%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM450+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 01:49:07 PM UTC 2026
% Result : Theorem 0.37s 1.07s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 467 ( 68 equ)
% Maximal formula atoms : 116 ( 19 avg)
% Number of connectives : 606 ( 163 ~; 179 |; 210 &)
% ( 20 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 70 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
<=> ( ? [X3] :
( aElementOf0(X2,X3)
& aElementOf0(X3,xS) )
& aInteger0(X2) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) ) ) ) )
& X1 != sz00
& aInteger0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2079,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).
fof(m__2144,hypothesis,
( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& X2 != sz00
& aInteger0(X2) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& X2 != sz00
& aInteger0(X2) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(c_0_3,negated_conjecture,
~ ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
<=> ( ? [X3] :
( aElementOf0(X2,X3)
& aElementOf0(X3,xS) )
& aInteger0(X2) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) ) ) ) )
& X1 != sz00
& aInteger0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_4,negated_conjecture,
~ ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz10,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
<=> ( ? [X3] :
( aElementOf0(X2,X3)
& aElementOf0(X3,xS) )
& aInteger0(X2) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) ) ) ) )
& X1 != sz00
& aInteger0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
fof(c_0_6,hypothesis,
( ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& X2 != sz00
& aInteger0(X2) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,X1,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& X2 != sz00
& aInteger0(X2) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_simplification,[status(thm)],[m__2144]) ).
fof(c_0_7,negated_conjecture,
! [X47,X48,X50,X51,X52,X54,X55,X56,X57] :
( ( X47 = sz00
| ~ aInteger0(X47)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X47),stldt0(sbsmnsldt0(xS))) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(esk13_1(X47),stldt0(sbsmnsldt0(xS))) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(esk13_1(X47),szAzrzSzezqlpdtcmdtrp0(sz10,X47)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(X57,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X57,sbsmnsldt0(xS))
| ~ aInteger0(X57) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X56,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X56,sbsmnsldt0(xS)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X56,stldt0(sbsmnsldt0(xS)))
| aInteger0(X56) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(X54,sbsmnsldt0(xS))
| ~ aElementOf0(X54,X55)
| ~ aElementOf0(X55,xS)
| ~ aInteger0(X54) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X52,sbsmnsldt0(xS))
| aElementOf0(X52,esk12_2(X47,X52)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X52,sbsmnsldt0(xS))
| aElementOf0(esk12_2(X47,X52),xS) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X52,sbsmnsldt0(xS))
| aInteger0(X52) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aSet0(sbsmnsldt0(xS)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(X50,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| ~ aInteger0(X50)
| ~ sdteqdtlpzmzozddtrp0(X50,sz10,X47) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(X50,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| ~ aInteger0(X50)
| ~ aDivisorOf0(X47,sdtpldt0(X50,smndt0(sz10))) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aElementOf0(X50,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| ~ aInteger0(X50)
| sdtasdt0(X47,X51) != sdtpldt0(X50,smndt0(sz10))
| ~ aInteger0(X51) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X48,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| sdteqdtlpzmzozddtrp0(X48,sz10,X47) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X48,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| aDivisorOf0(X47,sdtpldt0(X48,smndt0(sz10))) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X48,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| sdtasdt0(X47,esk11_2(X47,X48)) = sdtpldt0(X48,smndt0(sz10)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X48,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| aInteger0(esk11_2(X47,X48)) )
& ( X47 = sz00
| ~ aInteger0(X47)
| ~ aElementOf0(X48,szAzrzSzezqlpdtcmdtrp0(sz10,X47))
| aInteger0(X48) )
& ( X47 = sz00
| ~ aInteger0(X47)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X47)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])]) ).
fof(c_0_8,hypothesis,
! [X17,X19,X20,X21,X22] :
( stldt0(sbsmnsldt0(xS)) = cS2076
& ( aElementOf0(X22,stldt0(sbsmnsldt0(xS)))
| X22 != smndt0(sz10) )
& ( aElementOf0(X22,stldt0(sbsmnsldt0(xS)))
| X22 != sz10 )
& ( X22 = smndt0(sz10)
| X22 = sz10
| ~ aElementOf0(X22,stldt0(sbsmnsldt0(xS))) )
& ( aElementOf0(X21,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X21,sbsmnsldt0(xS))
| ~ aInteger0(X21) )
& ( ~ aElementOf0(X21,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X21,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X21,stldt0(sbsmnsldt0(xS)))
| aInteger0(X21) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X19,sbsmnsldt0(xS))
| ~ aElementOf0(X19,X20)
| ~ aElementOf0(X20,xS)
| ~ aInteger0(X19) )
& ( ~ aElementOf0(X17,sbsmnsldt0(xS))
| aElementOf0(X17,esk4_1(X17)) )
& ( ~ aElementOf0(X17,sbsmnsldt0(xS))
| aElementOf0(esk4_1(X17),xS) )
& ( ~ aElementOf0(X17,sbsmnsldt0(xS))
| aInteger0(X17) )
& aSet0(sbsmnsldt0(xS)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])]) ).
fof(c_0_9,hypothesis,
! [X23,X25,X26,X27,X28,X30,X32,X33,X34,X35,X37,X38,X39,X40,X42,X44,X45,X46] :
( ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)),stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X46,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X46,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40))) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X44,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| ~ aInteger0(X44)
| ~ sdteqdtlpzmzozddtrp0(X44,X40,esk9_1(X40)) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X44,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| ~ aInteger0(X44)
| ~ aDivisorOf0(esk9_1(X40),sdtpldt0(X44,smndt0(X40))) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X44,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| ~ aInteger0(X44)
| sdtasdt0(esk9_1(X40),X45) != sdtpldt0(X44,smndt0(X40))
| ~ aInteger0(X45) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X42,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| sdteqdtlpzmzozddtrp0(X42,X40,esk9_1(X40)) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X42,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| aDivisorOf0(esk9_1(X40),sdtpldt0(X42,smndt0(X40))) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X42,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| sdtasdt0(esk9_1(X40),esk10_2(X40,X42)) = sdtpldt0(X42,smndt0(X40)) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X42,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| aInteger0(esk10_2(X40,X42)) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X42,szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40)))
| aInteger0(X42) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X40,esk9_1(X40))) )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| esk9_1(X40) != sz00 )
& ( ~ aElementOf0(X40,stldt0(sbsmnsldt0(xS)))
| aInteger0(esk9_1(X40)) )
& ( aElementOf0(X39,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X39,sbsmnsldt0(xS))
| ~ aInteger0(X39) )
& ( ~ aElementOf0(X39,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X39,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X39,stldt0(sbsmnsldt0(xS)))
| aInteger0(X39) )
& ( aElementOf0(X37,sbsmnsldt0(xS))
| ~ aElementOf0(X37,X38)
| ~ aElementOf0(X38,xS)
| ~ aInteger0(X37) )
& ( ~ aElementOf0(X35,sbsmnsldt0(xS))
| aElementOf0(X35,esk8_1(X35)) )
& ( ~ aElementOf0(X35,sbsmnsldt0(xS))
| aElementOf0(esk8_1(X35),xS) )
& ( ~ aElementOf0(X35,sbsmnsldt0(xS))
| aInteger0(X35) )
& aSet0(sbsmnsldt0(xS))
& isClosed0(sbsmnsldt0(xS))
& isOpen0(stldt0(sbsmnsldt0(xS)))
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)),stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X34,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X34,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28))) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X32,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| ~ aInteger0(X32)
| ~ sdteqdtlpzmzozddtrp0(X32,X28,esk6_1(X28)) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X32,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| ~ aInteger0(X32)
| ~ aDivisorOf0(esk6_1(X28),sdtpldt0(X32,smndt0(X28))) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X32,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| ~ aInteger0(X32)
| sdtasdt0(esk6_1(X28),X33) != sdtpldt0(X32,smndt0(X28))
| ~ aInteger0(X33) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X30,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| sdteqdtlpzmzozddtrp0(X30,X28,esk6_1(X28)) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X30,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| aDivisorOf0(esk6_1(X28),sdtpldt0(X30,smndt0(X28))) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X30,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| sdtasdt0(esk6_1(X28),esk7_2(X28,X30)) = sdtpldt0(X30,smndt0(X28)) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X30,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| aInteger0(esk7_2(X28,X30)) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X30,szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28)))
| aInteger0(X30) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aSet0(szAzrzSzezqlpdtcmdtrp0(X28,esk6_1(X28))) )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| esk6_1(X28) != sz00 )
& ( ~ aElementOf0(X28,stldt0(sbsmnsldt0(xS)))
| aInteger0(esk6_1(X28)) )
& ( aElementOf0(X27,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X27,sbsmnsldt0(xS))
| ~ aInteger0(X27) )
& ( ~ aElementOf0(X27,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X27,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X27,stldt0(sbsmnsldt0(xS)))
| aInteger0(X27) )
& ( aElementOf0(X25,sbsmnsldt0(xS))
| ~ aElementOf0(X25,X26)
| ~ aElementOf0(X26,xS)
| ~ aInteger0(X25) )
& ( ~ aElementOf0(X23,sbsmnsldt0(xS))
| aElementOf0(X23,esk5_1(X23)) )
& ( ~ aElementOf0(X23,sbsmnsldt0(xS))
| aElementOf0(esk5_1(X23),xS) )
& ( ~ aElementOf0(X23,sbsmnsldt0(xS))
| aInteger0(X23) )
& aSet0(sbsmnsldt0(xS)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( ~ aInteger0(X1)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk6_1(X1)),stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
( X1 != sz10
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ aInteger0(X1)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),cS2076)
| X1 = sz00 ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
( ~ aElementOf0(X1,cS2076)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk6_1(X1)),cS2076) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_11]) ).
cnf(c_0_16,hypothesis,
aElementOf0(sz10,cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11])]) ).
cnf(c_0_17,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aInteger0(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| esk6_1(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ aInteger0(esk6_1(sz10))
| esk6_1(sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,hypothesis,
( ~ aElementOf0(X1,cS2076)
| aInteger0(esk6_1(X1)) ),
inference(rw,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,cS2076)
| esk6_1(X1) != sz00 ),
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_22,hypothesis,
esk6_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]) ).
cnf(c_0_23,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.46 % Problem : NUM450+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.52 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.90 % Computer : n010.cluster.edu
% 0.19/0.90 % Model : x86_64 x86_64
% 0.19/0.90 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.90 % Memory : 8046.5625MB
% 0.19/0.90 % OS : Linux 6.8.0-71-generic
% 0.19/0.90 % CPULimit : 300
% 0.19/0.90 % WCLimit : 300
% 0.19/0.90 % DateTime : Mon Sep 21 02:30:47 UTC 2026
% 0.19/0.91 % CPUTime :
% 0.19/0.91 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.96 Running first-order theorem proving
% 0.19/0.96 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/1.07 % Version: 3.5.1
% 0.37/1.07 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/1.07 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/1.07 % Starting new_bool_3 with 300s (1) cores
% 0.37/1.07 % Starting new_bool_1 with 300s (1) cores
% 0.37/1.07 % Starting sh5l with 300s (1) cores
% 0.37/1.07 % new_bool_1 with pid 4044397 completed with status 0
% 0.37/1.07 % Result found by new_bool_1
% 0.37/1.07 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/1.07 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/1.07 % Starting new_bool_3 with 300s (1) cores
% 0.37/1.07 % Starting new_bool_1 with 300s (1) cores
% 0.37/1.07 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.37/1.07 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/1.07 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.37/1.07 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/1.07 % Starting SubtermCWHack with 31s (1) cores
% 0.37/1.07 % SubtermCWHack with pid 4044406 completed with status 0
% 0.37/1.07 % Result found by SubtermCWHack
% 0.37/1.07 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/1.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/1.07 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/1.07 % Starting new_bool_3 with 300s (1) cores
% 0.37/1.07 % Starting new_bool_1 with 300s (1) cores
% 0.37/1.07 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.37/1.07 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/1.07 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.37/1.07 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/1.07 % Starting SubtermCWHack with 31s (1) cores
% 0.37/1.07 % Preprocessing time : 0.003 s
% 0.37/1.07
% 0.37/1.07 % Proof found!
% 0.37/1.07 % SZS status Theorem
% 0.37/1.07 % SZS output start CNFRefutation
% See solution above
% 0.37/1.07 % Parsed axioms : 46
% 0.37/1.07 % Removed by relevancy pruning/SinE : 4
% 0.37/1.07 % Initial clauses : 195
% 0.37/1.07 % Removed in clause preprocessing : 5
% 0.37/1.07 % Initial clauses in saturation : 190
% 0.37/1.07 % Processed clauses : 185
% 0.37/1.07 % ...of these trivial : 3
% 0.37/1.07 % ...subsumed : 44
% 0.37/1.07 % ...remaining for further processing : 138
% 0.37/1.07 % Other redundant clauses eliminated : 14
% 0.37/1.07 % Clauses deleted for lack of memory : 0
% 0.37/1.07 % Backward-subsumed : 0
% 0.37/1.07 % Backward-rewritten : 3
% 0.37/1.07 % Generated clauses : 199
% 0.37/1.07 % ...of the previous two non-redundant : 159
% 0.37/1.07 % ...aggressively subsumed : 0
% 0.37/1.07 % Contextual simplify-reflections : 3
% 0.37/1.07 % Paramodulations : 184
% 0.37/1.07 % Factorizations : 1
% 0.37/1.07 % NegExts : 0
% 0.37/1.07 % Equation resolutions : 14
% 0.37/1.07 % Disequality decompositions : 0
% 0.37/1.07 % Total rewrite steps : 122
% 0.37/1.07 % ...of those cached : 109
% 0.37/1.07 % Propositional unsat checks : 0
% 0.37/1.07 % Propositional check models : 0
% 0.37/1.07 % Propositional check unsatisfiable : 0
% 0.37/1.07 % Propositional clauses : 0
% 0.37/1.07 % Propositional clauses after purity: 0
% 0.37/1.07 % Propositional unsat core size : 0
% 0.37/1.07 % Propositional preprocessing time : 0.000
% 0.37/1.07 % Propositional encoding time : 0.000
% 0.37/1.07 % Propositional solver time : 0.000
% 0.37/1.07 % Success case prop preproc time : 0.000
% 0.37/1.07 % Success case prop encoding time : 0.000
% 0.37/1.07 % Success case prop solver time : 0.000
% 0.37/1.07 % Current number of processed clauses : 122
% 0.37/1.07 % Positive orientable unit clauses : 15
% 0.37/1.07 % Positive unorientable unit clauses: 0
% 0.37/1.07 % Negative unit clauses : 0
% 0.37/1.07 % Non-unit-clauses : 107
% 0.37/1.07 % Current number of unprocessed clauses: 163
% 0.37/1.07 % ...number of literals in the above : 773
% 0.37/1.07 % Current number of archived formulas : 0
% 0.37/1.07 % Current number of archived clauses : 3
% 0.37/1.07 % Clause-clause subsumption calls (NU) : 1335
% 0.37/1.07 % Rec. Clause-clause subsumption calls : 809
% 0.37/1.07 % Non-unit clause-clause subsumptions : 47
% 0.37/1.07 % Unit Clause-clause subsumption calls : 22
% 0.37/1.07 % Rewrite failures with RHS unbound : 0
% 0.37/1.07 % BW rewrite match attempts : 3
% 0.37/1.07 % BW rewrite match successes : 3
% 0.37/1.07 % Condensation attempts : 0
% 0.37/1.07 % Condensation successes : 0
% 0.37/1.07 % Termbank termtop insertions : 18085
% 0.37/1.07 % Search garbage collected termcells : 3482
% 0.37/1.07
% 0.37/1.07 % -------------------------------------------------
% 0.37/1.07 % User time : 0.021 s
% 0.37/1.07 % System time : 0.003 s
% 0.37/1.07 % Total time : 0.024 s
% 0.37/1.07 % Maximum resident set size: 4172 pages
% 0.37/1.07
% 0.37/1.07 % -------------------------------------------------
% 0.37/1.07 % User time : 0.023 s
% 0.37/1.07 % System time : 0.008 s
% 0.37/1.07 % Total time : 0.031 s
% 0.37/1.07 % Maximum resident set size: 4864 pages
% 0.37/1.07 % E exiting
%------------------------------------------------------------------------------