%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:35 PM UTC 2026
% Result : Theorem 92.81s 12.34s
% Output : CNFRefutation 92.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 41
% Syntax : Number of formulae : 181 ( 33 unt; 28 def)
% Number of atoms : 769 ( 149 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 898 ( 310 ~; 273 |; 265 &)
% ( 35 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 29 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 158 ( 132 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xS = cS2043
& ! [W0] :
( ( ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 )
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) )
=> aElementOf0(W0,xS) )
& ( aElementOf0(W0,xS)
=> ? [W1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
isFinite0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(W0) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f54,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f55,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f61,plain,
! [W0,W1,W2] :
( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f64,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f70,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f224,plain,
( xS = cS2043
& ! [W0] :
( ( aElementOf0(W0,xS)
| ! [W1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) != W0
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
| ~ isPrime0(W1)
| W1 = sz00
| ~ aInteger0(W1) ) )
& ( ? [W1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,xS) ) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f225,plain,
( xS = cS2043
& ! [W0] :
( aElementOf0(W0,xS)
| ! [W1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) != W0
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
| ~ isPrime0(W1)
| W1 = sz00
| ~ aInteger0(W1) ) )
& ! [W0] :
( ? [W1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
& isPrime0(W1)
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(miniscoping,[status(thm)],[f224]) ).
fof(f226,plain,
( xS = cS2043
& ! [W0] :
( aElementOf0(W0,xS)
| ! [W1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) != W0
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,sz00,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
& sdtasdt0(W1,sK17_skl(W2,W1,W0)) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(sK17_skl(W2,W1,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1)) )
| ~ isPrime0(W1)
| W1 = sz00
| ~ aInteger0(W1) ) )
& ! [W0] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK15_skl(W0)) = W0
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,sK15_skl(W0)))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sz00,sK15_skl(W0))
& ~ aDivisorOf0(sK15_skl(W0),sdtpldt0(W2,smndt0(sz00)))
& ! [W3] :
( sdtasdt0(sK15_skl(W0),W3) != sdtpldt0(W2,smndt0(sz00))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,sz00,sK15_skl(W0))
& aDivisorOf0(sK15_skl(W0),sdtpldt0(W2,smndt0(sz00)))
& sdtasdt0(sK15_skl(W0),sK16_skl(W2,W0)) = sdtpldt0(W2,smndt0(sz00))
& aInteger0(sK16_skl(W2,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,sK15_skl(W0))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK15_skl(W0)))
& isPrime0(sK15_skl(W0))
& sK15_skl(W0) != sz00
& aInteger0(sK15_skl(W0)) )
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(W1,sK15_skl(W0)),skolemize(W3,sK16_skl(W2,W0)),skolemize(W3,sK17_skl(W2,W1,W0))],[f225]) ).
fof(f227,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f252,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( ( ( W0 != smndt0(sz10)
& W0 != sz10 )
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ( W0 = smndt0(sz10)
| W0 = sz10
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f253,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( ( W0 != smndt0(sz10)
& W0 != sz10 )
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( W0 = smndt0(sz10)
| W0 = sz10
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ! [W0] :
( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f254,plain,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( ( W0 != smndt0(sz10)
& W0 != sz10 )
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( W0 = smndt0(sz10)
| W0 = sz10
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ! [W0] :
( ( aElementOf0(W0,sK18_skl(W0))
& aElementOf0(sK18_skl(W0),xS)
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(W1,sK18_skl(W0))],[f253]) ).
fof(f255,plain,
aSet0(sbsmnsldt0(xS)),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f261,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f266,plain,
! [X0] :
( X0 != smndt0(sz10)
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f267,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f268,plain,
isFinite0(xS),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f317,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f318,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [W0] :
( ( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) ) )
& ! [W0] :
( ( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(NNF_transformation,[status(thm)],[f317]) ).
fof(f319,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ! [W0] :
( ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(miniscoping,[status(thm)],[f318]) ).
fof(f320,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( ! [W1] :
( ~ aElementOf0(W0,W1)
| ~ aElementOf0(W1,xS) )
| ~ aInteger0(W0)
| aElementOf0(W0,sbsmnsldt0(xS)) )
& ! [W0] :
( ( aElementOf0(W0,sK26_skl(W0))
& aElementOf0(sK26_skl(W0),xS)
& aInteger0(W0) )
| ~ aElementOf0(W0,sbsmnsldt0(xS)) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ~ sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& ~ aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ! [W1] :
( sdtasdt0(xp,W1) != sdtpldt0(W0,smndt0(sz10))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& sdtasdt0(xp,sK25_skl(W0)) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(sK25_skl(W0))
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl]),skolemize(W1,sK25_skl(W0)),skolemize(W1,sK26_skl(W0))],[f319]) ).
fof(f321,plain,
aInteger0(xp),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f323,plain,
aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f324,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f342,plain,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdtasdt0(xp,sK28_skl) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(sK28_skl)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtasdt0(xp,sK27_skl) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl,sK28_skl]),skolemize(W0,sK27_skl),skolemize(W0,sK28_skl)],[f47]) ).
fof(f343,plain,
aInteger0(sK27_skl),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f348,plain,
aInteger0(sK28_skl),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f352,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f353,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f354,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(cnf_transformation,[status(thm)],[f353]) ).
fof(f397,definition,
( sQ8_spl
<=> sdtpldt0(sz10,xp) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( ~ sQ8_spl
| sdtpldt0(sz10,xp) = sz10 ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ9_spl
<=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ9_spl
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f354,f397,f400]) ).
fof(f405,definition,
( sQ10_spl
<=> aInteger0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ10_spl
| ~ aInteger0(sz10) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,definition,
( sQ11_spl
<=> aInteger0(xp) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( sQ11_spl
| ~ aInteger0(xp) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f412,plain,
! [X0] :
( ~ sQ8_spl
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
| ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f398,f62]) ).
fof(f413,definition,
! [X0] :
( sQ12_spl
<=> ( sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f414,plain,
! [X0] :
( ~ sQ12_spl
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f412,f413,f405,f408,f397]) ).
fof(f417,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f321]) ).
fof(f418,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f419,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f54]) ).
fof(f420,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f423,plain,
! [X0] :
( ~ sQ9_spl
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f401,f62]) ).
fof(f425,definition,
( sQ13_spl
<=> aInteger0(smndt0(xp)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ13_spl
| ~ aInteger0(smndt0(xp)) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f433,definition,
! [X0] :
( sQ15_spl
<=> ( sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp))
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f434,plain,
! [X0] :
( ~ sQ15_spl
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp))
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f423,f433,f405,f425,f400]) ).
fof(f438,plain,
( sQ13_spl
| ~ aInteger0(xp) ),
inference(resolution,[status(thm)],[f427,f56]) ).
fof(f439,plain,
( sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f438,f408,f425]) ).
fof(f461,plain,
! [X0] :
( X0 != smndt0(sz10)
| aElementOf0(X0,cS2076) ),
inference(backward_demodulation,[status(thm)],[f267,f266]) ).
fof(f549,definition,
( sQ26_spl
<=> aInteger0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ26_spl
| ~ aInteger0(sz00) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f594,definition,
( sQ31_spl
<=> aInteger0(smndt0(sz10)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ31_spl
| ~ aInteger0(smndt0(sz10)) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f607,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,cS2076) ),
inference(forward_demodulation,[status(thm)],[f267,f261]) ).
fof(f610,plain,
! [X0] :
( X0 != smndt0(sz10)
| aInteger0(X0) ),
inference(resolution,[status(thm)],[f607,f461]) ).
fof(f649,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f53]) ).
fof(f650,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f708,definition,
! [X0] :
( sQ45_spl
<=> ( ~ aInteger0(X0)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f709,plain,
! [X0] :
( ~ sQ45_spl
| ~ aInteger0(X0)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f738,plain,
( sQ31_spl
| ~ aInteger0(sz10) ),
inference(resolution,[status(thm)],[f596,f56]) ).
fof(f740,plain,
( sQ31_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f738,f405,f594]) ).
fof(f784,definition,
( sQ48_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ48_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f793,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f785,f322]) ).
fof(f794,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f942,plain,
! [X0] :
( ~ sQ45_spl
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f709]) ).
fof(f949,plain,
( ~ sQ45_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f54,f942]) ).
fof(f957,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f949]) ).
fof(f1029,definition,
( sQ64_spl
<=> aSet0(sbsmnsldt0(xS)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1031,plain,
( sQ64_spl
| ~ aSet0(sbsmnsldt0(xS)) ),
inference(component_clause,[status(thm)],[f1029]) ).
fof(f1039,definition,
! [X0] :
( sQ66_spl
<=> ( ~ aInteger0(X0)
| X0 != sz10 ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1040,plain,
! [X0] :
( ~ sQ66_spl
| ~ aInteger0(X0)
| X0 != sz10 ),
inference(component_clause,[status(thm)],[f1039]) ).
fof(f1057,definition,
( sQ69_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( sQ69_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f1057]) ).
fof(f1064,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1059,f227]) ).
fof(f1065,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f1064]) ).
fof(f1172,definition,
! [X0] :
( sQ77_spl
<=> ( X0 != smndt0(sz10)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
! [X0] :
( ~ sQ77_spl
| X0 != smndt0(sz10)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f1172]) ).
fof(f1328,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1031,f255]) ).
fof(f1329,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f1328]) ).
fof(f1614,definition,
( sQ134_spl
<=> sdtpldt0(smndt0(sz10),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1615,plain,
( ~ sQ134_spl
| sdtpldt0(smndt0(sz10),sz10) = sz00 ),
inference(component_clause,[status(thm)],[f1614]) ).
fof(f1616,plain,
( sQ134_spl
| sdtpldt0(smndt0(sz10),sz10) != sz00 ),
inference(component_clause,[status(thm)],[f1614]) ).
fof(f1654,definition,
( sQ141_spl
<=> sdtpldt0(sz00,xp) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( ~ sQ141_spl
| sdtpldt0(sz00,xp) = sz00 ),
inference(component_clause,[status(thm)],[f1654]) ).
fof(f1656,plain,
( sQ141_spl
| sdtpldt0(sz00,xp) != sz00 ),
inference(component_clause,[status(thm)],[f1654]) ).
fof(f2271,definition,
( sQ214_spl
<=> sdtpldt0(smndt0(xp),sz00) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2272,plain,
( ~ sQ214_spl
| sdtpldt0(smndt0(xp),sz00) = sz00 ),
inference(component_clause,[status(thm)],[f2271]) ).
fof(f2499,definition,
! [X0] :
( sQ242_spl
<=> ( ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2500,plain,
! [X0] :
( ~ sQ242_spl
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2499]) ).
fof(f2848,plain,
( ~ sQ214_spl
| sz00 = smndt0(xp)
| ~ aInteger0(smndt0(xp)) ),
inference(paramodulation,[status(thm)],[f2272,f66]) ).
fof(f2853,definition,
( sQ287_spl
<=> sz00 = smndt0(xp) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2854,plain,
( ~ sQ287_spl
| sz00 = smndt0(xp) ),
inference(component_clause,[status(thm)],[f2853]) ).
fof(f2856,plain,
( ~ sQ214_spl
| sQ287_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2848,f425,f2853,f2271]) ).
fof(f2869,plain,
( ~ sQ287_spl
| sz00 = sdtpldt0(sz00,xp)
| ~ aInteger0(xp) ),
inference(paramodulation,[status(thm)],[f2854,f70]) ).
fof(f2876,plain,
( ~ sQ287_spl
| sQ141_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2869,f408,f1654,f2853]) ).
fof(f2898,plain,
( ~ sQ141_spl
| xp = sz00
| ~ aInteger0(xp) ),
inference(paramodulation,[status(thm)],[f1655,f67]) ).
fof(f2902,plain,
( ~ sQ141_spl
| sQ48_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2898,f408,f784,f1654]) ).
fof(f2917,definition,
( sQ293_spl
<=> isFinite0(xS) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2919,plain,
( sQ293_spl
| ~ isFinite0(xS) ),
inference(component_clause,[status(thm)],[f2917]) ).
fof(f2963,plain,
( sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2919,f268]) ).
fof(f2964,plain,
sQ293_spl,
inference(contradiction_clause,[status(thm)],[f2963]) ).
fof(f3291,definition,
( sQ327_spl
<=> sbsmnsldt0(xS) = sbsmnsldt0(xS) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f3293,plain,
( sQ327_spl
| sbsmnsldt0(xS) != sbsmnsldt0(xS) ),
inference(component_clause,[status(thm)],[f3291]) ).
fof(f3318,plain,
( sQ327_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3293]) ).
fof(f3319,plain,
sQ327_spl,
inference(contradiction_clause,[status(thm)],[f3318]) ).
fof(f3466,plain,
! [X0] :
( ~ sQ242_spl
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2500]) ).
fof(f3475,plain,
( ~ sQ242_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f323,f3466]) ).
fof(f3479,plain,
~ sQ242_spl,
inference(contradiction_clause,[status(thm)],[f3475]) ).
fof(f3545,plain,
( ~ sQ66_spl
| sz10 != sz10 ),
inference(resolution,[status(thm)],[f1040,f54]) ).
fof(f3546,plain,
( ~ sQ66_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3545]) ).
fof(f3547,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f3546]) ).
fof(f3939,plain,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(resolution,[status(thm)],[f352,f324]) ).
fof(f4459,plain,
! [X0] :
( ~ sQ77_spl
| X0 != smndt0(sz10) ),
inference(forward_subsumption_resolution,[status(thm)],[f1173,f610]) ).
fof(f4469,plain,
( ~ sQ77_spl
| $false ),
inference(equality_resolution,[status(thm)],[f4459]) ).
fof(f4474,plain,
~ sQ77_spl,
inference(contradiction_clause,[status(thm)],[f4469]) ).
fof(f4647,definition,
( sQ429_spl
<=> aInteger0(sdtpldt0(sz10,smndt0(xp))) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f4649,plain,
( sQ429_spl
| ~ aInteger0(sdtpldt0(sz10,smndt0(xp))) ),
inference(component_clause,[status(thm)],[f4647]) ).
fof(f4798,definition,
( sQ444_spl
<=> aInteger0(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f4800,plain,
( sQ444_spl
| ~ aInteger0(sK27_skl) ),
inference(component_clause,[status(thm)],[f4798]) ).
fof(f4805,plain,
( sQ444_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4800,f343]) ).
fof(f4806,plain,
sQ444_spl,
inference(contradiction_clause,[status(thm)],[f4805]) ).
fof(f4973,definition,
( sQ460_spl
<=> aInteger0(sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f4975,plain,
( sQ460_spl
| ~ aInteger0(sK28_skl) ),
inference(component_clause,[status(thm)],[f4973]) ).
fof(f4986,plain,
( sQ460_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4975,f348]) ).
fof(f4987,plain,
sQ460_spl,
inference(contradiction_clause,[status(thm)],[f4986]) ).
fof(f5003,definition,
! [X0] :
( sQ464_spl
<=> ( ~ aInteger0(X0)
| sz00 != X0
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f5004,plain,
! [X0] :
( ~ sQ464_spl
| ~ aInteger0(X0)
| sz00 != X0
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f5003]) ).
fof(f5012,plain,
! [X0] :
( ~ sQ464_spl
| sz00 != X0
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5004]) ).
fof(f5050,plain,
( ~ sQ464_spl
| sz00 != sz00 ),
inference(resolution,[status(thm)],[f5012,f53]) ).
fof(f5056,plain,
( ~ sQ464_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5050]) ).
fof(f5057,plain,
~ sQ464_spl,
inference(contradiction_clause,[status(thm)],[f5056]) ).
fof(f5248,plain,
( sQ429_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4649,f3939]) ).
fof(f5249,plain,
sQ429_spl,
inference(contradiction_clause,[status(thm)],[f5248]) ).
fof(f6968,plain,
( ~ sQ134_spl
| ~ sQ12_spl
| sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(paramodulation,[status(thm)],[f1615,f414]) ).
fof(f6969,definition,
( sQ666_spl
<=> sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,xp) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f6970,plain,
( ~ sQ666_spl
| sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,xp) ),
inference(component_clause,[status(thm)],[f6969]) ).
fof(f6972,plain,
( ~ sQ134_spl
| ~ sQ12_spl
| sQ666_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f6968,f594,f6969,f413,f1614]) ).
fof(f6973,plain,
( ~ sQ666_spl
| ~ sQ134_spl
| sz00 = sdtpldt0(sz00,xp) ),
inference(forward_demodulation,[status(thm)],[f1615,f6970]) ).
fof(f6974,plain,
( ~ sQ666_spl
| ~ sQ134_spl
| sQ141_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6973,f1656]) ).
fof(f6975,plain,
( ~ sQ666_spl
| ~ sQ134_spl
| sQ141_spl ),
inference(contradiction_clause,[status(thm)],[f6974]) ).
fof(f7215,plain,
( sQ134_spl
| ~ aInteger0(sz10) ),
inference(resolution,[status(thm)],[f1616,f70]) ).
fof(f7216,plain,
( sQ134_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f7215,f405,f1614]) ).
fof(f7572,plain,
( ~ sQ134_spl
| ~ sQ15_spl
| sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,smndt0(xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(paramodulation,[status(thm)],[f1615,f434]) ).
fof(f7574,definition,
( sQ710_spl
<=> sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,smndt0(xp)) ),
introduced(definition,[new_symbols(definition,[sQ710_spl])],[split_symbol_definition]) ).
fof(f7575,plain,
( ~ sQ710_spl
| sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,smndt0(xp)) ),
inference(component_clause,[status(thm)],[f7574]) ).
fof(f7577,plain,
( ~ sQ134_spl
| ~ sQ15_spl
| sQ710_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f7572,f594,f7574,f433,f1614]) ).
fof(f7579,plain,
( ~ sQ710_spl
| ~ sQ134_spl
| sz00 = sdtpldt0(sz00,smndt0(xp)) ),
inference(forward_demodulation,[status(thm)],[f1615,f7575]) ).
fof(f7631,plain,
( ~ sQ710_spl
| ~ sQ134_spl
| sdtpldt0(smndt0(xp),sz00) = sz00
| ~ aInteger0(sz00)
| ~ aInteger0(smndt0(xp)) ),
inference(paramodulation,[status(thm)],[f7579,f64]) ).
fof(f7655,plain,
( ~ sQ710_spl
| ~ sQ134_spl
| sQ214_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7631,f425,f549,f2271,f1614,f7574]) ).
fof(f7657,plain,
$false,
inference(sat_refutation,[status(thm)],[f403,f416,f418,f420,f436,f439,f650,f740,f794,f957,f1065,f1329,f2856,f2876,f2902,f2964,f3319,f3479,f3547,f4474,f4806,f4987,f5057,f5249,f6972,f6975,f7216,f7577,f7655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:34:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 92.81/12.34 % Refutation found
% 92.81/12.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 92.81/12.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 74.06/12.41 % Elapsed time: 12.025511 seconds
% 74.06/12.41 % CPU time: 95.043334 seconds
% 74.06/12.41 % Total memory used: 493.057 MB
% 74.06/12.41 % Net memory used: 456.940 MB
%------------------------------------------------------------------------------