%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:24:22 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 13 unt; 8 def)
% Number of atoms : 1068 ( 157 equ)
% Maximal formula atoms : 56 ( 14 avg)
% Number of connectives : 1334 ( 340 ~; 281 |; 626 &)
% ( 39 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 4 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 292 ( 0 sgn 197 !; 95 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( aSet0(xS)
& ! [X0] :
( ( aElementOf0(X0,xS)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
=> aElementOf0(X0,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2046) ).
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(f54,plain,
( aSet0(xS)
& ! [X0] :
( ( aElementOf0(X0,xS)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X4] :
( aInteger0(X4)
& sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
& ( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& isPrime0(X5)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) )
& ( ( aInteger0(X6)
& ( ? [X8] :
( aInteger0(X8)
& sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8) )
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0 ) )
=> aElementOf0(X0,xS) ) )
& xS = cS2043 ),
inference(rectify,[],[f42]) ).
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(f114,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) ) ) ) ) )
& xS = cS2043 ),
inference(ennf_transformation,[],[f54]) ).
fof(f115,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) ) ) ) ) )
& xS = cS2043 ),
inference(flattening,[],[f114]) ).
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(f129,definition,
! [X5] :
( ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) )
| ~ sP6(X5) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f130,definition,
! [X1] :
( ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
| ~ sP7(X1) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f131,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP7(X1)
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& sP6(X5) ) ) ) )
& xS = cS2043 ),
inference(definition_folding,[],[f115,f130,f129]) ).
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(f191,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP7(X1)
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ~ isPrime0(X2)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& sP6(X2) ) ) ) )
& xS = cS2043 ),
inference(rectify,[],[f131]) ).
fof(f192,plain,
( aSet0(xS)
& ! [X0] :
( ( ( aInteger0(sK30(X0))
& sz00 != sK30(X0)
& isPrime0(sK30(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK30(X0)))
& sP7(sK30(X0))
& szAzrzSzezqlpdtcmdtrp0(sz00,sK30(X0)) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ~ isPrime0(X2)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& sP6(X2) ) ) ) )
& xS = cS2043 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X1,sK30(X0))],[f191]) ).
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(f342,plain,
xS = cS2043,
inference(cnf_transformation,[],[f192]) ).
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(f399,plain,
! [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f403,plain,
! [X4] :
( sz00 != sK35(X4)
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f206]) ).
fof(f404,plain,
! [X4] :
( aInteger0(sK35(X4))
| ~ aElementOf0(X4,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(f455,plain,
! [X4] :
( aElementOf0(X4,stldt0(sbsmnsldt0(cS2043)))
| sz10 != X4 ),
inference(definition_unfolding,[],[f356,f342]) ).
fof(f458,plain,
cS2076 = stldt0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f353,f342]) ).
fof(f468,plain,
! [X4] :
( aInteger0(sK35(X4))
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f404,f342]) ).
fof(f469,plain,
! [X4] :
( sz00 != sK35(X4)
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f403,f342]) ).
fof(f473,plain,
! [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)),stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f399,f342,f342]) ).
fof(f498,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f433,f342]) ).
fof(f516,plain,
aElementOf0(sz10,stldt0(sbsmnsldt0(cS2043))),
inference(equality_resolution,[],[f455]) ).
fof(f604,plain,
aElementOf0(sz10,cS2076),
inference(forward_demodulation,[],[f516,f458]) ).
fof(f1118,plain,
! [X4] :
( ~ aElementOf0(X4,cS2076)
| aInteger0(sK35(X4)) ),
inference(forward_demodulation,[],[f468,f458]) ).
fof(f1425,plain,
! [X4] :
( sz00 != sK35(X4)
| ~ aElementOf0(X4,cS2076) ),
inference(forward_demodulation,[],[f469,f458]) ).
fof(f1432,plain,
! [X0] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),cS2076)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_demodulation,[],[f498,f458]) ).
fof(f1448,plain,
aInteger0(sK35(sz10)),
inference(resolution,[],[f604,f1118]) ).
fof(f1517,definition,
( spl41_44
<=> sz00 = sK35(sz10) ),
introduced(definition,[new_symbols(definition,[spl41_44])],[avatar_definition]) ).
fof(f1518,plain,
( sz00 != sK35(sz10)
| spl41_44 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f1519,plain,
( sz00 = sK35(sz10)
| ~ spl41_44 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f2128,plain,
( sz00 != sz00
| ~ aElementOf0(sz10,cS2076)
| ~ spl41_44 ),
inference(superposition,[],[f1425,f1519]) ).
fof(f2129,plain,
( ~ aElementOf0(sz10,cS2076)
| ~ spl41_44 ),
inference(trivial_inequality_removal,[],[f2128]) ).
fof(f2130,plain,
( $false
| ~ spl41_44 ),
inference(forward_subsumption_resolution,[],[f2129,f604]) ).
fof(f2131,plain,
~ spl41_44,
inference(avatar_contradiction_clause,[],[f2130]) ).
fof(f2556,plain,
! [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)),cS2076)
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(forward_demodulation,[],[f473,f458]) ).
fof(f2557,plain,
! [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK35(X4)),cS2076)
| ~ aElementOf0(X4,cS2076) ),
inference(forward_demodulation,[],[f2556,f458]) ).
fof(f2560,plain,
( ~ aElementOf0(sz10,cS2076)
| ~ aInteger0(sK35(sz10))
| sz00 = sK35(sz10) ),
inference(resolution,[],[f2557,f1432]) ).
fof(f2565,plain,
( ~ aInteger0(sK35(sz10))
| sz00 = sK35(sz10) ),
inference(forward_subsumption_resolution,[],[f2560,f604]) ).
fof(f2566,plain,
sz00 = sK35(sz10),
inference(forward_subsumption_resolution,[],[f2565,f1448]) ).
fof(f2567,plain,
( $false
| spl41_44 ),
inference(forward_subsumption_resolution,[],[f2566,f1518]) ).
fof(f2568,plain,
spl41_44,
inference(avatar_contradiction_clause,[],[f2567]) ).
cnf(s107,plain,
~ spl41_44,
inference(sat_conversion,[],[f2131]) ).
cnf(s129,plain,
spl41_44,
inference(sat_conversion,[],[f2568]) ).
cnf(s130,plain,
$false,
inference(rat,[],[s107,s129]) ).
fof(f2569,plain,
$false,
inference(avatar_sat_refutation,[],[s130]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 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 19:58:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.33 Running first-order model finding
% 0.08/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.38 % (2696909)Will run a generic schedule for satisfiability detection.
% 0.08/0.38 % (2696915)% WARNING: option uhcvi not known.
% 0.08/0.38 % (2696920)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3312178779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.38 % (2696918)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=778906611:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.38 % (2696914)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=13663605_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.38 % (2696917)dis+10_1_sil=32000:sp=arity:random_seed=1323603163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.38 % (2696915)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1155771486:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.38 % (2696916)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2634784010:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.38 % (2696919)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1133009850:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.38 % TRYING [1]
% 0.08/0.38 % TRYING [2]
% 0.08/0.38 % TRYING [3]
% 0.08/0.38 % (2696917) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2696909-2696917"...
% 0.08/0.38 % (2696916) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2696909-2696916"...
% 0.08/0.38 % (2696917)...printing done.
% 0.08/0.38 % (2696917)Refutation found. Thanks to Tanya!
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.38 % (2696917)------------------------------
% 0.08/0.38 % (2696917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.38 % (2696917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.38 % (2696917)CaDiCaL version: 2.1.3
% 0.08/0.38 % (2696917)Termination reason: Refutation
% 0.08/0.38 % (2696917)Time elapsed: 0.023 s
% 0.08/0.38 % (2696917)Peak memory usage: 13 MB
% 0.08/0.38 % (2696917)Instructions burned: 70 (million)
% 0.08/0.38 % (2696909)Success in time 0.05 s
% 0.08/0.38 % Vampire exiting
%------------------------------------------------------------------------------