TSTP Solution File: NUM456+6 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM456+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 12:26:49 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 144 ( 25 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 182 ( 59 ~; 29 |; 75 &)
% ( 16 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 = sz10
| W0 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ) ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(W0,sz10,xp) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(W0,sz10,xp) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ) ).
fof(m__2203,hypothesis,
? [W0] :
( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ~ ( W0 = sz10
| W0 = smndt0(sz10)
| aElementOf0(W0,cS2200) ) ) ).
fof(m__,conjecture,
$false ).
fof(subgoal_0,plain,
$false,
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ $false,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [W0] :
( W0 != smndt0(sz10)
& W0 != sz10
& ~ aElementOf0(W0,cS2200)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aInteger0(W0)
& sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) ),
inference(canonicalize,[],[m__2203]) ).
fof(normalize_0_1,plain,
( xp != sz00
& aInteger0(xp)
& aSet0(sbsmnsldt0(xS))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& aInteger0(W0)
& sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) ) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ~ aInteger0(W0)
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) ) ) ),
inference(canonicalize,[],[m__2171]) ).
fof(normalize_0_2,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& aSet0(sbsmnsldt0(xS))
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) )
& ! [W0] :
( ~ aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ~ aInteger0(W0)
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) ) ) ),
inference(canonicalize,[],[m__2079]) ).
fof(normalize_0_3,plain,
aSet0(sbsmnsldt0(xS)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ~ aInteger0(W0)
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) ) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ~ aInteger0(W0)
| ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( xp != sz00
& aInteger0(xp)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& aInteger0(W0)
& sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) ) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) ) ) ),
inference(simplify,[],[normalize_0_1,normalize_0_3,normalize_0_5,normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [W0] :
( ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_10,normalize_0_12]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM456+6 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 14:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------