%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM444+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 02:24:29 PM UTC 2026
% Result : Theorem 8.58s 6.82s
% Output : CNFRefutation 8.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 9 unt; 9 def)
% Number of atoms : 1071 ( 128 equ)
% Maximal formula atoms : 92 ( 9 avg)
% Number of connectives : 1389 ( 428 ~; 389 |; 494 &)
% ( 12 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 7 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 273 ( 0 sgn 199 !; 74 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
fof(f42,conjecture,
( ! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( ( ( sdteqdtlpzmzozddtrp0(X1,X0,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(X0))
& aInteger0(X2) ) )
& ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X0) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ) )
& ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X0,cS1395) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ( ! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( ( ( sdteqdtlpzmzozddtrp0(X1,X0,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X1,smndt0(X0))
& aInteger0(X2) ) )
& ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X0) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ) )
& ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X0,cS1395) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
~ ( ! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( ( ( sdteqdtlpzmzozddtrp0(X1,X0,xq)
| aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
| ? [X5] :
( sdtpldt0(X1,smndt0(X0)) = sdtasdt0(xq,X5)
& aInteger0(X5) ) )
& ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
| ? [X4] :
( sdtpldt0(X2,smndt0(xa)) = sdtasdt0(xq,X4)
& aInteger0(X4) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( ( ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
| ? [X8] :
( sdtpldt0(X6,smndt0(xa)) = sdtasdt0(xq,X8)
& aInteger0(X8) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ? [X7] :
( sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( ! [X14] :
( ( ( ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
| ? [X16] :
( sdtpldt0(X14,smndt0(xa)) = sdtasdt0(xq,X16)
& aInteger0(X16) ) )
& aInteger0(X14) )
=> aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ? [X15] :
( sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X19] :
( ( ( ! [X20] :
( ( ( ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
| aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
| ? [X22] :
( sdtpldt0(X20,smndt0(X18)) = sdtasdt0(X19,X22)
& aInteger0(X22) ) )
& aInteger0(X20) )
=> aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
=> ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ? [X21] :
( sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18))
& aInteger0(X21) )
& aInteger0(X20) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
=> aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& sz00 != X19
& aInteger0(X19) ) ) ) ) ) )
& ( ( ! [X9] :
( ( ( ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
| ? [X11] :
( sdtpldt0(X9,smndt0(xa)) = sdtasdt0(xq,X11)
& aInteger0(X11) ) )
& aInteger0(X9) )
=> aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X10] :
( sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa))
& aInteger0(X10) )
& aInteger0(X9) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X13,cS1395) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f48,plain,
( ! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X5] :
( sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5)
| ~ aInteger0(X5) ) )
| ( ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X8] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ? [X7] :
( sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ( ( ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ! [X16] :
( sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ? [X15] :
( sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X19] :
( ( ! [X20] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X20,X18,X19)
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ! [X22] :
( sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22)
| ~ aInteger0(X22) ) )
| ~ aInteger0(X20)
| aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ? [X21] :
( sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18))
& aInteger0(X21) )
& aInteger0(X20) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X19
| ~ aInteger0(X19) ) ) )
| ( ! [X9] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X11] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X9)
| aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X10] :
( sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa))
& aInteger0(X10) )
& aInteger0(X9) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X13,cS1395) ) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f49,plain,
( ! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X5] :
( sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5)
| ~ aInteger0(X5) ) )
| ( ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X8] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ? [X7] :
( sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ( ( ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ! [X16] :
( sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ? [X15] :
( sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa))
& aInteger0(X15) )
& aInteger0(X14) ) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X19] :
( ( ! [X20] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X20,X18,X19)
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ! [X22] :
( sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22)
| ~ aInteger0(X22) ) )
| ~ aInteger0(X20)
| aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ? [X21] :
( sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18))
& aInteger0(X21) )
& aInteger0(X20) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X19
| ~ aInteger0(X19) ) ) )
| ( ! [X9] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X11] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X9)
| aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X10] :
( sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa))
& aInteger0(X10) )
& aInteger0(X9) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X13,cS1395) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f99,plain,
( ~ sP8
| ( sP5
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X17] :
( ( ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& ( aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP6 ) ),
inference(nnf_transformation,[],[f97]) ).
fof(f100,plain,
( ~ sP8
| ( sP5
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X17] :
( ( ~ aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& ( aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X17)
| aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP6 ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
( ~ sP8
| ( sP5
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X0) ) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP6 ) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
( ~ sP7
| ! [X9] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X11] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X9)
| aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X10] :
( sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa))
& aInteger0(X10) )
& aInteger0(X9) ) ) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f103,plain,
( ~ sP7
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
( ~ sP7
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK9(X0))
& aInteger0(sK9(X0))
& aInteger0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f103]) ).
fof(f105,plain,
( ~ sP6
| ? [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X19] :
( ( sP4(X18,X19)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X19
| ~ aInteger0(X19) ) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f106,plain,
( ~ sP6
| ? [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( ( sP4(X0,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ~ aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
( ~ sP6
| ( aElementOf0(sK10,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( ( sP4(sK10,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK10,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK10,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(sK11(X1),szAzrzSzezqlpdtcmdtrp0(sK10,X1))
& ~ aElementOf0(sK11(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X2,sK11(X1))],[f106]) ).
fof(f108,plain,
( ~ sP5
| ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ! [X16] :
( sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ? [X15] :
( sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa))
& aInteger0(X15) )
& aInteger0(X14) ) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f109,plain,
( ~ sP5
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) ) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
( ~ sP5
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK12(X0))
& aInteger0(sK12(X0))
& aInteger0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f109]) ).
fof(f111,plain,
! [X18,X19] :
( ~ sP4(X18,X19)
| ! [X20] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X20,X18,X19)
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ! [X22] :
( sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22)
| ~ aInteger0(X22) ) )
| ~ aInteger0(X20)
| aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ? [X21] :
( sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18))
& aInteger0(X21) )
& aInteger0(X20) ) ) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f112,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(rectify,[],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ! [X4] :
( sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK13(X0,X1,X2))
& aInteger0(sK13(X0,X1,X2))
& aInteger0(X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f112]) ).
fof(f114,plain,
! [X1] :
( ~ sP3(X1)
| ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP1
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f115,plain,
! [X0] :
( ~ sP3(X0)
| ( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP1
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ sP2(X0)
| ( sP0
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f123,plain,
( ! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X5] :
( sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5)
| ~ aInteger0(X5) ) )
| sP2(X0)
| sP3(X1) )
& ( sP8
| ( sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X12] :
( ( ~ aElementOf0(X12,cS1395)
| aInteger0(X12) )
& ( ~ aInteger0(X12)
| aElementOf0(X12,cS1395) ) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X13,cS1395) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f124,plain,
( ! [X2,X3] :
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ( ~ sdteqdtlpzmzozddtrp0(X3,X2,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(X2)))
& ! [X4] :
( sdtasdt0(xq,X4) != sdtpldt0(X3,smndt0(X2))
| ~ aInteger0(X4) ) )
| sP2(X2)
| sP3(X3) )
& ( sP8
| ( sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,cS1395) ) ) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
( ! [X2,X3] :
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ( ~ sdteqdtlpzmzozddtrp0(X3,X2,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(X2)))
& ! [X4] :
( sdtasdt0(xq,X4) != sdtpldt0(X3,smndt0(X2))
| ~ aInteger0(X4) ) )
| sP2(X2)
| sP3(X3) )
& ( sP8
| ( sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& aElementOf0(sK16,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(sK16,cS1395) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f124]) ).
fof(f147,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f148,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f150,plain,
( ~ sP8
| sP5 ),
inference(cnf_transformation,[],[f101]) ).
fof(f153,plain,
! [X0] :
( ~ sP8
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f157,plain,
( ~ sP8
| sP6 ),
inference(cnf_transformation,[],[f101]) ).
fof(f165,plain,
! [X0] :
( ~ sP7
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
( ~ sP6
| aElementOf0(sK10,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f107]) ).
fof(f167,plain,
! [X1] :
( ~ sP6
| sP4(sK10,X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f170,plain,
! [X1] :
( ~ sP6
| aElementOf0(sK11(X1),szAzrzSzezqlpdtcmdtrp0(sK10,X1))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f171,plain,
! [X1] :
( ~ sP6
| ~ aElementOf0(sK11(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f179,plain,
! [X0] :
( ~ sP5
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f188,plain,
! [X0] :
( ~ sP3(X0)
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f194,plain,
! [X0] :
( ~ sP2(X0)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f116]) ).
fof(f212,plain,
! [X2,X3] :
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X2,xq)
| sP2(X2)
| sP3(X3) ),
inference(cnf_transformation,[],[f125]) ).
fof(f215,plain,
( sP8
| sP7 ),
inference(cnf_transformation,[],[f125]) ).
fof(f218,plain,
! [X1] :
( sP8
| ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ),
inference(cnf_transformation,[],[f125]) ).
fof(f221,plain,
( sP8
| aElementOf0(sK16,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f222,plain,
( sP8
| ~ aElementOf0(sK16,cS1395) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_50,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f148]) ).
tcf(c_51,plain,
xq != sz00,
inference(cnf_transformation,[],[f147]) ).
tcf(c_52,plain,
( sP6
| ~ sP8 ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_56,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP8
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_59,plain,
( sP5
| ~ sP8 ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_60,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP7
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP6
| ~ aInteger0(X0)
| ~ aElementOf0(sK11(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_69,plain,
! [X0: $i] :
( aElementOf0(sK11(X0),szAzrzSzezqlpdtcmdtrp0(sK10,X0))
| ( X0 = sz00 )
| ~ sP6
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_72,plain,
! [X0: $i] :
( sP4(sK10,X0)
| ( X0 = sz00 )
| ~ sP6
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_73,plain,
( aElementOf0(sK10,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP6 ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_74,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP5
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_93,plain,
! [X0: $i] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_95,plain,
! [X0: $i] :
( ~ sP2(X0)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_114,negated_conjecture,
( sP8
| ~ aElementOf0(sK16,cS1395) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_115,negated_conjecture,
( sP8
| aElementOf0(sK16,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_118,negated_conjecture,
! [X0: $i] :
( sP8
| aElementOf0(X0,cS1395)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_121,negated_conjecture,
( sP7
| sP8 ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_124,negated_conjecture,
! [X0: $i,X1: $i] :
( sP2(X1)
| sP3(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,xq) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_2012,plain,
( aElementOf0(sK10,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP8 ),
inference(resolution,[status(thm)],[c_52,c_73]) ).
tcf(c_2019,plain,
! [X0: $i] :
( sP4(sK10,X0)
| ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[c_52,c_72]) ).
tcf(c_2061,plain,
! [X0: $i] :
( aElementOf0(sK11(X0),szAzrzSzezqlpdtcmdtrp0(sK10,X0))
| ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[c_52,c_69]) ).
tcf(c_2062,plain,
( aElementOf0(sK11(xq),szAzrzSzezqlpdtcmdtrp0(sK10,xq))
| ( xq = sz00 )
| ~ sP8
| ~ aInteger0(xq) ),
inference(instantiation,[status(thm)],[c_2061]) ).
tcf(c_2075,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0)
| ~ aElementOf0(sK11(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(resolution,[status(thm)],[c_52,c_68]) ).
tcf(c_2076,plain,
( ( xq = sz00 )
| ~ sP8
| ~ aInteger0(xq)
| ~ aElementOf0(sK11(xq),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(instantiation,[status(thm)],[c_2075]) ).
tcf(c_2331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X3,X2,X1)
| ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ( X2 != sK10 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2019,c_86]) ).
tcf(c_2332,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,sK10,X1)
| ( X1 = sz00 )
| ~ sP8
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK10,X1)) ),
inference(unflattening,[status(thm)],[c_2331]) ).
tcf(c_2403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aInteger0(X3)
| ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ( X2 != sK10 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2019,c_82]) ).
tcf(c_2404,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ( X1 = sz00 )
| ~ sP8
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK10,X1)) ),
inference(unflattening,[status(thm)],[c_2403]) ).
tcf(c_14294,plain,
( sP8
| ~ aInteger0(sK16) ),
inference(superposition,[status(thm)],[c_118,c_114]) ).
tcf(c_15055,plain,
! [X0: $i] :
( aElementOf0(sK11(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP3(sK11(X0)) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_15056,plain,
( aElementOf0(sK11(xq),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP3(sK11(xq)) ),
inference(instantiation,[status(thm)],[c_15055]) ).
tcf(c_15360,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(sK11(X0),sK10,X0)
| ( X0 = sz00 )
| ~ sP8
| ~ aInteger0(X0)
| ~ aElementOf0(sK11(X0),szAzrzSzezqlpdtcmdtrp0(sK10,X0)) ),
inference(instantiation,[status(thm)],[c_2332]) ).
tcf(c_15361,plain,
( sdteqdtlpzmzozddtrp0(sK11(xq),sK10,xq)
| ( xq = sz00 )
| ~ sP8
| ~ aInteger0(xq)
| ~ aElementOf0(sK11(xq),szAzrzSzezqlpdtcmdtrp0(sK10,xq)) ),
inference(instantiation,[status(thm)],[c_15360]) ).
tcf(c_16339,plain,
! [X0: $i,X1: $i] :
( sP2(X1)
| sP3(sK11(X0))
| ~ aInteger0(X1)
| ~ aInteger0(sK11(X0))
| ~ sdteqdtlpzmzozddtrp0(sK11(X0),X1,xq) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_16810,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK11(X0))
| ( X1 = sz00 )
| ~ sP8
| ~ aInteger0(X1)
| ~ aElementOf0(sK11(X0),szAzrzSzezqlpdtcmdtrp0(sK10,X1)) ),
inference(instantiation,[status(thm)],[c_2404]) ).
tcf(c_16821,plain,
( aInteger0(sK11(xq))
| ( xq = sz00 )
| ~ sP8
| ~ aInteger0(xq)
| ~ aElementOf0(sK11(xq),szAzrzSzezqlpdtcmdtrp0(sK10,xq)) ),
inference(instantiation,[status(thm)],[c_16810]) ).
tcf(c_22699,plain,
( sP2(sK10)
| sP3(sK11(xq))
| ~ aInteger0(sK10)
| ~ aInteger0(sK11(xq))
| ~ sdteqdtlpzmzozddtrp0(sK11(xq),sK10,xq) ),
inference(instantiation,[status(thm)],[c_16339]) ).
fof(f89,definition,
( ~ sP0
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f90,definition,
( ~ sP1
| ! [X6] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X8] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X8)
| ~ aInteger0(X8) ) )
| ~ aInteger0(X6)
| aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ? [X7] :
( sdtasdt0(xq,X7) = sdtpldt0(X6,smndt0(xa))
& aInteger0(X7) )
& aInteger0(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f91,definition,
! [X0] :
( ~ sP2(X0)
| ( sP0
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f92,definition,
! [X1] :
( ~ sP3(X1)
| ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP1
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f93,definition,
! [X18,X19] :
( ~ sP4(X18,X19)
| ! [X20] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X20,X18,X19)
& ~ aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ! [X22] :
( sdtpldt0(X20,smndt0(X18)) != sdtasdt0(X19,X22)
| ~ aInteger0(X22) ) )
| ~ aInteger0(X20)
| aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19)) )
& ( ~ aElementOf0(X20,szAzrzSzezqlpdtcmdtrp0(X18,X19))
| ( sdteqdtlpzmzozddtrp0(X20,X18,X19)
& aDivisorOf0(X19,sdtpldt0(X20,smndt0(X18)))
& ? [X21] :
( sdtasdt0(X19,X21) = sdtpldt0(X20,smndt0(X18))
& aInteger0(X21) )
& aInteger0(X20) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f94,definition,
( ~ sP5
| ! [X14] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X14,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ! [X16] :
( sdtpldt0(X14,smndt0(xa)) != sdtasdt0(xq,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X14)
| aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X14,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X14,smndt0(xa)))
& ? [X15] :
( sdtasdt0(xq,X15) = sdtpldt0(X14,smndt0(xa))
& aInteger0(X15) )
& aInteger0(X14) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f95,definition,
( ~ sP6
| ? [X18] :
( aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X19] :
( ( sP4(X18,X19)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X18,X19),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(X18,X19))
& ~ aElementOf0(X23,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X19
| ~ aInteger0(X19) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f96,definition,
( ~ sP7
| ! [X9] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X11] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X11)
| ~ aInteger0(X11) ) )
| ~ aInteger0(X9)
| aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X10] :
( sdtasdt0(xq,X10) = sdtpldt0(X9,smndt0(xa))
& aInteger0(X10) )
& aInteger0(X9) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f97,definition,
( ~ sP8
| ( sP5
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X17] :
( aElementOf0(X17,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X17,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X17) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f98,plain,
( ! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X5] :
( sdtpldt0(X1,smndt0(X0)) != sdtasdt0(xq,X5)
| ~ aInteger0(X5) ) )
| sP2(X0)
| sP3(X1) )
& ( sP8
| ( sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X12] :
( aElementOf0(X12,cS1395)
<=> aInteger0(X12) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X13] :
( aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X13,cS1395) ) ) ) ),
inference(definition_folding,[],[f49,f97,f96,f95,f94,f93,f92,f91,f90,f89]) ).
fof(f120,plain,
( ~ sP0
| ! [X2] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X2,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X2,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X2,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X2,smndt0(xa)))
& ? [X3] :
( sdtasdt0(xq,X3) = sdtpldt0(X2,smndt0(xa))
& aInteger0(X3) )
& aInteger0(X2) ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f121,plain,
( ~ sP0
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
( ~ sP0
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X0,smndt0(xa))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK15(X0))
& aInteger0(sK15(X0))
& aInteger0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f121]) ).
fof(f211,plain,
! [X0] :
( ~ sP0
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_106,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP0
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_289,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_121,c_59,c_74,c_60]) ).
tcf(c_295,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_289]) ).
tcf(c_14328,plain,
( sP8
| aInteger0(sK16) ),
inference(superposition,[status(thm)],[c_115,c_295]) ).
tcf(c_14331,plain,
sP8,
inference(global_subsumption_just,[status(thm)],[c_14328,c_14294,c_14328]) ).
tcf(c_14410,plain,
aElementOf0(sK10,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))),
inference(global_subsumption_just,[status(thm)],[c_2012,c_2012,c_14331]) ).
tcf(c_14505,plain,
~ sP2(sK10),
inference(superposition,[status(thm)],[c_14410,c_95]) ).
tcf(c_14766,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_56,c_14294,c_14328]) ).
tcf(c_14773,plain,
aInteger0(sK10),
inference(superposition,[status(thm)],[c_14410,c_14766]) ).
tcf(c_22701,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22699,c_16821,c_15361,c_15056,c_14773,c_14505,c_14331,c_2076,c_2062,c_51,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM444+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.44 % Computer : n017.cluster.edu
% 0.11/5.44 % Model : x86_64 x86_64
% 0.11/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.44 % Memory : 8046.5625MB
% 0.11/5.44 % OS : Linux 6.8.0-71-generic
% 0.11/5.44 % CPULimit : 300
% 0.11/5.44 % WCLimit : 300
% 0.11/5.44 % DateTime : Thu Sep 24 03:56:21 UTC 2026
% 0.11/5.44 % CPUTime :
% 0.11/5.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.47 Running first-order theorem proving
% 0.11/5.47 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.49
% 0.11/5.49 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.49
% 0.11/5.49 % Detected problem language: tptp
% 0.14/5.50 % Proving...
% 8.58/6.82 % SZS status Started for theBenchmark.p
% 8.58/6.82 % SZS status Theorem for theBenchmark.p
% 8.58/6.82
% 8.58/6.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.58/6.82
% 8.58/6.82 % ------ iProver source info
% 8.58/6.82
% 8.58/6.82 % git: date: 2026-07-19 20:42:38 +0200
% 8.58/6.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.58/6.82 % git: non_committed_changes: false
% 8.58/6.82
% 8.58/6.82 % ------ Parsing...
% 8.58/6.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.58/6.82
% 8.58/6.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 8.58/6.82
% 8.58/6.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.58/6.82
% 8.58/6.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.58/6.82 % ------ Proving...
% 8.58/6.82 % ------ Problem Properties
% 8.58/6.82
% 8.58/6.82 %
% 8.58/6.82 % clauses 108
% 8.58/6.82 % conjectures 9
% 8.58/6.82 % EPR 19
% 8.58/6.82 % Horn 65
% 8.58/6.82 % unary 6
% 8.58/6.82 % binary 29
% 8.58/6.82 % lits 385
% 8.58/6.82 % lits eq 66
% 8.58/6.82 % fd_pure 0
% 8.58/6.82 % fd_pseudo 0
% 8.58/6.82 % fd_cond 26
% 8.58/6.82 % fd_pseudo_cond 6
% 8.58/6.82 % AC symbols 0
% 8.58/6.82
% 8.58/6.82 % ------ Schedule dynamic 5 is on
% 8.58/6.82
% 8.58/6.82 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.58/6.82
% 8.58/6.82
% 8.58/6.82 % ------
% 8.58/6.82 % Current options:
% 8.58/6.82 % ------
% 8.58/6.82
% 8.58/6.82
% 8.58/6.82 %
% 8.58/6.82
% 8.58/6.82 % ------ Proving...
% 8.58/6.82 %
% 8.58/6.82
% 8.58/6.82 % SZS status Theorem for theBenchmark.p
% 8.58/6.82
% 8.58/6.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.58/6.83
% 8.58/6.83
%------------------------------------------------------------------------------