TSTP Solution File: NUM444+6 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM444+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:30:30 EDT 2023
% Result : Theorem 3.75s 1.16s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 124 ( 9 unt; 0 def)
% Number of atoms : 1127 ( 139 equ)
% Maximal formula atoms : 92 ( 9 avg)
% Number of connectives : 1434 ( 431 ~; 402 |; 516 &)
% ( 12 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 292 ( 0 sgn; 168 !; 83 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
( sz00 != xq
& 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))) ) ) )
& sz00 != X1
& 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))) ) ) )
& sz00 != X1
& 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,[],[f42]) ).
fof(f50,plain,
~ ( ! [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) ) )
& ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
| ? [X4] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X4)
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X5] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X5)
& aInteger0(X5) )
& aInteger0(X3) ) ) )
& 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)))
| ? [X7] :
( sdtpldt0(X6,smndt0(xa)) = sdtasdt0(xq,X7)
& aInteger0(X7) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X6,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ? [X8] :
( sdtpldt0(X6,smndt0(xa)) = sdtasdt0(xq,X8)
& aInteger0(X8) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ( ! [X9] :
( ( ( ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
| ? [X10] :
( sdtpldt0(X9,smndt0(xa)) = sdtasdt0(xq,X10)
& aInteger0(X10) ) )
& aInteger0(X9) )
=> aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X9,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ? [X11] :
( sdtpldt0(X9,smndt0(xa)) = sdtasdt0(xq,X11)
& aInteger0(X11) )
& aInteger0(X9) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X12] :
( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X13] :
( aElementOf0(X13,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X14] :
( ( ( ! [X15] :
( ( ( ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
| aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
| ? [X16] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X16)
& aInteger0(X16) ) )
& aInteger0(X15) )
=> aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
& ( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14))
=> ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
& aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ? [X17] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X17)
& aInteger0(X17) )
& aInteger0(X15) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X13,X14),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X18] :
( aElementOf0(X18,szAzrzSzezqlpdtcmdtrp0(X13,X14))
=> aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& sz00 != X14
& aInteger0(X14) ) ) ) ) ) )
& ( ( ! [X19] :
( ( ( ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
| ? [X20] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X20)
& aInteger0(X20) ) )
& aInteger0(X19) )
=> aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ? [X21] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X21)
& aInteger0(X21) )
& aInteger0(X19) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X22] :
( aElementOf0(X22,cS1395)
<=> aInteger0(X22) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X23] :
( aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X23,cS1395) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f104,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X13] :
( ! [X14] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X13,X14),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( ~ aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X18,szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
& ! [X15] :
( ( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14))
| ( ~ sdteqdtlpzmzozddtrp0(X15,X13,X14)
& ~ aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ! [X16] :
( sdtpldt0(X15,smndt0(X13)) != sdtasdt0(X14,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X15) )
& ( ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
& aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ? [X17] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X17)
& aInteger0(X17) )
& aInteger0(X15) )
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
| sz00 = X14
| ~ aInteger0(X14) )
& aElementOf0(X13,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ! [X12] :
( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X9] :
( ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X10] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X10)
| ~ aInteger0(X10) ) )
| ~ aInteger0(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)) ) ) )
| ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X23] :
( ~ aElementOf0(X23,cS1395)
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ! [X22] :
( aElementOf0(X22,cS1395)
<=> aInteger0(X22) )
& aSet0(cS1395)
& ! [X19] :
( ( aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X19,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ! [X20] :
( sdtpldt0(X19,smndt0(xa)) != sdtasdt0(xq,X20)
| ~ aInteger0(X20) ) )
| ~ aInteger0(X19) )
& ( ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ? [X21] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X21)
& aInteger0(X21) )
& aInteger0(X19) )
| ~ aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ! [X0,X1] :
( ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X1,smndt0(X0))
| ~ aInteger0(X2) ) )
| ( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X3,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X5] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f105,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X13] :
( ! [X14] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X13,X14),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( ~ aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X18,szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
& ! [X15] :
( ( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14))
| ( ~ sdteqdtlpzmzozddtrp0(X15,X13,X14)
& ~ aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ! [X16] :
( sdtpldt0(X15,smndt0(X13)) != sdtasdt0(X14,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X15) )
& ( ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
& aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ? [X17] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X17)
& aInteger0(X17) )
& aInteger0(X15) )
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
| sz00 = X14
| ~ aInteger0(X14) )
& aElementOf0(X13,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
& ! [X12] :
( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X9] :
( ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X10] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X10)
| ~ aInteger0(X10) ) )
| ~ aInteger0(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)) ) ) )
| ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X23] :
( ~ aElementOf0(X23,cS1395)
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ! [X22] :
( aElementOf0(X22,cS1395)
<=> aInteger0(X22) )
& aSet0(cS1395)
& ! [X19] :
( ( aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X19,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ! [X20] :
( sdtpldt0(X19,smndt0(xa)) != sdtasdt0(xq,X20)
| ~ aInteger0(X20) ) )
| ~ aInteger0(X19) )
& ( ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ? [X21] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X21)
& aInteger0(X21) )
& aInteger0(X19) )
| ~ aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ! [X0,X1] :
( ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X1,smndt0(X0))
| ~ aInteger0(X2) ) )
| ( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X3,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X5] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f104]) ).
fof(f115,plain,
( ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X3,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X5] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP6 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f116,plain,
( ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X6,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X6,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X6,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(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)) ) )
| ~ sP7 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f117,plain,
! [X0] :
( ( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP6
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f118,plain,
! [X1] :
( ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP9(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f119,plain,
( ! [X19] :
( ( aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X19,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ! [X20] :
( sdtpldt0(X19,smndt0(xa)) != sdtasdt0(xq,X20)
| ~ aInteger0(X20) ) )
| ~ aInteger0(X19) )
& ( ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ? [X21] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X21)
& aInteger0(X21) )
& aInteger0(X19) )
| ~ aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP10 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f120,plain,
! [X14,X13] :
( ! [X15] :
( ( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14))
| ( ~ sdteqdtlpzmzozddtrp0(X15,X13,X14)
& ~ aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ! [X16] :
( sdtpldt0(X15,smndt0(X13)) != sdtasdt0(X14,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X15) )
& ( ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
& aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ? [X17] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X17)
& aInteger0(X17) )
& aInteger0(X15) )
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14)) ) )
| ~ sP11(X14,X13) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f121,plain,
( ! [X9] :
( ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X10] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X10)
| ~ aInteger0(X10) ) )
| ~ aInteger0(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)) ) )
| ~ sP12 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f122,plain,
( ? [X13] :
( ! [X14] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X13,X14),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( ~ aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X18,szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
& sP11(X14,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
| sz00 = X14
| ~ aInteger0(X14) )
& aElementOf0(X13,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ sP13 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f123,plain,
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X23] :
( ~ aElementOf0(X23,cS1395)
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ! [X22] :
( aElementOf0(X22,cS1395)
<=> aInteger0(X22) )
& aSet0(cS1395)
& sP10
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP14 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f124,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP13
& ! [X12] :
( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP12 )
| sP14 )
& ! [X0,X1] :
( sP9(X1)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X1,smndt0(X0))
| ~ aInteger0(X2) ) )
| sP8(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
inference(definition_folding,[],[f105,f123,f122,f121,f120,f119,f118,f117,f116,f115]) ).
fof(f182,plain,
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X23] :
( ~ aElementOf0(X23,cS1395)
& aElementOf0(X23,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ! [X22] :
( ( aElementOf0(X22,cS1395)
| ~ aInteger0(X22) )
& ( aInteger0(X22)
| ~ aElementOf0(X22,cS1395) ) )
& aSet0(cS1395)
& sP10
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP14 ),
inference(nnf_transformation,[],[f123]) ).
fof(f183,plain,
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP10
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP14 ),
inference(rectify,[],[f182]) ).
fof(f184,plain,
( ? [X0] :
( ~ aElementOf0(X0,cS1395)
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ~ aElementOf0(sK29,cS1395)
& aElementOf0(sK29,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
introduced(choice_axiom,[]) ).
fof(f185,plain,
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ~ aElementOf0(sK29,cS1395)
& aElementOf0(sK29,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& sP10
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP14 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f183,f184]) ).
fof(f186,plain,
( ? [X13] :
( ! [X14] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X13,X14),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X18] :
( ~ aElementOf0(X18,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X18,szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
& sP11(X14,X13)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X13,X14)) )
| sz00 = X14
| ~ aInteger0(X14) )
& aElementOf0(X13,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ sP13 ),
inference(nnf_transformation,[],[f122]) ).
fof(f187,plain,
( ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP11(X1,X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ sP13 ),
inference(rectify,[],[f186]) ).
fof(f188,plain,
( ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& sP11(X1,X0)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK30,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK30,X1)) )
& sP11(X1,sK30)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK30,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK30,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ),
introduced(choice_axiom,[]) ).
fof(f189,plain,
! [X1] :
( ? [X2] :
( ~ aElementOf0(X2,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK30,X1)) )
=> ( ~ aElementOf0(sK31(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(sK31(X1),szAzrzSzezqlpdtcmdtrp0(sK30,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f190,plain,
( ( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK30,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(sK31(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(sK31(X1),szAzrzSzezqlpdtcmdtrp0(sK30,X1))
& sP11(X1,sK30)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK30,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK30,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| ~ sP13 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f187,f189,f188]) ).
fof(f191,plain,
( ! [X9] :
( ( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X9,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X9,smndt0(xa)))
& ! [X10] :
( sdtpldt0(X9,smndt0(xa)) != sdtasdt0(xq,X10)
| ~ aInteger0(X10) ) )
| ~ aInteger0(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)) ) )
| ~ sP12 ),
inference(nnf_transformation,[],[f121]) ).
fof(f192,plain,
( ! [X0] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP12 ),
inference(rectify,[],[f191]) ).
fof(f193,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X2) )
=> ( sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK32(X0))
& aInteger0(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
( ! [X0] :
( ( 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) )
& ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK32(X0))
& aInteger0(sK32(X0))
& aInteger0(X0) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP12 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f192,f193]) ).
fof(f195,plain,
! [X14,X13] :
( ! [X15] :
( ( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14))
| ( ~ sdteqdtlpzmzozddtrp0(X15,X13,X14)
& ~ aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ! [X16] :
( sdtpldt0(X15,smndt0(X13)) != sdtasdt0(X14,X16)
| ~ aInteger0(X16) ) )
| ~ aInteger0(X15) )
& ( ( sdteqdtlpzmzozddtrp0(X15,X13,X14)
& aDivisorOf0(X14,sdtpldt0(X15,smndt0(X13)))
& ? [X17] :
( sdtpldt0(X15,smndt0(X13)) = sdtasdt0(X14,X17)
& aInteger0(X17) )
& aInteger0(X15) )
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X13,X14)) ) )
| ~ sP11(X14,X13) ),
inference(nnf_transformation,[],[f120]) ).
fof(f196,plain,
! [X0,X1] :
( ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X2,X1,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X2,smndt0(X1)))
& ! [X3] :
( sdtpldt0(X2,smndt0(X1)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,X1,X0)
& aDivisorOf0(X0,sdtpldt0(X2,smndt0(X1)))
& ? [X4] :
( sdtpldt0(X2,smndt0(X1)) = sdtasdt0(X0,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0)) ) )
| ~ sP11(X0,X1) ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ? [X4] :
( sdtpldt0(X2,smndt0(X1)) = sdtasdt0(X0,X4)
& aInteger0(X4) )
=> ( sdtpldt0(X2,smndt0(X1)) = sdtasdt0(X0,sK33(X0,X1,X2))
& aInteger0(sK33(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
! [X0,X1] :
( ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X2,X1,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X2,smndt0(X1)))
& ! [X3] :
( sdtpldt0(X2,smndt0(X1)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,X1,X0)
& aDivisorOf0(X0,sdtpldt0(X2,smndt0(X1)))
& sdtpldt0(X2,smndt0(X1)) = sdtasdt0(X0,sK33(X0,X1,X2))
& aInteger0(sK33(X0,X1,X2))
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0)) ) )
| ~ sP11(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f196,f197]) ).
fof(f199,plain,
( ! [X19] :
( ( aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X19,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ! [X20] :
( sdtpldt0(X19,smndt0(xa)) != sdtasdt0(xq,X20)
| ~ aInteger0(X20) ) )
| ~ aInteger0(X19) )
& ( ( sdteqdtlpzmzozddtrp0(X19,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X19,smndt0(xa)))
& ? [X21] :
( sdtpldt0(X19,smndt0(xa)) = sdtasdt0(xq,X21)
& aInteger0(X21) )
& aInteger0(X19) )
| ~ aElementOf0(X19,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP10 ),
inference(nnf_transformation,[],[f119]) ).
fof(f200,plain,
( ! [X0] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP10 ),
inference(rectify,[],[f199]) ).
fof(f201,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X2) )
=> ( sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK34(X0))
& aInteger0(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f202,plain,
( ! [X0] :
( ( 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) )
& ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK34(X0))
& aInteger0(sK34(X0))
& aInteger0(X0) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP10 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f200,f201]) ).
fof(f203,plain,
! [X1] :
( ( aElementOf0(X1,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP9(X1) ),
inference(nnf_transformation,[],[f118]) ).
fof(f204,plain,
! [X0] :
( ( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP7
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP9(X0) ),
inference(rectify,[],[f203]) ).
fof(f205,plain,
! [X0] :
( ( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sP6
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f210,plain,
( ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X4] :
( sdtpldt0(X3,smndt0(xa)) != sdtasdt0(xq,X4)
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X5] :
( sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP6 ),
inference(nnf_transformation,[],[f115]) ).
fof(f211,plain,
( ! [X0] :
( ( 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) )
& ( ( 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)) ) )
| ~ sP6 ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(xq,X2) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X2) )
=> ( sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK36(X0))
& aInteger0(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f213,plain,
( ! [X0] :
( ( 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) )
& ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK36(X0))
& aInteger0(sK36(X0))
& aInteger0(X0) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
| ~ sP6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f211,f212]) ).
fof(f214,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP13
& ! [X12] :
( ( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X12) )
& ( ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) )
| ~ aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP12 )
| sP14 )
& ! [X0,X1] :
( sP9(X1)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X1,smndt0(X0))
| ~ aInteger0(X2) ) )
| sP8(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f215,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP13
& ! [X12] :
( ( aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X12) )
& ( ( ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X12) )
| ~ aElementOf0(X12,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP12 )
| sP14 )
& ! [X0,X1] :
( sP9(X1)
| ( ~ sdteqdtlpzmzozddtrp0(X1,X0,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X0)))
& ! [X2] :
( sdtasdt0(xq,X2) != sdtpldt0(X1,smndt0(X0))
| ~ aInteger0(X2) ) )
| sP8(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f214]) ).
fof(f216,plain,
( ( ( ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP13
& ! [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)))
& sP12 )
| sP14 )
& ! [X1,X2] :
( sP9(X2)
| ( ~ sdteqdtlpzmzozddtrp0(X2,X1,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X2,smndt0(X1)))
& ! [X3] :
( sdtasdt0(xq,X3) != sdtpldt0(X2,smndt0(X1))
| ~ aInteger0(X3) ) )
| sP8(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ) ),
inference(rectify,[],[f215]) ).
fof(f322,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f323,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f325,plain,
( sP10
| ~ sP14 ),
inference(cnf_transformation,[],[f185]) ).
fof(f327,plain,
! [X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,cS1395)
| ~ sP14 ),
inference(cnf_transformation,[],[f185]) ).
fof(f328,plain,
! [X1] :
( aElementOf0(X1,cS1395)
| ~ aInteger0(X1)
| ~ sP14 ),
inference(cnf_transformation,[],[f185]) ).
fof(f329,plain,
( aElementOf0(sK29,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP14 ),
inference(cnf_transformation,[],[f185]) ).
fof(f330,plain,
( ~ aElementOf0(sK29,cS1395)
| ~ sP14 ),
inference(cnf_transformation,[],[f185]) ).
fof(f332,plain,
( aElementOf0(sK30,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP13 ),
inference(cnf_transformation,[],[f190]) ).
fof(f334,plain,
! [X1] :
( sP11(X1,sK30)
| sz00 = X1
| ~ aInteger0(X1)
| ~ sP13 ),
inference(cnf_transformation,[],[f190]) ).
fof(f335,plain,
! [X1] :
( aElementOf0(sK31(X1),szAzrzSzezqlpdtcmdtrp0(sK30,X1))
| sz00 = X1
| ~ aInteger0(X1)
| ~ sP13 ),
inference(cnf_transformation,[],[f190]) ).
fof(f336,plain,
! [X1] :
( ~ aElementOf0(sK31(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sz00 = X1
| ~ aInteger0(X1)
| ~ sP13 ),
inference(cnf_transformation,[],[f190]) ).
fof(f338,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP12 ),
inference(cnf_transformation,[],[f194]) ).
fof(f346,plain,
! [X2,X0,X1] :
( aInteger0(X2)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f350,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X2,X1,X0)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,X0))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f354,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP10 ),
inference(cnf_transformation,[],[f202]) ).
fof(f365,plain,
! [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f368,plain,
! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f378,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP6 ),
inference(cnf_transformation,[],[f213]) ).
fof(f388,plain,
! [X2,X1] :
( sP9(X2)
| ~ sdteqdtlpzmzozddtrp0(X2,X1,xq)
| sP8(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f389,plain,
( sP12
| sP14 ),
inference(cnf_transformation,[],[f216]) ).
fof(f391,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP14 ),
inference(cnf_transformation,[],[f216]) ).
fof(f392,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP14 ),
inference(cnf_transformation,[],[f216]) ).
fof(f394,plain,
( sP13
| sP14 ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_153,plain,
sz00 != xq,
inference(cnf_transformation,[],[f323]) ).
cnf(c_154,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f322]) ).
cnf(c_157,plain,
( ~ aElementOf0(sK29,cS1395)
| ~ sP14 ),
inference(cnf_transformation,[],[f330]) ).
cnf(c_158,plain,
( ~ sP14
| aElementOf0(sK29,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f329]) ).
cnf(c_159,plain,
( ~ aInteger0(X0)
| ~ sP14
| aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f328]) ).
cnf(c_160,plain,
( ~ aElementOf0(X0,cS1395)
| ~ sP14
| aInteger0(X0) ),
inference(cnf_transformation,[],[f327]) ).
cnf(c_162,plain,
( ~ sP14
| sP10 ),
inference(cnf_transformation,[],[f325]) ).
cnf(c_165,plain,
( ~ aElementOf0(sK31(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X0)
| ~ sP13
| X0 = sz00 ),
inference(cnf_transformation,[],[f336]) ).
cnf(c_166,plain,
( ~ aInteger0(X0)
| ~ sP13
| X0 = sz00
| aElementOf0(sK31(X0),szAzrzSzezqlpdtcmdtrp0(sK30,X0)) ),
inference(cnf_transformation,[],[f335]) ).
cnf(c_167,plain,
( ~ aInteger0(X0)
| ~ sP13
| X0 = sz00
| sP11(X0,sK30) ),
inference(cnf_transformation,[],[f334]) ).
cnf(c_169,plain,
( ~ sP13
| aElementOf0(sK30,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f332]) ).
cnf(c_177,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP12
| aInteger0(X0) ),
inference(cnf_transformation,[],[f338]) ).
cnf(c_181,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ sP11(X2,X1)
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f350]) ).
cnf(c_185,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ sP11(X2,X1)
| aInteger0(X0) ),
inference(cnf_transformation,[],[f346]) ).
cnf(c_193,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP10
| aInteger0(X0) ),
inference(cnf_transformation,[],[f354]) ).
cnf(c_194,plain,
( ~ sP9(X0)
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f365]) ).
cnf(c_199,plain,
( ~ sP8(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f368]) ).
cnf(c_217,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sP6
| aInteger0(X0) ),
inference(cnf_transformation,[],[f378]) ).
cnf(c_220,negated_conjecture,
( sP14
| sP13 ),
inference(cnf_transformation,[],[f394]) ).
cnf(c_222,negated_conjecture,
( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sP14 ),
inference(cnf_transformation,[],[f392]) ).
cnf(c_223,negated_conjecture,
( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X0)
| sP14 ),
inference(cnf_transformation,[],[f391]) ).
cnf(c_225,negated_conjecture,
( sP14
| sP12 ),
inference(cnf_transformation,[],[f389]) ).
cnf(c_226,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X0,X1,xq)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sP9(X0)
| sP8(X1) ),
inference(cnf_transformation,[],[f388]) ).
cnf(c_361,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_217,c_225,c_162,c_193,c_177]) ).
cnf(c_365,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_193,c_361]) ).
cnf(c_2929,plain,
( aElementOf0(sK30,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sP14 ),
inference(resolution,[status(thm)],[c_220,c_169]) ).
cnf(c_2950,plain,
( ~ aInteger0(X0)
| X0 = sz00
| sP11(X0,sK30)
| sP14 ),
inference(resolution,[status(thm)],[c_220,c_167]) ).
cnf(c_2964,plain,
( ~ aInteger0(X0)
| X0 = sz00
| aElementOf0(sK31(X0),szAzrzSzezqlpdtcmdtrp0(sK30,X0))
| sP14 ),
inference(resolution,[status(thm)],[c_220,c_166]) ).
cnf(c_2978,plain,
( ~ aElementOf0(sK31(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X0)
| X0 = sz00
| sP14 ),
inference(resolution,[status(thm)],[c_220,c_165]) ).
cnf(c_3028,plain,
( X0 != X1
| X2 != sK30
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ~ aInteger0(X0)
| X0 = sz00
| aInteger0(X3)
| sP14 ),
inference(resolution_lifted,[status(thm)],[c_2950,c_185]) ).
cnf(c_3029,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK30,X1))
| ~ aInteger0(X1)
| X1 = sz00
| aInteger0(X0)
| sP14 ),
inference(unflattening,[status(thm)],[c_3028]) ).
cnf(c_3099,plain,
( X0 != X1
| X2 != sK30
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ~ aInteger0(X0)
| X0 = sz00
| sdteqdtlpzmzozddtrp0(X3,X2,X1)
| sP14 ),
inference(resolution_lifted,[status(thm)],[c_2950,c_181]) ).
cnf(c_3100,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK30,X1))
| ~ aInteger0(X1)
| X1 = sz00
| sdteqdtlpzmzozddtrp0(X0,sK30,X1)
| sP14 ),
inference(unflattening,[status(thm)],[c_3099]) ).
cnf(c_22338,plain,
( ~ aElementOf0(sK30,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sP14 ),
inference(superposition,[status(thm)],[c_2929,c_222]) ).
cnf(c_22339,plain,
( aInteger0(sK30)
| sP14 ),
inference(superposition,[status(thm)],[c_2929,c_223]) ).
cnf(c_22510,plain,
( ~ aInteger0(X0)
| X0 = sz00
| aInteger0(sK31(X0))
| sP14 ),
inference(superposition,[status(thm)],[c_2964,c_3029]) ).
cnf(c_22567,plain,
( ~ sP14
| aInteger0(sK29) ),
inference(superposition,[status(thm)],[c_158,c_365]) ).
cnf(c_22614,plain,
( ~ aInteger0(X0)
| X0 = sz00
| sdteqdtlpzmzozddtrp0(sK31(X0),sK30,X0)
| sP14 ),
inference(superposition,[status(thm)],[c_2964,c_3100]) ).
cnf(c_22628,plain,
( ~ aInteger0(sK31(xq))
| ~ aInteger0(xq)
| ~ aInteger0(sK30)
| sz00 = xq
| sP9(sK31(xq))
| sP8(sK30)
| sP14 ),
inference(superposition,[status(thm)],[c_22614,c_226]) ).
cnf(c_22629,plain,
( ~ aInteger0(sK31(xq))
| ~ aInteger0(sK30)
| sP9(sK31(xq))
| sP8(sK30)
| sP14 ),
inference(forward_subsumption_resolution,[status(thm)],[c_22628,c_153,c_154]) ).
cnf(c_22635,plain,
( ~ aInteger0(sK31(xq))
| sP9(sK31(xq))
| sP8(sK30)
| sP14 ),
inference(global_subsumption_just,[status(thm)],[c_22629,c_22339,c_22629]) ).
cnf(c_22645,plain,
( ~ aInteger0(xq)
| sz00 = xq
| sP9(sK31(xq))
| sP8(sK30)
| sP14 ),
inference(superposition,[status(thm)],[c_22510,c_22635]) ).
cnf(c_22646,plain,
( sP9(sK31(xq))
| sP8(sK30)
| sP14 ),
inference(forward_subsumption_resolution,[status(thm)],[c_22645,c_153,c_154]) ).
cnf(c_22700,plain,
( ~ aInteger0(sK29)
| ~ sP14 ),
inference(superposition,[status(thm)],[c_159,c_157]) ).
cnf(c_22703,plain,
~ sP14,
inference(global_subsumption_just,[status(thm)],[c_160,c_22567,c_22700]) ).
cnf(c_22714,plain,
~ aElementOf0(sK30,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(backward_subsumption_resolution,[status(thm)],[c_22338,c_22703]) ).
cnf(c_22719,plain,
( ~ aElementOf0(sK31(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aInteger0(X0)
| X0 = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[c_2978,c_22703]) ).
cnf(c_22806,plain,
( sP8(sK30)
| sP9(sK31(xq)) ),
inference(global_subsumption_just,[status(thm)],[c_22646,c_22646,c_22703]) ).
cnf(c_22807,plain,
( sP9(sK31(xq))
| sP8(sK30) ),
inference(renaming,[status(thm)],[c_22806]) ).
cnf(c_22862,plain,
~ sP8(sK30),
inference(superposition,[status(thm)],[c_199,c_22714]) ).
cnf(c_22867,plain,
sP9(sK31(xq)),
inference(backward_subsumption_resolution,[status(thm)],[c_22807,c_22862]) ).
cnf(c_23203,plain,
( ~ sP9(sK31(X0))
| ~ aInteger0(X0)
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_194,c_22719]) ).
cnf(c_23632,plain,
( ~ aInteger0(xq)
| sz00 = xq ),
inference(superposition,[status(thm)],[c_22867,c_23203]) ).
cnf(c_23633,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23632,c_153,c_154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM444+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:00:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.75/1.16 % SZS status Started for theBenchmark.p
% 3.75/1.16 % SZS status Theorem for theBenchmark.p
% 3.75/1.16
% 3.75/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.75/1.16
% 3.75/1.16 ------ iProver source info
% 3.75/1.16
% 3.75/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.75/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.75/1.16 git: non_committed_changes: false
% 3.75/1.16 git: last_make_outside_of_git: false
% 3.75/1.16
% 3.75/1.16 ------ Parsing...
% 3.75/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.75/1.16
% 3.75/1.16 ------ 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: 2 0s sf_e pe_s pe_e
% 3.75/1.16
% 3.75/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.75/1.16
% 3.75/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.16 ------ Proving...
% 3.75/1.16 ------ Problem Properties
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16 clauses 156
% 3.75/1.16 conjectures 9
% 3.75/1.16 EPR 33
% 3.75/1.16 Horn 99
% 3.75/1.16 unary 5
% 3.75/1.16 binary 38
% 3.75/1.16 lits 557
% 3.75/1.16 lits eq 73
% 3.75/1.16 fd_pure 0
% 3.75/1.16 fd_pseudo 0
% 3.75/1.16 fd_cond 28
% 3.75/1.16 fd_pseudo_cond 9
% 3.75/1.16 AC symbols 0
% 3.75/1.16
% 3.75/1.16 ------ Schedule dynamic 5 is on
% 3.75/1.16
% 3.75/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16 ------
% 3.75/1.16 Current options:
% 3.75/1.16 ------
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16 ------ Proving...
% 3.75/1.16
% 3.75/1.16
% 3.75/1.16 % SZS status Theorem for theBenchmark.p
% 3.75/1.16
% 3.75/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.16
% 3.75/1.17
%------------------------------------------------------------------------------