%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM449+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:42:55 PM UTC 2026
% Result : CounterSatisfiable 1.35s 0.70s
% Output : Saturation 1.35s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
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(f11,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aInteger0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> sdteqdtlpzmzozddtrp0(W0,W0,W1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2,W3] :
( ( aInteger0(W3)
& W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( ( sdteqdtlpzmzozddtrp0(W1,W3,W2)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1,W2,W3] :
( ( W3 != sz00
& aInteger0(W3)
& W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,sdtasdt0(W2,W3))
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W3)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aInteger0(W0)
=> ( ? [W1] :
( isPrime0(W1)
& aDivisorOf0(W1,W0) )
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> ! [W2] :
( W2 = sdtbsmnsldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> ! [W2] :
( W2 = sdtslmnbsdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,definition,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> aSubsetOf0(W1,cS1395) )
& aSet0(W0) )
=> ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ! [W1] :
( W1 = stldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ~ aElementOf0(W2,W0)
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,definition,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> ! [W2] :
( W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ( isOpen0(W0)
<=> ! [W1] :
( aElementOf0(W1,W0)
=> ? [W2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
& W2 != sz00
& aInteger0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ( isClosed0(W0)
<=> isOpen0(stldt0(W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> ( isOpen0(W1)
& aSubsetOf0(W1,cS1395) ) )
& aSet0(W0) )
=> isOpen0(sbsmnsldt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [W0,W1] :
( ( isOpen0(W1)
& isOpen0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [W0,W1] :
( ( isClosed0(W1)
& isClosed0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isClosed0(sdtbsmnsldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> ( isClosed0(W1)
& aSubsetOf0(W1,cS1395) ) )
& isFinite0(W0)
& aSet0(W0) )
=> isClosed0(sbsmnsldt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W0,W1] :
( ( W1 != sz00
& aInteger0(W1)
& aInteger0(W0) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),cS1395) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
xS = cS2043,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
isFinite0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
isClosed0(sbsmnsldt0(xS)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ isClosed0(sbsmnsldt0(xS)),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f50,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f51,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f52,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f53,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,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(f59,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)],[f58]) ).
fof(f60,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f61,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f63,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f66,plain,
! [X0] :
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [W0,W1,W2] :
( sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f69,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f73,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f76,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f79,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [W0] :
( ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f82,plain,
! [X0] :
( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f85,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f87,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( sdtasdt0(W1,sK0_skl(W1,W0)) = W0
& aInteger0(sK0_skl(W1,W0))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( X1 != sz00
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1] :
( aInteger0(sK0_skl(X1,X0))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0_skl(X1,X0)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f94,plain,
! [X0,X1,X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f95,plain,
! [W0,W1,W2] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f96,plain,
! [W0,W1,W2] :
( ( ( ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| sdteqdtlpzmzozddtrp0(W0,W1,W2) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
! [W0,W1] :
( sdteqdtlpzmzozddtrp0(W0,W0,W1)
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f100,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [W0,W1,W2] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f102,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [W0,W1,W2,W3] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W3)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X3)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [W0,W1,W2,W3] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W3)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,sdtasdt0(W2,W3))
| W3 = sz00
| ~ aInteger0(W3)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| X3 = sz00
| ~ aInteger0(X3)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X1,X3)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| X3 = sz00
| ~ aInteger0(X3)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
! [W0] :
( ( ? [W1] :
( isPrime0(W1)
& aDivisorOf0(W1,W0) )
<=> ( W0 != smndt0(sz10)
& W0 != sz10 ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f111,plain,
! [W0] :
( ( ( W0 = smndt0(sz10)
| W0 = sz10
| ? [W1] :
( isPrime0(W1)
& aDivisorOf0(W1,W0) ) )
& ( ( W0 != smndt0(sz10)
& W0 != sz10 )
| ! [W1] :
( ~ isPrime0(W1)
| ~ aDivisorOf0(W1,W0) ) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [W0] :
( ( ( W0 = smndt0(sz10)
| W0 = sz10
| ( isPrime0(sK1_skl(W0))
& aDivisorOf0(sK1_skl(W0),W0) ) )
& ( ( W0 != smndt0(sz10)
& W0 != sz10 )
| ! [W1] :
( ~ isPrime0(W1)
| ~ aDivisorOf0(W1,W0) ) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W1,sK1_skl(W0))],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( X0 != sz10
| ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( X0 != smndt0(sz10)
| ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0] :
( X0 = smndt0(sz10)
| X0 = sz10
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f116,plain,
! [X0] :
( X0 = smndt0(sz10)
| X0 = sz10
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f123,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f124,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f126,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK2_skl(W1,W0),W0)
& aElementOf0(sK2_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W2,sK2_skl(W1,W0))],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( aElementOf0(sK2_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aElementOf0(sK2_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f133,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtbsmnsldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) ) )
& aSet0(W2) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f134,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( aElementOf0(sK3_skl(W2,W1,W0),W1)
| aElementOf0(sK3_skl(W2,W1,W0),W0) )
& aInteger0(sK3_skl(W2,W1,W0)) )
| aElementOf0(sK3_skl(W2,W1,W0),W2) )
& ( ( ~ aElementOf0(sK3_skl(W2,W1,W0),W1)
& ~ aElementOf0(sK3_skl(W2,W1,W0),W0) )
| ~ aInteger0(sK3_skl(W2,W1,W0))
| ~ aElementOf0(sK3_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f135]) ).
fof(f137,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( aInteger0(X3)
| ~ aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(X2,X1,X0),X0)
| ~ aInteger0(sK3_skl(X2,X1,X0))
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(X2,X1,X0),X1)
| ~ aInteger0(sK3_skl(X2,X1,X0))
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f144,plain,
! [X0,X1,X2] :
( aInteger0(sK3_skl(X2,X1,X0))
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f145,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,X1,X0),X1)
| aElementOf0(sK3_skl(X2,X1,X0),X0)
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f146,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtslmnbsdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) ) )
& aSet0(W2) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f147,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f148,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtslmnbsdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> sP0_prd(W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(formula_renaming,[status(thm)],[f146,f147]) ).
fof(f149,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtslmnbsdt0(W0,W1) )
& ( ( ! [W3] :
( ( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtslmnbsdt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtslmnbsdt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtslmnbsdt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f151,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP0_prd(sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ~ sP0_prd(sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtslmnbsdt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtslmnbsdt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W3,sK4_skl(W2,W1,W0))],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtslmnbsdt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X1,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtslmnbsdt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X0)
| aElementOf0(X3,X2)
| X2 != sdtslmnbsdt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ sP0_prd(sK4_skl(X2,X1,X0),X1,X0)
| ~ aElementOf0(sK4_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtslmnbsdt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
! [X0,X1,X2] :
( sP0_prd(sK4_skl(X2,X1,X0),X1,X0)
| aElementOf0(sK4_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtslmnbsdt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f157,plain,
! [W0] :
( ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) )
| ? [W1] :
( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f158,definition,
! [W0,W1] :
( sP1_prd(W1,W0)
<=> ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f159,plain,
! [W0] :
( ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) )
| ? [W1] : sP1_prd(W1,W0)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f157,f158]) ).
fof(f160,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = sbsmnsldt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ( ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != sbsmnsldt0(W0) ) )
| ? [W1] : sP1_prd(W1,W0)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = sbsmnsldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != sbsmnsldt0(W0) ) )
| ? [W1] : sP1_prd(W1,W0)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( aElementOf0(sK7_skl(W1,W0),sK8_skl(W1,W0))
& aElementOf0(sK8_skl(W1,W0),W0)
& aInteger0(sK7_skl(W1,W0)) )
| aElementOf0(sK7_skl(W1,W0),W1) )
& ( ! [W3] :
( ~ aElementOf0(sK7_skl(W1,W0),W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(sK7_skl(W1,W0))
| ~ aElementOf0(sK7_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = sbsmnsldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( ~ aElementOf0(W2,W3)
| ~ aElementOf0(W3,W0) )
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( aElementOf0(W2,sK6_skl(W2,W1,W0))
& aElementOf0(sK6_skl(W2,W1,W0),W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != sbsmnsldt0(W0) ) )
| sP1_prd(sK5_skl(W0),W0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(W1,sK5_skl(W0)),skolemize(W3,sK6_skl(W2,W1,W0)),skolemize(W2,sK7_skl(W1,W0)),skolemize(W3,sK8_skl(W1,W0))],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,X1)
| X1 != sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1,X2] :
( aElementOf0(sK6_skl(X2,X1,X0),X0)
| ~ aElementOf0(X2,X1)
| X1 != sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f166,plain,
! [X0,X1,X2] :
( aElementOf0(X2,sK6_skl(X2,X1,X0))
| ~ aElementOf0(X2,X1)
| X1 != sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,X1)
| X1 != sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK7_skl(X1,X0),X2)
| ~ aElementOf0(X2,X0)
| ~ aInteger0(sK7_skl(X1,X0))
| ~ aElementOf0(sK7_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f169,plain,
! [X0,X1] :
( aInteger0(sK7_skl(X1,X0))
| aElementOf0(sK7_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f170,plain,
! [X0,X1] :
( aElementOf0(sK8_skl(X1,X0),X0)
| aElementOf0(sK7_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f171,plain,
! [X0,X1] :
( aElementOf0(sK7_skl(X1,X0),sK8_skl(X1,X0))
| aElementOf0(sK7_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = sbsmnsldt0(X0)
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f172,plain,
! [W0] :
( ! [W1] :
( W1 = stldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ~ aElementOf0(W2,W0)
& aInteger0(W2) ) )
& aSet0(W1) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f173,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f175,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( ~ aElementOf0(sK9_skl(W1,W0),W0)
& aInteger0(sK9_skl(W1,W0)) )
| aElementOf0(sK9_skl(W1,W0),W1) )
& ( aElementOf0(sK9_skl(W1,W0),W0)
| ~ aInteger0(sK9_skl(W1,W0))
| ~ aElementOf0(sK9_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(W2,sK9_skl(W1,W0))],[f174]) ).
fof(f176,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f179,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f180,plain,
! [X0,X1] :
( aElementOf0(sK9_skl(X1,X0),X0)
| ~ aInteger0(sK9_skl(X1,X0))
| ~ aElementOf0(sK9_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f181,plain,
! [X0,X1] :
( aInteger0(sK9_skl(X1,X0))
| aElementOf0(sK9_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aElementOf0(sK9_skl(X1,X0),X0)
| aElementOf0(sK9_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f183,plain,
! [W0,W1] :
( ! [W2] :
( W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) ) )
& aSet0(W2) ) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f184,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1) )
& ( ( ! [W3] :
( ( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != szAzrzSzezqlpdtcmdtrp0(W0,W1) ) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != szAzrzSzezqlpdtcmdtrp0(W0,W1) ) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(sK10_skl(W2,W1,W0),W0,W1)
& aInteger0(sK10_skl(W2,W1,W0)) )
| aElementOf0(sK10_skl(W2,W1,W0),W2) )
& ( ~ sdteqdtlpzmzozddtrp0(sK10_skl(W2,W1,W0),W0,W1)
| ~ aInteger0(sK10_skl(W2,W1,W0))
| ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = szAzrzSzezqlpdtcmdtrp0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sdteqdtlpzmzozddtrp0(W3,W0,W1)
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sdteqdtlpzmzozddtrp0(W3,W0,W1)
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != szAzrzSzezqlpdtcmdtrp0(W0,W1) ) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f185]) ).
fof(f187,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( aInteger0(X3)
| ~ aElementOf0(X3,X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f189,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f190,plain,
! [X0,X1,X2,X3] :
( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ sdteqdtlpzmzozddtrp0(sK10_skl(X2,X1,X0),X0,X1)
| ~ aInteger0(sK10_skl(X2,X1,X0))
| ~ aElementOf0(sK10_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f192,plain,
! [X0,X1,X2] :
( aInteger0(sK10_skl(X2,X1,X0))
| aElementOf0(sK10_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f193,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X2,X1,X0),X0,X1)
| aElementOf0(sK10_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f194,plain,
! [W0] :
( ( isOpen0(W0)
<=> ! [W1] :
( ? [W2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
& W2 != sz00
& aInteger0(W2) )
| ~ aElementOf0(W1,W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f195,plain,
! [W0] :
( ( ( ? [W1] :
( ! [W2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
| W2 = sz00
| ~ aInteger0(W2) )
& aElementOf0(W1,W0) )
| isOpen0(W0) )
& ( ! [W1] :
( ? [W2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0)
& W2 != sz00
& aInteger0(W2) )
| ~ aElementOf0(W1,W0) )
| ~ isOpen0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
! [W0] :
( ( ( ( ! [W2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK12_skl(W0),W2),W0)
| W2 = sz00
| ~ aInteger0(W2) )
& aElementOf0(sK12_skl(W0),W0) )
| isOpen0(W0) )
& ( ! [W1] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,sK11_skl(W1,W0)),W0)
& sK11_skl(W1,W0) != sz00
& aInteger0(sK11_skl(W1,W0)) )
| ~ aElementOf0(W1,W0) )
| ~ isOpen0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(W2,sK11_skl(W1,W0)),skolemize(W1,sK12_skl(W0))],[f195]) ).
fof(f197,plain,
! [X0,X1] :
( aInteger0(sK11_skl(X1,X0))
| ~ aElementOf0(X1,X0)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( sK11_skl(X1,X0) != sz00
| ~ aElementOf0(X1,X0)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f199,plain,
! [X0,X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,sK11_skl(X1,X0)),X0)
| ~ aElementOf0(X1,X0)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f200,plain,
! [X0] :
( aElementOf0(sK12_skl(X0),X0)
| isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f201,plain,
! [X0,X1] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK12_skl(X0),X1),X0)
| X1 = sz00
| ~ aInteger0(X1)
| isOpen0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f202,plain,
! [W0] :
( ( isClosed0(W0)
<=> isOpen0(stldt0(W0)) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f203,plain,
! [W0] :
( ( ( ~ isOpen0(stldt0(W0))
| isClosed0(W0) )
& ( isOpen0(stldt0(W0))
| ~ isClosed0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( isOpen0(stldt0(X0))
| ~ isClosed0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
! [X0] :
( ~ isOpen0(stldt0(X0))
| isClosed0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f206,plain,
! [W0] :
( isOpen0(sbsmnsldt0(W0))
| ? [W1] :
( ( ~ isOpen0(W1)
| ~ aSubsetOf0(W1,cS1395) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f207,plain,
! [W0] :
( isOpen0(sbsmnsldt0(W0))
| ( ( ~ isOpen0(sK13_skl(W0))
| ~ aSubsetOf0(sK13_skl(W0),cS1395) )
& aElementOf0(sK13_skl(W0),W0) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(W1,sK13_skl(W0))],[f206]) ).
fof(f208,plain,
! [X0] :
( isOpen0(sbsmnsldt0(X0))
| aElementOf0(sK13_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0] :
( isOpen0(sbsmnsldt0(X0))
| ~ isOpen0(sK13_skl(X0))
| ~ aSubsetOf0(sK13_skl(X0),cS1395)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f210,plain,
! [W0,W1] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ isOpen0(W1)
| ~ isOpen0(W0)
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f211,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
! [W0,W1] :
( isClosed0(sdtbsmnsldt0(W0,W1))
| ~ isClosed0(W1)
| ~ isClosed0(W0)
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f213,plain,
! [X0,X1] :
( isClosed0(sdtbsmnsldt0(X0,X1))
| ~ isClosed0(X1)
| ~ isClosed0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f214,plain,
! [W0] :
( isClosed0(sbsmnsldt0(W0))
| ? [W1] :
( ( ~ isClosed0(W1)
| ~ aSubsetOf0(W1,cS1395) )
& aElementOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f215,plain,
! [W0] :
( isClosed0(sbsmnsldt0(W0))
| ( ( ~ isClosed0(sK14_skl(W0))
| ~ aSubsetOf0(sK14_skl(W0),cS1395) )
& aElementOf0(sK14_skl(W0),W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(W1,sK14_skl(W0))],[f214]) ).
fof(f216,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| aElementOf0(sK14_skl(X0),X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ~ isClosed0(sK14_skl(X0))
| ~ aSubsetOf0(sK14_skl(X0),cS1395)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f218,plain,
! [W0,W1] :
( ( isClosed0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),cS1395) )
| W1 = sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f219,plain,
! [X0,X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
xS = cS2043,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f222,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f223,plain,
isFinite0(xS),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f224,plain,
~ isClosed0(sbsmnsldt0(xS)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f225,plain,
! [W0,W1,W3] :
( ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aInteger0(W3)
| sP0_prd(W3,W1,W0) )
& ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f147]) ).
fof(f226,plain,
( ! [W0,W1,W3] :
( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aInteger0(W3)
| sP0_prd(W3,W1,W0) )
& ! [W0,W1,W3] :
( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0)
& aInteger0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f225]) ).
fof(f227,plain,
! [X0,X1,X2] :
( aInteger0(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f229,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f230,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X0,X2)
| ~ aInteger0(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f231,plain,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
| ~ aElementOf0(W1,W0)
| sP1_prd(W1,W0) )
& ( ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ sP1_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f158]) ).
fof(f232,plain,
( ! [W0,W1] :
( aSubsetOf0(W1,cS1395)
| ~ aElementOf0(W1,W0)
| sP1_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ sP1_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f233,plain,
! [X0,X1] :
( aElementOf0(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f234,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f235,plain,
! [X0,X1] :
( aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X0,X1)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f236,plain,
! [X0] :
( ~ aDivisorOf0(sz00,X0)
| ~ aInteger0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f91]) ).
fof(f237,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f238,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10)
| ~ aInteger0(sz10) ),
inference(destructive_equality_resolution,[status(thm)],[f113]) ).
fof(f239,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(destructive_equality_resolution,[status(thm)],[f114]) ).
fof(f240,plain,
! [X0,X1] :
( aSet0(sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f241,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f138]) ).
fof(f242,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X1)
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f139]) ).
fof(f243,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X1)
| ~ aInteger0(X2)
| aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f245,plain,
! [X0,X1] :
( aSet0(sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f152]) ).
fof(f246,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f153]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| aElementOf0(X2,sdtslmnbsdt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f154]) ).
fof(f248,plain,
! [X0] :
( aSet0(sbsmnsldt0(X0))
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f163]) ).
fof(f249,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,sbsmnsldt0(X0))
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f164]) ).
fof(f250,plain,
! [X0,X1] :
( aElementOf0(sK6_skl(X1,sbsmnsldt0(X0),X0),X0)
| ~ aElementOf0(X1,sbsmnsldt0(X0))
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f165]) ).
fof(f251,plain,
! [X0,X1] :
( aElementOf0(X1,sK6_skl(X1,sbsmnsldt0(X0),X0))
| ~ aElementOf0(X1,sbsmnsldt0(X0))
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f166]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(X0))
| sP1_prd(sK5_skl(X0),X0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f167]) ).
fof(f253,plain,
! [X0] :
( aSet0(stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f176]) ).
fof(f254,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f177]) ).
fof(f255,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f178]) ).
fof(f256,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f179]) ).
fof(f257,plain,
! [X0,X1] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f187]) ).
fof(f258,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f259,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f189]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ sdteqdtlpzmzozddtrp0(X2,X0,X1)
| ~ aInteger0(X2)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f190]) ).
fof(f261,plain,
! [X0] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f50,f220]) ).
fof(f262,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00))
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f261,f50]) ).
fof(f263,definition,
( sQ0_spl
<=> sz00 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f266,definition,
( sQ1_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f262,f263,f266]) ).
fof(f270,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10))
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f261]) ).
fof(f271,plain,
! [X0] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f220]) ).
fof(f272,definition,
( sQ2_spl
<=> sz10 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ2_spl
| sz10 = sz00 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f274,plain,
( sQ2_spl
| sz10 != sz00 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ3_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ3_spl
| isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10)) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f270,f272,f275]) ).
fof(f279,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,sz10))
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f271,f51]) ).
fof(f280,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,sz00))
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f271,f50]) ).
fof(f281,definition,
( sQ4_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ4_spl
| isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,sz10)) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f279,f272,f281]) ).
fof(f285,definition,
( sQ5_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f280,f263,f285]) ).
fof(f291,plain,
aInteger0(smndt0(sz00)),
inference(resolution,[status(thm)],[f53,f50]) ).
fof(f292,plain,
! [X0] :
( aInteger0(sdtpldt0(sz00,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f55,f50]) ).
fof(f293,plain,
! [X0] :
( aInteger0(sdtasdt0(sz00,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f57,f50]) ).
fof(f294,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f59,f50]) ).
fof(f295,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sdtpldt0(X0,sz00),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f59,f50]) ).
fof(f296,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,sz00)) = sdtpldt0(sdtpldt0(X0,X1),sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f59,f50]) ).
fof(f297,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f61,f50]) ).
fof(f298,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(resolution,[status(thm)],[f63,f50]) ).
fof(f300,plain,
sdtpldt0(sz00,smndt0(sz00)) = sz00,
inference(resolution,[status(thm)],[f66,f50]) ).
fof(f301,plain,
sz00 = sdtpldt0(smndt0(sz00),sz00),
inference(resolution,[status(thm)],[f67,f50]) ).
fof(f302,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f69,f50]) ).
fof(f303,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(sz00,X1)) = sdtasdt0(sdtasdt0(X0,sz00),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f69,f50]) ).
fof(f304,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,sz00)) = sdtasdt0(sdtasdt0(X0,X1),sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f69,f50]) ).
fof(f305,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f71,f50]) ).
fof(f306,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f73]) ).
fof(f307,plain,
( ~ sQ2_spl
| sdtasdt0(sz00,sz00) = sz00 ),
inference(resolution,[status(thm)],[f306,f50]) ).
fof(f308,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sdtasdt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f74]) ).
fof(f310,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f76,f50]) ).
fof(f311,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f76,f50]) ).
fof(f312,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sz00)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz00))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f76,f50]) ).
fof(f314,plain,
! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,sz00),X1) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(sz00,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f77,f50]) ).
fof(f315,plain,
! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X1,sz00))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f77,f50]) ).
fof(f317,plain,
sz00 = sdtasdt0(sz00,sz00),
inference(resolution,[status(thm)],[f80,f50]) ).
fof(f318,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(smndt0(sz00),X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f82]) ).
fof(f320,plain,
! [X0] :
( ~ sQ2_spl
| smndt0(X0) = sdtasdt0(X0,smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f83]) ).
fof(f326,definition,
( sQ6_spl
<=> aInteger0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( sQ6_spl
| ~ aInteger0(sz00) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f330,definition,
( sQ7_spl
<=> aInteger0(smndt0(sz00)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ7_spl
| aInteger0(smndt0(sz00)) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f332,plain,
( sQ7_spl
| ~ aInteger0(smndt0(sz00)) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ8_spl
<=> smndt0(sz00) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ8_spl
| smndt0(sz00) = sz00 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f335,plain,
( sQ8_spl
| smndt0(sz00) != sz00 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f339,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f57]) ).
fof(f340,plain,
! [X0] :
( X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,sz00)) ),
inference(resolution,[status(thm)],[f339,f50]) ).
fof(f341,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sz00,sz00,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f100,f50]) ).
fof(f353,definition,
! [X0,X1] :
( sQ11_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,X1,sz00)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f363,plain,
! [X0] :
( ~ sQ2_spl
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10)
| ~ aInteger0(sz00) ),
inference(forward_demodulation,[status(thm)],[f273,f238]) ).
fof(f364,plain,
! [X0] :
( ~ sQ2_spl
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz00)
| ~ aInteger0(sz00) ),
inference(forward_demodulation,[status(thm)],[f273,f363]) ).
fof(f365,plain,
! [X0] :
( ~ sQ2_spl
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f50]) ).
fof(f368,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz10)
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f115]) ).
fof(f369,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz00)
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f368]) ).
fof(f370,plain,
( ~ sQ2_spl
| sz00 = smndt0(sz00)
| sz00 = sz00
| aDivisorOf0(sK1_skl(sz00),sz00) ),
inference(resolution,[status(thm)],[f369,f50]) ).
fof(f371,definition,
( sQ12_spl
<=> aDivisorOf0(sK1_skl(sz00),sz00) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ12_spl
| aDivisorOf0(sK1_skl(sz00),sz00) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( ~ sQ2_spl
| sQ8_spl
| sQ0_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f370,f371,f263,f333,f272]) ).
fof(f375,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz10)
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f116]) ).
fof(f376,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz00)
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f375]) ).
fof(f377,plain,
( ~ sQ2_spl
| sz00 = smndt0(sz00)
| sz00 = sz00
| isPrime0(sK1_skl(sz00)) ),
inference(resolution,[status(thm)],[f376,f50]) ).
fof(f378,definition,
( sQ13_spl
<=> isPrime0(sK1_skl(sz00)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( ~ sQ13_spl
| isPrime0(sK1_skl(sz00)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ13_spl
| ~ isPrime0(sK1_skl(sz00)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ2_spl
| sQ8_spl
| sQ0_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f377,f378,f263,f333,f272]) ).
fof(f382,plain,
! [X0] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f257,f50]) ).
fof(f383,plain,
! [X0,X1] :
( aInteger0(sK10_skl(X1,X0,sz00))
| aElementOf0(sK10_skl(X1,X0,sz00),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(sz00,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f192,f50]) ).
fof(f384,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X1,X0,sz00),sz00,X0)
| aElementOf0(sK10_skl(X1,X0,sz00),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(sz00,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f193,f50]) ).
fof(f385,plain,
! [X0] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS1395)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f219,f50]) ).
fof(f386,plain,
! [X0] :
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ~ aElementOf0(X0,cS2076)
| ~ aSubsetOf0(sbsmnsldt0(xS),cS1395) ),
inference(paramodulation,[status(thm)],[f222,f255]) ).
fof(f387,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,cS2076)
| ~ aSubsetOf0(sbsmnsldt0(xS),cS1395) ),
inference(paramodulation,[status(thm)],[f222,f254]) ).
fof(f388,definition,
( sQ14_spl
<=> aSubsetOf0(sbsmnsldt0(xS),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ14_spl
| ~ aSubsetOf0(sbsmnsldt0(xS),cS1395) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,definition,
! [X0] :
( sQ15_spl
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ~ aElementOf0(X0,cS2076) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f386,f388,f391]) ).
fof(f395,definition,
! [X0] :
( sQ16_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,cS2076) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ16_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f387,f388,f395]) ).
fof(f399,plain,
( isClosed0(sbsmnsldt0(xS))
| aElementOf0(sK14_skl(xS),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f223,f216]) ).
fof(f400,definition,
( sQ17_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( sQ17_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,definition,
( sQ18_spl
<=> aElementOf0(sK14_skl(xS),xS) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f406,definition,
( sQ19_spl
<=> isClosed0(sbsmnsldt0(xS)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ19_spl
| isClosed0(sbsmnsldt0(xS)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( sQ19_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f399,f400,f403,f406]) ).
fof(f410,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f50]) ).
fof(f411,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f412,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f224]) ).
fof(f413,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f415,plain,
! [X0] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),X0),cS1395)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f219]) ).
fof(f416,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X1,X0,smndt0(sz00)),smndt0(sz00),X0)
| aElementOf0(sK10_skl(X1,X0,smndt0(sz00)),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f193]) ).
fof(f417,plain,
! [X0,X1] :
( aInteger0(sK10_skl(X1,X0,smndt0(sz00)))
| aElementOf0(sK10_skl(X1,X0,smndt0(sz00)),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f192]) ).
fof(f418,plain,
! [X0] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f257]) ).
fof(f419,plain,
( ~ sQ2_spl
| smndt0(sz00) = smndt0(sz00)
| smndt0(sz00) = sz00
| isPrime0(sK1_skl(smndt0(sz00))) ),
inference(resolution,[status(thm)],[f291,f376]) ).
fof(f420,plain,
( ~ sQ2_spl
| smndt0(sz00) = smndt0(sz00)
| smndt0(sz00) = sz00
| aDivisorOf0(sK1_skl(smndt0(sz00)),smndt0(sz00)) ),
inference(resolution,[status(thm)],[f291,f369]) ).
fof(f421,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(smndt0(sz00),smndt0(sz00),X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f100]) ).
fof(f422,plain,
! [X0] :
( X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,smndt0(sz00))) ),
inference(resolution,[status(thm)],[f291,f339]) ).
fof(f425,plain,
sz00 = sdtasdt0(sz00,smndt0(sz00)),
inference(resolution,[status(thm)],[f291,f80]) ).
fof(f426,plain,
sdtasdt0(smndt0(sz00),sz00) = sz00,
inference(resolution,[status(thm)],[f291,f79]) ).
fof(f427,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00)) = sdtpldt0(sdtasdt0(X0,smndt0(sz00)),sdtasdt0(smndt0(sz00),smndt0(sz00)))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f77]) ).
fof(f431,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(smndt0(sz00),smndt0(sz00))) = sdtpldt0(sdtasdt0(X0,smndt0(sz00)),sdtasdt0(X0,smndt0(sz00)))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f76]) ).
fof(f432,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,smndt0(sz00))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,smndt0(sz00)))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f76]) ).
fof(f434,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(smndt0(sz00),X1)) = sdtpldt0(sdtasdt0(X0,smndt0(sz00)),sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f76]) ).
fof(f438,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(smndt0(sz00),smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f69]) ).
fof(f439,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,X1),smndt0(sz00))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f69]) ).
fof(f441,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(smndt0(sz00),X1)) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f69]) ).
fof(f442,plain,
sz00 = sdtpldt0(smndt0(smndt0(sz00)),smndt0(sz00)),
inference(resolution,[status(thm)],[f291,f67]) ).
fof(f443,plain,
sdtpldt0(smndt0(sz00),smndt0(smndt0(sz00))) = sz00,
inference(resolution,[status(thm)],[f291,f66]) ).
fof(f444,plain,
smndt0(sz00) = sdtpldt0(sz00,smndt0(sz00)),
inference(resolution,[status(thm)],[f291,f64]) ).
fof(f447,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(smndt0(sz00),smndt0(sz00))) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f59]) ).
fof(f449,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(smndt0(sz00),smndt0(sz00))) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f59]) ).
fof(f454,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,smndt0(sz00)))
| smndt0(sz00) = sz00 ),
inference(resolution,[status(thm)],[f291,f261]) ).
fof(f455,plain,
! [X0] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f291,f220]) ).
fof(f456,definition,
( sQ20_spl
<=> isPrime0(sK1_skl(smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f459,definition,
( sQ21_spl
<=> smndt0(sz00) = smndt0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| sQ21_spl
| sQ8_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f419,f456,f333,f459,f272]) ).
fof(f463,definition,
( sQ22_spl
<=> aDivisorOf0(sK1_skl(smndt0(sz00)),smndt0(sz00)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ2_spl
| sQ21_spl
| sQ8_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f420,f463,f333,f459,f272]) ).
fof(f467,definition,
( sQ23_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ23_spl
| isClosed0(szAzrzSzezqlpdtcmdtrp0(sz00,smndt0(sz00))) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ23_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f454,f333,f467]) ).
fof(f479,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,smndt0(sz00))) = sdtpldt0(sdtpldt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f295,f291]) ).
fof(f481,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(smndt0(sz00),sz00)) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f296,f291]) ).
fof(f486,definition,
! [X0,X1] :
( sQ24_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz00))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,smndt0(smndt0(sz00)))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),smndt0(sz00)))
| smndt0(sz00) = sz00 ),
inference(resolution,[status(thm)],[f455,f291]) ).
fof(f496,plain,
( isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00))
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f455,f50]) ).
fof(f497,definition,
( sQ26_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ26_spl
| isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),smndt0(sz00))) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( sQ26_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f495,f333,f497]) ).
fof(f501,definition,
( sQ27_spl
<=> isClosed0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ27_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f496,f263,f501]) ).
fof(f509,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| X0 = sz00
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f334,f376]) ).
fof(f510,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| X0 = sz00
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f334,f369]) ).
fof(f512,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| smndt0(X0) = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f334,f320]) ).
fof(f514,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| sdtasdt0(sz00,X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f334,f318]) ).
fof(f519,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f509]) ).
fof(f520,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f510]) ).
fof(f523,definition,
! [X0,X1] :
( sQ28_spl
<=> ( ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f524,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f548,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f298,f294]) ).
fof(f549,plain,
! [X0] :
( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(sz00,sz00,X0)
| X0 = sz00
| ~ aInteger0(X0)
| ~ aInteger0(sz00)
| ~ aInteger0(sz00) ),
inference(paramodulation,[status(thm)],[f300,f98]) ).
fof(f550,definition,
! [X0] :
( sQ29_spl
<=> ( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(sz00,sz00,X0)
| X0 = sz00
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( sQ29_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f549,f326,f550]) ).
fof(f554,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f307,f302]) ).
fof(f558,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f303,f50]) ).
fof(f560,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f304,f50]) ).
fof(f563,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f310]) ).
fof(f579,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz00),sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(sz00,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f315,f50]) ).
fof(f587,plain,
( sz00 = sz00
| aDivisorOf0(sz00,sdtasdt0(sz00,sz00)) ),
inference(resolution,[status(thm)],[f340,f50]) ).
fof(f588,definition,
( sQ30_spl
<=> aDivisorOf0(sz00,sdtasdt0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ0_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f587,f588,f263]) ).
fof(f592,plain,
( sdteqdtlpzmzozddtrp0(sz00,sz00,sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f341,f50]) ).
fof(f593,definition,
( sQ31_spl
<=> sdteqdtlpzmzozddtrp0(sz00,sz00,sz00) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ31_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f592,f263,f593]) ).
fof(f597,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00))
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f382,f50]) ).
fof(f598,definition,
( sQ32_spl
<=> aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( sQ32_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f597,f263,f598]) ).
fof(f602,plain,
! [X0] :
( aInteger0(sK10_skl(X0,sz00,sz00))
| aElementOf0(sK10_skl(X0,sz00,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f383,f50]) ).
fof(f603,definition,
! [X0] :
( sQ33_spl
<=> ( aInteger0(sK10_skl(X0,sz00,sz00))
| aElementOf0(sK10_skl(X0,sz00,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz00) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( sQ33_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f602,f263,f603]) ).
fof(f607,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz00,sz00),sz00,sz00)
| aElementOf0(sK10_skl(X0,sz00,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f384,f50]) ).
fof(f608,definition,
! [X0] :
( sQ34_spl
<=> ( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz00,sz00),sz00,sz00)
| aElementOf0(sK10_skl(X0,sz00,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz00) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( sQ34_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f607,f263,f608]) ).
fof(f612,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00),cS1395)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f385,f50]) ).
fof(f613,definition,
( sQ35_spl
<=> aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sz00),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ35_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f612,f263,f613]) ).
fof(f617,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00),cS1395)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f415,f50]) ).
fof(f618,definition,
( sQ36_spl
<=> aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ36_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f617,f263,f618]) ).
fof(f622,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f332]) ).
fof(f623,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f622]) ).
fof(f624,definition,
( sQ37_spl
<=> aInteger0(smndt0(sz10)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( ~ sQ37_spl
| aInteger0(smndt0(sz10)) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f626,plain,
( sQ37_spl
| ~ aInteger0(smndt0(sz10)) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,definition,
! [X0] :
( sQ38_spl
<=> ( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,smndt0(sz10)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f628,plain,
! [X0] :
( ~ sQ38_spl
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,smndt0(sz10)) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f239,f624,f627]) ).
fof(f631,definition,
( sQ39_spl
<=> aInteger0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( sQ39_spl
| ~ aInteger0(sz10) ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f634,definition,
! [X0] :
( sQ40_spl
<=> ( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f635,plain,
! [X0] :
( ~ sQ40_spl
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,plain,
( sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f238,f631,f634]) ).
fof(f640,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz00,smndt0(sz00)),smndt0(sz00),sz00)
| aElementOf0(sK10_skl(X0,sz00,smndt0(sz00)),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f416,f50]) ).
fof(f641,definition,
! [X0] :
( sQ41_spl
<=> ( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz00,smndt0(sz00)),smndt0(sz00),sz00)
| aElementOf0(sK10_skl(X0,sz00,smndt0(sz00)),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ41_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f640,f263,f641]) ).
fof(f645,plain,
! [X0] :
( aInteger0(sK10_skl(X0,sz00,smndt0(sz00)))
| aElementOf0(sK10_skl(X0,sz00,smndt0(sz00)),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f417,f50]) ).
fof(f646,definition,
! [X0] :
( sQ42_spl
<=> ( aInteger0(sK10_skl(X0,sz00,smndt0(sz00)))
| aElementOf0(sK10_skl(X0,sz00,smndt0(sz00)),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( sQ42_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f645,f263,f646]) ).
fof(f650,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00))
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f418,f50]) ).
fof(f651,definition,
( sQ43_spl
<=> aSet0(szAzrzSzezqlpdtcmdtrp0(smndt0(sz00),sz00)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( sQ43_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f650,f263,f651]) ).
fof(f655,plain,
( sdteqdtlpzmzozddtrp0(smndt0(sz00),smndt0(sz00),sz00)
| sz00 = sz00 ),
inference(resolution,[status(thm)],[f421,f50]) ).
fof(f656,definition,
( sQ44_spl
<=> sdteqdtlpzmzozddtrp0(smndt0(sz00),smndt0(sz00),sz00) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( sQ44_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f655,f263,f656]) ).
fof(f660,plain,
( sz00 = sz00
| aDivisorOf0(sz00,sdtasdt0(sz00,smndt0(sz00))) ),
inference(resolution,[status(thm)],[f422,f50]) ).
fof(f661,definition,
( sQ45_spl
<=> aDivisorOf0(sz00,sdtasdt0(sz00,smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( sQ0_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f660,f661,f263]) ).
fof(f696,plain,
( sz00 = smndt0(sz10)
| sz00 = sz10
| isPrime0(sK1_skl(sz00)) ),
inference(resolution,[status(thm)],[f116,f50]) ).
fof(f697,definition,
( sQ47_spl
<=> sz00 = smndt0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( ~ sQ47_spl
| sz00 = smndt0(sz10) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f700,plain,
( sQ47_spl
| sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f696,f378,f272,f697]) ).
fof(f701,plain,
( sz00 = smndt0(sz10)
| sz00 = sz10
| aDivisorOf0(sK1_skl(sz00),sz00) ),
inference(resolution,[status(thm)],[f115,f50]) ).
fof(f702,plain,
( sQ47_spl
| sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f701,f371,f272,f697]) ).
fof(f703,plain,
smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10)),
inference(resolution,[status(thm)],[f83,f50]) ).
fof(f704,plain,
( ~ sQ7_spl
| smndt0(smndt0(sz00)) = sdtasdt0(smndt0(sz00),smndt0(sz10)) ),
inference(resolution,[status(thm)],[f331,f83]) ).
fof(f705,plain,
( ~ sQ7_spl
| smndt0(sz00) = smndt0(sz10)
| smndt0(sz00) = sz10
| aDivisorOf0(sK1_skl(smndt0(sz00)),smndt0(sz00)) ),
inference(resolution,[status(thm)],[f331,f115]) ).
fof(f706,plain,
( ~ sQ7_spl
| smndt0(sz00) = smndt0(sz10)
| smndt0(sz00) = sz10
| isPrime0(sK1_skl(smndt0(sz00))) ),
inference(resolution,[status(thm)],[f331,f116]) ).
fof(f707,plain,
( ~ sQ7_spl
| sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))) = sdtpldt0(sdtasdt0(smndt0(sz00),smndt0(sz00)),sdtasdt0(smndt0(sz00),smndt0(sz00))) ),
inference(resolution,[status(thm)],[f331,f431]) ).
fof(f710,plain,
( ~ sQ7_spl
| sdtasdt0(sdtpldt0(smndt0(sz00),smndt0(sz00)),smndt0(sz00)) = sdtpldt0(sdtasdt0(smndt0(sz00),smndt0(sz00)),sdtasdt0(smndt0(sz00),smndt0(sz00))) ),
inference(resolution,[status(thm)],[f331,f427]) ).
fof(f731,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(sz00,smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f331,f303]) ).
fof(f734,plain,
! [X0] :
( ~ sQ7_spl
| sdtpldt0(X0,sdtpldt0(smndt0(sz00),sz00)) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f331,f296]) ).
fof(f755,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(smndt0(sz00),smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f331,f69]) ).
fof(f761,plain,
( ~ sQ7_spl
| smndt0(sz00) = sdtpldt0(sz00,smndt0(sz00)) ),
inference(resolution,[status(thm)],[f331,f64]) ).
fof(f773,definition,
( sQ48_spl
<=> smndt0(sz00) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ48_spl
| smndt0(sz00) = sz10 ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,definition,
( sQ49_spl
<=> smndt0(sz00) = smndt0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( ~ sQ49_spl
| smndt0(sz00) = smndt0(sz10) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f779,plain,
( ~ sQ7_spl
| sQ49_spl
| sQ48_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f705,f463,f773,f776,f330]) ).
fof(f780,plain,
( ~ sQ7_spl
| sQ49_spl
| sQ48_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f706,f456,f773,f776,f330]) ).
fof(f842,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f731]) ).
fof(f845,plain,
! [X0] :
( ~ sQ7_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f301,f734]) ).
fof(f849,plain,
( ~ sQ7_spl
| smndt0(sz00) = sz00 ),
inference(forward_demodulation,[status(thm)],[f300,f761]) ).
fof(f850,plain,
( ~ sQ7_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f335]) ).
fof(f851,plain,
( ~ sQ7_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f857,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sz00 = sz00
| isPrime0(sK1_skl(sz00)) ),
inference(resolution,[status(thm)],[f519,f50]) ).
fof(f859,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sQ0_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f857,f378,f263,f333,f272]) ).
fof(f860,plain,
! [X0,X1] :
( ~ sQ7_spl
| sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,smndt0(smndt0(sz00)))
| smndt0(sz10) = sz00
| ~ aInteger0(smndt0(sz10))
| smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f704,f107]) ).
fof(f861,plain,
! [X0,X1] :
( ~ sQ7_spl
| sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz00))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,smndt0(smndt0(sz00)))
| smndt0(sz10) = sz00
| ~ aInteger0(smndt0(sz10))
| smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f704,f106]) ).
fof(f863,definition,
! [X0,X1] :
( sQ63_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,smndt0(smndt0(sz00)))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( sQ47_spl
| ~ sQ37_spl
| sQ8_spl
| ~ sQ7_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f860,f863,f330,f333,f624,f697]) ).
fof(f867,plain,
( sQ47_spl
| ~ sQ37_spl
| sQ8_spl
| ~ sQ7_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f861,f486,f330,f333,f624,f697]) ).
fof(f869,plain,
( ~ sQ7_spl
| sdtasdt0(sdtpldt0(smndt0(sz00),smndt0(sz00)),smndt0(sz00)) = sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))) ),
inference(forward_demodulation,[status(thm)],[f707,f710]) ).
fof(f870,plain,
! [X0,X1] :
( ~ sQ7_spl
| sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz00))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))))
| smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00))
| sdtpldt0(smndt0(sz00),smndt0(sz00)) = sz00
| ~ aInteger0(sdtpldt0(smndt0(sz00),smndt0(sz00)))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f869,f107]) ).
fof(f871,plain,
! [X0,X1] :
( ~ sQ7_spl
| sdteqdtlpzmzozddtrp0(X0,X1,sdtpldt0(smndt0(sz00),smndt0(sz00)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))))
| smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00))
| sdtpldt0(smndt0(sz00),smndt0(sz00)) = sz00
| ~ aInteger0(sdtpldt0(smndt0(sz00),smndt0(sz00)))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f869,f106]) ).
fof(f872,plain,
( ~ sQ7_spl
| smndt0(sz00) = sz00
| sdtpldt0(smndt0(sz00),smndt0(sz00)) = sz00
| sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))) != sz00
| ~ aInteger0(smndt0(sz00))
| ~ aInteger0(sdtpldt0(smndt0(sz00),smndt0(sz00))) ),
inference(paramodulation,[status(thm)],[f869,f85]) ).
fof(f873,definition,
! [X0,X1] :
( sQ64_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,X1,smndt0(sz00))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f876,definition,
( sQ65_spl
<=> aInteger0(sdtpldt0(smndt0(sz00),smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f878,plain,
( sQ65_spl
| ~ aInteger0(sdtpldt0(smndt0(sz00),smndt0(sz00))) ),
inference(component_clause,[status(thm)],[f876]) ).
fof(f879,definition,
( sQ66_spl
<=> sdtpldt0(smndt0(sz00),smndt0(sz00)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ8_spl
| ~ sQ7_spl
| sQ66_spl
| ~ sQ65_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f870,f873,f876,f879,f330,f333]) ).
fof(f883,definition,
! [X0,X1] :
( sQ67_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,X1,sdtpldt0(smndt0(sz00),smndt0(sz00)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( sQ8_spl
| ~ sQ7_spl
| sQ66_spl
| ~ sQ65_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f871,f883,f876,f879,f330,f333]) ).
fof(f887,definition,
( sQ68_spl
<=> sdtasdt0(smndt0(sz00),sdtpldt0(smndt0(sz00),smndt0(sz00))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( sQ8_spl
| sQ66_spl
| ~ sQ68_spl
| ~ sQ7_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f872,f876,f330,f887,f879,f333]) ).
fof(f917,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sz00 = sz00
| aDivisorOf0(sK1_skl(sz00),sz00) ),
inference(resolution,[status(thm)],[f520,f50]) ).
fof(f919,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sQ0_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f917,f371,f263,f333,f272]) ).
fof(f924,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz00,smndt0(sz00))) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,smndt0(sz00)))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f432,f50]) ).
fof(f925,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,smndt0(sz00)))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f300,f924]) ).
fof(f927,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(smndt0(sz00),sz00)) = sdtpldt0(sdtasdt0(X0,smndt0(sz00)),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f434,f50]) ).
fof(f928,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,smndt0(sz00)),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f301,f927]) ).
fof(f937,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f439,f50]) ).
fof(f938,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f937]) ).
fof(f940,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(smndt0(sz00),sz00)) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f441,f50]) ).
fof(f941,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f426,f940]) ).
fof(f942,plain,
! [X0] :
( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(smndt0(smndt0(sz00)),sz00,X0)
| X0 = sz00
| ~ aInteger0(X0)
| ~ aInteger0(sz00)
| ~ aInteger0(smndt0(smndt0(sz00))) ),
inference(paramodulation,[status(thm)],[f442,f98]) ).
fof(f943,definition,
( sQ69_spl
<=> aInteger0(smndt0(smndt0(sz00))) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( sQ69_spl
| ~ aInteger0(smndt0(smndt0(sz00))) ),
inference(component_clause,[status(thm)],[f943]) ).
fof(f946,definition,
! [X0] :
( sQ70_spl
<=> ( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(smndt0(smndt0(sz00)),sz00,X0)
| X0 = sz00
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( sQ70_spl
| ~ sQ6_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f942,f943,f326,f946]) ).
fof(f950,plain,
! [X0] :
( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(smndt0(sz00),smndt0(sz00),X0)
| X0 = sz00
| ~ aInteger0(X0)
| ~ aInteger0(smndt0(sz00))
| ~ aInteger0(smndt0(sz00)) ),
inference(paramodulation,[status(thm)],[f443,f98]) ).
fof(f951,definition,
! [X0] :
( sQ71_spl
<=> ( ~ aDivisorOf0(X0,sz00)
| sdteqdtlpzmzozddtrp0(smndt0(sz00),smndt0(sz00),X0)
| X0 = sz00
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f954,plain,
( sQ71_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f950,f330,f951]) ).
fof(f959,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(smndt0(sz00),smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f987,f438]) ).
fof(f970,plain,
( ~ sQ7_spl
| smndt0(smndt0(sz00)) = sdtasdt0(sz00,smndt0(sz10)) ),
inference(backward_demodulation,[status(thm)],[f987,f704]) ).
fof(f987,plain,
smndt0(sz00) = sz00,
inference(forward_demodulation,[status(thm)],[f300,f444]) ).
fof(f988,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(sz00)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f987,f98]) ).
fof(f995,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f959]) ).
fof(f996,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f995]) ).
fof(f997,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f996]) ).
fof(f1015,plain,
( ~ sQ7_spl
| smndt0(sz00) = sdtasdt0(sz00,smndt0(sz10)) ),
inference(forward_demodulation,[status(thm)],[f987,f970]) ).
fof(f1016,plain,
( ~ sQ7_spl
| sz00 = sdtasdt0(sz00,smndt0(sz10)) ),
inference(forward_demodulation,[status(thm)],[f987,f1015]) ).
fof(f1034,plain,
( ~ sQ6_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f988,f523,f326]) ).
fof(f1037,plain,
sdtasdt0(smndt0(sz10),sz00) = smndt0(sz00),
inference(resolution,[status(thm)],[f82,f50]) ).
fof(f1038,plain,
sdtasdt0(smndt0(sz10),sz00) = sz00,
inference(forward_demodulation,[status(thm)],[f987,f1037]) ).
fof(f1039,plain,
sz00 = sdtasdt0(sz10,sz00),
inference(resolution,[status(thm)],[f74,f50]) ).
fof(f1040,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(resolution,[status(thm)],[f73,f50]) ).
fof(f1041,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f842]) ).
fof(f1043,plain,
! [X0] :
( ~ sQ7_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f845]) ).
fof(f1056,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(sz00,smndt0(sz00))) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f755]) ).
fof(f1057,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1056]) ).
fof(f1058,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1057]) ).
fof(f1059,plain,
! [X0] :
( ~ sQ7_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1058]) ).
fof(f1079,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,smndt0(sz00))) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f447]) ).
fof(f1080,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1079]) ).
fof(f1081,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1080]) ).
fof(f1082,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1081]) ).
fof(f1083,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1082]) ).
fof(f1086,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,smndt0(sz00))) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f449]) ).
fof(f1087,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1086]) ).
fof(f1088,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1087]) ).
fof(f1089,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1088]) ).
fof(f1090,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1089]) ).
fof(f1110,plain,
( ~ sQ7_spl
| sdtasdt0(sz10,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(sz10,sz00),sz00) ),
inference(resolution,[status(thm)],[f51,f1059]) ).
fof(f1112,plain,
( ~ sQ7_spl
| sdtpldt0(sz10,sz00) = sdtpldt0(sdtpldt0(sz10,sz00),sz00) ),
inference(resolution,[status(thm)],[f51,f1043]) ).
fof(f1113,plain,
( ~ sQ7_spl
| sdtasdt0(sz10,sz00) = sdtasdt0(sdtasdt0(sz10,sz00),sz00) ),
inference(resolution,[status(thm)],[f51,f1041]) ).
fof(f1114,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(resolution,[status(thm)],[f51,f73]) ).
fof(f1115,plain,
sz10 = sdtasdt0(sz10,sz10),
inference(resolution,[status(thm)],[f51,f74]) ).
fof(f1116,plain,
sdtasdt0(smndt0(sz10),sz10) = smndt0(sz10),
inference(resolution,[status(thm)],[f51,f82]) ).
fof(f1120,plain,
smndt0(sz10) = sdtasdt0(sz10,smndt0(sz10)),
inference(resolution,[status(thm)],[f51,f83]) ).
fof(f1121,plain,
( sz10 = smndt0(sz10)
| sz10 = sz10
| aDivisorOf0(sK1_skl(sz10),sz10) ),
inference(resolution,[status(thm)],[f51,f115]) ).
fof(f1122,plain,
( sz10 = smndt0(sz10)
| sz10 = sz10
| isPrime0(sK1_skl(sz10)) ),
inference(resolution,[status(thm)],[f51,f116]) ).
fof(f1124,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10),cS1395)
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f385]) ).
fof(f1125,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz10,sz00),sz00,sz10)
| aElementOf0(sK10_skl(X0,sz10,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz10)
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f384]) ).
fof(f1126,plain,
! [X0] :
( aInteger0(sK10_skl(X0,sz10,sz00))
| aElementOf0(sK10_skl(X0,sz10,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz10)
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f383]) ).
fof(f1127,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10))
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f382]) ).
fof(f1128,plain,
( sdteqdtlpzmzozddtrp0(sz00,sz00,sz10)
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f51,f341]) ).
fof(f1129,plain,
( sz10 = sz00
| aDivisorOf0(sz10,sdtasdt0(sz10,sz00)) ),
inference(resolution,[status(thm)],[f51,f340]) ).
fof(f1130,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz10),sz00) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(sz10,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f315]) ).
fof(f1131,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz00),sz10) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(sz00,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f314]) ).
fof(f1132,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz10,sz00)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f312]) ).
fof(f1133,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f311]) ).
fof(f1134,plain,
sdtasdt0(sz10,sz00) = sdtpldt0(sdtasdt0(sz10,sz00),sdtasdt0(sz10,sz00)),
inference(resolution,[status(thm)],[f51,f563]) ).
fof(f1135,plain,
sdtasdt0(sz10,sz00) = sdtasdt0(sz00,sz10),
inference(resolution,[status(thm)],[f51,f305]) ).
fof(f1136,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz10,sz00)) = sdtasdt0(sdtasdt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f304]) ).
fof(f1137,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz00,sz10)) = sdtasdt0(sdtasdt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f303]) ).
fof(f1138,plain,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f51,f297]) ).
fof(f1139,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz10,sz00)) = sdtpldt0(sdtpldt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f296]) ).
fof(f1140,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtpldt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f295]) ).
fof(f1141,plain,
aInteger0(sdtasdt0(sz00,sz10)),
inference(resolution,[status(thm)],[f51,f293]) ).
fof(f1142,plain,
aInteger0(sdtpldt0(sz00,sz10)),
inference(resolution,[status(thm)],[f51,f292]) ).
fof(f1143,plain,
! [X0] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),cS1395)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f219]) ).
fof(f1144,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(sK10_skl(X1,X0,sz10),sz10,X0)
| aElementOf0(sK10_skl(X1,X0,sz10),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(sz10,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f193]) ).
fof(f1145,plain,
! [X0,X1] :
( aInteger0(sK10_skl(X1,X0,sz10))
| aElementOf0(sK10_skl(X1,X0,sz10),X1)
| ~ aSet0(X1)
| X1 = szAzrzSzezqlpdtcmdtrp0(sz10,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f192]) ).
fof(f1146,plain,
! [X0] :
( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X0))
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f257]) ).
fof(f1147,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(sz10,sz10,X0)
| X0 = sz00
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f100]) ).
fof(f1148,plain,
! [X0] :
( X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,sz10)) ),
inference(resolution,[status(thm)],[f51,f339]) ).
fof(f1149,plain,
sz00 = sdtasdt0(sz00,sz10),
inference(resolution,[status(thm)],[f51,f80]) ).
fof(f1150,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(resolution,[status(thm)],[f51,f79]) ).
fof(f1151,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz10),sz10) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(sz10,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f77]) ).
fof(f1152,plain,
! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sz10) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X1,sz10))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f77]) ).
fof(f1153,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz10),sz10) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(sz10,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f77]) ).
fof(f1154,plain,
! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,sz10),X1) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(sz10,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f77]) ).
fof(f1155,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f76]) ).
fof(f1156,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz10))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f76]) ).
fof(f1157,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f76]) ).
fof(f1158,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f76]) ).
fof(f1159,plain,
! [X0] :
( sdtasdt0(X0,sz10) = sdtasdt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f71]) ).
fof(f1160,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz10,sz10)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f69]) ).
fof(f1161,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,sz10)) = sdtasdt0(sdtasdt0(X0,X1),sz10)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f69]) ).
fof(f1162,plain,
! [X0] :
( sdtasdt0(X0,sdtasdt0(sz10,sz10)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f69]) ).
fof(f1163,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtasdt0(sz10,X1)) = sdtasdt0(sdtasdt0(X0,sz10),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f69]) ).
fof(f1164,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f51,f67]) ).
fof(f1165,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolution,[status(thm)],[f51,f66]) ).
fof(f1166,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f51,f64]) ).
fof(f1167,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[f51,f63]) ).
fof(f1168,plain,
! [X0] :
( sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f61]) ).
fof(f1169,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f59]) ).
fof(f1170,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtpldt0(X0,X1),sz10)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f59]) ).
fof(f1171,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f59]) ).
fof(f1172,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtpldt0(X0,sz10),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f59]) ).
fof(f1173,plain,
! [X0] :
( aInteger0(sdtasdt0(sz10,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f57]) ).
fof(f1174,plain,
! [X0] :
( aInteger0(sdtpldt0(sz10,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f51,f55]) ).
fof(f1175,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[f51,f53]) ).
fof(f1178,definition,
( sQ72_spl
<=> aDivisorOf0(sK1_skl(sz10),sz10) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1182,definition,
( sQ73_spl
<=> isPrime0(sK1_skl(sz10)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1186,definition,
( sQ74_spl
<=> sz10 = sz10 ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1189,definition,
( sQ75_spl
<=> sz10 = smndt0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1190,plain,
( ~ sQ75_spl
| sz10 = smndt0(sz10) ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1192,plain,
( sQ75_spl
| sQ74_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1121,f1178,f1186,f1189]) ).
fof(f1193,plain,
( sQ75_spl
| sQ74_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1122,f1182,f1186,f1189]) ).
fof(f1195,definition,
( sQ76_spl
<=> aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1198,plain,
( sQ76_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1124,f272,f1195]) ).
fof(f1199,definition,
! [X0] :
( sQ77_spl
<=> ( sdteqdtlpzmzozddtrp0(sK10_skl(X0,sz10,sz00),sz00,sz10)
| aElementOf0(sK10_skl(X0,sz10,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz10) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( sQ77_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1125,f272,f1199]) ).
fof(f1203,definition,
! [X0] :
( sQ78_spl
<=> ( aInteger0(sK10_skl(X0,sz10,sz00))
| aElementOf0(sK10_skl(X0,sz10,sz00),X0)
| ~ aSet0(X0)
| X0 = szAzrzSzezqlpdtcmdtrp0(sz00,sz10) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( sQ78_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1126,f272,f1203]) ).
fof(f1207,definition,
( sQ79_spl
<=> aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1210,plain,
( sQ79_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1127,f272,f1207]) ).
fof(f1211,definition,
( sQ80_spl
<=> sdteqdtlpzmzozddtrp0(sz00,sz00,sz10) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1214,plain,
( sQ80_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1128,f272,f1211]) ).
fof(f1215,definition,
( sQ81_spl
<=> aDivisorOf0(sz10,sdtasdt0(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1218,plain,
( sQ2_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1129,f1215,f272]) ).
fof(f1220,plain,
( sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f633,f51]) ).
fof(f1221,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f1220]) ).
fof(f1242,plain,
( sQ37_spl
| ~ sQ49_spl
| ~ aInteger0(sz00) ),
inference(backward_demodulation,[status(thm)],[f1247,f626]) ).
fof(f1243,plain,
! [X0] :
( ~ sQ49_spl
| sdtasdt0(sz00,X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f1247,f82]) ).
fof(f1244,plain,
! [X0] :
( ~ sQ49_spl
| smndt0(X0) = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f1247,f83]) ).
fof(f1245,plain,
! [X0] :
( ~ sQ49_spl
| X0 = sz00
| X0 = sz10
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f1247,f115]) ).
fof(f1246,plain,
! [X0] :
( ~ sQ49_spl
| X0 = sz00
| X0 = sz10
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f1247,f116]) ).
fof(f1247,plain,
( ~ sQ49_spl
| sz00 = smndt0(sz10) ),
inference(forward_demodulation,[status(thm)],[f987,f777]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ sQ49_spl
| ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz10,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(sz10)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f1247,f98]) ).
fof(f1249,plain,
( sQ37_spl
| ~ sQ49_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1242,f326,f776,f624]) ).
fof(f1250,definition,
! [X0,X1] :
( sQ82_spl
<=> ( ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz10,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1251,plain,
! [X0,X1] :
( ~ sQ82_spl
| ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz10,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f1250]) ).
fof(f1253,plain,
( ~ sQ49_spl
| ~ sQ39_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1248,f1250,f631,f776]) ).
fof(f1254,plain,
( ~ sQ48_spl
| sz00 = sz10 ),
inference(forward_demodulation,[status(thm)],[f987,f774]) ).
fof(f1258,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f376]) ).
fof(f1259,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1258]) ).
fof(f1260,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f479]) ).
fof(f1261,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1260]) ).
fof(f1262,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1261]) ).
fof(f1263,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f481]) ).
fof(f1264,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,smndt0(sz00)),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1263]) ).
fof(f1265,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1264]) ).
fof(f1267,plain,
( sz00 = sz00
| sz00 = sz00
| ~ aInteger0(sz00)
| ~ aInteger0(sz00) ),
inference(resolution,[status(thm)],[f317,f85]) ).
fof(f1268,plain,
! [X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,sz00)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sz00)
| sz00 = sz00
| ~ aInteger0(sz00)
| sz00 = sz00
| ~ aInteger0(sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(paramodulation,[status(thm)],[f317,f107]) ).
fof(f1271,plain,
( sQ0_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1267,f326,f263]) ).
fof(f1272,plain,
( sQ0_spl
| ~ sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1268,f353,f326,f263]) ).
fof(f1275,plain,
! [X0] :
( sdtasdt0(sdtpldt0(X0,sz00),sz00) = sdtpldt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f579]) ).
fof(f1276,plain,
sdtasdt0(sdtpldt0(sz10,sz00),sz00) = sdtpldt0(sdtasdt0(sz10,sz00),sz00),
inference(resolution,[status(thm)],[f1275,f51]) ).
fof(f1286,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f560]) ).
fof(f1287,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f558]) ).
fof(f1288,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f369]) ).
fof(f1289,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1288]) ).
fof(f1290,plain,
! [X0] :
( ~ sQ2_spl
| smndt0(X0) = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f320]) ).
fof(f1291,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(sz00,X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f318]) ).
fof(f1302,plain,
( sQ65_spl
| ~ aInteger0(sdtpldt0(sz00,smndt0(sz00))) ),
inference(forward_demodulation,[status(thm)],[f987,f878]) ).
fof(f1303,plain,
( sQ65_spl
| ~ aInteger0(sdtpldt0(sz00,sz00)) ),
inference(forward_demodulation,[status(thm)],[f987,f1302]) ).
fof(f1304,plain,
( sQ65_spl
| ~ aInteger0(sz00) ),
inference(forward_demodulation,[status(thm)],[f298,f1303]) ).
fof(f1305,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1304,f50]) ).
fof(f1306,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f1305]) ).
fof(f1313,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ isPrime0(sK1_skl(sz00)) ),
inference(resolution,[status(thm)],[f372,f365]) ).
fof(f1314,plain,
( ~ sQ12_spl
| sdtasdt0(sK1_skl(sz00),sK0_skl(sK1_skl(sz00),sz00)) = sz00
| ~ aInteger0(sz00) ),
inference(resolution,[status(thm)],[f372,f93]) ).
fof(f1315,plain,
( ~ sQ12_spl
| aInteger0(sK0_skl(sK1_skl(sz00),sz00))
| ~ aInteger0(sz00) ),
inference(resolution,[status(thm)],[f372,f92]) ).
fof(f1316,plain,
( ~ sQ12_spl
| aInteger0(sK1_skl(sz00))
| ~ aInteger0(sz00) ),
inference(resolution,[status(thm)],[f372,f90]) ).
fof(f1317,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1313,f379]) ).
fof(f1318,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1317]) ).
fof(f1320,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f302]) ).
fof(f1334,plain,
sz00 = sdtasdt0(sz00,smndt0(sz10)),
inference(forward_demodulation,[status(thm)],[f987,f703]) ).
fof(f1379,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f938]) ).
fof(f1380,plain,
( sQ69_spl
| ~ aInteger0(smndt0(sz00)) ),
inference(forward_demodulation,[status(thm)],[f987,f945]) ).
fof(f1381,plain,
( sQ69_spl
| ~ aInteger0(sz00) ),
inference(forward_demodulation,[status(thm)],[f987,f1380]) ).
fof(f1382,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1381,f50]) ).
fof(f1383,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f1382]) ).
fof(f1388,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f997]) ).
fof(f1399,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(smndt0(sz00),X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f82]) ).
fof(f1400,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(sz00,X0) = smndt0(X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1399]) ).
fof(f1401,plain,
! [X0] :
( ~ sQ2_spl
| smndt0(X0) = sdtasdt0(X0,smndt0(sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f83]) ).
fof(f1402,plain,
! [X0] :
( ~ sQ2_spl
| smndt0(X0) = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1401]) ).
fof(f1403,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz10)
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f115]) ).
fof(f1404,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz00)
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1403]) ).
fof(f1405,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1404]) ).
fof(f1406,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| aDivisorOf0(sK1_skl(X0),X0)
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1405]) ).
fof(f1430,plain,
! [X0,X1] :
( ~ sQ82_spl
| ~ sQ2_spl
| ~ aDivisorOf0(X1,sdtpldt0(X0,sz00))
| sdteqdtlpzmzozddtrp0(X0,sz00,X1)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1251]) ).
fof(f1442,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz10)
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f116]) ).
fof(f1443,plain,
! [X0] :
( ~ sQ2_spl
| X0 = smndt0(sz00)
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1442]) ).
fof(f1444,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f987,f1443]) ).
fof(f1445,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| isPrime0(sK1_skl(X0))
| ~ aInteger0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1444]) ).
fof(f1473,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1136]) ).
fof(f1474,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f1473]) ).
fof(f1475,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1474]) ).
fof(f1476,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1137]) ).
fof(f1477,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f1476]) ).
fof(f1478,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1477]) ).
fof(f1482,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1139]) ).
fof(f1483,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz10),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1482]) ).
fof(f1484,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1483]) ).
fof(f1485,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1140]) ).
fof(f1486,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1485]) ).
fof(f1487,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1486]) ).
fof(f1539,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz10)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1160]) ).
fof(f1540,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1539]) ).
fof(f1541,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f1540]) ).
fof(f1542,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1541]) ).
fof(f1543,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1542]) ).
fof(f1546,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz10)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1162]) ).
fof(f1547,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sdtasdt0(sz00,sz00)) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1546]) ).
fof(f1548,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f317,f1547]) ).
fof(f1549,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1548]) ).
fof(f1550,plain,
! [X0] :
( ~ sQ2_spl
| sdtasdt0(X0,sz00) = sdtasdt0(sdtasdt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1549]) ).
fof(f1565,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1169]) ).
fof(f1566,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1565]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1566]) ).
fof(f1568,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1567]) ).
fof(f1569,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1568]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1171]) ).
fof(f1573,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1572]) ).
fof(f1574,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz10),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f298,f1573]) ).
fof(f1575,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz10)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1574]) ).
fof(f1576,plain,
! [X0] :
( ~ sQ2_spl
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz00),sz00)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1575]) ).
fof(model,axiom,
( sQ0_spl
| sQ2_spl
| sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ19_spl
| sQ24_spl
| sQ28_spl
| sQ29_spl
| sQ37_spl
| sQ38_spl
| sQ39_spl
| sQ40_spl
| sQ47_spl
| sQ48_spl
| sQ65_spl
| sQ66_spl
| sQ69_spl
| sQ70_spl
| sQ71_spl
| sQ74_spl
| sQ75_spl
| sQ82_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM449+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 : Mon Sep 21 02:30:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.35/0.70 % SZS status CounterSatisfiable for theBenchmark: Theorem is counter-satisfiable, conjecture is false
% 1.35/0.70 % SZS output start Saturation for theBenchmark
% See solution above
% 1.79/0.72 % Elapsed time: 0.343809 seconds
% 1.79/0.72 % CPU time: 2.408229 seconds
% 1.79/0.72 % Total memory used: 139.878 MB
% 1.79/0.72 % Net memory used: 136.204 MB
%------------------------------------------------------------------------------