%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM437+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 2.83s 1.29s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 3 unt; 3 def)
% Number of atoms : 555 ( 58 equ)
% Maximal formula atoms : 29 ( 9 avg)
% Number of connectives : 719 ( 220 ~; 185 |; 273 &)
% ( 11 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 182 ( 133 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(X0,cS1395)
& ! [X1] :
( aElementOf0(X1,X0)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& 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)
& ( ? [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)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,X0) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0) ) )
& isOpen0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1750) ).
fof(f38,conjecture,
( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
=> ? [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,sbsmnsldt0(xS)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS)) ) ) ) )
| isOpen0(sbsmnsldt0(xS)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f39,negated_conjecture,
~ ( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
=> ? [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,sbsmnsldt0(xS)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS)) ) ) ) )
| isOpen0(sbsmnsldt0(xS)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,cS1395) )
& aSubsetOf0(X0,cS1395)
& ! [X3] :
( aElementOf0(X3,X0)
=> ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
& ( ( aInteger0(X5)
& ( ? [X7] :
( aInteger0(X7)
& sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7) )
| aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
| sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& ! [X8] :
( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> aElementOf0(X8,X0) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0) ) )
& isOpen0(X0) ) ) ),
inference(rectify,[],[f37]) ).
fof(f41,plain,
~ ( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
=> ? [X3] :
( aInteger0(X3)
& sz00 != X3
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) ) )
& ( ( aInteger0(X4)
& ( ? [X6] :
( aInteger0(X6)
& sdtpldt0(X4,smndt0(X2)) = sdtasdt0(X3,X6) )
| aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
| sdteqdtlpzmzozddtrp0(X4,X2,X3) ) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) ) ) )
=> ( ! [X7] :
( aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3))
=> aElementOf0(X7,sbsmnsldt0(xS)) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS)) ) ) ) )
| isOpen0(sbsmnsldt0(xS)) ) ),
inference(rectify,[],[f39]) ).
fof(f46,plain,
( aSet0(xS)
& ! [X0] :
( ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,X0) )
& aSubsetOf0(X0,cS1395)
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
& ! [X8] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0) )
| ~ aElementOf0(X3,X0) )
& isOpen0(X0) )
| ~ aElementOf0(X0,xS) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
( aSet0(xS)
& ! [X0] :
( ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,X0) )
& aSubsetOf0(X0,cS1395)
& ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
& ! [X8] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0) )
| ~ aElementOf0(X3,X0) )
& isOpen0(X0) )
| ~ aElementOf0(X0,xS) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) ) ) )
& aElementOf0(X2,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f49,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) ) ) )
& aElementOf0(X2,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f87,definition,
! [X3,X4] :
( ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
| ~ sP0(X3,X4) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f88,definition,
! [X0] :
( ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP0(X3,X4)
& ! [X8] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0) )
| ~ aElementOf0(X3,X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f89,plain,
( aSet0(xS)
& ! [X0] :
( ( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,X0) )
& aSubsetOf0(X0,cS1395)
& sP1(X0)
& isOpen0(X0) )
| ~ aElementOf0(X0,xS) ) ),
inference(definition_folding,[],[f47,f88,f87]) ).
fof(f90,definition,
! [X2,X3] :
( ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) )
| ~ sP2(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f91,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(definition_folding,[],[f49,f90]) ).
fof(f95,plain,
! [X0] :
( ! [X3] :
( ? [X4] :
( aInteger0(X4)
& sz00 != X4
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP0(X3,X4)
& ! [X8] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0) )
| ~ aElementOf0(X3,X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( aInteger0(X2)
& sz00 != X2
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& sP0(X1,X2)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0) )
| ~ aElementOf0(X1,X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ( aInteger0(sK5(X0,X1))
& sz00 != sK5(X0,X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)))
& sP0(X1,sK5(X0,X1))
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)),X0) )
| ~ aElementOf0(X1,X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f96]) ).
fof(f101,plain,
( aSet0(xS)
& ! [X0] :
( ( aSet0(cS1395)
& ! [X1] :
( ( aElementOf0(X1,cS1395)
| ~ aInteger0(X1) )
& ( aInteger0(X1)
| ~ aElementOf0(X1,cS1395) ) )
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,cS1395)
| ~ aElementOf0(X2,X0) )
& aSubsetOf0(X0,cS1395)
& sP1(X0)
& isOpen0(X0) )
| ~ aElementOf0(X0,xS) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f102,plain,
! [X2,X3] :
( ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X3,X5) = sdtpldt0(X4,smndt0(X2)) )
& aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& sdteqdtlpzmzozddtrp0(X4,X2,X3) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X2,X3))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(X2)) != sdtasdt0(X3,X6) )
& ~ aDivisorOf0(X3,sdtpldt0(X4,smndt0(X2)))
& ~ sdteqdtlpzmzozddtrp0(X4,X2,X3) ) ) )
| ~ sP2(X2,X3) ),
inference(nnf_transformation,[],[f90]) ).
fof(f103,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) ) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( ( aInteger0(X2)
& aInteger0(sK7(X0,X1,X2))
& sdtpldt0(X2,smndt0(X0)) = sdtasdt0(X1,sK7(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) ) ) )
| ~ sP2(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f103]) ).
fof(f105,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f106,plain,
( ? [X2] :
( ! [X3] :
( ~ aInteger0(X3)
| sz00 = X3
| ( ? [X7] :
( ~ aElementOf0(X7,sbsmnsldt0(xS))
& aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(X2,X3)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X2,X3),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X2,X3))
& sP2(X2,X3) ) )
& aElementOf0(X2,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) ) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
( ? [X0] :
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ? [X2] :
( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sP2(X0,X1) ) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X3,X5) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ~ aElementOf0(sK9(X1),sbsmnsldt0(xS))
& aElementOf0(sK9(X1),szAzrzSzezqlpdtcmdtrp0(sK8,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK8,X1),sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK8,X1))
& sP2(sK8,X1) ) )
& aElementOf0(sK8,sbsmnsldt0(xS))
& ~ isOpen0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& aElementOf0(sK10(X3),xS)
& aElementOf0(X3,sK10(X3)) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X2,sK9(X1)),skolemize(X5,sK10(X3))],[f107]) ).
fof(f133,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,sK5(X0,X1)))
| aElementOf0(X3,X0)
| ~ aElementOf0(X1,X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X0,X1] :
( sz00 != sK5(X0,X1)
| ~ aElementOf0(X1,X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X1] :
( aInteger0(sK5(X0,X1))
| ~ aElementOf0(X1,X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f147,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sP1(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| aInteger0(X2)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f163,plain,
! [X3] :
( aElementOf0(X3,sK10(X3))
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f164,plain,
! [X3] :
( aElementOf0(sK10(X3),xS)
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f166,plain,
! [X3,X4] :
( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
aElementOf0(sK8,sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X1] :
( sP2(sK8,X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f173,plain,
! [X1] :
( aElementOf0(sK9(X1),szAzrzSzezqlpdtcmdtrp0(sK8,X1))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f174,plain,
! [X1] :
( ~ aElementOf0(sK9(X1),sbsmnsldt0(xS))
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f242,plain,
! [X0,X1] :
( ~ aElementOf0(sK9(X0),X1)
| ~ aElementOf0(X1,xS)
| ~ aInteger0(sK9(X0))
| sz00 = X0
| ~ aInteger0(X0) ),
inference(resolution,[],[f166,f174]) ).
fof(f368,plain,
! [X0] :
( aInteger0(sK9(X0))
| ~ sP2(sK8,X0)
| sz00 = X0
| ~ aInteger0(X0) ),
inference(resolution,[],[f162,f173]) ).
fof(f371,plain,
! [X0] :
( aInteger0(sK9(X0))
| sz00 = X0
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f368,f170]) ).
fof(f689,plain,
! [X0] :
( aElementOf0(sK9(sK5(X0,sK8)),X0)
| ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| sz00 = sK5(X0,sK8)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(resolution,[],[f133,f173]) ).
fof(f698,plain,
! [X0] :
( aElementOf0(sK9(sK5(X0,sK8)),X0)
| ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(forward_subsumption_resolution,[],[f689,f136]) ).
fof(f701,plain,
! [X0] :
( aElementOf0(sK9(sK5(X0,sK8)),X0)
| ~ aElementOf0(sK8,X0)
| ~ sP1(X0) ),
inference(forward_subsumption_resolution,[],[f698,f137]) ).
fof(f703,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK9(sK5(X0,sK8)))
| sz00 = sK5(X0,sK8)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(resolution,[],[f701,f242]) ).
fof(f722,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK9(sK5(X0,sK8)))
| ~ aInteger0(sK5(X0,sK8)) ),
inference(forward_subsumption_resolution,[],[f703,f136]) ).
fof(f725,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK9(sK5(X0,sK8))) ),
inference(forward_subsumption_resolution,[],[f722,f137]) ).
fof(f727,plain,
! [X0] :
( ~ aInteger0(sK9(sK5(X0,sK8)))
| ~ aElementOf0(X0,xS)
| ~ aElementOf0(sK8,X0) ),
inference(forward_subsumption_resolution,[],[f725,f147]) ).
fof(f761,plain,
! [X0] :
( sz00 = sK5(X0,sK8)
| ~ aElementOf0(sK8,X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(resolution,[],[f727,f371]) ).
fof(f1426,plain,
! [X0] :
( sz00 != sz00
| ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(sK8,X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(superposition,[],[f136,f761]) ).
fof(f1443,plain,
! [X0] :
( sz00 != sz00
| ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(duplicate_literal_removal,[],[f1426]) ).
fof(f1444,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS)
| ~ aInteger0(sK5(X0,sK8)) ),
inference(trivial_inequality_removal,[],[f1443]) ).
fof(f1457,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ sP1(X0)
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f1444,f137]) ).
fof(f1464,plain,
! [X0] :
( ~ aElementOf0(sK8,X0)
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f1457,f147]) ).
fof(f1479,plain,
( ~ aElementOf0(sK10(sK8),xS)
| ~ aElementOf0(sK8,sbsmnsldt0(xS)) ),
inference(resolution,[],[f1464,f163]) ).
fof(f1481,plain,
~ aElementOf0(sK8,sbsmnsldt0(xS)),
inference(forward_subsumption_resolution,[],[f1479,f164]) ).
fof(f1487,plain,
$false,
inference(forward_subsumption_resolution,[],[f1481,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM437+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 19:55:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.83/1.29 % (1561641)Detected formulas, will run a generic FOF schedule.
% 2.83/1.29 % (1561652)dis-21_1_sil=8000:lcm=predicate:random_seed=3542406659: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)
% 2.83/1.29 % (1561652)Instruction limit reached!
% 2.83/1.29 % (1561652)------------------------------
% 2.83/1.29 % (1561652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (1561652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (1561652)CaDiCaL version: 2.1.3
% 2.83/1.29 % (1561652)Termination reason: Instruction limit
% 2.83/1.29 % (1561652)Termination phase: Saturation
% 2.83/1.29 % (1561652)Time elapsed: 0.041 s
% 2.83/1.29 % (1561652)Peak memory usage: 89 MB
% 2.83/1.29 % (1561652)Instructions burned: 132 (million)
% 2.83/1.29 % (1561650)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3306694642:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.29 % (1561646)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=3295640083:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.29 % (1561651)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2519342620:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.29 % (1561649)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4108742311:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.29 % (1561647)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=2727668885:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.29 % (1561648)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=349475569:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.29 % (1561650)First to succeed.
% 2.83/1.29 % (1561650)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1561641"
% 2.83/1.29 % (1561649)Also succeeded, but the first one will report.
% 2.83/1.29 % (1561654)lrs+10_1_sil=8000:sp=occurrence:random_seed=2158749617:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.83/1.29 % (1561651)Instruction limit reached!
% 2.83/1.29 % (1561651)------------------------------
% 2.83/1.29 % (1561651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (1561651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (1561651)CaDiCaL version: 2.1.3
% 2.83/1.29 % (1561651)Termination reason: Instruction limit
% 2.83/1.29 % (1561651)Termination phase: Saturation
% 2.83/1.29 % (1561651)Time elapsed: 0.100 s
% 2.83/1.29 % (1561651)Peak memory usage: 90 MB
% 2.83/1.29 % (1561651)Instructions burned: 140 (million)
% 2.83/1.29 % (1561654)Instruction limit reached!
% 2.83/1.29 % (1561654)------------------------------
% 2.83/1.29 % (1561654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (1561654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (1561654)CaDiCaL version: 2.1.3
% 2.83/1.29 % (1561654)Termination reason: Instruction limit
% 2.83/1.29 % (1561654)Termination phase: Saturation
% 2.83/1.29 % (1561654)Time elapsed: 0.093 s
% 2.83/1.29 % (1561654)Peak memory usage: 92 MB
% 2.83/1.29 % (1561654)Instructions burned: 287 (million)
% 2.83/1.29 % (1561662)lrs+10_1_sil=32000:urr=on:br=off:random_seed=426498711:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.83/1.29 % (1561663)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2124220382:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.83/1.29 % (1561650)Refutation found. Thanks to Tanya!
% 2.83/1.29 % SZS status Theorem for theBenchmark
% 2.83/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.49 % (1561650)------------------------------
% 3.74/1.49 % (1561650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.49 % (1561650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.49 % (1561650)CaDiCaL version: 2.1.3
% 3.74/1.49 % (1561650)Termination reason: Refutation
% 3.74/1.49 % (1561650)Time elapsed: 0.034 s
% 3.74/1.49 % (1561650)Peak memory usage: 89 MB
% 3.74/1.49 % (1561650)Instructions burned: 52 (million)
% 3.74/1.49 % (1561650)------------------------------
% 3.74/1.49 % (1561650)------------------------------
% 3.74/1.49 % (1561641)Success in time 0.447 s
% 3.74/1.49 % Vampire exiting
%------------------------------------------------------------------------------