%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM438+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:11 PM UTC 2026
% Result : Theorem 7.01s 2.62s
% Output : Refutation 12.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 17
% Syntax : Number of formulae : 171 ( 22 unt; 11 def)
% Number of atoms : 1257 ( 196 equ)
% Maximal formula atoms : 54 ( 7 avg)
% Number of connectives : 1578 ( 492 ~; 557 |; 457 &)
% ( 28 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 7 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 341 ( 0 sgn 284 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f17,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModMul) ).
fof(f34,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1)
& X1 != sz00 )
=> ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(f38,axiom,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xB)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,cS1395) )
& aSubsetOf0(xB,cS1395)
& ! [X0] :
( aElementOf0(X0,xA)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,xA) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),xA) ) )
& isOpen0(xA)
& ! [X0] :
( aElementOf0(X0,xB)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,xB) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),xB) ) )
& isOpen0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(f39,conjecture,
( ( aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,sdtslmnbsdt0(xA,xB)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sdtslmnbsdt0(xA,xB)) ) ) ) )
| isOpen0(sdtslmnbsdt0(xA,xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ( aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,sdtslmnbsdt0(xA,xB)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sdtslmnbsdt0(xA,xB)) ) ) ) )
| isOpen0(sdtslmnbsdt0(xA,xB)) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f47,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,xB)
=> aElementOf0(X3,cS1395) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( aElementOf0(X4,xA)
=> ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5))
=> ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(X4)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& sdteqdtlpzmzozddtrp0(X6,X4,X5) ) )
& ( ( aInteger0(X6)
& ( ? [X8] :
( aInteger0(X8)
& sdtpldt0(X6,smndt0(X4)) = sdtasdt0(X5,X8) )
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
| sdteqdtlpzmzozddtrp0(X6,X4,X5) ) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) ) )
& ! [X9] :
( aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X4,X5))
=> aElementOf0(X9,xA) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) ) )
& isOpen0(xA)
& ! [X10] :
( aElementOf0(X10,xB)
=> ? [X11] :
( aInteger0(X11)
& sz00 != X11
& aSet0(szAzrzSzezqlpdtcmdtrp0(X10,X11))
& ! [X12] :
( ( aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11))
=> ( aInteger0(X12)
& ? [X13] :
( aInteger0(X13)
& sdtasdt0(X11,X13) = sdtpldt0(X12,smndt0(X10)) )
& aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& sdteqdtlpzmzozddtrp0(X12,X10,X11) ) )
& ( ( aInteger0(X12)
& ( ? [X14] :
( aInteger0(X14)
& sdtpldt0(X12,smndt0(X10)) = sdtasdt0(X11,X14) )
| aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
| sdteqdtlpzmzozddtrp0(X12,X10,X11) ) )
=> aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11)) ) )
& ! [X15] :
( aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X10,X11))
=> aElementOf0(X15,xB) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,X11),xB) ) )
& isOpen0(xB) ),
inference(rectify,[],[f38]) ).
fof(f48,plain,
~ ( ( aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtslmnbsdt0(xA,xB))
=> ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X5] :
( aInteger0(X5)
& sdtpldt0(X3,smndt0(X1)) = sdtasdt0(X2,X5) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ) )
=> ( ! [X6] :
( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X6,sdtslmnbsdt0(xA,xB)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB)) ) ) ) )
| isOpen0(sdtslmnbsdt0(xA,xB)) ) ),
inference(rectify,[],[f40]) ).
fof(f52,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f52]) ).
fof(f69,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f69]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X3) )
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3)
| sz00 = X3 ),
inference(ennf_transformation,[],[f23]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X3) )
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3)
| sz00 = X3 ),
inference(flattening,[],[f80]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(ennf_transformation,[],[f34]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(flattening,[],[f91]) ).
fof(f97,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(X4)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& sdteqdtlpzmzozddtrp0(X6,X4,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(X4)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& ~ sdteqdtlpzmzozddtrp0(X6,X4,X5) ) ) )
& ! [X9] :
( aElementOf0(X9,xA)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X10] :
( ? [X11] :
( aInteger0(X11)
& sz00 != X11
& aSet0(szAzrzSzezqlpdtcmdtrp0(X10,X11))
& ! [X12] :
( ( ( aInteger0(X12)
& ? [X13] :
( aInteger0(X13)
& sdtasdt0(X11,X13) = sdtpldt0(X12,smndt0(X10)) )
& aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& sdteqdtlpzmzozddtrp0(X12,X10,X11) )
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& ( aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11))
| ~ aInteger0(X12)
| ( ! [X14] :
( ~ aInteger0(X14)
| sdtpldt0(X12,smndt0(X10)) != sdtasdt0(X11,X14) )
& ~ aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& ~ sdteqdtlpzmzozddtrp0(X12,X10,X11) ) ) )
& ! [X15] :
( aElementOf0(X15,xB)
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,X11),xB) )
| ~ aElementOf0(X10,xB) )
& isOpen0(xB) ),
inference(ennf_transformation,[],[f47]) ).
fof(f98,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(X4)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& sdteqdtlpzmzozddtrp0(X6,X4,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(X4)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& ~ sdteqdtlpzmzozddtrp0(X6,X4,X5) ) ) )
& ! [X9] :
( aElementOf0(X9,xA)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X10] :
( ? [X11] :
( aInteger0(X11)
& sz00 != X11
& aSet0(szAzrzSzezqlpdtcmdtrp0(X10,X11))
& ! [X12] :
( ( ( aInteger0(X12)
& ? [X13] :
( aInteger0(X13)
& sdtasdt0(X11,X13) = sdtpldt0(X12,smndt0(X10)) )
& aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& sdteqdtlpzmzozddtrp0(X12,X10,X11) )
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& ( aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11))
| ~ aInteger0(X12)
| ( ! [X14] :
( ~ aInteger0(X14)
| sdtpldt0(X12,smndt0(X10)) != sdtasdt0(X11,X14) )
& ~ aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& ~ sdteqdtlpzmzozddtrp0(X12,X10,X11) ) ) )
& ! [X15] :
( aElementOf0(X15,xB)
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,X11),xB) )
| ~ aElementOf0(X10,xB) )
& isOpen0(xB) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
( ? [X1] :
( ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ( ? [X6] :
( ~ aElementOf0(X6,sdtslmnbsdt0(xA,xB))
& aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X3,smndt0(X1)) != sdtasdt0(X2,X5) )
& ~ aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ~ sdteqdtlpzmzozddtrp0(X3,X1,X2) ) ) ) ) )
& aElementOf0(X1,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f100,plain,
( ? [X1] :
( ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ( ? [X6] :
( ~ aElementOf0(X6,sdtslmnbsdt0(xA,xB))
& aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X3,smndt0(X1)) != sdtasdt0(X2,X5) )
& ~ aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ~ sdteqdtlpzmzozddtrp0(X3,X1,X2) ) ) ) ) )
& aElementOf0(X1,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) ),
inference(flattening,[],[f99]) ).
fof(f110,definition,
! [X10,X11] :
( ! [X12] :
( ( ( aInteger0(X12)
& ? [X13] :
( aInteger0(X13)
& sdtasdt0(X11,X13) = sdtpldt0(X12,smndt0(X10)) )
& aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& sdteqdtlpzmzozddtrp0(X12,X10,X11) )
| ~ aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& ( aElementOf0(X12,szAzrzSzezqlpdtcmdtrp0(X10,X11))
| ~ aInteger0(X12)
| ( ! [X14] :
( ~ aInteger0(X14)
| sdtpldt0(X12,smndt0(X10)) != sdtasdt0(X11,X14) )
& ~ aDivisorOf0(X11,sdtpldt0(X12,smndt0(X10)))
& ~ sdteqdtlpzmzozddtrp0(X12,X10,X11) ) ) )
| ~ sP6(X10,X11) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f111,definition,
! [X4,X5] :
( ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(X4)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& sdteqdtlpzmzozddtrp0(X6,X4,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(X4)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(X4)))
& ~ sdteqdtlpzmzozddtrp0(X6,X4,X5) ) ) )
| ~ sP7(X4,X5) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f112,plain,
( aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( aElementOf0(X2,cS1395)
<=> aInteger0(X2) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sP7(X4,X5)
& ! [X9] :
( aElementOf0(X9,xA)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X10] :
( ? [X11] :
( aInteger0(X11)
& sz00 != X11
& aSet0(szAzrzSzezqlpdtcmdtrp0(X10,X11))
& sP6(X10,X11)
& ! [X15] :
( aElementOf0(X15,xB)
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,X11),xB) )
| ~ aElementOf0(X10,xB) )
& isOpen0(xB) ),
inference(definition_folding,[],[f98,f111,f110]) ).
fof(f113,definition,
! [X1,X2] :
( ! [X3] :
( ( ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X3,smndt0(X1)) != sdtasdt0(X2,X5) )
& ~ aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ~ sdteqdtlpzmzozddtrp0(X3,X1,X2) ) ) )
| ~ sP8(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f114,plain,
( ? [X1] :
( ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ( ? [X6] :
( ~ aElementOf0(X6,sdtslmnbsdt0(xA,xB))
& aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& sP8(X1,X2) ) )
& aElementOf0(X1,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
<=> ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) ) ) ),
inference(definition_folding,[],[f100,f113]) ).
fof(f151,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| ~ aElementOf0(X3,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(nnf_transformation,[],[f92]) ).
fof(f152,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| ~ aElementOf0(X3,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1) )
& ( ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X0,X1) )
| ~ aElementOf0(X4,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(rectify,[],[f152]) ).
fof(f154,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aInteger0(sK19(X0,X1,X2))
| ~ sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1)
| ~ aElementOf0(sK19(X0,X1,X2),X2) )
& ( ( aInteger0(sK19(X0,X1,X2))
& sdteqdtlpzmzozddtrp0(sK19(X0,X1,X2),X0,X1) )
| aElementOf0(sK19(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1) )
& ( ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X0,X1) )
| ~ aElementOf0(X4,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1,X2))],[f153]) ).
fof(f166,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sP7(X4,X5)
& ! [X9] :
( aElementOf0(X9,xA)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X10] :
( ? [X11] :
( aInteger0(X11)
& sz00 != X11
& aSet0(szAzrzSzezqlpdtcmdtrp0(X10,X11))
& sP6(X10,X11)
& ! [X15] :
( aElementOf0(X15,xB)
| ~ aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(X10,X11)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X10,X11),xB) )
| ~ aElementOf0(X10,xB) )
& isOpen0(xB) ),
inference(nnf_transformation,[],[f112]) ).
fof(f167,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,X5))
& sP7(X4,X5)
& ! [X6] :
( aElementOf0(X6,xA)
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,X5)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,X5),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X7] :
( ? [X8] :
( aInteger0(X8)
& sz00 != X8
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,X8))
& sP6(X7,X8)
& ! [X9] :
( aElementOf0(X9,xB)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,X8)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,X8),xB) )
| ~ aElementOf0(X7,xB) )
& isOpen0(xB) ),
inference(rectify,[],[f166]) ).
fof(f168,plain,
( aSet0(cS1395)
& ! [X0] :
( ( aElementOf0(X0,cS1395)
| ~ aInteger0(X0) )
& ( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,cS1395)
| ~ aElementOf0(X1,xA) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X2] :
( ( aElementOf0(X2,cS1395)
| ~ aInteger0(X2) )
& ( aInteger0(X2)
| ~ aElementOf0(X2,cS1395) ) )
& aSet0(xB)
& ! [X3] :
( aElementOf0(X3,cS1395)
| ~ aElementOf0(X3,xB) )
& aSubsetOf0(xB,cS1395)
& ! [X4] :
( ( aInteger0(sK25(X4))
& sz00 != sK25(X4)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X4,sK25(X4)))
& sP7(X4,sK25(X4))
& ! [X6] :
( aElementOf0(X6,xA)
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK25(X4))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X4,sK25(X4)),xA) )
| ~ aElementOf0(X4,xA) )
& isOpen0(xA)
& ! [X7] :
( ( aInteger0(sK26(X7))
& sz00 != sK26(X7)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X7,sK26(X7)))
& sP6(X7,sK26(X7))
& ! [X9] :
( aElementOf0(X9,xB)
| ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,sK26(X7))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X7,sK26(X7)),xB) )
| ~ aElementOf0(X7,xB) )
& isOpen0(xB) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X5,sK25(X4)),skolemize(X8,sK26(X7))],[f167]) ).
fof(f169,plain,
! [X1,X2] :
( ! [X3] :
( ( ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtpldt0(X3,smndt0(X1)) != sdtasdt0(X2,X5) )
& ~ aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ~ sdteqdtlpzmzozddtrp0(X3,X1,X2) ) ) )
| ~ sP8(X1,X2) ),
inference(nnf_transformation,[],[f113]) ).
fof(f170,plain,
! [X0,X1] :
( ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ~ sdteqdtlpzmzozddtrp0(X2,X0,X1) ) ) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f169]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X2] :
( ( ( aInteger0(X2)
& aInteger0(sK27(X0,X1,X2))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK27(X0,X1,X2))
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(X0)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ~ sdteqdtlpzmzozddtrp0(X2,X0,X1) ) ) )
| ~ sP8(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X3,sK27(X0,X1,X2))],[f170]) ).
fof(f172,plain,
( ? [X1] :
( ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ( ? [X6] :
( ~ aElementOf0(X6,sdtslmnbsdt0(xA,xB))
& aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& sP8(X1,X2) ) )
& aElementOf0(X1,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( ( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
| ~ aInteger0(X0)
| ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,xB) )
& ( ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) )
| ~ aElementOf0(X0,sdtslmnbsdt0(xA,xB)) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f173,plain,
( ? [X1] :
( ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ( ? [X6] :
( ~ aElementOf0(X6,sdtslmnbsdt0(xA,xB))
& aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& sP8(X1,X2) ) )
& aElementOf0(X1,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X0] :
( ( aElementOf0(X0,sdtslmnbsdt0(xA,xB))
| ~ aInteger0(X0)
| ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,xB) )
& ( ( aInteger0(X0)
& aElementOf0(X0,xA)
& aElementOf0(X0,xB) )
| ~ aElementOf0(X0,sdtslmnbsdt0(xA,xB)) ) ) ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
( ? [X0] :
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ? [X2] :
( ~ aElementOf0(X2,sdtslmnbsdt0(xA,xB))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sP8(X0,X1) ) )
& aElementOf0(X0,sdtslmnbsdt0(xA,xB)) )
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X3] :
( ( aElementOf0(X3,sdtslmnbsdt0(xA,xB))
| ~ aInteger0(X3)
| ~ aElementOf0(X3,xA)
| ~ aElementOf0(X3,xB) )
& ( ( aInteger0(X3)
& aElementOf0(X3,xA)
& aElementOf0(X3,xB) )
| ~ aElementOf0(X3,sdtslmnbsdt0(xA,xB)) ) ) ),
inference(rectify,[],[f173]) ).
fof(f175,plain,
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ~ aElementOf0(sK29(X1),sdtslmnbsdt0(xA,xB))
& aElementOf0(sK29(X1),szAzrzSzezqlpdtcmdtrp0(sK28,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK28,X1),sdtslmnbsdt0(xA,xB))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK28,X1))
& sP8(sK28,X1) ) )
& aElementOf0(sK28,sdtslmnbsdt0(xA,xB))
& ~ isOpen0(sdtslmnbsdt0(xA,xB))
& aSet0(sdtslmnbsdt0(xA,xB))
& ! [X3] :
( ( aElementOf0(X3,sdtslmnbsdt0(xA,xB))
| ~ aInteger0(X3)
| ~ aElementOf0(X3,xA)
| ~ aElementOf0(X3,xB) )
& ( ( aInteger0(X3)
& aElementOf0(X3,xA)
& aElementOf0(X3,xB) )
| ~ aElementOf0(X3,sdtslmnbsdt0(xA,xB)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29]),skolemize(X0,sK28),skolemize(X2,sK29(X1))],[f174]) ).
fof(f180,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f197,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sdteqdtlpzmzozddtrp0(X0,X1,X3)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3)
| sz00 = X3 ),
inference(cnf_transformation,[],[f81]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3)
| sz00 = X3 ),
inference(cnf_transformation,[],[f81]) ).
fof(f262,plain,
! [X2,X0,X1,X4] :
( sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aElementOf0(X4,X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f264,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f296,plain,
! [X9,X7] :
( ~ aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(X7,sK26(X7)))
| aElementOf0(X9,xB)
| ~ aElementOf0(X7,xB) ),
inference(cnf_transformation,[],[f168]) ).
fof(f299,plain,
! [X7] :
( sz00 != sK26(X7)
| ~ aElementOf0(X7,xB) ),
inference(cnf_transformation,[],[f168]) ).
fof(f300,plain,
! [X7] :
( ~ aElementOf0(X7,xB)
| aInteger0(sK26(X7)) ),
inference(cnf_transformation,[],[f168]) ).
fof(f303,plain,
! [X6,X4] :
( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(X4,sK25(X4)))
| aElementOf0(X6,xA)
| ~ aElementOf0(X4,xA) ),
inference(cnf_transformation,[],[f168]) ).
fof(f306,plain,
! [X4] :
( sz00 != sK25(X4)
| ~ aElementOf0(X4,xA) ),
inference(cnf_transformation,[],[f168]) ).
fof(f307,plain,
! [X4] :
( ~ aElementOf0(X4,xA)
| aInteger0(sK25(X4)) ),
inference(cnf_transformation,[],[f168]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f328,plain,
! [X3] :
( aElementOf0(X3,xB)
| ~ aElementOf0(X3,sdtslmnbsdt0(xA,xB)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f329,plain,
! [X3] :
( aElementOf0(X3,xA)
| ~ aElementOf0(X3,sdtslmnbsdt0(xA,xB)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f330,plain,
! [X3] :
( aInteger0(X3)
| ~ aElementOf0(X3,sdtslmnbsdt0(xA,xB)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f331,plain,
! [X3] :
( aElementOf0(X3,sdtslmnbsdt0(xA,xB))
| ~ aInteger0(X3)
| ~ aElementOf0(X3,xA)
| ~ aElementOf0(X3,xB) ),
inference(cnf_transformation,[],[f175]) ).
fof(f334,plain,
aElementOf0(sK28,sdtslmnbsdt0(xA,xB)),
inference(cnf_transformation,[],[f175]) ).
fof(f335,plain,
! [X1] :
( sP8(sK28,X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f338,plain,
! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| aElementOf0(sK29(X1),szAzrzSzezqlpdtcmdtrp0(sK28,X1)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f339,plain,
! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ~ aElementOf0(sK29(X1),sdtslmnbsdt0(xA,xB)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f352,plain,
! [X0,X1,X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(equality_resolution,[],[f264]) ).
fof(f354,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(equality_resolution,[],[f262]) ).
fof(f355,definition,
sF30 = sdtslmnbsdt0(xA,xB),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f356,plain,
sdtslmnbsdt0(xA,xB) = sF30,
inference(reorient_equations,[],[f355]) ).
fof(f357,plain,
! [X1] :
( ~ aElementOf0(sK29(X1),sF30)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_folding,[],[f339,f356]) ).
fof(f358,definition,
! [X1] : sF31(X1) = szAzrzSzezqlpdtcmdtrp0(sK28,X1),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f359,plain,
! [X1] : szAzrzSzezqlpdtcmdtrp0(sK28,X1) = sF31(X1),
inference(reorient_equations,[],[f358]) ).
fof(f360,plain,
! [X1] :
( aElementOf0(sK29(X1),sF31(X1))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_folding,[],[f338,f359]) ).
fof(f363,plain,
aElementOf0(sK28,sF30),
inference(definition_folding,[],[f334,f356]) ).
fof(f366,plain,
! [X3] :
( ~ aElementOf0(X3,xB)
| ~ aInteger0(X3)
| ~ aElementOf0(X3,xA)
| aElementOf0(X3,sF30) ),
inference(definition_folding,[],[f331,f356]) ).
fof(f367,plain,
! [X3] :
( ~ aElementOf0(X3,sF30)
| aInteger0(X3) ),
inference(definition_folding,[],[f330,f356]) ).
fof(f368,plain,
! [X3] :
( ~ aElementOf0(X3,sF30)
| aElementOf0(X3,xA) ),
inference(definition_folding,[],[f329,f356]) ).
fof(f369,plain,
! [X3] :
( ~ aElementOf0(X3,sF30)
| aElementOf0(X3,xB) ),
inference(definition_folding,[],[f328,f356]) ).
fof(f387,plain,
aInteger0(sK28),
inference(resolution,[],[f367,f363]) ).
fof(f388,plain,
aElementOf0(sK28,xA),
inference(resolution,[],[f368,f363]) ).
fof(f389,plain,
aElementOf0(sK28,xB),
inference(resolution,[],[f369,f363]) ).
fof(f390,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sF31(X0))
| aInteger0(X1)
| ~ sP8(sK28,X0) ),
inference(superposition,[],[f327,f359]) ).
fof(f403,plain,
aInteger0(sK26(sK28)),
inference(resolution,[],[f300,f389]) ).
fof(f410,plain,
! [X0] :
( aInteger0(sK29(X0))
| ~ sP8(sK28,X0)
| sz00 = X0
| ~ aInteger0(X0) ),
inference(resolution,[],[f390,f360]) ).
fof(f411,plain,
! [X0] :
( aInteger0(sK29(X0))
| sz00 = X0
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f410,f335]) ).
fof(f412,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sF31(X0))
| sdteqdtlpzmzozddtrp0(X1,sK28,X0)
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(superposition,[],[f354,f359]) ).
fof(f413,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sF31(X0))
| sdteqdtlpzmzozddtrp0(X1,sK28,X0)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f412,f387]) ).
fof(f414,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sK29(X0),sK28,X0)
| ~ aInteger0(X0)
| sz00 = X0
| sz00 = X0
| ~ aInteger0(X0) ),
inference(resolution,[],[f413,f360]) ).
fof(f415,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sK29(X0),sK28,X0)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f417,plain,
! [X0] :
( ~ aElementOf0(X0,sF31(sK26(sK28)))
| aElementOf0(X0,xB)
| ~ aElementOf0(sK28,xB) ),
inference(superposition,[],[f296,f359]) ).
fof(f418,plain,
! [X0] :
( ~ aElementOf0(X0,sF31(sK26(sK28)))
| aElementOf0(X0,xB) ),
inference(forward_subsumption_resolution,[],[f417,f389]) ).
fof(f422,definition,
( spl32_7
<=> sz00 = sK26(sK28) ),
introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition]) ).
fof(f423,plain,
( sz00 != sK26(sK28)
| spl32_7 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f424,plain,
( sz00 = sK26(sK28)
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f438,plain,
aInteger0(sK25(sK28)),
inference(resolution,[],[f307,f388]) ).
fof(f439,plain,
! [X0] :
( ~ aElementOf0(X0,sF31(sK25(sK28)))
| aElementOf0(X0,xA)
| ~ aElementOf0(sK28,xA) ),
inference(superposition,[],[f303,f359]) ).
fof(f440,plain,
! [X0] :
( ~ aElementOf0(X0,sF31(sK25(sK28)))
| aElementOf0(X0,xA) ),
inference(forward_subsumption_resolution,[],[f439,f388]) ).
fof(f444,definition,
( spl32_9
<=> sz00 = sK25(sK28) ),
introduced(definition,[new_symbols(definition,[spl32_9])],[avatar_definition]) ).
fof(f445,plain,
( sz00 != sK25(sK28)
| spl32_9 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f446,plain,
( sz00 = sK25(sK28)
| ~ spl32_9 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f553,plain,
( sz00 != sz00
| ~ aElementOf0(sK28,xB)
| ~ spl32_7 ),
inference(superposition,[],[f299,f424]) ).
fof(f554,plain,
( ~ aElementOf0(sK28,xB)
| ~ spl32_7 ),
inference(trivial_inequality_removal,[],[f553]) ).
fof(f555,plain,
( $false
| ~ spl32_7 ),
inference(forward_subsumption_resolution,[],[f554,f389]) ).
fof(f556,plain,
~ spl32_7,
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f711,plain,
! [X0,X1] :
( aElementOf0(X1,sF31(X0))
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,sK28,X0)
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(superposition,[],[f352,f359]) ).
fof(f714,plain,
! [X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X1,sK28,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,sF31(X0))
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f711,f387]) ).
fof(f870,plain,
( sz00 != sz00
| ~ aElementOf0(sK28,xA)
| ~ spl32_9 ),
inference(superposition,[],[f306,f446]) ).
fof(f873,plain,
( ~ aElementOf0(sK28,xA)
| ~ spl32_9 ),
inference(trivial_inequality_removal,[],[f870]) ).
fof(f876,plain,
( $false
| ~ spl32_9 ),
inference(forward_subsumption_resolution,[],[f873,f388]) ).
fof(f877,plain,
~ spl32_9,
inference(avatar_contradiction_clause,[],[f876]) ).
fof(f1421,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X0)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1))
| sz00 = sdtasdt0(X0,X1) ),
inference(resolution,[],[f209,f415]) ).
fof(f1432,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X0)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1421,f197]) ).
fof(f1434,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X0)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1432,f387]) ).
fof(f1436,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X0)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(forward_subsumption_resolution,[],[f1434,f180]) ).
fof(f1449,plain,
! [X0,X1] :
( ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| aElementOf0(sK29(sdtasdt0(X0,X1)),sF31(X0))
| ~ aInteger0(X0)
| sz00 = X0 ),
inference(resolution,[],[f1436,f714]) ).
fof(f1458,plain,
! [X0,X1] :
( aElementOf0(sK29(sdtasdt0(X0,X1)),sF31(X0))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sK29(sdtasdt0(X0,X1))) ),
inference(duplicate_literal_removal,[],[f1449]) ).
fof(f1468,plain,
! [X0] :
( ~ aInteger0(sK25(sK28))
| sz00 = sK25(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(sK29(sdtasdt0(sK25(sK28),X0)))
| aElementOf0(sK29(sdtasdt0(sK25(sK28),X0)),xA) ),
inference(resolution,[],[f1458,f440]) ).
fof(f1475,plain,
! [X0] :
( sz00 = sK25(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(sK29(sdtasdt0(sK25(sK28),X0)))
| aElementOf0(sK29(sdtasdt0(sK25(sK28),X0)),xA) ),
inference(forward_subsumption_resolution,[],[f1468,f438]) ).
fof(f1478,plain,
( ! [X0] :
( aElementOf0(sK29(sdtasdt0(sK25(sK28),X0)),xA)
| sz00 = X0
| ~ aInteger0(sK29(sdtasdt0(sK25(sK28),X0)))
| ~ aInteger0(X0) )
| spl32_9 ),
inference(forward_subsumption_resolution,[],[f1475,f445]) ).
fof(f1500,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X1)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1))
| sz00 = sdtasdt0(X0,X1) ),
inference(resolution,[],[f208,f415]) ).
fof(f1517,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X1)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(sK28)
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1500,f197]) ).
fof(f1521,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X1)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1517,f387]) ).
fof(f1525,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK29(sdtasdt0(X0,X1)),sK28,X1)
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(forward_subsumption_resolution,[],[f1521,f180]) ).
fof(f1543,plain,
! [X0,X1] :
( ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sK29(sdtasdt0(X0,X1)))
| aElementOf0(sK29(sdtasdt0(X0,X1)),sF31(X1))
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(resolution,[],[f1525,f714]) ).
fof(f1554,plain,
! [X0,X1] :
( aElementOf0(sK29(sdtasdt0(X0,X1)),sF31(X1))
| ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(sK29(sdtasdt0(X0,X1))) ),
inference(duplicate_literal_removal,[],[f1543]) ).
fof(f1566,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| ~ aInteger0(sK26(sK28))
| sz00 = sK26(sK28)
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),xB) ),
inference(resolution,[],[f1554,f418]) ).
fof(f1575,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = X0
| sz00 = sK26(sK28)
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),xB) ),
inference(forward_subsumption_resolution,[],[f1566,f403]) ).
fof(f1578,plain,
( ! [X0] :
( aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),xB)
| sz00 = X0
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| ~ aInteger0(X0) )
| spl32_7 ),
inference(forward_subsumption_resolution,[],[f1575,f423]) ).
fof(f1608,plain,
( ! [X0] :
( sz00 = X0
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| ~ aInteger0(X0)
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| ~ aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),xA)
| aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),sF30) )
| spl32_7 ),
inference(resolution,[],[f1578,f366]) ).
fof(f1609,plain,
( ! [X0] :
( ~ aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),xA)
| ~ aInteger0(sK29(sdtasdt0(X0,sK26(sK28))))
| ~ aInteger0(X0)
| sz00 = X0
| aElementOf0(sK29(sdtasdt0(X0,sK26(sK28))),sF30) )
| spl32_7 ),
inference(duplicate_literal_removal,[],[f1608]) ).
fof(f1610,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| ~ aInteger0(sK25(sK28))
| sz00 = sK25(sK28)
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| sz00 = sK26(sK28)
| ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9 ),
inference(resolution,[],[f1609,f1478]) ).
fof(f1611,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| ~ aInteger0(sK25(sK28))
| sz00 = sK25(sK28)
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| sz00 = sK26(sK28)
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9 ),
inference(duplicate_literal_removal,[],[f1610]) ).
fof(f1612,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| sz00 = sK25(sK28)
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| sz00 = sK26(sK28)
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9 ),
inference(forward_subsumption_resolution,[],[f1611,f438]) ).
fof(f1613,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| sz00 = sK26(sK28)
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9 ),
inference(forward_subsumption_resolution,[],[f1612,f445]) ).
fof(f1614,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9 ),
inference(forward_subsumption_resolution,[],[f1613,f423]) ).
fof(f1615,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| spl32_7
| spl32_9 ),
inference(forward_subsumption_resolution,[],[f1614,f403]) ).
fof(f1617,definition,
( spl32_88
<=> aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30) ),
introduced(definition,[new_symbols(definition,[spl32_88])],[avatar_definition]) ).
fof(f1619,plain,
( aElementOf0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))),sF30)
| ~ spl32_88 ),
inference(avatar_component_clause,[],[f1617]) ).
fof(f1621,definition,
( spl32_89
<=> aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28)))) ),
introduced(definition,[new_symbols(definition,[spl32_89])],[avatar_definition]) ).
fof(f1623,plain,
( ~ aInteger0(sK29(sdtasdt0(sK25(sK28),sK26(sK28))))
| spl32_89 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f1624,plain,
( spl32_88
| ~ spl32_89
| spl32_7
| spl32_9 ),
inference(avatar_split_clause,[],[f1615,f444,f422,f1621,f1617]) ).
fof(f1625,plain,
( sz00 = sdtasdt0(sK25(sK28),sK26(sK28))
| ~ aInteger0(sdtasdt0(sK25(sK28),sK26(sK28)))
| spl32_89 ),
inference(resolution,[],[f1623,f411]) ).
fof(f1627,definition,
( spl32_90
<=> aInteger0(sdtasdt0(sK25(sK28),sK26(sK28))) ),
introduced(definition,[new_symbols(definition,[spl32_90])],[avatar_definition]) ).
fof(f1628,plain,
( aInteger0(sdtasdt0(sK25(sK28),sK26(sK28)))
| ~ spl32_90 ),
inference(avatar_component_clause,[],[f1627]) ).
fof(f1629,plain,
( ~ aInteger0(sdtasdt0(sK25(sK28),sK26(sK28)))
| spl32_90 ),
inference(avatar_component_clause,[],[f1627]) ).
fof(f1631,definition,
( spl32_91
<=> sz00 = sdtasdt0(sK25(sK28),sK26(sK28)) ),
introduced(definition,[new_symbols(definition,[spl32_91])],[avatar_definition]) ).
fof(f1633,plain,
( sz00 = sdtasdt0(sK25(sK28),sK26(sK28))
| ~ spl32_91 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f1634,plain,
( ~ spl32_90
| spl32_91
| spl32_89 ),
inference(avatar_split_clause,[],[f1625,f1621,f1631,f1627]) ).
fof(f1635,plain,
( ~ aInteger0(sK25(sK28))
| ~ aInteger0(sK26(sK28))
| spl32_90 ),
inference(resolution,[],[f1629,f180]) ).
fof(f1636,plain,
( ~ aInteger0(sK26(sK28))
| spl32_90 ),
inference(forward_subsumption_resolution,[],[f1635,f438]) ).
fof(f1637,plain,
( $false
| spl32_90 ),
inference(forward_subsumption_resolution,[],[f1636,f403]) ).
fof(f1638,plain,
spl32_90,
inference(avatar_contradiction_clause,[],[f1637]) ).
fof(f1639,plain,
( sz00 = sdtasdt0(sK25(sK28),sK26(sK28))
| ~ aInteger0(sdtasdt0(sK25(sK28),sK26(sK28)))
| ~ spl32_88 ),
inference(resolution,[],[f1619,f357]) ).
fof(f1643,plain,
( sz00 = sdtasdt0(sK25(sK28),sK26(sK28))
| ~ spl32_88
| ~ spl32_90 ),
inference(forward_subsumption_resolution,[],[f1639,f1628]) ).
fof(f1644,plain,
( spl32_91
| ~ spl32_88
| ~ spl32_90 ),
inference(avatar_split_clause,[],[f1643,f1627,f1617,f1631]) ).
fof(f1656,plain,
( sz00 != sz00
| sz00 = sK26(sK28)
| sz00 = sK25(sK28)
| ~ aInteger0(sK25(sK28))
| ~ aInteger0(sK26(sK28))
| ~ spl32_91 ),
inference(superposition,[],[f197,f1633]) ).
fof(f1665,plain,
( sz00 = sK26(sK28)
| sz00 = sK25(sK28)
| ~ aInteger0(sK25(sK28))
| ~ aInteger0(sK26(sK28))
| ~ spl32_91 ),
inference(trivial_inequality_removal,[],[f1656]) ).
fof(f1674,plain,
( sz00 = sK25(sK28)
| ~ aInteger0(sK25(sK28))
| ~ aInteger0(sK26(sK28))
| spl32_7
| ~ spl32_91 ),
inference(forward_subsumption_resolution,[],[f1665,f423]) ).
fof(f1686,plain,
( ~ aInteger0(sK25(sK28))
| ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9
| ~ spl32_91 ),
inference(forward_subsumption_resolution,[],[f1674,f445]) ).
fof(f1696,plain,
( ~ aInteger0(sK26(sK28))
| spl32_7
| spl32_9
| ~ spl32_91 ),
inference(forward_subsumption_resolution,[],[f1686,f438]) ).
fof(f1714,plain,
( $false
| spl32_7
| spl32_9
| ~ spl32_91 ),
inference(forward_subsumption_resolution,[],[f1696,f403]) ).
fof(f1715,plain,
( spl32_7
| spl32_9
| ~ spl32_91 ),
inference(avatar_contradiction_clause,[],[f1714]) ).
cnf(s13,plain,
~ spl32_7,
inference(sat_conversion,[],[f556]) ).
cnf(s27,plain,
~ spl32_9,
inference(sat_conversion,[],[f877]) ).
cnf(s64,plain,
( spl32_7
| spl32_9
| spl32_88
| ~ spl32_89 ),
inference(sat_conversion,[],[f1624]) ).
cnf(s65,plain,
( spl32_89
| ~ spl32_90
| spl32_91 ),
inference(sat_conversion,[],[f1634]) ).
cnf(s66,plain,
spl32_90,
inference(sat_conversion,[],[f1638]) ).
cnf(s67,plain,
( ~ spl32_88
| ~ spl32_90
| spl32_91 ),
inference(sat_conversion,[],[f1644]) ).
cnf(s69,plain,
( spl32_7
| spl32_9
| ~ spl32_91 ),
inference(sat_conversion,[],[f1715]) ).
cnf(s76,plain,
( spl32_89
| spl32_91 ),
inference(rat,[],[s65,s66]) ).
cnf(s77,plain,
~ spl32_91,
inference(rat,[],[s69,s27,s13]) ).
cnf(s78,plain,
~ spl32_88,
inference(rat,[],[s67,s66,s77]) ).
cnf(s79,plain,
spl32_89,
inference(rat,[],[s76,s77]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s64,s13,s27,s79,s78]) ).
fof(f1746,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM438+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 19:55:24 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.01/2.61 % (1562178)Detected formulas, will run a generic FOF schedule.
% 7.01/2.61 % (1562287)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=505029078:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.01/2.61 % (1562288)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=917035082:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.01/2.61 % (1562285)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2466485595:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.01/2.61 % (1562290)dis-21_1_sil=8000:lcm=predicate:random_seed=3446746981:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.01/2.61 % (1562284)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=674717777:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.01/2.61 % (1562289)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2929735301:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.01/2.61 % (1562287)Instruction limit reached!
% 7.01/2.61 % (1562287)------------------------------
% 7.01/2.61 % (1562287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562287)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562287)Termination reason: Instruction limit
% 7.01/2.61 % (1562287)Termination phase: Saturation
% 7.01/2.61 % (1562287)Time elapsed: 0.041 s
% 7.01/2.61 % (1562287)Peak memory usage: 89 MB
% 7.01/2.61 % (1562287)Instructions burned: 111 (million)
% 7.01/2.61 % (1562286)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2434269011:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.01/2.61 % (1562288)Instruction limit reached!
% 7.01/2.61 % (1562288)------------------------------
% 7.01/2.61 % (1562288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562288)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562288)Termination reason: Instruction limit
% 7.01/2.61 % (1562288)Termination phase: Saturation
% 7.01/2.61 % (1562288)Time elapsed: 0.078 s
% 7.01/2.61 % (1562288)Peak memory usage: 88 MB
% 7.01/2.61 % (1562288)Instructions burned: 119 (million)
% 7.01/2.61 % (1562290)Instruction limit reached!
% 7.01/2.61 % (1562290)------------------------------
% 7.01/2.61 % (1562290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562290)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562290)Termination reason: Instruction limit
% 7.01/2.61 % (1562290)Termination phase: Saturation
% 7.01/2.61 % (1562290)Time elapsed: 0.091 s
% 7.01/2.61 % (1562290)Peak memory usage: 89 MB
% 7.01/2.61 % (1562290)Instructions burned: 129 (million)
% 7.01/2.61 % (1562289)Instruction limit reached!
% 7.01/2.61 % (1562289)------------------------------
% 7.01/2.61 % (1562289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562289)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562289)Termination reason: Instruction limit
% 7.01/2.61 % (1562289)Termination phase: Saturation
% 7.01/2.61 % (1562289)Time elapsed: 0.109 s
% 7.01/2.61 % (1562289)Peak memory usage: 89 MB
% 7.01/2.61 % (1562289)Instructions burned: 139 (million)
% 7.01/2.61 % (1562297)lrs+10_1_sil=8000:sp=occurrence:random_seed=2503176457:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.01/2.61 % (1562297)Instruction limit reached!
% 7.01/2.61 % (1562297)------------------------------
% 7.01/2.61 % (1562297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562297)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562297)Termination reason: Instruction limit
% 7.01/2.61 % (1562297)Termination phase: Saturation
% 7.01/2.61 % (1562297)Time elapsed: 0.140 s
% 7.01/2.61 % (1562297)Peak memory usage: 91 MB
% 7.01/2.61 % (1562297)Instructions burned: 286 (million)
% 7.01/2.61 % (1562320)lrs+10_1_sil=32000:urr=on:br=off:random_seed=960038531:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.01/2.61 % (1562327)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2130577892:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.01/2.61 % (1562328)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2916559212:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.01/2.61 % (1562320)Instruction limit reached!
% 7.01/2.61 % (1562320)------------------------------
% 7.01/2.61 % (1562320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562320)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562320)Termination reason: Instruction limit
% 7.01/2.61 % (1562320)Termination phase: Saturation
% 7.01/2.61 % (1562320)Time elapsed: 0.144 s
% 7.01/2.61 % (1562320)Peak memory usage: 91 MB
% 7.01/2.61 % (1562320)Instructions burned: 158 (million)
% 7.01/2.61 % (1562338)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3762267059:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.01/2.61 % (1562328)Instruction limit reached!
% 7.01/2.61 % (1562328)------------------------------
% 7.01/2.61 % (1562328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562328)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562328)Termination reason: Instruction limit
% 7.01/2.61 % (1562328)Termination phase: Saturation
% 7.01/2.61 % (1562328)Time elapsed: 0.216 s
% 7.01/2.61 % (1562328)Peak memory usage: 95 MB
% 7.01/2.61 % (1562328)Instructions burned: 249 (million)
% 7.01/2.61 % (1562338)Instruction limit reached!
% 7.01/2.61 % (1562338)------------------------------
% 7.01/2.61 % (1562338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562338)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562338)Termination reason: Instruction limit
% 7.01/2.61 % (1562338)Termination phase: Saturation
% 7.01/2.61 % (1562338)Time elapsed: 0.162 s
% 7.01/2.61 % (1562338)Peak memory usage: 90 MB
% 7.01/2.61 % (1562338)Instructions burned: 295 (million)
% 7.01/2.61 % (1562327)Instruction limit reached!
% 7.01/2.61 % (1562327)------------------------------
% 7.01/2.61 % (1562327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562327)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562327)Termination reason: Instruction limit
% 7.01/2.61 % (1562327)Termination phase: Saturation
% 7.01/2.61 % (1562327)Time elapsed: 0.341 s
% 7.01/2.61 % (1562327)Peak memory usage: 92 MB
% 7.01/2.61 % (1562327)Instructions burned: 326 (million)
% 7.01/2.61 % (1562348)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2494235844:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 7.01/2.61 % (1562350)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3197479619:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 7.01/2.61 % (1562351)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1260986392:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 7.01/2.61 % (1562352)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3505707000:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.01/2.61 % (1562351)Instruction limit reached!
% 7.01/2.61 % (1562351)------------------------------
% 7.01/2.61 % (1562351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.61 % (1562351)CaDiCaL version: 2.1.3
% 7.01/2.61 % (1562351)Termination reason: Instruction limit
% 7.01/2.61 % (1562351)Termination phase: Saturation
% 7.01/2.61 % (1562351)Time elapsed: 0.059 s
% 7.01/2.61 % (1562351)Peak memory usage: 89 MB
% 7.01/2.61 % (1562351)Instructions burned: 128 (million)
% 7.01/2.61 % (1562350)Instruction limit reached!
% 7.01/2.61 % (1562350)------------------------------
% 7.01/2.61 % (1562350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.61 % (1562350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.62 % (1562350)CaDiCaL version: 2.1.3
% 7.01/2.62 % (1562350)Termination reason: Instruction limit
% 7.01/2.62 % (1562350)Termination phase: Saturation
% 7.01/2.62 % (1562350)Time elapsed: 0.120 s
% 7.01/2.62 % (1562350)Peak memory usage: 90 MB
% 7.01/2.62 % (1562350)Instructions burned: 113 (million)
% 7.01/2.62 % (1562352)Instruction limit reached!
% 7.01/2.62 % (1562352)------------------------------
% 7.01/2.62 % (1562352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.62 % (1562352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.62 % (1562352)CaDiCaL version: 2.1.3
% 7.01/2.62 % (1562352)Termination reason: Instruction limit
% 7.01/2.62 % (1562352)Termination phase: Saturation
% 7.01/2.62 % (1562352)Time elapsed: 0.088 s
% 7.01/2.62 % (1562352)Peak memory usage: 89 MB
% 7.01/2.62 % (1562352)Instructions burned: 114 (million)
% 7.01/2.62 % (1562363)lrs+10_1_sil=8000:sp=occurrence:random_seed=1724298704:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 7.01/2.62 % (1562284)First to succeed.
% 7.01/2.62 % (1562284)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1562178"
% 7.01/2.62 % (1562365)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2212560786:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 7.01/2.62 % (1562364)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3409052294:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 7.01/2.62 % (1562363)Instruction limit reached!
% 7.01/2.62 % (1562363)------------------------------
% 7.01/2.62 % (1562363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.01/2.62 % (1562363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.01/2.62 % (1562363)CaDiCaL version: 2.1.3
% 7.01/2.62 % (1562363)Termination reason: Instruction limit
% 7.01/2.62 % (1562363)Termination phase: Saturation
% 7.01/2.62 % (1562363)Time elapsed: 0.355 s
% 7.01/2.62 % (1562363)Peak memory usage: 98 MB
% 7.01/2.62 % (1562363)Instructions burned: 908 (million)
% 7.01/2.62 % (1562284)Refutation found. Thanks to Tanya!
% 7.01/2.62 % SZS status Theorem for theBenchmark
% 7.01/2.62 % SZS output start Proof for theBenchmark
% See solution above
% 12.99/2.91 % (1562284)------------------------------
% 12.99/2.91 % (1562284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.99/2.91 % (1562284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.99/2.91 % (1562284)CaDiCaL version: 2.1.3
% 12.99/2.91 % (1562284)Termination reason: Refutation
% 12.99/2.91 % (1562284)Time elapsed: 1.223 s
% 12.99/2.91 % (1562284)Peak memory usage: 132 MB
% 12.99/2.91 % (1562284)Instructions burned: 1189 (million)
% 12.99/2.91 % (1562284)------------------------------
% 12.99/2.91 % (1562284)------------------------------
% 12.99/2.91 % (1562178)Success in time 1.733 s
% 12.99/2.91 % Vampire exiting
%------------------------------------------------------------------------------