%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM444+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:24:20 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 14 unt; 11 def)
% Number of atoms : 849 ( 89 equ)
% Maximal formula atoms : 92 ( 6 avg)
% Number of connectives : 1028 ( 307 ~; 360 |; 274 &)
% ( 21 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 12 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 195 ( 0 sgn 143 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
fof(f42,conjecture,
( ! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> ( ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(X0)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X1,X0,xq) ) )
=> ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
=> ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X0,cS1395) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) ) ) )
& ( ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ( ! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> ( ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(X0)) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X1,X0,xq) ) )
=> ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
=> ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) ) )
=> ( ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X0,cS1395) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) ) ) )
& ( ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [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(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f45,plain,
~ ( ! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> ( ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
& ( ( aInteger0(X2)
& ( ? [X4] :
( aInteger0(X4)
& sdtpldt0(X2,smndt0(xa)) = sdtasdt0(xq,X4) )
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X2,xa,xq) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& ( ? [X5] :
( aInteger0(X5)
& sdtpldt0(X1,smndt0(X0)) = sdtasdt0(xq,X5) )
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X1,X0,xq) ) )
=> ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X6,xa,xq) ) )
& ( ( aInteger0(X6)
& ( ? [X8] :
( aInteger0(X8)
& sdtpldt0(X6,smndt0(xa)) = sdtasdt0(xq,X8) )
| aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X6,xa,xq) ) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
=> ( ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X9] :
( ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X9)
& ? [X10] :
( aInteger0(X10)
& sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X9,xa,xq) ) )
& ( ( aInteger0(X9)
& ( ? [X11] :
( aInteger0(X11)
& sdtpldt0(X9,smndt0(xa)) = sdtasdt0(xq,X11) )
| aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X9,xa,xq) ) )
=> aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( aSet0(cS1395)
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) ) )
=> ( ! [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X13,cS1395) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395) ) ) )
& ( ! [X14] :
( ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X14,xa,xq) ) )
& ( ( aInteger0(X14)
& ( ? [X16] :
( aInteger0(X16)
& sdtpldt0(X14,smndt0(xa)) = sdtasdt0(xq,X16) )
| aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X14,xa,xq) ) )
=> aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
=> ( ( ( aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X17)
& ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ! [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X19] :
( aInteger0(X19)
& sz00 != X19
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ! [X20] :
( ( aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
=> ( aInteger0(X20)
& ? [X21] :
( aInteger0(X21)
& sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18)) )
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& sdteqdtlpzmzozddtrp0(X20,X18,X19) ) )
& ( ( aInteger0(X20)
& ( ? [X22] :
( aInteger0(X22)
& sdtpldt0(X20,smndt0(X18)) = sdtasdt0(X19,X22) )
| aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
| sdteqdtlpzmzozddtrp0(X20,X18,X19) ) )
=> aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) ) ) )
=> ( ! [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
=> aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ) )
| isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f105,plain,
( ( ( ? [X13] :
( ~ aElementOf0(X13,cS1395)
& aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& aSet0(cS1395)
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X9] :
( ( ( aInteger0(X9)
& ? [X10] :
( aInteger0(X10)
& sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X9,xa,xq) )
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X9)
| ( ! [X11] :
( ~ aInteger0(X11)
| sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11) )
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X9,xa,xq) ) ) ) )
| ( ? [X18] :
( ! [X19] :
( ~ aInteger0(X19)
| sz00 = X19
| ( ? [X23] :
( ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ! [X20] :
( ( ( aInteger0(X20)
& ? [X21] :
( aInteger0(X21)
& sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18)) )
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& sdteqdtlpzmzozddtrp0(X20,X18,X19) )
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ~ aInteger0(X20)
| ( ! [X22] :
( ~ aInteger0(X22)
| sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22) )
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ~ sdteqdtlpzmzozddtrp0(X20,X18,X19) ) ) ) ) )
& aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X17)
& ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X14] :
( ( ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X14,xa,xq) )
| ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X14)
| ( ! [X16] :
( ~ aInteger0(X16)
| sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16) )
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X14,xa,xq) ) ) ) ) )
& ! [X0,X1] :
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X6,xa,xq) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X8) )
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X6,xa,xq) ) ) )
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4) )
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X2,xa,xq) ) ) ) )
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5) )
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ~ sdteqdtlpzmzozddtrp0(X1,X0,xq) )
| ~ aInteger0(X0)
| ~ aInteger0(X1) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f106,plain,
( ( ( ? [X13] :
( ~ aElementOf0(X13,cS1395)
& aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& aSet0(cS1395)
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X9] :
( ( ( aInteger0(X9)
& ? [X10] :
( aInteger0(X10)
& sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X9,xa,xq) )
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X9)
| ( ! [X11] :
( ~ aInteger0(X11)
| sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11) )
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X9,xa,xq) ) ) ) )
| ( ? [X18] :
( ! [X19] :
( ~ aInteger0(X19)
| sz00 = X19
| ( ? [X23] :
( ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ! [X20] :
( ( ( aInteger0(X20)
& ? [X21] :
( aInteger0(X21)
& sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18)) )
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& sdteqdtlpzmzozddtrp0(X20,X18,X19) )
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ~ aInteger0(X20)
| ( ! [X22] :
( ~ aInteger0(X22)
| sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22) )
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ~ sdteqdtlpzmzozddtrp0(X20,X18,X19) ) ) ) ) )
& aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( aInteger0(X17)
& ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X14] :
( ( ( aInteger0(X14)
& ? [X15] :
( aInteger0(X15)
& sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X14,xa,xq) )
| ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X14)
| ( ! [X16] :
( ~ aInteger0(X16)
| sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16) )
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X14,xa,xq) ) ) ) ) )
& ! [X0,X1] :
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X6,xa,xq) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X8) )
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X6,xa,xq) ) ) )
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X2,xa,xq) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4) )
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X2,xa,xq) ) ) ) )
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5) )
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ~ sdteqdtlpzmzozddtrp0(X1,X0,xq) )
| ~ aInteger0(X0)
| ~ aInteger0(X1) ) ),
inference(flattening,[],[f105]) ).
fof(f210,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f211,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f237,plain,
! [X19,X12,X20] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| sdteqdtlpzmzozddtrp0(X20,sK15,X19)
| sz00 = X19
| ~ aInteger0(X19)
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f239,plain,
! [X19,X12,X20] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| aInteger0(X20)
| sz00 = X19
| ~ aInteger0(X19)
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f246,plain,
! [X19,X20] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| sdteqdtlpzmzozddtrp0(X20,sK15,X19)
| sz00 = X19
| ~ aInteger0(X19)
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f248,plain,
! [X19,X20] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| aInteger0(X20)
| sz00 = X19
| ~ aInteger0(X19)
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f271,plain,
! [X19,X12] :
( aElementOf0(sK23(X19),szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| sz00 = X19
| ~ aInteger0(X19)
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f272,plain,
! [X19,X12] :
( ~ aElementOf0(sK23(X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sz00 = X19
| ~ aInteger0(X19)
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f277,plain,
! [X19] :
( aElementOf0(sK23(X19),szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| sz00 = X19
| ~ aInteger0(X19)
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f278,plain,
! [X19] :
( ~ aElementOf0(sK23(X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sz00 = X19
| ~ aInteger0(X19)
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f313,plain,
! [X9] :
( ~ sP17(X9)
| aInteger0(X9)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f343,plain,
! [X17] :
( sP20(X17)
| ~ aInteger0(X17)
| aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f345,plain,
! [X17] :
( ~ sP20(X17)
| aInteger0(X17) ),
inference(cnf_transformation,[],[f106]) ).
fof(f348,plain,
! [X14] :
( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X14)
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f363,plain,
! [X9,X14] :
( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X14)
| sP17(X9) ),
inference(cnf_transformation,[],[f106]) ).
fof(f376,plain,
! [X13] :
( ~ sP19(X13)
| aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f377,plain,
! [X13] :
( ~ sP19(X13)
| ~ aElementOf0(X13,cS1395) ),
inference(cnf_transformation,[],[f106]) ).
fof(f378,plain,
! [X12] :
( ~ sP18(X12)
| aElementOf0(X12,cS1395)
| ~ aInteger0(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f383,plain,
( aElementOf0(sK15,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f386,plain,
! [X12] :
( aElementOf0(sK15,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f389,plain,
! [X17] :
( ~ sP20(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f390,plain,
! [X17] :
( sP20(X17)
| ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP19(sK16) ),
inference(cnf_transformation,[],[f106]) ).
fof(f395,plain,
! [X17,X12] :
( ~ sP20(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f396,plain,
! [X17,X12] :
( sP20(X17)
| ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP18(X12) ),
inference(cnf_transformation,[],[f106]) ).
fof(f402,plain,
! [X1] :
( ~ sP14(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f408,plain,
! [X0,X1] :
( sP14(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f461,definition,
( spl27_1
<=> sP19(sK16) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f463,plain,
( sP19(sK16)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f485,definition,
( spl27_6
<=> ! [X12] : sP18(X12) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f486,plain,
( ! [X12] : sP18(X12)
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f496,definition,
( spl27_8
<=> ! [X9] : sP17(X9) ),
introduced(definition,[new_symbols(definition,[spl27_8])],[avatar_definition]) ).
fof(f497,plain,
( ! [X9] : sP17(X9)
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f510,definition,
( spl27_10
<=> ! [X20,X19] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| ~ aInteger0(X19)
| sz00 = X19
| sdteqdtlpzmzozddtrp0(X20,sK15,X19) ) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f511,plain,
( ! [X19,X20] :
( sdteqdtlpzmzozddtrp0(X20,sK15,X19)
| ~ aInteger0(X19)
| sz00 = X19
| ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19)) )
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f518,definition,
( spl27_12
<=> ! [X20,X19] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| ~ aInteger0(X19)
| sz00 = X19
| aInteger0(X20) ) ),
introduced(definition,[new_symbols(definition,[spl27_12])],[avatar_definition]) ).
fof(f519,plain,
( ! [X19,X20] :
( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| ~ aInteger0(X19)
| sz00 = X19
| aInteger0(X20) )
| ~ spl27_12 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f524,plain,
( spl27_6
| spl27_10 ),
inference(avatar_split_clause,[],[f237,f510,f485]) ).
fof(f526,plain,
( spl27_6
| spl27_12 ),
inference(avatar_split_clause,[],[f239,f518,f485]) ).
fof(f533,plain,
( spl27_1
| spl27_10 ),
inference(avatar_split_clause,[],[f246,f510,f461]) ).
fof(f535,plain,
( spl27_1
| spl27_12 ),
inference(avatar_split_clause,[],[f248,f518,f461]) ).
fof(f570,definition,
( spl27_19
<=> ! [X19] :
( aElementOf0(sK23(X19),szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| ~ aInteger0(X19)
| sz00 = X19 ) ),
introduced(definition,[new_symbols(definition,[spl27_19])],[avatar_definition]) ).
fof(f571,plain,
( ! [X19] :
( aElementOf0(sK23(X19),szAzrzSzezqlpdtcmdtrp0(sK15,X19))
| ~ aInteger0(X19)
| sz00 = X19 )
| ~ spl27_19 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f574,definition,
( spl27_20
<=> ! [X19] :
( ~ aElementOf0(sK23(X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X19)
| sz00 = X19 ) ),
introduced(definition,[new_symbols(definition,[spl27_20])],[avatar_definition]) ).
fof(f575,plain,
( ! [X19] :
( ~ aElementOf0(sK23(X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X19)
| sz00 = X19 )
| ~ spl27_20 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f579,plain,
( spl27_6
| spl27_19 ),
inference(avatar_split_clause,[],[f271,f570,f485]) ).
fof(f580,plain,
( spl27_6
| spl27_20 ),
inference(avatar_split_clause,[],[f272,f574,f485]) ).
fof(f585,plain,
( spl27_1
| spl27_19 ),
inference(avatar_split_clause,[],[f277,f570,f461]) ).
fof(f586,plain,
( spl27_1
| spl27_20 ),
inference(avatar_split_clause,[],[f278,f574,f461]) ).
fof(f644,definition,
( spl27_30
<=> ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X6) ) ),
introduced(definition,[new_symbols(definition,[spl27_30])],[avatar_definition]) ).
fof(f645,plain,
( ! [X6] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X6) )
| ~ spl27_30 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f690,plain,
( spl27_1
| spl27_30 ),
inference(avatar_split_clause,[],[f348,f644,f461]) ).
fof(f705,plain,
( spl27_8
| spl27_30 ),
inference(avatar_split_clause,[],[f363,f644,f496]) ).
fof(f720,definition,
( spl27_35
<=> aElementOf0(sK15,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
introduced(definition,[new_symbols(definition,[spl27_35])],[avatar_definition]) ).
fof(f722,plain,
( aElementOf0(sK15,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ spl27_35 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f723,plain,
( spl27_1
| spl27_35 ),
inference(avatar_split_clause,[],[f383,f720,f461]) ).
fof(f726,plain,
( spl27_6
| spl27_35 ),
inference(avatar_split_clause,[],[f386,f720,f485]) ).
fof(f730,definition,
( spl27_36
<=> ! [X17] :
( ~ sP20(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ),
introduced(definition,[new_symbols(definition,[spl27_36])],[avatar_definition]) ).
fof(f731,plain,
( ! [X17] :
( ~ sP20(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ spl27_36 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f732,plain,
( spl27_1
| spl27_36 ),
inference(avatar_split_clause,[],[f389,f730,f461]) ).
fof(f734,definition,
( spl27_37
<=> ! [X17] :
( sP20(X17)
| ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ),
introduced(definition,[new_symbols(definition,[spl27_37])],[avatar_definition]) ).
fof(f735,plain,
( ! [X17] :
( sP20(X17)
| ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ spl27_37 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f736,plain,
( spl27_1
| spl27_37 ),
inference(avatar_split_clause,[],[f390,f734,f461]) ).
fof(f741,plain,
( spl27_6
| spl27_36 ),
inference(avatar_split_clause,[],[f395,f730,f485]) ).
fof(f742,plain,
( spl27_6
| spl27_37 ),
inference(avatar_split_clause,[],[f396,f734,f485]) ).
fof(f799,plain,
( ! [X0] :
( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X0) )
| ~ spl27_37 ),
inference(resolution,[],[f735,f345]) ).
fof(f801,plain,
( ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0) )
| ~ spl27_36 ),
inference(resolution,[],[f343,f731]) ).
fof(f805,plain,
( ! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| aInteger0(sK23(X0))
| ~ aInteger0(X0)
| sz00 = X0 )
| ~ spl27_12
| ~ spl27_19 ),
inference(resolution,[],[f519,f571]) ).
fof(f806,plain,
( ! [X0] :
( aInteger0(sK23(X0))
| sz00 = X0
| ~ aInteger0(X0) )
| ~ spl27_12
| ~ spl27_19 ),
inference(duplicate_literal_removal,[],[f805]) ).
fof(f811,plain,
( ! [X0] :
( aElementOf0(sK23(X0),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(sK23(X0))
| ~ aInteger0(X0)
| sz00 = X0 )
| ~ spl27_20
| ~ spl27_36 ),
inference(resolution,[],[f801,f575]) ).
fof(f812,plain,
( ! [X0] :
( aElementOf0(sK23(X0),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| sz00 = X0 )
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_36 ),
inference(forward_subsumption_resolution,[],[f811,f806]) ).
fof(f844,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(resolution,[],[f408,f402]) ).
fof(f845,plain,
( ! [X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f844,f799]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ spl27_30
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f845,f645]) ).
fof(f849,plain,
( ! [X0] :
( ~ aElementOf0(sK15,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xq)
| sz00 = xq
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK15,xq)) )
| ~ spl27_10
| ~ spl27_30
| ~ spl27_37 ),
inference(resolution,[],[f847,f511]) ).
fof(f851,plain,
( ! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xq)
| sz00 = xq
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK15,xq)) )
| ~ spl27_10
| ~ spl27_30
| ~ spl27_35
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f849,f722]) ).
fof(f857,plain,
( ! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sz00 = xq
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK15,xq)) )
| ~ spl27_10
| ~ spl27_30
| ~ spl27_35
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f851,f211]) ).
fof(f858,plain,
( ! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK15,xq))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ spl27_10
| ~ spl27_30
| ~ spl27_35
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f857,f210]) ).
fof(f892,plain,
( ~ aElementOf0(sK23(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xq)
| sz00 = xq
| ~ spl27_10
| ~ spl27_19
| ~ spl27_30
| ~ spl27_35
| ~ spl27_37 ),
inference(resolution,[],[f858,f571]) ).
fof(f893,plain,
( ~ aInteger0(xq)
| sz00 = xq
| ~ spl27_10
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_30
| ~ spl27_35
| ~ spl27_36
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f892,f812]) ).
fof(f894,plain,
( sz00 = xq
| ~ spl27_10
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_30
| ~ spl27_35
| ~ spl27_36
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f893,f211]) ).
fof(f895,plain,
( $false
| ~ spl27_10
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_30
| ~ spl27_35
| ~ spl27_36
| ~ spl27_37 ),
inference(forward_subsumption_resolution,[],[f894,f210]) ).
fof(f896,plain,
( ~ spl27_10
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_30
| ~ spl27_35
| ~ spl27_36
| ~ spl27_37 ),
inference(avatar_contradiction_clause,[],[f895]) ).
fof(f897,plain,
( aElementOf0(sK16,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ spl27_1 ),
inference(resolution,[],[f463,f376]) ).
fof(f898,plain,
( ~ aElementOf0(sK16,cS1395)
| ~ spl27_1 ),
inference(resolution,[],[f463,f377]) ).
fof(f900,plain,
( ! [X0] :
( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
| ~ spl27_6 ),
inference(resolution,[],[f486,f378]) ).
fof(f906,plain,
( ! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ spl27_8 ),
inference(resolution,[],[f497,f313]) ).
fof(f925,plain,
( aInteger0(sK16)
| ~ spl27_1
| ~ spl27_30 ),
inference(resolution,[],[f897,f645]) ).
fof(f944,plain,
( ~ aInteger0(sK16)
| ~ spl27_1
| ~ spl27_6 ),
inference(resolution,[],[f900,f898]) ).
fof(f945,plain,
( $false
| ~ spl27_1
| ~ spl27_6
| ~ spl27_30 ),
inference(forward_subsumption_resolution,[],[f944,f925]) ).
fof(f946,plain,
( ~ spl27_1
| ~ spl27_6
| ~ spl27_30 ),
inference(avatar_contradiction_clause,[],[f945]) ).
fof(f950,plain,
( spl27_30
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f906,f496,f644]) ).
cnf(s25,plain,
( spl27_6
| spl27_10 ),
inference(sat_conversion,[],[f524]) ).
cnf(s27,plain,
( spl27_6
| spl27_12 ),
inference(sat_conversion,[],[f526]) ).
cnf(s34,plain,
( spl27_1
| spl27_10 ),
inference(sat_conversion,[],[f533]) ).
cnf(s36,plain,
( spl27_1
| spl27_12 ),
inference(sat_conversion,[],[f535]) ).
cnf(s56,plain,
( spl27_6
| spl27_19 ),
inference(sat_conversion,[],[f579]) ).
cnf(s57,plain,
( spl27_6
| spl27_20 ),
inference(sat_conversion,[],[f580]) ).
cnf(s62,plain,
( spl27_1
| spl27_19 ),
inference(sat_conversion,[],[f585]) ).
cnf(s63,plain,
( spl27_1
| spl27_20 ),
inference(sat_conversion,[],[f586]) ).
cnf(s125,plain,
( spl27_1
| spl27_30 ),
inference(sat_conversion,[],[f690]) ).
cnf(s140,plain,
( spl27_8
| spl27_30 ),
inference(sat_conversion,[],[f705]) ).
cnf(s154,plain,
( spl27_1
| spl27_35 ),
inference(sat_conversion,[],[f723]) ).
cnf(s157,plain,
( spl27_6
| spl27_35 ),
inference(sat_conversion,[],[f726]) ).
cnf(s160,plain,
( spl27_1
| spl27_36 ),
inference(sat_conversion,[],[f732]) ).
cnf(s161,plain,
( spl27_1
| spl27_37 ),
inference(sat_conversion,[],[f736]) ).
cnf(s166,plain,
( spl27_6
| spl27_36 ),
inference(sat_conversion,[],[f741]) ).
cnf(s167,plain,
( spl27_6
| spl27_37 ),
inference(sat_conversion,[],[f742]) ).
cnf(s199,plain,
( ~ spl27_10
| ~ spl27_12
| ~ spl27_19
| ~ spl27_20
| ~ spl27_30
| ~ spl27_35
| ~ spl27_36
| ~ spl27_37 ),
inference(sat_conversion,[],[f896]) ).
cnf(s202,plain,
( ~ spl27_1
| ~ spl27_6
| ~ spl27_30 ),
inference(sat_conversion,[],[f946]) ).
cnf(s203,plain,
( ~ spl27_8
| spl27_30 ),
inference(sat_conversion,[],[f950]) ).
cnf(s207,plain,
spl27_1,
inference(rat,[],[s199,s34,s36,s62,s63,s125,s154,s160,s161]) ).
cnf(s209,plain,
spl27_30,
inference(rat,[],[s140,s203]) ).
cnf(s210,plain,
~ spl27_6,
inference(rat,[],[s202,s207,s209]) ).
cnf(s214,plain,
spl27_37,
inference(rat,[],[s167,s210]) ).
cnf(s215,plain,
spl27_36,
inference(rat,[],[s166,s210]) ).
cnf(s216,plain,
spl27_35,
inference(rat,[],[s157,s210]) ).
cnf(s226,plain,
spl27_20,
inference(rat,[],[s57,s210]) ).
cnf(s227,plain,
spl27_19,
inference(rat,[],[s56,s210]) ).
cnf(s230,plain,
spl27_12,
inference(rat,[],[s27,s210]) ).
cnf(s232,plain,
spl27_10,
inference(rat,[],[s25,s210]) ).
cnf(s234,plain,
$false,
inference(rat,[],[s199,s214,s215,s216,s209,s226,s227,s230,s232]) ).
fof(f951,plain,
$false,
inference(avatar_sat_refutation,[],[s234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM444+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:00:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.46 % (3839575)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (3839585)% WARNING: option uhcvi not known.
% 0.15/0.46 % (3839589)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3117108066:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (3839584)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2538348967_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (3839587)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=456433290:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (3839585)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3215096317:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (3839588)dis+10_1_sil=32000:sp=arity:random_seed=3680603555:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (3839592)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1233887994:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (3839591)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=579052320:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (3839589) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3839575-3839589"...
% 0.15/0.46 % (3839589)...printing done.
% 0.15/0.46 % (3839589)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (3839589)------------------------------
% 0.15/0.47 % (3839589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (3839589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (3839589)CaDiCaL version: 2.1.3
% 0.15/0.47 % (3839589)Termination reason: Refutation
% 0.15/0.47 % (3839589)Time elapsed: 0.014 s
% 0.15/0.47 % (3839589)Peak memory usage: 13 MB
% 0.15/0.47 % (3839589)Instructions burned: 45 (million)
% 0.15/0.47 % (3839575)Success in time 0.043 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------