X12,X13) )
| ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X12,X13))
| ~ aInteger0(X14)
| ( ! [X16] :
( ~ aInteger0(X16)
| sdtpldt0(X14,smndt0(X12)) != sdtasdt0(X13,X16) )
& ~ aDivisorOf0(X13,sdtpldt0(X14,smndt0(X12)))
& ~ sdteqdtlpzmzozddtrp0(X14,X12,X13) ) ) )
| ~ sP0(X12,X13) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f98,definition,
! [X5,X6] :
( ! [X7] :
( ( ( aInteger0(X7)
& ? [X8] :
( aInteger0(X8)
& sdtasdt0(X6,X8) = sdtpldt0(X7,smndt0(X5)) )
& aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& sdteqdtlpzmzozddtrp0(X7,X5,X6) )
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& ( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6))
| ~ aInteger0(X7)
| ( ! [X9] :
( ~ aInteger0(X9)
| sdtpldt0(X7,smndt0(X5)) != sdtasdt0(X6,X9) )
& ~ aDivisorOf0(X6,sdtpldt0(X7,smndt0(X5)))
& ~ sdteqdtlpzmzozddtrp0(X7,X5,X6) ) ) )
| ~ sP1(X5,X6) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f99,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( aElementOf0(X4,stldt0(xA))
<=> ( aInteger0(X4)
& ~ aElementOf0(X4,xA) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sP1(X5,X6)
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,xB) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP0(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(xB))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) )
| ~ aElementOf0(X12,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(definition_folding,[],[f50,f98,f97]) ).
fof(f100,definition,
! [X2,X3] :
( ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) )
| ~ sP2(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f101,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ) ) ),
inference(definition_folding,[],[f53,f100]) ).
fof(f114,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( ( aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| aElementOf0(X4,xA) )
& ( ( aInteger0(X4)
& ~ aElementOf0(X4,xA) )
| ~ aElementOf0(X4,stldt0(xA)) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sP1(X5,X6)
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( ( aElementOf0(X11,stldt0(xB))
| ~ aInteger0(X11)
| aElementOf0(X11,xB) )
& ( ( aInteger0(X11)
& ~ aElementOf0(X11,xB) )
| ~ aElementOf0(X11,stldt0(xB)) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP0(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(xB))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) )
| ~ aElementOf0(X12,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(nnf_transformation,[],[f99]) ).
fof(f115,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( ( aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| aElementOf0(X4,xA) )
& ( ( aInteger0(X4)
& ~ aElementOf0(X4,xA) )
| ~ aElementOf0(X4,stldt0(xA)) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sP1(X5,X6)
& ! [X10] :
( aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X11] :
( ( aElementOf0(X11,stldt0(xB))
| ~ aInteger0(X11)
| aElementOf0(X11,xB) )
& ( ( aInteger0(X11)
& ~ aElementOf0(X11,xB) )
| ~ aElementOf0(X11,stldt0(xB)) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP0(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(xB))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(xB)) )
| ~ aElementOf0(X12,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( ( aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| aElementOf0(X4,xA) )
& ( ( aInteger0(X4)
& ~ aElementOf0(X4,xA) )
| ~ aElementOf0(X4,stldt0(xA)) ) )
& ! [X5] :
( ? [X6] :
( aInteger0(X6)
& sz00 != X6
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,X6))
& sP1(X5,X6)
& ! [X7] :
( aElementOf0(X7,stldt0(xA))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,X6)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,X6),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X8] :
( ( aElementOf0(X8,stldt0(xB))
| ~ aInteger0(X8)
| aElementOf0(X8,xB) )
& ( ( aInteger0(X8)
& ~ aElementOf0(X8,xB) )
| ~ aElementOf0(X8,stldt0(xB)) ) )
& ! [X9] :
( ? [X10] :
( aInteger0(X10)
& sz00 != X10
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& sP0(X9,X10)
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(xB)) )
| ~ aElementOf0(X9,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X4] :
( ( aElementOf0(X4,stldt0(xA))
| ~ aInteger0(X4)
| aElementOf0(X4,xA) )
& ( ( aInteger0(X4)
& ~ aElementOf0(X4,xA) )
| ~ aElementOf0(X4,stldt0(xA)) ) )
& ! [X5] :
( ( aInteger0(sK9(X5))
& sz00 != sK9(X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5)))
& sP1(X5,sK9(X5))
& ! [X7] :
( aElementOf0(X7,stldt0(xA))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X5,sK9(X5)),stldt0(xA)) )
| ~ aElementOf0(X5,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X8] :
( ( aElementOf0(X8,stldt0(xB))
| ~ aInteger0(X8)
| aElementOf0(X8,xB) )
& ( ( aInteger0(X8)
& ~ aElementOf0(X8,xB) )
| ~ aElementOf0(X8,stldt0(xB)) ) )
& ! [X9] :
( ( aInteger0(sK10(X9))
& sz00 != sK10(X9)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9)))
& sP0(X9,sK10(X9))
& ! [X11] :
( aElementOf0(X11,stldt0(xB))
| ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,sK10(X9)),stldt0(xB)) )
| ~ aElementOf0(X9,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X6,sK9(X5)),skolemize(X10,sK10(X9))],[f116]) ).
fof(f118,plain,
( aSet0(stldt0(xA))
& ! [X0] :
( ( aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0)
| aElementOf0(X0,xA) )
& ( ( aInteger0(X0)
& ~ aElementOf0(X0,xA) )
| ~ aElementOf0(X0,stldt0(xA)) ) )
& aSet0(cS1395)
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,stldt0(xA)) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X3] :
( ( aElementOf0(X3,stldt0(xB))
| ~ aInteger0(X3)
| aElementOf0(X3,xB) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,xB) )
| ~ aElementOf0(X3,stldt0(xB)) ) )
& aSet0(cS1395)
& ! [X4] :
( ( aElementOf0(X4,cS1395)
| ~ aInteger0(X4) )
& ( aInteger0(X4)
| ~ aElementOf0(X4,cS1395) ) )
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X6] :
( ( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X6)
| ( ~ aElementOf0(X6,xA)
& ~ aElementOf0(X6,xB) ) )
& ( ( aInteger0(X6)
& ( aElementOf0(X6,xA)
| aElementOf0(X6,xB) ) )
| ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( ( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X7)
| aElementOf0(X7,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X7)
& ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X8] :
( ( aElementOf0(X8,stldt0(xA))
| ~ aInteger0(X8)
| aElementOf0(X8,xA) )
& ( ( aInteger0(X8)
& ~ aElementOf0(X8,xA) )
| ~ aElementOf0(X8,stldt0(xA)) ) )
& ! [X9] :
( ( aElementOf0(X9,stldt0(xB))
| ~ aInteger0(X9)
| aElementOf0(X9,xB) )
& ( ( aInteger0(X9)
& ~ aElementOf0(X9,xB) )
| ~ aElementOf0(X9,stldt0(xB)) ) )
& ! [X10] :
( ( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X10)
| ~ aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,stldt0(xB)) )
& ( ( aInteger0(X10)
& aElementOf0(X10,stldt0(xA))
& aElementOf0(X10,stldt0(xB)) )
| ~ aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(nnf_transformation,[],[f51]) ).
fof(f119,plain,
( aSet0(stldt0(xA))
& ! [X0] :
( ( aElementOf0(X0,stldt0(xA))
| ~ aInteger0(X0)
| aElementOf0(X0,xA) )
& ( ( aInteger0(X0)
& ~ aElementOf0(X0,xA) )
| ~ aElementOf0(X0,stldt0(xA)) ) )
& aSet0(cS1395)
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,stldt0(xA)) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X3] :
( ( aElementOf0(X3,stldt0(xB))
| ~ aInteger0(X3)
| aElementOf0(X3,xB) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,xB) )
| ~ aElementOf0(X3,stldt0(xB)) ) )
& aSet0(cS1395)
& ! [X4] :
( ( aElementOf0(X4,cS1395)
| ~ aInteger0(X4) )
& ( aInteger0(X4)
| ~ aElementOf0(X4,cS1395) ) )
& ! [X5] :
( aElementOf0(X5,cS1395)
| ~ aElementOf0(X5,stldt0(xB)) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X6] :
( ( aElementOf0(X6,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X6)
| ( ~ aElementOf0(X6,xA)
& ~ aElementOf0(X6,xB) ) )
& ( ( aInteger0(X6)
& ( aElementOf0(X6,xA)
| aElementOf0(X6,xB) ) )
| ~ aElementOf0(X6,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X7] :
( ( aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X7)
| aElementOf0(X7,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X7)
& ~ aElementOf0(X7,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [X8] :
( ( aElementOf0(X8,stldt0(xA))
| ~ aInteger0(X8)
| aElementOf0(X8,xA) )
& ( ( aInteger0(X8)
& ~ aElementOf0(X8,xA) )
| ~ aElementOf0(X8,stldt0(xA)) ) )
& ! [X9] :
( ( aElementOf0(X9,stldt0(xB))
| ~ aInteger0(X9)
| aElementOf0(X9,xB) )
& ( ( aInteger0(X9)
& ~ aElementOf0(X9,xB) )
| ~ aElementOf0(X9,stldt0(xB)) ) )
& ! [X10] :
( ( aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X10)
| ~ aElementOf0(X10,stldt0(xA))
| ~ aElementOf0(X10,stldt0(xB)) )
& ( ( aInteger0(X10)
& aElementOf0(X10,stldt0(xA))
& aElementOf0(X10,stldt0(xB)) )
| ~ aElementOf0(X10,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(flattening,[],[f118]) ).
fof(f123,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( ( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X1)
| aElementOf0(X1,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( ( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| ( ~ aElementOf0(X0,xA)
& ~ aElementOf0(X0,xB) ) )
& ( ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) )
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f124,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( ( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X1)
| aElementOf0(X1,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X0] :
( ( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| ( ~ aElementOf0(X0,xA)
& ~ aElementOf0(X0,xB) ) )
& ( ( aInteger0(X0)
& ( aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) )
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
( ? [X0] :
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ? [X2] :
( ~ aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sP2(X0,X1) ) )
& aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X3)
| aElementOf0(X3,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X4] :
( ( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X4)
| ( ~ aElementOf0(X4,xA)
& ~ aElementOf0(X4,xB) ) )
& ( ( aInteger0(X4)
& ( aElementOf0(X4,xA)
| aElementOf0(X4,xB) ) )
| ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ~ aElementOf0(sK13(X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK13(X1),szAzrzSzezqlpdtcmdtrp0(sK12,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK12,X1),stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK12,X1))
& sP2(sK12,X1) ) )
& aElementOf0(sK12,stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X3)
| aElementOf0(X3,sdtbsmnsldt0(xA,xB)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sdtbsmnsldt0(xA,xB)) )
| ~ aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ~ isClosed0(sdtbsmnsldt0(xA,xB))
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X4] :
( ( aElementOf0(X4,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X4)
| ( ~ aElementOf0(X4,xA)
& ~ aElementOf0(X4,xB) ) )
& ( ( aInteger0(X4)
& ( aElementOf0(X4,xA)
| aElementOf0(X4,xB) ) )
| ~ aElementOf0(X4,sdtbsmnsldt0(xA,xB)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X2,sK13(X1))],[f125]) ).
fof(f177,plain,
isOpen0(stldt0(xB)),
inference(cnf_transformation,[],[f117]) ).
fof(f189,plain,
isOpen0(stldt0(xA)),
inference(cnf_transformation,[],[f117]) ).
fof(f212,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(cnf_transformation,[],[f119]) ).
fof(f232,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf_transformation,[],[f119]) ).
fof(f241,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf_transformation,[],[f119]) ).
fof(f268,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf_transformation,[],[f126]) ).
fof(f341,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(X1,cS1395)
| ~ isOpen0(X0)
| ~ isOpen0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f1009,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xA))
| ~ isOpen0(stldt0(xB)) ),
inference(superposition,[],[f341,f212]) ).
fof(f1012,plain,
( ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xA))
| ~ isOpen0(stldt0(xB)) ),
inference(forward_subsumption_resolution,[],[f1009,f268]) ).
fof(f1013,plain,
( ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xA))
| ~ isOpen0(stldt0(xB)) ),
inference(forward_subsumption_resolution,[],[f1012,f241]) ).
fof(f1014,plain,
( ~ isOpen0(stldt0(xA))
| ~ isOpen0(stldt0(xB)) ),
inference(forward_subsumption_resolution,[],[f1013,f232]) ).
fof(f1015,plain,
~ isOpen0(stldt0(xB)),
inference(forward_subsumption_resolution,[],[f1014,f189]) ).
fof(f1016,plain,
$false,
inference(forward_subsumption_resolution,[],[f1015,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 19:56:00 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.04/1.20 % (2361125)Detected formulas, will run a generic FOF schedule.
% 2.04/1.20 % (2361165)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4267780086:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.04/1.20 % (2361165)First to succeed.
% 2.04/1.20 % (2361165)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2361125"
% 2.04/1.20 % (2361164)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3954928666:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.04/1.20 % (2361161)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1319840458:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.04/1.20 % (2361162)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=797707058:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.04/1.20 % (2361163)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1140169316:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.04/1.20 % (2361167)dis-21_1_sil=8000:lcm=predicate:random_seed=4202992999:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.04/1.20 % (2361166)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1151145549:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.04/1.20 % (2361164)Also succeeded, but the first one will report.
% 2.04/1.20 % (2361166)Also succeeded, but the first one will report.
% 2.04/1.20 % (2361167)Instruction limit reached!
% 2.04/1.20 % (2361167)------------------------------
% 2.04/1.20 % (2361167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/1.20 % (2361167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/1.20 % (2361167)CaDiCaL version: 2.1.3
% 2.04/1.20 % (2361167)Termination reason: Instruction limit
% 2.04/1.20 % (2361167)Termination phase: Saturation
% 2.04/1.20 % (2361167)Time elapsed: 0.075 s
% 2.04/1.20 % (2361167)Peak memory usage: 89 MB
% 2.04/1.20 % (2361167)Instructions burned: 131 (million)
% 2.04/1.20 % (2361165)Refutation found. Thanks to Tanya!
% 2.04/1.20 % SZS status Theorem for theBenchmark
% 2.04/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.30 % (2361165)------------------------------
% 0.16/1.30 % (2361165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.30 % (2361165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.30 % (2361165)CaDiCaL version: 2.1.3
% 0.16/1.30 % (2361165)Termination reason: Refutation
% 0.16/1.30 % (2361165)Time elapsed: 0.012 s
% 0.16/1.30 % (2361165)Peak memory usage: 89 MB
% 0.16/1.30 % (2361165)Instructions burned: 35 (million)
% 0.16/1.30 % (2361165)------------------------------
% 0.16/1.30 % (2361165)------------------------------
% 0.16/1.30 % (2361125)Success in time 0.313 s
% 0.16/1.30 % Vampire exiting
%------------------------------------------------------------------------------