%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM450+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 : n012.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 12:15:14 PM UTC 2026
% Result : Theorem 0.58s 0.86s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 5 unt; 5 def)
% Number of atoms : 808 ( 92 equ)
% Maximal formula atoms : 56 ( 17 avg)
% Number of connectives : 1020 ( 257 ~; 209 |; 482 &)
% ( 38 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 235 ( 162 !; 73 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,axiom,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( X0 = sz10
| X0 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(f45,axiom,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [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(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [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(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(f46,conjecture,
? [X0] :
( aInteger0(X0)
& X0 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
=> ( ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( aInteger0(X0)
& X0 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
=> ( ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f55,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
<=> ( sz10 = X3
| smndt0(sz10) = X3 ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(rectify,[],[f43]) ).
fof(f56,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
=> ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
& ( ( aInteger0(X5)
& ( ? [X7] :
( aInteger0(X7)
& sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7) )
| aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
| sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& ! [X8] :
( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) ) )
& ! [X12] :
( aElementOf0(X12,stldt0(sbsmnsldt0(xS)))
=> ? [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(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) ) ) ),
inference(rectify,[],[f45]) ).
fof(f57,plain,
~ ? [X0] :
( aInteger0(X0)
& X0 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
& ( ( aInteger0(X1)
& ( ? [X3] :
( aInteger0(X3)
& sdtpldt0(X1,smndt0(sz10)) = sdtasdt0(X0,X3) )
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X4] :
( aElementOf0(X4,sbsmnsldt0(xS))
<=> ( aInteger0(X4)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X4,X5) ) ) ) )
=> ( ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) ) )
=> ( ! [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
=> aElementOf0(X7,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
inference(rectify,[],[f47]) ).
fof(f116,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) ) )
& ! [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(sbsmnsldt0(xS)))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS))) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f117,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
& ! [X8] :
( aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) ) )
& ! [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(sbsmnsldt0(xS)))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS))) ) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X4] :
( aElementOf0(X4,sbsmnsldt0(xS))
<=> ( aInteger0(X4)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X4,X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ! [X1] :
( ( ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
| ~ aInteger0(X1)
| ( ! [X3] :
( ~ aInteger0(X3)
| sdtpldt0(X1,smndt0(sz10)) != sdtasdt0(X0,X3) )
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f119,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X4] :
( aElementOf0(X4,sbsmnsldt0(xS))
<=> ( aInteger0(X4)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X4,X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ! [X1] :
( ( ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
| ~ aInteger0(X1)
| ( ! [X3] :
( ~ aInteger0(X3)
| sdtpldt0(X1,smndt0(sz10)) != sdtasdt0(X0,X3) )
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) ) ) ) ),
inference(flattening,[],[f118]) ).
fof(f132,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) ) ) )
| ~ sP8(X12,X13) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f133,definition,
! [X3,X4] :
( ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
| ~ sP9(X3,X4) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f134,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP9(X3,X4)
& ! [X8] :
( aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( aElementOf0(X9,sbsmnsldt0(xS))
<=> ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) ) )
& ! [X11] :
( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP8(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS))) ) ),
inference(definition_folding,[],[f117,f133,f132]) ).
fof(f135,definition,
! [X0] :
( ! [X1] :
( ( ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X0,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,X0) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0))
| ~ aInteger0(X1)
| ( ! [X3] :
( ~ aInteger0(X3)
| sdtpldt0(X1,smndt0(sz10)) != sdtasdt0(X0,X3) )
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X1,sz10,X0) ) ) )
| ~ sP10(X0) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f136,definition,
( ! [X4] :
( aElementOf0(X4,sbsmnsldt0(xS))
<=> ( aInteger0(X4)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X4,X5) ) ) )
| ~ sP11 ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f137,definition,
( ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) ) )
| ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f138,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ( ? [X7] :
( ~ aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
& sP12
& aSet0(sbsmnsldt0(xS))
& sP11
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& sP10(X0) ) ),
inference(definition_folding,[],[f119,f137,f136,f135]) ).
fof(f193,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X3
& smndt0(sz10) != X3 ) )
& ( sz10 = X3
| smndt0(sz10) = X3
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(nnf_transformation,[],[f55]) ).
fof(f194,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X3
& smndt0(sz10) != X3 ) )
& ( sz10 = X3
| smndt0(sz10) = X3
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(flattening,[],[f193]) ).
fof(f195,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X0,X2) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ( aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X4
& smndt0(sz10) != X4 ) )
& ( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(rectify,[],[f194]) ).
fof(f196,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& aElementOf0(sK31(X0),xS)
& aElementOf0(X0,sK31(X0)) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ( aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X4
& smndt0(sz10) != X4 ) )
& ( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X2,sK31(X0))],[f195]) ).
fof(f203,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP9(X3,X4)
& ! [X8] :
( aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( ( aElementOf0(X9,sbsmnsldt0(xS))
| ~ aInteger0(X9)
| ! [X10] :
( ~ aElementOf0(X10,xS)
| ~ aElementOf0(X9,X10) ) )
& ( ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) )
| ~ aElementOf0(X9,sbsmnsldt0(xS)) ) )
& ! [X11] :
( ( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X11)
| aElementOf0(X11,sbsmnsldt0(xS)) )
& ( ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) )
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP8(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS))) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f204,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP9(X3,X4)
& ! [X8] :
( aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X9] :
( ( aElementOf0(X9,sbsmnsldt0(xS))
| ~ aInteger0(X9)
| ! [X10] :
( ~ aElementOf0(X10,xS)
| ~ aElementOf0(X9,X10) ) )
& ( ( aInteger0(X9)
& ? [X10] :
( aElementOf0(X10,xS)
& aElementOf0(X9,X10) ) )
| ~ aElementOf0(X9,sbsmnsldt0(xS)) ) )
& ! [X11] :
( ( aElementOf0(X11,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X11)
| aElementOf0(X11,sbsmnsldt0(xS)) )
& ( ( aInteger0(X11)
& ~ aElementOf0(X11,sbsmnsldt0(xS)) )
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) )
& ! [X12] :
( ? [X13] :
( aInteger0(X13)
& sz00 != X13
& aSet0(szAzrzSzezqlpdtcmdtrp0(X12,X13))
& sP8(X12,X13)
& ! [X17] :
( aElementOf0(X17,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(X12,X13)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X12,X13),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X12,stldt0(sbsmnsldt0(xS))) ) ),
inference(flattening,[],[f203]) ).
fof(f205,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X0,X2) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sP9(X4,X5)
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ~ aInteger0(X7)
| ! [X8] :
( ~ aElementOf0(X8,xS)
| ~ aElementOf0(X7,X8) ) )
& ( ( aInteger0(X7)
& ? [X9] :
( aElementOf0(X9,xS)
& aElementOf0(X7,X9) ) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& ! [X10] :
( ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X10)
| aElementOf0(X10,sbsmnsldt0(xS)) )
& ( ( aInteger0(X10)
& ~ aElementOf0(X10,sbsmnsldt0(xS)) )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X11] :
( ? [X12] :
( aInteger0(X12)
& sz00 != X12
& aSet0(szAzrzSzezqlpdtcmdtrp0(X11,X12))
& sP8(X11,X12)
& ! [X13] :
( aElementOf0(X13,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,X12)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,X12),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& aElementOf0(sK34(X0),xS)
& aElementOf0(X0,sK34(X0)) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ( aInteger0(sK35(X4))
& sz00 != sK35(X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)))
& sP9(X4,sK35(X4))
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ~ aInteger0(X7)
| ! [X8] :
( ~ aElementOf0(X8,xS)
| ~ aElementOf0(X7,X8) ) )
& ( ( aInteger0(X7)
& aElementOf0(sK36(X7),xS)
& aElementOf0(X7,sK36(X7)) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& ! [X10] :
( ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X10)
| aElementOf0(X10,sbsmnsldt0(xS)) )
& ( ( aInteger0(X10)
& ~ aElementOf0(X10,sbsmnsldt0(xS)) )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& ! [X11] :
( ( aInteger0(sK37(X11))
& sz00 != sK37(X11)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11)))
& sP8(X11,sK37(X11))
& ! [X13] :
( aElementOf0(X13,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11)),stldt0(sbsmnsldt0(xS))) )
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37]),skolemize(X2,sK34(X0)),skolemize(X5,sK35(X4)),skolemize(X9,sK36(X7)),skolemize(X12,sK37(X11))],[f205]) ).
fof(f216,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ( ? [X1] :
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,X0)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
& sP12
& aSet0(sbsmnsldt0(xS))
& sP11
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& sP10(X0) ) ),
inference(rectify,[],[f138]) ).
fof(f217,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ( ~ aElementOf0(sK40(X0),stldt0(sbsmnsldt0(xS)))
& aElementOf0(sK40(X0),szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
& sP12
& aSet0(sbsmnsldt0(xS))
& sP11
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
& sP10(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X1,sK40(X0))],[f216]) ).
fof(f353,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnf_transformation,[],[f196]) ).
fof(f356,plain,
! [X4] :
( aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| sz10 != X4 ),
inference(cnf_transformation,[],[f196]) ).
fof(f383,plain,
! [X11] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f387,plain,
! [X11] :
( sz00 != sK37(X11)
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f388,plain,
! [X11] :
( aInteger0(sK37(X11))
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f433,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f217]) ).
fof(f452,plain,
aElementOf0(sz10,stldt0(sbsmnsldt0(xS))),
inference(equality_resolution,[],[f356]) ).
fof(f540,plain,
aElementOf0(sz10,cS2076),
inference(forward_demodulation,[],[f452,f353]) ).
fof(f598,plain,
! [X11] :
( ~ aElementOf0(X11,cS2076)
| aInteger0(sK37(X11)) ),
inference(forward_demodulation,[],[f388,f353]) ).
fof(f713,plain,
! [X11] :
( sz00 != sK37(X11)
| ~ aElementOf0(X11,cS2076) ),
inference(forward_demodulation,[],[f387,f353]) ).
fof(f721,plain,
! [X0] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),cS2076)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_demodulation,[],[f433,f353]) ).
fof(f961,plain,
! [X11] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11)),cS2076)
| ~ aElementOf0(X11,stldt0(sbsmnsldt0(xS))) ),
inference(forward_demodulation,[],[f383,f353]) ).
fof(f962,plain,
! [X11] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X11,sK37(X11)),cS2076)
| ~ aElementOf0(X11,cS2076) ),
inference(forward_demodulation,[],[f961,f353]) ).
fof(f963,plain,
( ~ aElementOf0(sz10,cS2076)
| ~ aInteger0(sK37(sz10))
| sz00 = sK37(sz10) ),
inference(resolution,[],[f962,f721]) ).
fof(f966,plain,
( ~ aElementOf0(sz10,cS2076)
| sz00 = sK37(sz10) ),
inference(forward_subsumption_resolution,[],[f963,f598]) ).
fof(f967,plain,
~ aElementOf0(sz10,cS2076),
inference(forward_subsumption_resolution,[],[f966,f713]) ).
fof(f968,plain,
$false,
inference(forward_subsumption_resolution,[],[f967,f540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM450+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 19:58:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.58/0.86 % (2696506)Detected formulas, will run a generic FOF schedule.
% 0.58/0.86 % (2696512)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=280879125:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.58/0.86 % (2696515)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1870233313:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.58/0.86 % (2696514)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2665600255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.58/0.86 % (2696517)dis-21_1_sil=8000:lcm=predicate:random_seed=36347687: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)
% 0.58/0.86 % (2696513)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=3906867853:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.58/0.86 % (2696511)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=2535873299:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.58/0.86 % (2696516)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4104097035:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.58/0.86 % (2696516)First to succeed.
% 0.58/0.86 % (2696516)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2696506"
% 0.58/0.86 % (2696515)Also succeeded, but the first one will report.
% 0.58/0.86 % (2696517)Instruction limit reached!
% 0.58/0.86 % (2696517)------------------------------
% 0.58/0.86 % (2696517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/0.86 % (2696517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.86 % (2696517)CaDiCaL version: 2.1.3
% 0.58/0.86 % (2696517)Termination reason: Instruction limit
% 0.58/0.86 % (2696517)Termination phase: Saturation
% 0.58/0.86 % (2696517)Time elapsed: 0.036 s
% 0.58/0.86 % (2696517)Peak memory usage: 89 MB
% 0.58/0.86 % (2696517)Instructions burned: 133 (million)
% 0.58/0.86 % (2696514)Instruction limit reached!
% 0.58/0.86 % (2696514)------------------------------
% 0.58/0.86 % (2696514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/0.86 % (2696514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.86 % (2696514)CaDiCaL version: 2.1.3
% 0.58/0.86 % (2696514)Termination reason: Instruction limit
% 0.58/0.86 % (2696514)Termination phase: Saturation
% 0.58/0.86 % (2696514)Time elapsed: 0.037 s
% 0.58/0.86 % (2696514)Peak memory usage: 90 MB
% 0.58/0.86 % (2696514)Instructions burned: 110 (million)
% 0.58/0.86 % (2696526)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3522624352:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.58/0.86 % (2696525)lrs+10_1_sil=8000:sp=occurrence:random_seed=239549856:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.58/0.86 % (2696516)Refutation found. Thanks to Tanya!
% 0.58/0.86 % SZS status Theorem for theBenchmark
% 0.58/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/0.95 % (2696516)------------------------------
% 2.47/0.95 % (2696516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/0.95 % (2696516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.95 % (2696516)CaDiCaL version: 2.1.3
% 2.47/0.95 % (2696516)Termination reason: Refutation
% 2.47/0.95 % (2696516)Time elapsed: 0.022 s
% 2.47/0.95 % (2696516)Peak memory usage: 89 MB
% 2.47/0.95 % (2696516)Instructions burned: 33 (million)
% 2.47/0.95 % (2696516)------------------------------
% 2.47/0.95 % (2696516)------------------------------
% 2.47/0.95 % (2696506)Success in time 0.321 s
% 2.47/0.95 % Vampire exiting
%------------------------------------------------------------------------------