%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM442+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:24:28 PM UTC 2026
% Result : Theorem 15.06s 2.83s
% Output : CNFRefutation 15.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 135 ( 12 unt; 5 def)
% Number of atoms : 1015 ( 128 equ)
% Maximal formula atoms : 56 ( 7 avg)
% Number of connectives : 1335 ( 455 ~; 459 |; 356 &)
% ( 18 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 15 ( 13 usr; 5 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 279 ( 0 sgn 226 !; 53 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
=> sdteqdtlpzmzozddtrp0(X1,X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( ( aInteger0(X3)
& X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X3,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) )
=> sdteqdtlpzmzozddtrp0(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
fof(f34,axiom,
! [X0,X1] :
( ( X1 != sz00
& aInteger0(X1)
& aInteger0(X0) )
=> ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(f41,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1962) ).
fof(f42,conjecture,
( ( ! [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ( ( ! [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,
~ ( ( ! [X5] :
( ( ( ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
| ? [X7] :
( sdtpldt0(X5,smndt0(xa)) = sdtasdt0(xq,X7)
& aInteger0(X7) ) )
& aInteger0(X5) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ? [X6] :
( sdtasdt0(xq,X6) = sdtpldt0(X5,smndt0(xa))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ( ! [X8] :
( aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
=> ( isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X9] :
( aElementOf0(X9,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
=> ? [X10] :
( ( ( ! [X11] :
( ( ( ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
| aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
| ? [X13] :
( sdtpldt0(X11,smndt0(X9)) = sdtasdt0(X10,X13)
& aInteger0(X13) ) )
& aInteger0(X11) )
=> aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& ( aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
=> ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
& aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ? [X12] :
( sdtasdt0(X10,X12) = sdtpldt0(X11,smndt0(X9))
& aInteger0(X12) )
& aInteger0(X11) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ! [X14] :
( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X9,X10))
=> aElementOf0(X14,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
& sz00 != X10
& aInteger0(X10) ) ) ) ) ) )
& ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X2] :
( sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,X2)
& 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) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X3] :
( aElementOf0(X3,cS1395)
<=> aInteger0(X3) )
& aSet0(cS1395) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
| ! [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> aElementOf0(X4,cS1395) ) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f48,plain,
( ( ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X5,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ? [X6] :
( sdtasdt0(xq,X6) = sdtpldt0(X5,smndt0(xa))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X8] :
( aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X9] :
( aElementOf0(X9,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X10] :
( ( ! [X11] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X11,X9,X10)
& ~ aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ! [X13] :
( sdtpldt0(X11,smndt0(X9)) != sdtasdt0(X10,X13)
| ~ aInteger0(X13) ) )
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& ( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
| ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
& aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ? [X12] :
( sdtasdt0(X10,X12) = sdtpldt0(X11,smndt0(X9))
& aInteger0(X12) )
& aInteger0(X11) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X14] :
( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aElementOf0(X14,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X10
| ~ aInteger0(X10) ) ) )
| ( ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( aElementOf0(X3,cS1395)
<=> aInteger0(X3) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X4,cS1395) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f49,plain,
( ( ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X5,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ? [X6] :
( sdtasdt0(xq,X6) = sdtpldt0(X5,smndt0(xa))
& aInteger0(X6) )
& aInteger0(X5) ) ) )
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X8] :
( aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X9] :
( aElementOf0(X9,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X10] :
( ( ! [X11] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X11,X9,X10)
& ~ aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ! [X13] :
( sdtpldt0(X11,smndt0(X9)) != sdtasdt0(X10,X13)
| ~ aInteger0(X13) ) )
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& ( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
| ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
& aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ? [X12] :
( sdtasdt0(X10,X12) = sdtpldt0(X11,smndt0(X9))
& aInteger0(X12) )
& aInteger0(X11) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X14] :
( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aElementOf0(X14,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X10
| ~ aInteger0(X10) ) ) )
| ( ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( aElementOf0(X3,cS1395)
<=> aInteger0(X3) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X4,cS1395) ) ) ),
inference(flattening,[],[f48]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(flattening,[],[f63]) ).
fof(f86,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f87,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f86]) ).
fof(f95,plain,
( ~ sP4
| ( sP1
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& ( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP2 ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f96,plain,
( ~ sP4
| ( sP1
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X8] :
( ( ~ aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& ( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X8)
| aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP2 ) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
( ~ sP4
| ( sP1
& ~ 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)))
& sP2 ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
( ~ sP3
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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(nnf_transformation,[],[f92]) ).
fof(f99,plain,
( ~ sP3
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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,sK5(X0))
& aInteger0(sK5(X0))
& aInteger0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f98]) ).
fof(f100,plain,
( ~ sP2
| ? [X9] :
( aElementOf0(X9,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X10] :
( ( sP0(X9,X10)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X14] :
( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aElementOf0(X14,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X10
| ~ aInteger0(X10) ) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f101,plain,
( ~ sP2
| ? [X0] :
( aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( ( sP0(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,[],[f100]) ).
fof(f102,plain,
( ~ sP2
| ( aElementOf0(sK6,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X1] :
( ( sP0(sK6,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK6,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK6,X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(sK7(X1),szAzrzSzezqlpdtcmdtrp0(sK6,X1))
& ~ aElementOf0(sK7(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) )
| sz00 = X1
| ~ aInteger0(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X2,sK7(X1))],[f101]) ).
fof(f103,plain,
( ~ sP1
| ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X5,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ? [X6] :
( sdtasdt0(xq,X6) = sdtpldt0(X5,smndt0(xa))
& aInteger0(X6) )
& aInteger0(X5) ) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f104,plain,
( ~ sP1
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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,[],[f103]) ).
fof(f105,plain,
( ~ sP1
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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,sK8(X0))
& aInteger0(sK8(X0))
& aInteger0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f104]) ).
fof(f109,plain,
( sP4
| ( sP3
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( ~ aElementOf0(X3,cS1395)
| aInteger0(X3) )
& ( ~ aInteger0(X3)
| aElementOf0(X3,cS1395) ) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X4,cS1395) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f110,plain,
( sP4
| ( sP3
& 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,[],[f109]) ).
fof(f111,plain,
( sP4
| ( sP3
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X1] :
( ( ~ aElementOf0(X1,cS1395)
| aInteger0(X1) )
& ( ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& aElementOf0(sK10,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(sK10,cS1395) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f110]) ).
fof(f129,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f130,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aInteger0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ! [X2] :
( ( szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdteqdtlpzmzozddtrp0(X4,X0,X1)
& aInteger0(X4) ) )
& ( ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK16(X0,X1,X2),X2)
| ( sdteqdtlpzmzozddtrp0(sK16(X0,X1,X2),X0,X1)
& aInteger0(sK16(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK16(X0,X1,X2),X2)
| ~ sdteqdtlpzmzozddtrp0(sK16(X0,X1,X2),X0,X1)
| ~ aInteger0(sK16(X0,X1,X2)) ) )
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1,X2))],[f131]) ).
fof(f133,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f134,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f135,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f41]) ).
fof(f136,plain,
( ~ sP4
| sP1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f138,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f139,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f140,plain,
! [X0] :
( ~ sP4
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f143,plain,
( ~ sP4
| sP2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f147,plain,
! [X0] :
( ~ sP3
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ),
inference(cnf_transformation,[],[f99]) ).
fof(f151,plain,
! [X0] :
( ~ sP3
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f152,plain,
( ~ sP2
| aElementOf0(sK6,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f102]) ).
fof(f153,plain,
! [X1] :
( ~ sP2
| sP0(sK6,X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
! [X1] :
( ~ sP2
| aElementOf0(sK7(X1),szAzrzSzezqlpdtcmdtrp0(sK6,X1))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f157,plain,
! [X1] :
( ~ sP2
| ~ aElementOf0(sK7(X1),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f161,plain,
! [X0] :
( ~ sP1
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ),
inference(cnf_transformation,[],[f105]) ).
fof(f165,plain,
! [X0] :
( ~ sP1
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f174,plain,
( sP4
| sP3 ),
inference(cnf_transformation,[],[f111]) ).
fof(f177,plain,
! [X1] :
( sP4
| ~ aInteger0(X1)
| aElementOf0(X1,cS1395) ),
inference(cnf_transformation,[],[f111]) ).
fof(f180,plain,
( sP4
| aElementOf0(sK10,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f181,plain,
( sP4
| ~ aElementOf0(sK10,cS1395) ),
inference(cnf_transformation,[],[f111]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f201,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f233,plain,
! [X2,X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f248,plain,
! [X0,X1,X4] :
( sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ),
inference(equality_resolution,[],[f233]) ).
tcf(c_49,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f135]) ).
tcf(c_50,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f134]) ).
tcf(c_51,plain,
xq != sz00,
inference(cnf_transformation,[],[f133]) ).
tcf(c_52,plain,
( sP2
| ~ sP4 ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_55,plain,
! [X0: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP4
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_56,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP4
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_57,plain,
! [X0: $i] :
( ~ sP4
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_59,plain,
( sP1
| ~ sP4 ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_60,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP3
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_64,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ sP3
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP2
| ~ aInteger0(X0)
| ~ aElementOf0(sK7(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_69,plain,
! [X0: $i] :
( aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(sK6,X0))
| ( X0 = sz00 )
| ~ sP2
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_72,plain,
! [X0: $i] :
( sP0(sK6,X0)
| ( X0 = sz00 )
| ~ sP2
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_73,plain,
( aElementOf0(sK6,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP2 ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_74,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ sP1
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_78,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ sP1
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_90,negated_conjecture,
( sP4
| ~ aElementOf0(sK10,cS1395) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_91,negated_conjecture,
( sP4
| aElementOf0(sK10,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_94,negated_conjecture,
! [X0: $i] :
( sP4
| aElementOf0(X0,cS1395)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_97,negated_conjecture,
( sP3
| sP4 ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ( X2 = sz00 )
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_231,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_97,c_59,c_74,c_60]) ).
tcf(c_233,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_231]) ).
tcf(c_235,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_78,c_97,c_59,c_78,c_64]) ).
tcf(c_238,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_235]) ).
tcf(c_1722,plain,
( aElementOf0(sK6,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP4 ),
inference(resolution,[status(thm)],[c_52,c_73]) ).
tcf(c_1729,plain,
! [X0: $i] :
( sP0(sK6,X0)
| ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[c_52,c_72]) ).
tcf(c_1771,plain,
! [X0: $i] :
( aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(sK6,X0))
| ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[c_52,c_69]) ).
tcf(c_1772,plain,
( aElementOf0(sK7(xq),szAzrzSzezqlpdtcmdtrp0(sK6,xq))
| ( xq = sz00 )
| ~ sP4
| ~ aInteger0(xq) ),
inference(instantiation,[status(thm)],[c_1771]) ).
tcf(c_1785,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0)
| ~ aElementOf0(sK7(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(resolution,[status(thm)],[c_52,c_68]) ).
tcf(c_1786,plain,
( ( xq = sz00 )
| ~ sP4
| ~ aInteger0(xq)
| ~ aElementOf0(sK7(xq),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(instantiation,[status(thm)],[c_1785]) ).
tcf(c_13307,plain,
( sP4
| ~ aInteger0(sK10) ),
inference(superposition,[status(thm)],[c_94,c_90]) ).
tcf(c_13325,plain,
( sP4
| aInteger0(sK10) ),
inference(superposition,[status(thm)],[c_91,c_233]) ).
tcf(c_13328,plain,
sP4,
inference(global_subsumption_just,[status(thm)],[c_13325,c_13307,c_13325]) ).
tcf(c_13350,plain,
aElementOf0(sK6,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))),
inference(global_subsumption_just,[status(thm)],[c_1722,c_1722,c_13328]) ).
tcf(c_13660,plain,
! [X0: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_56,c_13307,c_13325]) ).
tcf(c_13666,plain,
aInteger0(sK6),
inference(superposition,[status(thm)],[c_13350,c_13660]) ).
tcf(c_13799,plain,
! [X0: $i] :
( aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(sK7(X0),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP4
| ~ aInteger0(sK7(X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_13800,plain,
( aElementOf0(sK7(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(sK7(xq),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ sP4
| ~ aInteger0(sK7(xq)) ),
inference(instantiation,[status(thm)],[c_13799]) ).
tcf(c_14135,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(xa,X0,xq) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_14365,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,sK6,X2)
| ( X2 = sz00 )
| ~ aInteger0(sK6)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,sK6,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_14380,plain,
! [X0: $i] :
( ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_57,c_13307,c_13325]) ).
tcf(c_14381,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aElementOf0(X0,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ),
inference(renaming,[status(thm)],[c_14380]) ).
tcf(c_14387,plain,
~ aElementOf0(sK6,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(superposition,[status(thm)],[c_13350,c_14381]) ).
tcf(c_15002,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(xa,X0,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_17192,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,sK6,X1)
| ( X1 = sz00 )
| ~ aInteger0(sK6)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sK7(X1))
| ~ sdteqdtlpzmzozddtrp0(sK7(X1),sK6,X1)
| ~ sdteqdtlpzmzozddtrp0(X0,sK7(X1),X1) ),
inference(instantiation,[status(thm)],[c_14365]) ).
tcf(c_17361,plain,
( ( xq = sz00 )
| ~ aInteger0(sK6)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ sdteqdtlpzmzozddtrp0(sK6,xa,xq) ),
inference(superposition,[status(thm)],[c_151,c_14387]) ).
tcf(c_17363,plain,
~ sdteqdtlpzmzozddtrp0(sK6,xa,xq),
inference(forward_subsumption_resolution,[status(thm)],[c_17361,c_51,c_13666,c_50,c_49]) ).
tcf(c_18042,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(sK7(X0),xa,xq)
| ~ aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_18045,plain,
( sdteqdtlpzmzozddtrp0(sK7(xq),xa,xq)
| ~ aElementOf0(sK7(xq),szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(instantiation,[status(thm)],[c_18042]) ).
tcf(c_18857,plain,
( sdteqdtlpzmzozddtrp0(sK6,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(sK6)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ sdteqdtlpzmzozddtrp0(xa,sK6,xq) ),
inference(instantiation,[status(thm)],[c_14135]) ).
tcf(c_23183,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(xa,sK7(X0),xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(sK7(X0))
| ~ sdteqdtlpzmzozddtrp0(sK7(X0),xa,xq) ),
inference(instantiation,[status(thm)],[c_15002]) ).
tcf(c_23189,plain,
( sdteqdtlpzmzozddtrp0(xa,sK7(xq),xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(sK7(xq))
| ~ sdteqdtlpzmzozddtrp0(sK7(xq),xa,xq) ),
inference(instantiation,[status(thm)],[c_23183]) ).
tcf(c_33069,plain,
( sdteqdtlpzmzozddtrp0(xa,sK6,xq)
| ( xq = sz00 )
| ~ aInteger0(sK6)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(sK7(xq))
| ~ sdteqdtlpzmzozddtrp0(xa,sK7(xq),xq)
| ~ sdteqdtlpzmzozddtrp0(sK7(xq),sK6,xq) ),
inference(instantiation,[status(thm)],[c_17192]) ).
fof(f89,definition,
! [X9,X10] :
( ~ sP0(X9,X10)
| ! [X11] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X11,X9,X10)
& ~ aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ! [X13] :
( sdtpldt0(X11,smndt0(X9)) != sdtasdt0(X10,X13)
| ~ aInteger0(X13) ) )
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& ( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
| ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
& aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ? [X12] :
( sdtasdt0(X10,X12) = sdtpldt0(X11,smndt0(X9))
& aInteger0(X12) )
& aInteger0(X11) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f90,definition,
( ~ sP1
| ! [X5] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X5,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ! [X7] :
( sdtpldt0(X5,smndt0(xa)) != sdtasdt0(xq,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X5)
| aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X5,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X5,smndt0(xa)))
& ? [X6] :
( sdtasdt0(xq,X6) = sdtpldt0(X5,smndt0(xa))
& aInteger0(X6) )
& aInteger0(X5) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f91,definition,
( ~ sP2
| ? [X9] :
( aElementOf0(X9,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ! [X10] :
( ( sP0(X9,X10)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X9,X10),stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X14] :
( aElementOf0(X14,szAzrzSzezqlpdtcmdtrp0(X9,X10))
& ~ aElementOf0(X14,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) )
| sz00 = X10
| ~ aInteger0(X10) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f92,definition,
( ~ sP3
| ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ 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) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f93,definition,
( ~ sP4
| ( sP1
& ~ isClosed0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X8] :
( aElementOf0(X8,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
<=> ( ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aInteger0(X8) ) )
& aSet0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ isOpen0(stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f94,plain,
( sP4
| ( sP3
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( aElementOf0(X3,cS1395)
<=> aInteger0(X3) )
& aSet0(cS1395)
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(xa,xq),cS1395)
& ? [X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(X4,cS1395) ) ) ),
inference(definition_folding,[],[f49,f93,f92,f91,f90,f89]) ).
fof(f106,plain,
! [X9,X10] :
( ~ sP0(X9,X10)
| ! [X11] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X11,X9,X10)
& ~ aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ! [X13] :
( sdtpldt0(X11,smndt0(X9)) != sdtasdt0(X10,X13)
| ~ aInteger0(X13) ) )
| ~ aInteger0(X11)
| aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10)) )
& ( ~ aElementOf0(X11,szAzrzSzezqlpdtcmdtrp0(X9,X10))
| ( sdteqdtlpzmzozddtrp0(X11,X9,X10)
& aDivisorOf0(X10,sdtpldt0(X11,smndt0(X9)))
& ? [X12] :
( sdtasdt0(X10,X12) = sdtpldt0(X11,smndt0(X9))
& aInteger0(X12) )
& aInteger0(X11) ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f107,plain,
! [X0,X1] :
( ~ sP0(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,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sP0(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,sK9(X0,X1,X2))
& aInteger0(sK9(X0,X1,X2))
& aInteger0(X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f107]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X0)
| ~ sP0(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sP0(X1,X2)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_2041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X3,X2,X1)
| ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ( X2 != sK6 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1729,c_86]) ).
tcf(c_2042,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,sK6,X1)
| ( X1 = sz00 )
| ~ sP4
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK6,X1)) ),
inference(unflattening,[status(thm)],[c_2041]) ).
tcf(c_2113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aInteger0(X3)
| ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| ( X2 != sK6 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1729,c_82]) ).
tcf(c_2114,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ( X1 = sz00 )
| ~ sP4
| ~ aInteger0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sK6,X1)) ),
inference(unflattening,[status(thm)],[c_2113]) ).
tcf(c_13937,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(sK7(X0),sK6,X0)
| ( X0 = sz00 )
| ~ sP4
| ~ aInteger0(X0)
| ~ aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(sK6,X0)) ),
inference(instantiation,[status(thm)],[c_2042]) ).
tcf(c_13938,plain,
( sdteqdtlpzmzozddtrp0(sK7(xq),sK6,xq)
| ( xq = sz00 )
| ~ sP4
| ~ aInteger0(xq)
| ~ aElementOf0(sK7(xq),szAzrzSzezqlpdtcmdtrp0(sK6,xq)) ),
inference(instantiation,[status(thm)],[c_13937]) ).
tcf(c_14878,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK7(X0))
| ( X1 = sz00 )
| ~ sP4
| ~ aInteger0(X1)
| ~ aElementOf0(sK7(X0),szAzrzSzezqlpdtcmdtrp0(sK6,X1)) ),
inference(instantiation,[status(thm)],[c_2114]) ).
tcf(c_14889,plain,
( aInteger0(sK7(xq))
| ( xq = sz00 )
| ~ sP4
| ~ aInteger0(xq)
| ~ aElementOf0(sK7(xq),szAzrzSzezqlpdtcmdtrp0(sK6,xq)) ),
inference(instantiation,[status(thm)],[c_14878]) ).
tcf(c_33075,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33069,c_23189,c_18857,c_18045,c_17363,c_14889,c_13938,c_13800,c_13666,c_13328,c_1786,c_1772,c_51,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM442+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:03:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 15.06/2.83 % SZS status Started for theBenchmark.p
% 15.06/2.83 % SZS status Theorem for theBenchmark.p
% 15.06/2.83
% 15.06/2.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.06/2.83
% 15.06/2.83 % ------ iProver source info
% 15.06/2.83
% 15.06/2.83 % git: date: 2026-07-19 20:42:38 +0200
% 15.06/2.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.06/2.83 % git: non_committed_changes: false
% 15.06/2.83
% 15.06/2.83 % ------ Parsing...
% 15.06/2.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.06/2.83
% 15.06/2.83 % ------ 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 %
% 15.06/2.83
% 15.06/2.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.06/2.83
% 15.06/2.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.06/2.83 % ------ Proving...
% 15.06/2.83 % ------ Problem Properties
% 15.06/2.83
% 15.06/2.83 %
% 15.06/2.83 % clauses 95
% 15.06/2.83 % conjectures 7
% 15.06/2.83 % EPR 16
% 15.06/2.83 % Horn 54
% 15.06/2.83 % unary 5
% 15.06/2.83 % binary 24
% 15.06/2.83 % lits 346
% 15.06/2.83 % lits eq 63
% 15.06/2.83 % fd_pure 0
% 15.06/2.83 % fd_pseudo 0
% 15.06/2.83 % fd_cond 26
% 15.06/2.83 % fd_pseudo_cond 6
% 15.06/2.83 % AC symbols 0
% 15.06/2.83
% 15.06/2.83 % ------ Schedule dynamic 5 is on
% 15.06/2.83
% 15.06/2.83 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.06/2.83
% 15.06/2.83
% 15.06/2.83 % ------
% 15.06/2.83 % Current options:
% 15.06/2.83 % ------
% 15.06/2.83
% 15.06/2.83
% 15.06/2.83 %
% 15.06/2.83
% 15.06/2.83 % ------ Proving...
% 15.06/2.83 %
% 15.06/2.83
% 15.06/2.83 % SZS status Theorem for theBenchmark.p
% 15.06/2.83
% 15.06/2.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.06/2.84
% 15.06/2.84
%------------------------------------------------------------------------------