%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM507+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:47 PM UTC 2026
% Result : Theorem 29.31s 4.31s
% Output : CNFRefutation 29.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 481
% Syntax : Number of formulae : 1911 ( 49 unt; 440 def)
% Number of atoms : 7825 (1012 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 10684 (4770 ~;5280 |; 132 &)
% ( 445 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 442 ( 440 usr; 436 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 948 ( 941 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,sdtpldt0(W1,W2))
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( W1 != sz00
& doDivides0(W0,W1) )
=> sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( sdtlseqdt0(xk,xp)
& xk != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f56,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
sz10 != sz00,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f59,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f64,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f68,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f73,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f75,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f80,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f81,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f84,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f87,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
! [W0,W1] :
( ( W1 = sz00
& W0 = sz00 )
| sdtpldt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = sz00
| sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( X1 = sz00
| sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f93,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f95,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( aNaturalNumber0(sK0_skl(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0_skl(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f100,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f101,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [W0,W1] :
( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ! [W2] :
( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) = X1
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f107,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f109,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f111,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f114,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
| ~ aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f116,plain,
! [X0,X1,X2] :
( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f120,plain,
! [W0,W1,W2] :
( ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ sdtlseqdt0(W1,W2)
| W1 = W2
| W0 = sz00
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f122,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
! [X0,X1,X2] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f124,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f125,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f127,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
! [W0,W1] :
( sdtlseqdt0(W1,sdtasdt0(W1,W0))
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f129,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
! [W0,W1] :
( iLess0(W0,W1)
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f133,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f135,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f135]) ).
fof(f138,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sK1_skl(X1,X0))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f141,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [X0,X1,X2] :
( X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f145,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W1,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f147,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [W0,W1,W2] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f149,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f151,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [W0,W1] :
( sdtlseqdt0(W0,W1)
| W1 = sz00
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f153,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| X1 = sz00
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
! [W0,W1] :
( ! [W2] :
( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0)
| ~ aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f155,plain,
! [X0,X1,X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
! [W0] :
( ( isPrime0(W0)
<=> ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 ) )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f157,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
! [W0] :
( ( ( ( sK2_skl(W0) != W0
& sK2_skl(W0) != sz10
& doDivides0(sK2_skl(W0),W0)
& aNaturalNumber0(sK2_skl(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f157]) ).
fof(f159,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
! [X0] :
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f161,plain,
! [X0,X1] :
( X1 = X0
| X1 = sz10
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f171,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f172,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
! [W0,W1,W2] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(W2,sdtasdt0(W0,W1))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f175,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f177,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f178,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f179,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f180,plain,
xn != xp,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f181,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f182,plain,
xm != xp,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f183,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f184,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f185,plain,
( xk != sz10
& xk != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f186,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f190,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f191,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f192,plain,
isPrime0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f193,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f194,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f195,plain,
xk != xp,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f196,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f197,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f198,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f199,definition,
( sQ0_spl
<=> sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ0_spl
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f201,plain,
( sQ0_spl
| sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ1_spl
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ1_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f198,f199,f202]) ).
fof(f206,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f208,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f104]) ).
fof(f209,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(sdtpldt0(X0,X1),X0)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f105]) ).
fof(f212,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f139]) ).
fof(f213,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f214,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f144]) ).
fof(f215,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X0 = sz00
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f145]) ).
fof(f216,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(destructive_equality_resolution,[status(thm)],[f159]) ).
fof(f217,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(destructive_equality_resolution,[status(thm)],[f160]) ).
fof(f219,definition,
( sQ2_spl
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ2_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ3_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ3_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
( sQ4_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ4_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f229,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[status(thm)],[f216,f56]) ).
fof(f230,plain,
~ isPrime0(sz10),
inference(forward_subsumption_resolution,[status(thm)],[f217,f57]) ).
fof(f232,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f114,f179]) ).
fof(f233,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f114,f178]) ).
fof(f234,definition,
( sQ5_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ5_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f241,definition,
( sQ7_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ7_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ8_spl
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f232,f241,f222,f244]) ).
fof(f248,definition,
( sQ9_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ9_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ10_spl
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f233,f248,f222,f251]) ).
fof(f255,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f173]) ).
fof(f256,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f171]) ).
fof(f258,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f259,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f172]) ).
fof(f260,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f263,plain,
( ~ sQ0_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f200,f64]) ).
fof(f274,definition,
( sQ13_spl
<=> sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ13_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( ~ sQ0_spl
| sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f263,f222,f219,f274,f199]) ).
fof(f280,plain,
( sQ2_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f221,f60]) ).
fof(f281,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f280,f248,f241,f219]) ).
fof(f282,plain,
( xp = xk
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f109,f196]) ).
fof(f284,plain,
( xp = xm
| ~ sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f109,f183]) ).
fof(f285,plain,
( xp = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f109,f181]) ).
fof(f288,definition,
( sQ14_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f291,definition,
( sQ15_spl
<=> sdtlseqdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ15_spl
| ~ sdtlseqdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
( sQ16_spl
<=> xp = xk ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ16_spl
| xp = xk ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f282,f222,f288,f291,f294]) ).
fof(f298,definition,
( sQ17_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ17_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f304,definition,
( sQ19_spl
<=> xk = xr ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f308,definition,
( sQ20_spl
<=> sdtlseqdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f311,definition,
( sQ21_spl
<=> xp = xm ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( ~ sQ21_spl
| xp = xm ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,plain,
( sQ21_spl
| ~ sQ20_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f284,f222,f241,f308,f311]) ).
fof(f315,definition,
( sQ22_spl
<=> sdtlseqdt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f318,definition,
( sQ23_spl
<=> xp = xn ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ23_spl
| xp = xn ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( sQ23_spl
| ~ sQ22_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f285,f222,f248,f315,f318]) ).
fof(f322,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f180]) ).
fof(f323,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f182]) ).
fof(f325,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f190]) ).
fof(f327,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f195]) ).
fof(f329,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f339,definition,
( sQ24_spl
<=> sdtlseqdt0(xr,xk) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ15_spl
| sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f293,f114]) ).
fof(f344,definition,
( sQ25_spl
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ15_spl
| sQ25_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f343,f288,f222,f344,f291]) ).
fof(f351,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f84,f69]) ).
fof(f354,plain,
! [X0,X1] :
( X1 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f84]) ).
fof(f355,definition,
( sQ26_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ26_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,definition,
! [X0] :
( sQ27_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f351,f355,f358]) ).
fof(f363,definition,
! [X0] :
( sQ28_spl
<=> ~ aNaturalNumber0(X0) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f364,plain,
! [X0] :
( ~ sQ28_spl
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,definition,
! [X1] :
( sQ29_spl
<=> ( X1 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f354,f363,f366]) ).
fof(f370,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f56]) ).
fof(f371,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f373,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f85,f68]) ).
fof(f378,definition,
! [X0] :
( sQ30_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ30_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f373,f355,f378]) ).
fof(f385,plain,
( ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f57,f364]) ).
fof(f392,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f399,definition,
( sQ31_spl
<=> aNaturalNumber0(sdtpldt0(xm,xp)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ31_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ32_spl
<=> aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ32_spl
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f407,plain,
( sQ31_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f401,f60]) ).
fof(f408,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f407,f241,f222,f399]) ).
fof(f417,plain,
! [X0,X1] :
( X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = X0
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[f109,f129]) ).
fof(f424,plain,
! [X0,X1] :
( X1 = sz00
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = X0
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f417]) ).
fof(f425,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f60]) ).
fof(f429,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f196]) ).
fof(f430,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f193]) ).
fof(f431,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f183]) ).
fof(f432,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f181]) ).
fof(f435,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f114]) ).
fof(f437,definition,
! [X0] :
( sQ33_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f438,plain,
! [X0] :
( ~ sQ33_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f429,f437,f288,f222]) ).
fof(f441,definition,
! [X0] :
( sQ34_spl
<=> ( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f442,plain,
! [X0] :
( ~ sQ34_spl
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f430,f441,f298,f288]) ).
fof(f445,definition,
! [X0] :
( sQ35_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f446,plain,
! [X0] :
( ~ sQ35_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f431,f445,f241,f222]) ).
fof(f449,definition,
! [X0] :
( sQ36_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f450,plain,
! [X0] :
( ~ sQ36_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f432,f449,f248,f222]) ).
fof(f456,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f435]) ).
fof(f459,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X0)
| X0 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f116]) ).
fof(f460,definition,
! [X0] :
( sQ37_spl
<=> ( ~ sdtlseqdt0(X0,X0)
| X0 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ28_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f459,f460,f363]) ).
fof(f464,plain,
! [X0] :
( ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(X0,sdtpldt0(sz00,X0))
| X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0)) ),
inference(resolution,[status(thm)],[f69,f116]) ).
fof(f465,plain,
! [X0] :
( ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(sdtpldt0(sz00,X0),X0)
| sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(sdtpldt0(sz00,X0)) ),
inference(resolution,[status(thm)],[f69,f116]) ).
fof(f466,definition,
! [X0] :
( sQ38_spl
<=> ( ~ sdtlseqdt0(X0,sdtpldt0(sz00,X0))
| X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ26_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f464,f466,f355]) ).
fof(f470,definition,
! [X0] :
( sQ39_spl
<=> ( ~ sdtlseqdt0(sdtpldt0(sz00,X0),X0)
| sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(sdtpldt0(sz00,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ26_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f465,f470,f355]) ).
fof(f476,plain,
! [X0] :
( ~ sQ35_spl
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f446,f114]) ).
fof(f478,definition,
! [X0] :
( sQ40_spl
<=> ( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f479,plain,
! [X0] :
( ~ sQ40_spl
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( ~ sQ35_spl
| ~ sQ7_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f476,f478,f241,f445]) ).
fof(f483,plain,
! [X0] :
( ~ sQ40_spl
| sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f484,plain,
! [X0] :
( ~ sQ36_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f450,f114]) ).
fof(f486,definition,
! [X0] :
( sQ41_spl
<=> ( sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0] :
( ~ sQ41_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( ~ sQ36_spl
| ~ sQ9_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f484,f486,f248,f449]) ).
fof(f491,plain,
! [X0] :
( ~ sQ41_spl
| sdtlseqdt0(xn,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f487]) ).
fof(f492,plain,
! [X0] :
( ~ sQ34_spl
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f442,f114]) ).
fof(f493,plain,
( ~ sQ34_spl
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f442,f107]) ).
fof(f494,definition,
! [X0] :
( sQ42_spl
<=> ( sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0] :
( ~ sQ42_spl
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( ~ sQ34_spl
| ~ sQ17_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f492,f494,f298,f441]) ).
fof(f498,plain,
( ~ sQ34_spl
| sQ24_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f493,f298,f339,f441]) ).
fof(f499,plain,
! [X0] :
( ~ sQ42_spl
| sdtlseqdt0(xr,X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f495]) ).
fof(f500,plain,
( ~ sQ33_spl
| sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f438,f193]) ).
fof(f501,plain,
! [X0] :
( ~ sQ33_spl
| sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f438,f114]) ).
fof(f503,definition,
( sQ43_spl
<=> sdtlseqdt0(xr,xp) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ43_spl
| sdtlseqdt0(xr,xp) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( ~ sQ33_spl
| sQ43_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f500,f298,f503,f437]) ).
fof(f507,definition,
! [X0] :
( sQ44_spl
<=> ( sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ33_spl
| ~ sQ14_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f501,f507,f288,f437]) ).
fof(f513,plain,
! [X0] :
( ~ sQ43_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f504,f111]) ).
fof(f514,plain,
( ~ sQ43_spl
| xp = xr
| ~ sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f504,f109]) ).
fof(f515,definition,
! [X0] :
( sQ45_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f516,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( ~ sQ43_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f513,f515,f298,f222,f503]) ).
fof(f519,definition,
( sQ46_spl
<=> sdtlseqdt0(xp,xr) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ46_spl
| ~ sdtlseqdt0(xp,xr) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ47_spl
<=> xp = xr ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( ~ sQ47_spl
| xp = xr ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( ~ sQ43_spl
| sQ47_spl
| ~ sQ46_spl
| ~ sQ17_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f514,f222,f298,f519,f522,f503]) ).
fof(f542,plain,
( sQ46_spl
| ~ sQ47_spl
| ~ sdtlseqdt0(xr,xr) ),
inference(forward_demodulation,[status(thm)],[f523,f521]) ).
fof(f544,plain,
( sQ46_spl
| ~ sQ47_spl
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f542,f107]) ).
fof(f545,definition,
( sQ48_spl
<=> sdtlseqdt0(xr,xr) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ48_spl
| sdtlseqdt0(xr,xr) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( sQ48_spl
| ~ sdtlseqdt0(xr,xr) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f549,plain,
( sQ46_spl
| ~ sQ47_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f544,f298,f522,f519]) ).
fof(f550,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0)
| sz10 = sz00
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f87,f76]) ).
fof(f553,definition,
( sQ49_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f555,plain,
( sQ49_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f556,definition,
( sQ50_spl
<=> sz10 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( ~ sQ50_spl
| sz10 = sz00 ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,definition,
! [X0] :
( sQ51_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( sQ51_spl
| sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f550,f553,f556,f559]) ).
fof(f564,definition,
! [X0] :
( sQ52_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f565,plain,
! [X0] :
( ~ sQ52_spl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f569,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f58]) ).
fof(f570,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f571,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f555,f57]) ).
fof(f572,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f582,plain,
( sQ5_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f236,f60]) ).
fof(f583,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f582,f219,f222,f234]) ).
fof(f591,plain,
( ~ sQ47_spl
| sdtlseqdt0(xm,xr) ),
inference(forward_demodulation,[status(thm)],[f523,f183]) ).
fof(f592,plain,
! [X0] :
( ~ sQ47_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f591,f111]) ).
fof(f593,plain,
( ~ sQ47_spl
| xr = xm
| ~ sdtlseqdt0(xr,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f591,f109]) ).
fof(f594,definition,
! [X0] :
( sQ54_spl
<=> ( sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f595,plain,
! [X0] :
( ~ sQ54_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,plain,
( ~ sQ47_spl
| ~ sQ17_spl
| ~ sQ7_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f592,f594,f241,f298,f522]) ).
fof(f598,definition,
( sQ55_spl
<=> sdtlseqdt0(xr,xm) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( ~ sQ55_spl
| sdtlseqdt0(xr,xm) ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f600,plain,
( sQ55_spl
| ~ sdtlseqdt0(xr,xm) ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f601,definition,
( sQ56_spl
<=> xr = xm ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ56_spl
| xr = xm ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f603,plain,
( sQ56_spl
| xr != xm ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,plain,
( ~ sQ47_spl
| sQ56_spl
| ~ sQ55_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f593,f298,f241,f598,f601,f522]) ).
fof(f605,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X3,sdtpldt0(X2,X1))
| ~ sdtlseqdt0(X3,sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtpldt0(X2,X0))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f117,f111]) ).
fof(f607,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X3,sdtpldt0(X2,X1))
| ~ sdtlseqdt0(X3,sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f60]) ).
fof(f609,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(sdtpldt0(X0,sz00),X0)
| sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00)) ),
inference(resolution,[status(thm)],[f118,f68]) ).
fof(f611,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,sz00))
| X0 = sdtpldt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f118,f68]) ).
fof(f614,definition,
! [X0] :
( sQ57_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ sdtlseqdt0(sdtpldt0(X0,sz00),X0)
| sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00)) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ26_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f609,f614,f355]) ).
fof(f618,definition,
! [X0] :
( sQ58_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ sdtlseqdt0(X0,sdtpldt0(X0,sz00))
| X0 = sdtpldt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( ~ sQ26_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f611,f618,f355]) ).
fof(f625,plain,
( ~ sQ47_spl
| xk != xr ),
inference(forward_demodulation,[status(thm)],[f523,f195]) ).
fof(f627,plain,
( ~ sQ47_spl
| sdtlseqdt0(xk,xr) ),
inference(forward_demodulation,[status(thm)],[f523,f196]) ).
fof(f629,plain,
( ~ sQ47_spl
| xr = xk
| ~ sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f627,f109]) ).
fof(f634,plain,
( ~ sQ47_spl
| sQ19_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f629,f298,f288,f339,f304,f522]) ).
fof(f635,plain,
( ~ sQ47_spl
| sdtlseqdt0(xn,xr) ),
inference(forward_demodulation,[status(thm)],[f523,f181]) ).
fof(f637,plain,
( ~ sQ47_spl
| xr = xn
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f635,f109]) ).
fof(f638,definition,
! [X0] :
( sQ60_spl
<=> ( sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f642,definition,
( sQ61_spl
<=> sdtlseqdt0(xr,xn) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ61_spl
| ~ sdtlseqdt0(xr,xn) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,definition,
( sQ62_spl
<=> xr = xn ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ62_spl
| xr = xn ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( ~ sQ47_spl
| sQ62_spl
| ~ sQ61_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f637,f298,f248,f642,f645,f522]) ).
fof(f649,plain,
( ~ sQ47_spl
| ~ sdtlseqdt0(xr,xm) ),
inference(forward_demodulation,[status(thm)],[f523,f179]) ).
fof(f650,plain,
( ~ sQ47_spl
| sdtlseqdt0(xm,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f649,f114]) ).
fof(f651,definition,
( sQ63_spl
<=> sdtlseqdt0(xm,xr) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f652,plain,
( ~ sQ63_spl
| sdtlseqdt0(xm,xr) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,plain,
( ~ sQ47_spl
| sQ63_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f650,f241,f298,f651,f522]) ).
fof(f657,definition,
( sQ64_spl
<=> sdtlseqdt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ64_spl
| sdtlseqdt0(xn,xr) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f664,definition,
! [X0] :
( sQ65_spl
<=> ( sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f668,definition,
( sQ66_spl
<=> xr = xr ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f673,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f88,f75]) ).
fof(f676,definition,
! [X0] :
( sQ67_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ67_spl
| sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f673,f553,f556,f676]) ).
fof(f683,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f90,f68]) ).
fof(f685,definition,
( sQ68_spl
<=> sz00 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( sQ68_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f683,f355,f685]) ).
fof(f733,plain,
! [X0,X1] :
( ~ sQ41_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f491,f111]) ).
fof(f734,plain,
! [X0] :
( ~ sQ41_spl
| X0 = xn
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f491,f109]) ).
fof(f735,definition,
! [X0,X1] :
( sQ71_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( ~ sQ41_spl
| ~ sQ9_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f733,f735,f248,f486]) ).
fof(f739,definition,
! [X0] :
( sQ72_spl
<=> ( X0 = xn
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( ~ sQ41_spl
| ~ sQ9_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f734,f739,f248,f486]) ).
fof(f745,plain,
! [X0,X1] :
( ~ sQ42_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f499,f111]) ).
fof(f746,plain,
! [X0] :
( ~ sQ42_spl
| X0 = xr
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f499,f109]) ).
fof(f747,definition,
! [X0,X1] :
( sQ73_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( ~ sQ42_spl
| ~ sQ17_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f745,f747,f298,f494]) ).
fof(f751,definition,
! [X0] :
( sQ74_spl
<=> ( X0 = xr
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ42_spl
| ~ sQ17_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f746,f751,f298,f494]) ).
fof(f759,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f516,f114]) ).
fof(f763,definition,
! [X0] :
( sQ75_spl
<=> ( sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( ~ sQ45_spl
| ~ sQ17_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f759,f763,f298,f515]) ).
fof(f776,definition,
! [X0] :
( sQ76_spl
<=> ( ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f777,plain,
! [X0] :
( ~ sQ76_spl
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f783,plain,
! [X0] :
( sK0_skl(sz00,X0) = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f98,f91]) ).
fof(f784,plain,
! [X0] :
( X0 = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f98,f90]) ).
fof(f787,definition,
! [X0] :
( sQ77_spl
<=> ( sK0_skl(sz00,X0) = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( ~ sQ26_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f783,f787,f355]) ).
fof(f791,definition,
! [X0] :
( sQ78_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( ~ sQ26_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f784,f791,f355]) ).
fof(f802,plain,
! [X0] :
( ~ sQ13_spl
| sdtlseqdt0(sdtpldt0(X0,xr),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f275,f119]) ).
fof(f803,plain,
! [X0] :
( ~ sQ13_spl
| sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(X0,xr))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f275,f119]) ).
fof(f804,plain,
( ~ sQ13_spl
| xr = sz00
| sdtpldt0(xp,sdtpldt0(xn,xm)) != sz00
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f275,f91]) ).
fof(f806,plain,
! [X0] :
( ~ sQ13_spl
| sdtpldt0(X0,xr) != sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f275,f118]) ).
fof(f807,plain,
! [X0] :
( ~ sQ13_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) != sdtpldt0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f275,f118]) ).
fof(f808,plain,
! [X0] :
( ~ sQ13_spl
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),X0),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xr)
| X0 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f275,f117]) ).
fof(f809,plain,
! [X0] :
( ~ sQ13_spl
| sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(sdtpldt0(xn,xm),X0))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,X0)
| xr = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f275,f117]) ).
fof(f810,plain,
! [X0] :
( ~ sQ13_spl
| sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xr)
| X0 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f275,f116]) ).
fof(f811,plain,
! [X0] :
( ~ sQ13_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) != sdtpldt0(sdtpldt0(xn,xm),X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,X0)
| xr = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f275,f116]) ).
fof(f812,plain,
( ~ sQ13_spl
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f275,f425]) ).
fof(f813,plain,
( ~ sQ13_spl
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f275,f64]) ).
fof(f816,definition,
! [X0] :
( sQ79_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,xr),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f802,f816,f219,f298,f274]) ).
fof(f820,definition,
! [X0] :
( sQ80_spl
<=> ( sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(X0,xr))
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| sQ80_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f803,f219,f820,f298,f274]) ).
fof(f824,definition,
( sQ81_spl
<=> sdtpldt0(xp,sdtpldt0(xn,xm)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f827,definition,
( sQ82_spl
<=> xr = sz00 ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( ~ sQ82_spl
| xr = sz00 ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f830,plain,
( ~ sQ13_spl
| sQ82_spl
| ~ sQ81_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f804,f219,f298,f824,f827,f274]) ).
fof(f831,definition,
( sQ83_spl
<=> sdtpldt0(xn,xm) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( ~ sQ83_spl
| sdtpldt0(xn,xm) = sz00 ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f835,definition,
! [X0] :
( sQ84_spl
<=> ( sdtpldt0(X0,xr) != sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f838,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f806,f835,f219,f298,f274]) ).
fof(f839,definition,
! [X0] :
( sQ85_spl
<=> ( sdtpldt0(xp,sdtpldt0(xn,xm)) != sdtpldt0(X0,xr)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f842,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| sQ85_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f807,f219,f839,f298,f274]) ).
fof(f843,definition,
! [X0] :
( sQ86_spl
<=> ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),X0),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ sdtlseqdt0(X0,xr)
| X0 = xr
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f846,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f808,f843,f298,f219,f274]) ).
fof(f847,definition,
! [X0] :
( sQ87_spl
<=> ( sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(sdtpldt0(xn,xm),X0))
| ~ sdtlseqdt0(xr,X0)
| xr = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| sQ87_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f809,f298,f847,f219,f274]) ).
fof(f851,definition,
! [X0] :
( sQ88_spl
<=> ( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xr)
| X0 = xr
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f810,f851,f298,f219,f274]) ).
fof(f855,definition,
! [X0] :
( sQ89_spl
<=> ( sdtpldt0(xp,sdtpldt0(xn,xm)) != sdtpldt0(sdtpldt0(xn,xm),X0)
| ~ sdtlseqdt0(xr,X0)
| xr = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f858,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| sQ89_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f811,f298,f855,f219,f274]) ).
fof(f859,definition,
( sQ90_spl
<=> sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ90_spl
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(component_clause,[status(thm)],[f859]) ).
fof(f862,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| sQ90_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f812,f219,f859,f298,f274]) ).
fof(f863,definition,
( sQ91_spl
<=> sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( ~ sQ13_spl
| sQ91_spl
| ~ sQ2_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f813,f298,f219,f863,f274]) ).
fof(f869,plain,
! [X0] :
( ~ sQ90_spl
| sdtlseqdt0(X0,sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f860,f111]) ).
fof(f870,plain,
( ~ sQ90_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[f860,f109]) ).
fof(f871,definition,
! [X0] :
( sQ92_spl
<=> ( sdtlseqdt0(X0,sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f874,plain,
( ~ sQ90_spl
| ~ sQ32_spl
| ~ sQ2_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f869,f871,f219,f402,f859]) ).
fof(f875,definition,
( sQ93_spl
<=> sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f877,plain,
( sQ93_spl
| ~ sdtlseqdt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f875]) ).
fof(f878,definition,
( sQ94_spl
<=> sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f879,plain,
( ~ sQ94_spl
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm) ),
inference(component_clause,[status(thm)],[f878]) ).
fof(f881,plain,
( ~ sQ90_spl
| sQ94_spl
| ~ sQ93_spl
| ~ sQ2_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f870,f402,f219,f875,f878,f859]) ).
fof(f882,plain,
( sQ93_spl
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f877,f114]) ).
fof(f883,plain,
( sQ93_spl
| sQ90_spl
| ~ sQ32_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f882,f219,f402,f859,f875]) ).
fof(f888,plain,
! [X0] :
( ~ sQ94_spl
| sdtlseqdt0(sdtpldt0(X0,sdtpldt0(xn,xm)),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f879,f119]) ).
fof(f889,plain,
! [X0] :
( ~ sQ94_spl
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(X0,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xp,X0)
| xp = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f879,f119]) ).
fof(f892,plain,
! [X0] :
( ~ sQ94_spl
| sdtpldt0(X0,sdtpldt0(xn,xm)) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f879,f118]) ).
fof(f893,plain,
! [X0] :
( ~ sQ94_spl
| sdtpldt0(xn,xm) != sdtpldt0(X0,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xp,X0)
| xp = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f879,f118]) ).
fof(f894,plain,
! [X0] :
( ~ sQ94_spl
| sdtlseqdt0(sdtpldt0(xp,X0),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f879,f117]) ).
fof(f895,plain,
! [X0] :
( ~ sQ94_spl
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,X0))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f879,f117]) ).
fof(f896,plain,
! [X0] :
( ~ sQ94_spl
| sdtpldt0(xp,X0) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f879,f116]) ).
fof(f897,plain,
! [X0] :
( ~ sQ94_spl
| sdtpldt0(xn,xm) != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f879,f116]) ).
fof(f898,plain,
( ~ sQ94_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtlseqdt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f879,f425]) ).
fof(f900,definition,
! [X0] :
( sQ95_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,sdtpldt0(xn,xm)),sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f903,plain,
( ~ sQ94_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f888,f900,f222,f219,f878]) ).
fof(f904,definition,
! [X0] :
( sQ96_spl
<=> ( sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(X0,sdtpldt0(xn,xm)))
| ~ sdtlseqdt0(xp,X0)
| xp = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( ~ sQ94_spl
| ~ sQ2_spl
| sQ96_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f889,f222,f904,f219,f878]) ).
fof(f909,definition,
( sQ97_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( ~ sQ97_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f909]) ).
fof(f913,definition,
! [X0] :
( sQ98_spl
<=> ( sdtpldt0(X0,sdtpldt0(xn,xm)) != sdtpldt0(xn,xm)
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ94_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f892,f913,f222,f219,f878]) ).
fof(f917,definition,
! [X0] :
( sQ99_spl
<=> ( sdtpldt0(xn,xm) != sdtpldt0(X0,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xp,X0)
| xp = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f920,plain,
( ~ sQ94_spl
| ~ sQ2_spl
| sQ99_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f893,f222,f917,f219,f878]) ).
fof(f921,definition,
! [X0] :
( sQ100_spl
<=> ( sdtlseqdt0(sdtpldt0(xp,X0),sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( ~ sQ94_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f894,f921,f219,f222,f878]) ).
fof(f925,definition,
! [X0] :
( sQ101_spl
<=> ( sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,X0))
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f928,plain,
( ~ sQ94_spl
| ~ sQ3_spl
| sQ101_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f895,f219,f925,f222,f878]) ).
fof(f929,definition,
! [X0] :
( sQ102_spl
<=> ( sdtpldt0(xp,X0) != sdtpldt0(xn,xm)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| X0 = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ94_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f896,f929,f219,f222,f878]) ).
fof(f933,definition,
! [X0] :
( sQ103_spl
<=> ( sdtpldt0(xn,xm) != sdtpldt0(xp,X0)
| ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtpldt0(xn,xm) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f936,plain,
( ~ sQ94_spl
| ~ sQ3_spl
| sQ103_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f897,f219,f933,f222,f878]) ).
fof(f937,definition,
( sQ104_spl
<=> sdtlseqdt0(xp,sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f938,plain,
( ~ sQ104_spl
| sdtlseqdt0(xp,sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f937]) ).
fof(f939,plain,
( sQ104_spl
| ~ sdtlseqdt0(xp,sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f937]) ).
fof(f940,plain,
( ~ sQ94_spl
| ~ sQ2_spl
| sQ104_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f898,f222,f937,f219,f878]) ).
fof(f943,plain,
( ~ sQ0_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,xp)
| xr = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f200,f116]) ).
fof(f959,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ43_spl
| sQ47_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f943,f298,f222,f522,f503,f219,f199]) ).
fof(f1005,plain,
! [X0] :
( ~ sQ76_spl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f777]) ).
fof(f1021,plain,
( ~ sQ97_spl
| ~ isPrime0(xp) ),
inference(backward_demodulation,[status(thm)],[f910,f229]) ).
fof(f1029,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1021,f176]) ).
fof(f1030,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f1029]) ).
fof(f1035,plain,
( ~ sQ62_spl
| ~ sdtlseqdt0(xp,xr) ),
inference(backward_demodulation,[status(thm)],[f646,f178]) ).
fof(f1041,plain,
( ~ sQ62_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1035,f519,f645]) ).
fof(f1044,plain,
( ~ sQ56_spl
| ~ sdtlseqdt0(xp,xr) ),
inference(backward_demodulation,[status(thm)],[f602,f179]) ).
fof(f1048,plain,
( ~ sQ56_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1044,f519,f601]) ).
fof(f1062,definition,
( sQ116_spl
<=> sz10 = xr ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1063,plain,
( ~ sQ116_spl
| sz10 = xr ),
inference(component_clause,[status(thm)],[f1062]) ).
fof(f1070,definition,
! [X0] :
( sQ118_spl
<=> ( X0 = xr
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1071,plain,
! [X0] :
( ~ sQ118_spl
| X0 = xr
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1070]) ).
fof(f1081,plain,
( ~ sQ116_spl
| ~ isPrime0(xr) ),
inference(backward_demodulation,[status(thm)],[f1063,f230]) ).
fof(f1082,plain,
( ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1081,f192]) ).
fof(f1083,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f1082]) ).
fof(f1091,plain,
( ~ sQ76_spl
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f1005,f57]) ).
fof(f1100,plain,
( ~ sQ76_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1091,f556,f776]) ).
fof(f1109,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(sdtpldt0(X0,X1),X0)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f60]) ).
fof(f1111,plain,
( ~ sQ118_spl
| sz10 = xr ),
inference(resolution,[status(thm)],[f1071,f57]) ).
fof(f1120,plain,
( ~ sQ118_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1111,f1062,f1070]) ).
fof(f1134,plain,
( ~ sQ83_spl
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f832,f425]) ).
fof(f1135,plain,
( ~ sQ83_spl
| sdtpldt0(xm,xn) = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f832,f64]) ).
fof(f1138,definition,
( sQ120_spl
<=> sdtlseqdt0(xn,sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1140,plain,
( sQ120_spl
| ~ sdtlseqdt0(xn,sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1138]) ).
fof(f1141,definition,
( sQ121_spl
<=> xm = sdtmndt0(sz00,xn) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( ~ sQ121_spl
| xm = sdtmndt0(sz00,xn) ),
inference(component_clause,[status(thm)],[f1141]) ).
fof(f1177,definition,
( sQ130_spl
<=> sdtlseqdt0(xn,sz00) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1178,plain,
( ~ sQ130_spl
| sdtlseqdt0(xn,sz00) ),
inference(component_clause,[status(thm)],[f1177]) ).
fof(f1179,plain,
( sQ130_spl
| ~ sdtlseqdt0(xn,sz00) ),
inference(component_clause,[status(thm)],[f1177]) ).
fof(f1180,plain,
( ~ sQ83_spl
| ~ sQ7_spl
| sQ130_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1134,f248,f1177,f241,f831]) ).
fof(f1181,definition,
( sQ131_spl
<=> sdtpldt0(xm,xn) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1182,plain,
( ~ sQ131_spl
| sdtpldt0(xm,xn) = sz00 ),
inference(component_clause,[status(thm)],[f1181]) ).
fof(f1184,plain,
( ~ sQ83_spl
| sQ131_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1135,f241,f248,f1181,f831]) ).
fof(f1187,plain,
! [X0] :
( ~ sQ130_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1178,f111]) ).
fof(f1188,plain,
( ~ sQ130_spl
| sz00 = xn
| ~ sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1178,f109]) ).
fof(f1189,definition,
! [X0] :
( sQ132_spl
<=> ( sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1190,plain,
! [X0] :
( ~ sQ132_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1192,plain,
( ~ sQ130_spl
| ~ sQ26_spl
| ~ sQ9_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1187,f1189,f248,f355,f1177]) ).
fof(f1193,definition,
( sQ133_spl
<=> sdtlseqdt0(sz00,xn) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1194,plain,
( ~ sQ133_spl
| sdtlseqdt0(sz00,xn) ),
inference(component_clause,[status(thm)],[f1193]) ).
fof(f1195,plain,
( sQ133_spl
| ~ sdtlseqdt0(sz00,xn) ),
inference(component_clause,[status(thm)],[f1193]) ).
fof(f1196,definition,
( sQ134_spl
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1197,plain,
( ~ sQ134_spl
| sz00 = xn ),
inference(component_clause,[status(thm)],[f1196]) ).
fof(f1198,plain,
( sQ134_spl
| sz00 != xn ),
inference(component_clause,[status(thm)],[f1196]) ).
fof(f1199,plain,
( ~ sQ130_spl
| sQ134_spl
| ~ sQ133_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1188,f355,f248,f1193,f1196,f1177]) ).
fof(f1200,plain,
( ~ sQ134_spl
| sz10 != xn ),
inference(backward_demodulation,[status(thm)],[f1197,f58]) ).
fof(f1202,plain,
( ~ sQ134_spl
| ~ isPrime0(xn) ),
inference(backward_demodulation,[status(thm)],[f1197,f229]) ).
fof(f1205,plain,
! [X0] :
( ~ sQ63_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f652,f111]) ).
fof(f1206,plain,
( ~ sQ63_spl
| xr = xm
| ~ sdtlseqdt0(xr,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f652,f109]) ).
fof(f1207,plain,
( ~ sQ63_spl
| ~ sQ17_spl
| ~ sQ7_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1205,f594,f241,f298,f651]) ).
fof(f1208,plain,
( ~ sQ63_spl
| sQ56_spl
| ~ sQ55_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1206,f298,f241,f598,f601,f651]) ).
fof(f1209,plain,
! [X0] :
( ~ sQ64_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f658,f111]) ).
fof(f1210,plain,
( ~ sQ64_spl
| xr = xn
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f658,f109]) ).
fof(f1211,plain,
( ~ sQ64_spl
| ~ sQ17_spl
| ~ sQ9_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1209,f638,f248,f298,f657]) ).
fof(f1212,plain,
( ~ sQ64_spl
| sQ62_spl
| ~ sQ61_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1210,f298,f248,f642,f645,f657]) ).
fof(f1215,plain,
( sQ61_spl
| sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f644,f114]) ).
fof(f1216,plain,
( sQ61_spl
| sQ64_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1215,f248,f298,f657,f642]) ).
fof(f1238,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ134_spl
| X0 = xn
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f565]) ).
fof(f1240,plain,
( ~ sQ52_spl
| ~ sQ134_spl
| sz10 = xn ),
inference(resolution,[status(thm)],[f1238,f57]) ).
fof(f1248,plain,
( ~ sQ52_spl
| ~ sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1240,f1200]) ).
fof(f1249,plain,
( ~ sQ52_spl
| ~ sQ134_spl ),
inference(contradiction_clause,[status(thm)],[f1248]) ).
fof(f1250,plain,
( sQ133_spl
| sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1195,f114]) ).
fof(f1251,plain,
( sQ133_spl
| sQ130_spl
| ~ sQ26_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1250,f248,f355,f1177,f1193]) ).
fof(f1264,plain,
! [X0] :
( ~ sQ131_spl
| X0 = xm
| sdtpldt0(X0,xn) != sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1182,f85]) ).
fof(f1266,plain,
( ~ sQ131_spl
| ~ aNaturalNumber0(xn)
| xn = sdtmndt0(sz00,xm)
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1182,f1109]) ).
fof(f1267,plain,
! [X0] :
( ~ sQ131_spl
| sdtlseqdt0(sdtpldt0(X0,xn),sz00)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f1182,f119]) ).
fof(f1268,plain,
! [X0] :
( ~ sQ131_spl
| sdtlseqdt0(sz00,sdtpldt0(X0,xn))
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1182,f119]) ).
fof(f1269,plain,
! [X0] :
( ~ sQ131_spl
| sdtlseqdt0(sdtpldt0(xm,X0),sz00)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f1182,f117]) ).
fof(f1270,plain,
! [X0] :
( ~ sQ131_spl
| sdtlseqdt0(sz00,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1182,f117]) ).
fof(f1271,plain,
! [X0] :
( ~ sQ131_spl
| sdtpldt0(xm,X0) != sz00
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f1182,f116]) ).
fof(f1272,plain,
! [X0] :
( ~ sQ131_spl
| sz00 != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1182,f116]) ).
fof(f1273,plain,
( ~ sQ131_spl
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1182,f425]) ).
fof(f1275,definition,
! [X0] :
( sQ135_spl
<=> ( X0 = xm
| sdtpldt0(X0,xn) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1278,plain,
( ~ sQ131_spl
| ~ sQ7_spl
| sQ135_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1264,f248,f1275,f241,f1181]) ).
fof(f1280,definition,
( sQ136_spl
<=> sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
( sQ136_spl
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(component_clause,[status(thm)],[f1280]) ).
fof(f1283,definition,
( sQ137_spl
<=> xn = sdtmndt0(sz00,xm) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1284,plain,
( ~ sQ137_spl
| xn = sdtmndt0(sz00,xm) ),
inference(component_clause,[status(thm)],[f1283]) ).
fof(f1286,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| sQ137_spl
| ~ sQ136_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1266,f241,f1280,f1283,f248,f1181]) ).
fof(f1287,definition,
! [X0] :
( sQ138_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,xn),sz00)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1290,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1267,f1287,f241,f248,f1181]) ).
fof(f1291,definition,
! [X0] :
( sQ139_spl
<=> ( sdtlseqdt0(sz00,sdtpldt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1294,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| sQ139_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1268,f241,f1291,f248,f1181]) ).
fof(f1295,definition,
! [X0] :
( sQ140_spl
<=> ( sdtlseqdt0(sdtpldt0(xm,X0),sz00)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1298,plain,
( ~ sQ131_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1269,f1295,f248,f241,f1181]) ).
fof(f1299,definition,
! [X0] :
( sQ141_spl
<=> ( sdtlseqdt0(sz00,sdtpldt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( ~ sQ131_spl
| ~ sQ7_spl
| sQ141_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1270,f248,f1299,f241,f1181]) ).
fof(f1303,definition,
! [X0] :
( sQ142_spl
<=> ( sdtpldt0(xm,X0) != sz00
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( ~ sQ131_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1271,f1303,f248,f241,f1181]) ).
fof(f1307,definition,
! [X0] :
( sQ143_spl
<=> ( sz00 != sdtpldt0(xm,X0)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1310,plain,
( ~ sQ131_spl
| ~ sQ7_spl
| sQ143_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1272,f248,f1307,f241,f1181]) ).
fof(f1311,definition,
( sQ144_spl
<=> sdtlseqdt0(xm,sz00) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1312,plain,
( ~ sQ144_spl
| sdtlseqdt0(xm,sz00) ),
inference(component_clause,[status(thm)],[f1311]) ).
fof(f1313,plain,
( sQ144_spl
| ~ sdtlseqdt0(xm,sz00) ),
inference(component_clause,[status(thm)],[f1311]) ).
fof(f1314,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| sQ144_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1273,f241,f1311,f248,f1181]) ).
fof(f1316,plain,
! [X0] :
( ~ sQ144_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1312,f111]) ).
fof(f1317,plain,
( ~ sQ144_spl
| sz00 = xm
| ~ sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1312,f109]) ).
fof(f1318,definition,
! [X0] :
( sQ145_spl
<=> ( sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( ~ sQ144_spl
| ~ sQ26_spl
| ~ sQ7_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1316,f1318,f241,f355,f1311]) ).
fof(f1322,definition,
( sQ146_spl
<=> sdtlseqdt0(sz00,xm) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1323,plain,
( ~ sQ146_spl
| sdtlseqdt0(sz00,xm) ),
inference(component_clause,[status(thm)],[f1322]) ).
fof(f1324,plain,
( sQ146_spl
| ~ sdtlseqdt0(sz00,xm) ),
inference(component_clause,[status(thm)],[f1322]) ).
fof(f1325,definition,
( sQ147_spl
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1326,plain,
( ~ sQ147_spl
| sz00 = xm ),
inference(component_clause,[status(thm)],[f1325]) ).
fof(f1328,plain,
( ~ sQ144_spl
| sQ147_spl
| ~ sQ146_spl
| ~ sQ7_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1317,f355,f241,f1322,f1325,f1311]) ).
fof(f1329,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f127,f111]) ).
fof(f1330,plain,
! [X0] :
( X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f127,f109]) ).
fof(f1331,definition,
! [X0,X1] :
( sQ148_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( ~ sQ49_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1329,f1331,f553]) ).
fof(f1335,definition,
! [X0] :
( sQ149_spl
<=> ( X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1338,plain,
( ~ sQ49_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1330,f1335,f553]) ).
fof(f1341,plain,
! [X0] :
( X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0)
| iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f133,f127]) ).
fof(f1342,plain,
( ~ sQ63_spl
| iLess0(xm,xr)
| xm = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f133,f652]) ).
fof(f1343,plain,
( iLess0(xm,xp)
| xm = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f133,f183]) ).
fof(f1344,plain,
( ~ sQ130_spl
| iLess0(xn,sz00)
| xn = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f133,f1178]) ).
fof(f1345,plain,
( ~ sQ64_spl
| iLess0(xn,xr)
| xn = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f133,f658]) ).
fof(f1346,plain,
( iLess0(xn,xp)
| xn = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f133,f181]) ).
fof(f1348,plain,
( iLess0(xk,xp)
| xk = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f133,f196]) ).
fof(f1355,definition,
! [X0] :
( sQ150_spl
<=> ( X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0)
| iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1358,plain,
( sQ150_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f1341,f553,f1355]) ).
fof(f1359,definition,
( sQ151_spl
<=> iLess0(xm,xr) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1362,plain,
( ~ sQ63_spl
| sQ151_spl
| sQ56_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1342,f241,f298,f601,f1359,f651]) ).
fof(f1363,definition,
( sQ152_spl
<=> iLess0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1366,plain,
( sQ152_spl
| sQ21_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1343,f241,f222,f311,f1363]) ).
fof(f1367,definition,
( sQ153_spl
<=> iLess0(xn,sz00) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1370,plain,
( ~ sQ130_spl
| sQ153_spl
| sQ134_spl
| ~ sQ26_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1344,f248,f355,f1196,f1367,f1177]) ).
fof(f1371,definition,
( sQ154_spl
<=> iLess0(xn,xr) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1374,plain,
( ~ sQ64_spl
| sQ154_spl
| sQ62_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1345,f248,f298,f645,f1371,f657]) ).
fof(f1375,definition,
( sQ155_spl
<=> iLess0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( sQ155_spl
| sQ23_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1346,f248,f222,f318,f1375]) ).
fof(f1383,definition,
( sQ157_spl
<=> iLess0(xk,xp) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( sQ157_spl
| sQ16_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1348,f288,f222,f294,f1383]) ).
fof(f1399,plain,
! [X0] :
( ~ sQ147_spl
| sdtlseqdt0(sz10,X0)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f1326,f127]) ).
fof(f1414,plain,
( ~ sQ134_spl
| ~ sQ147_spl
| xm = xn ),
inference(forward_demodulation,[status(thm)],[f1326,f1197]) ).
fof(f1419,plain,
( sQ1_spl
| ~ sQ134_spl
| ~ sQ147_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_demodulation,[status(thm)],[f1414,f204]) ).
fof(f1420,plain,
( sQ1_spl
| ~ sQ134_spl
| ~ sQ147_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xm),xr),sdtpldt0(sdtpldt0(xm,xm),xp)) ),
inference(forward_demodulation,[status(thm)],[f1414,f1419]) ).
fof(f1421,plain,
( sQ1_spl
| ~ sQ134_spl
| ~ sQ147_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xm))
| ~ sdtlseqdt0(xr,xp)
| xr = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1420,f117]) ).
fof(f1423,definition,
( sQ159_spl
<=> aNaturalNumber0(sdtpldt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1425,plain,
( sQ159_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xm)) ),
inference(component_clause,[status(thm)],[f1423]) ).
fof(f1426,plain,
( sQ1_spl
| ~ sQ134_spl
| ~ sQ147_spl
| ~ sQ159_spl
| ~ sQ43_spl
| sQ47_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1421,f298,f222,f522,f503,f1423,f1325,f1196,f202]) ).
fof(f1427,definition,
( sQ160_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1429,plain,
( sQ160_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xm),xp)) ),
inference(component_clause,[status(thm)],[f1427]) ).
fof(f1430,definition,
( sQ161_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xm),xr)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1432,plain,
( sQ161_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xm),xr)) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1445,plain,
( ~ sQ134_spl
| ~ sQ62_spl
| ~ isPrime0(xr) ),
inference(forward_demodulation,[status(thm)],[f646,f1202]) ).
fof(f1446,plain,
( ~ sQ134_spl
| ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1445,f192]) ).
fof(f1447,plain,
( ~ sQ134_spl
| ~ sQ62_spl ),
inference(contradiction_clause,[status(thm)],[f1446]) ).
fof(f1454,plain,
( sQ146_spl
| ~ sQ56_spl
| ~ sdtlseqdt0(sz00,xr) ),
inference(forward_demodulation,[status(thm)],[f602,f1324]) ).
fof(f1455,plain,
( sQ146_spl
| ~ sQ56_spl
| sdtlseqdt0(xr,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1454,f114]) ).
fof(f1456,definition,
( sQ163_spl
<=> sdtlseqdt0(xr,sz00) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1457,plain,
( ~ sQ163_spl
| sdtlseqdt0(xr,sz00) ),
inference(component_clause,[status(thm)],[f1456]) ).
fof(f1459,plain,
( sQ146_spl
| ~ sQ56_spl
| sQ163_spl
| ~ sQ26_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1455,f298,f355,f1456,f601,f1322]) ).
fof(f1474,plain,
( sQ144_spl
| ~ sQ56_spl
| ~ sdtlseqdt0(xr,sz00) ),
inference(forward_demodulation,[status(thm)],[f602,f1313]) ).
fof(f1475,plain,
( sQ144_spl
| ~ sQ56_spl
| sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1474,f114]) ).
fof(f1476,definition,
( sQ164_spl
<=> sdtlseqdt0(sz00,xr) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1477,plain,
( ~ sQ164_spl
| sdtlseqdt0(sz00,xr) ),
inference(component_clause,[status(thm)],[f1476]) ).
fof(f1478,plain,
( sQ164_spl
| ~ sdtlseqdt0(sz00,xr) ),
inference(component_clause,[status(thm)],[f1476]) ).
fof(f1479,plain,
( sQ144_spl
| ~ sQ56_spl
| sQ164_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1475,f355,f298,f1476,f601,f1311]) ).
fof(f1482,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f62]) ).
fof(f1493,plain,
( sQ1_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,xp)
| xr = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f204,f117]) ).
fof(f1495,plain,
( sQ1_spl
| ~ sQ2_spl
| ~ sQ43_spl
| sQ47_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1493,f298,f222,f522,f503,f219,f202]) ).
fof(f1524,plain,
( ~ sQ163_spl
| ~ sQ134_spl
| sdtlseqdt0(xr,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f1457]) ).
fof(f1525,plain,
( ~ sQ163_spl
| ~ sQ134_spl
| sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1524,f644]) ).
fof(f1526,plain,
( ~ sQ163_spl
| ~ sQ134_spl
| sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f1525]) ).
fof(f1527,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| sdtlseqdt0(xn,xr) ),
inference(forward_demodulation,[status(thm)],[f1197,f1477]) ).
fof(f1528,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| iLess0(xn,xr)
| xn = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1527,f133]) ).
fof(f1529,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ134_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1527,f111]) ).
fof(f1530,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| xr = xn
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1527,f109]) ).
fof(f1531,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| sQ154_spl
| sQ62_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1528,f248,f298,f645,f1371,f1196,f1476]) ).
fof(f1532,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| ~ sQ17_spl
| ~ sQ9_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1529,f638,f248,f298,f1196,f1476]) ).
fof(f1533,plain,
( ~ sQ164_spl
| ~ sQ134_spl
| sQ62_spl
| ~ sQ61_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1530,f298,f248,f642,f645,f1196,f1476]) ).
fof(f1534,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f62]) ).
fof(f1535,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f177]) ).
fof(f1536,plain,
! [X0] :
( doDivides0(X0,xk)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f191]) ).
fof(f1538,definition,
! [X0] :
( sQ165_spl
<=> ( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1541,definition,
( sQ166_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( sQ166_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1541]) ).
fof(f1544,plain,
( ~ sQ166_spl
| ~ sQ3_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f1535,f1538,f222,f1541]) ).
fof(f1545,definition,
! [X0] :
( sQ167_spl
<=> ( doDivides0(X0,xk)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1548,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f1536,f1545,f298,f288]) ).
fof(f1551,plain,
( sQ146_spl
| sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f1324,f114]) ).
fof(f1552,plain,
( sQ146_spl
| sQ144_spl
| ~ sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1551,f241,f355,f1311,f1322]) ).
fof(f1559,plain,
( sQ164_spl
| sdtlseqdt0(xr,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1478,f114]) ).
fof(f1560,plain,
( sQ164_spl
| sQ163_spl
| ~ sQ26_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1559,f298,f355,f1456,f1476]) ).
fof(f1595,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f194,f147]) ).
fof(f1596,definition,
! [X0] :
( sQ168_spl
<=> ( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1599,plain,
( ~ sQ166_spl
| ~ sQ17_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f1595,f1596,f298,f1541]) ).
fof(f1602,plain,
( ~ sQ144_spl
| iLess0(xm,sz00)
| xm = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f1312,f133]) ).
fof(f1605,definition,
( sQ169_spl
<=> iLess0(xm,sz00) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1608,plain,
( ~ sQ144_spl
| sQ169_spl
| sQ147_spl
| ~ sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1602,f241,f355,f1325,f1605,f1311]) ).
fof(f1612,plain,
( sQ133_spl
| ~ sQ147_spl
| ~ sdtlseqdt0(xm,xn) ),
inference(backward_demodulation,[status(thm)],[f1326,f1195]) ).
fof(f1617,plain,
( sQ134_spl
| ~ sQ147_spl
| xm != xn ),
inference(backward_demodulation,[status(thm)],[f1326,f1198]) ).
fof(f1624,plain,
( ~ sQ163_spl
| ~ sQ147_spl
| sdtlseqdt0(xr,xm) ),
inference(forward_demodulation,[status(thm)],[f1326,f1457]) ).
fof(f1625,plain,
( ~ sQ163_spl
| ~ sQ147_spl
| sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1624,f600]) ).
fof(f1626,plain,
( ~ sQ163_spl
| ~ sQ147_spl
| sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f1625]) ).
fof(f1627,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ147_spl
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1326,f565]) ).
fof(f1628,plain,
( ~ sQ52_spl
| ~ sQ147_spl
| xn = xm ),
inference(resolution,[status(thm)],[f1627,f171]) ).
fof(f1638,plain,
( ~ sQ52_spl
| ~ sQ147_spl
| sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1628,f1617]) ).
fof(f1639,plain,
( ~ sQ52_spl
| ~ sQ147_spl
| sQ134_spl ),
inference(contradiction_clause,[status(thm)],[f1638]) ).
fof(f1640,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1534,f1482]) ).
fof(f1645,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f153,f177]) ).
fof(f1646,plain,
( sdtlseqdt0(xr,sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f153,f194]) ).
fof(f1650,definition,
( sQ170_spl
<=> sdtasdt0(xn,xm) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( ~ sQ170_spl
| sdtasdt0(xn,xm) = sz00 ),
inference(component_clause,[status(thm)],[f1650]) ).
fof(f1653,definition,
( sQ171_spl
<=> sdtlseqdt0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1654,plain,
( ~ sQ171_spl
| sdtlseqdt0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1653]) ).
fof(f1656,plain,
( sQ171_spl
| sQ170_spl
| ~ sQ166_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1645,f222,f1541,f1650,f1653]) ).
fof(f1657,definition,
( sQ172_spl
<=> sdtlseqdt0(xr,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1658,plain,
( ~ sQ172_spl
| sdtlseqdt0(xr,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1659,plain,
( sQ172_spl
| ~ sdtlseqdt0(xr,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1660,plain,
( sQ172_spl
| sQ170_spl
| ~ sQ166_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1646,f298,f1541,f1650,f1657]) ).
fof(f1661,definition,
( sQ173_spl
<=> xk = sz00 ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1662,plain,
( ~ sQ173_spl
| xk = sz00 ),
inference(component_clause,[status(thm)],[f1661]) ).
fof(f1669,plain,
( ~ sQ173_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1662,f186]) ).
fof(f1670,plain,
~ sQ173_spl,
inference(contradiction_clause,[status(thm)],[f1669]) ).
fof(f1671,plain,
( ~ sQ163_spl
| iLess0(xr,sz00)
| xr = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1457,f133]) ).
fof(f1672,plain,
! [X0] :
( ~ sQ163_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1457,f111]) ).
fof(f1673,plain,
( ~ sQ163_spl
| sz00 = xr
| ~ sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1457,f109]) ).
fof(f1674,definition,
( sQ174_spl
<=> iLess0(xr,sz00) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1677,plain,
( ~ sQ163_spl
| sQ174_spl
| sQ82_spl
| ~ sQ26_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1671,f298,f355,f827,f1674,f1456]) ).
fof(f1678,definition,
! [X0] :
( sQ175_spl
<=> ( sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1681,plain,
( ~ sQ163_spl
| ~ sQ26_spl
| ~ sQ17_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f1672,f1678,f298,f355,f1456]) ).
fof(f1682,plain,
( ~ sQ163_spl
| sQ82_spl
| ~ sQ164_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1673,f355,f298,f1476,f827,f1456]) ).
fof(f1703,plain,
! [X0] :
( ~ sQ55_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f599,f111]) ).
fof(f1709,definition,
! [X0] :
( sQ177_spl
<=> ( sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1712,plain,
( ~ sQ55_spl
| ~ sQ7_spl
| ~ sQ17_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f1703,f1709,f298,f241,f598]) ).
fof(f1752,plain,
( ~ sQ164_spl
| iLess0(sz00,xr)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1477,f133]) ).
fof(f1753,plain,
! [X0] :
( ~ sQ164_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1477,f111]) ).
fof(f1755,definition,
( sQ178_spl
<=> iLess0(sz00,xr) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1758,plain,
( ~ sQ164_spl
| sQ178_spl
| sQ82_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1752,f355,f298,f827,f1755,f1476]) ).
fof(f1759,definition,
! [X0] :
( sQ179_spl
<=> ( sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( ~ sQ164_spl
| ~ sQ17_spl
| ~ sQ26_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f1753,f1759,f355,f298,f1476]) ).
fof(f1775,plain,
( ~ sQ82_spl
| ~ isPrime0(xr) ),
inference(backward_demodulation,[status(thm)],[f828,f229]) ).
fof(f1785,plain,
( ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1775,f192]) ).
fof(f1786,plain,
~ sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1785]) ).
fof(f1787,plain,
( xp = sdtasdt0(xn,xm)
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f161,f177]) ).
fof(f1788,plain,
( xr = sdtasdt0(xn,xm)
| xr = sz10
| ~ aNaturalNumber0(xr)
| ~ isPrime0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f161,f194]) ).
fof(f1792,definition,
( sQ180_spl
<=> isPrime0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1794,plain,
( sQ180_spl
| ~ isPrime0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1792]) ).
fof(f1795,definition,
( sQ181_spl
<=> xp = sz10 ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1796,plain,
( ~ sQ181_spl
| xp = sz10 ),
inference(component_clause,[status(thm)],[f1795]) ).
fof(f1798,definition,
( sQ182_spl
<=> xp = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1799,plain,
( ~ sQ182_spl
| xp = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1798]) ).
fof(f1800,plain,
( sQ182_spl
| xp != sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1798]) ).
fof(f1801,plain,
( sQ182_spl
| sQ181_spl
| ~ sQ3_spl
| ~ sQ180_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f1787,f1541,f1792,f222,f1795,f1798]) ).
fof(f1802,definition,
( sQ183_spl
<=> xr = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1803,plain,
( ~ sQ183_spl
| xr = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1802]) ).
fof(f1804,plain,
( sQ183_spl
| xr != sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1802]) ).
fof(f1805,plain,
( sQ183_spl
| sQ116_spl
| ~ sQ17_spl
| ~ sQ180_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f1788,f1541,f1792,f298,f1062,f1802]) ).
fof(f1817,plain,
( ~ sQ181_spl
| ~ isPrime0(xp) ),
inference(backward_demodulation,[status(thm)],[f1796,f230]) ).
fof(f1820,plain,
( ~ sQ181_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1817,f176]) ).
fof(f1821,plain,
~ sQ181_spl,
inference(contradiction_clause,[status(thm)],[f1820]) ).
fof(f1857,plain,
( ~ sQ121_spl
| sdtpldt0(xn,xm) = sz00
| ~ sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1142,f208]) ).
fof(f1859,plain,
( ~ sQ121_spl
| sQ83_spl
| ~ sQ130_spl
| ~ sQ26_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1857,f248,f355,f1177,f831,f1141]) ).
fof(f1863,plain,
( ~ sQ133_spl
| iLess0(sz00,xn)
| sz00 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1194,f133]) ).
fof(f1864,plain,
! [X0] :
( ~ sQ133_spl
| sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1194,f111]) ).
fof(f1866,definition,
( sQ185_spl
<=> iLess0(sz00,xn) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1869,plain,
( ~ sQ133_spl
| sQ185_spl
| sQ134_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1863,f355,f248,f1196,f1866,f1193]) ).
fof(f1870,definition,
! [X0] :
( sQ186_spl
<=> ( sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1873,plain,
( ~ sQ133_spl
| ~ sQ9_spl
| ~ sQ26_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f1864,f1870,f355,f248,f1193]) ).
fof(f1899,plain,
! [X0] :
( ~ sQ147_spl
| iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1399,f133]) ).
fof(f1900,plain,
! [X0,X1] :
( ~ sQ147_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1399,f111]) ).
fof(f1901,plain,
! [X0] :
( ~ sQ147_spl
| X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1399,f109]) ).
fof(f1902,definition,
! [X0] :
( sQ187_spl
<=> ( iLess0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
( ~ sQ147_spl
| ~ sQ49_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f1899,f1902,f553,f1325]) ).
fof(f1906,definition,
! [X0,X1] :
( sQ188_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1909,plain,
( ~ sQ147_spl
| ~ sQ49_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f1900,f1906,f553,f1325]) ).
fof(f1910,definition,
! [X0] :
( sQ189_spl
<=> ( X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1913,plain,
( ~ sQ147_spl
| ~ sQ49_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f1901,f1910,f553,f1325]) ).
fof(f1953,plain,
( ~ sQ137_spl
| sdtpldt0(xm,xn) = sz00
| ~ sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1284,f208]) ).
fof(f1955,plain,
( ~ sQ137_spl
| sQ131_spl
| ~ sQ144_spl
| ~ sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1953,f241,f355,f1311,f1181,f1283]) ).
fof(f1987,plain,
( sQ144_spl
| ~ sQ134_spl
| ~ sdtlseqdt0(xm,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f1313]) ).
fof(f1988,plain,
( sQ144_spl
| ~ sQ134_spl
| sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1987,f114]) ).
fof(f1989,definition,
( sQ190_spl
<=> sdtlseqdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1990,plain,
( ~ sQ190_spl
| sdtlseqdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1989]) ).
fof(f1991,plain,
( sQ190_spl
| ~ sdtlseqdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1989]) ).
fof(f1992,plain,
( sQ144_spl
| ~ sQ134_spl
| sQ190_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1988,f248,f241,f1989,f1196,f1311]) ).
fof(f1993,plain,
( ~ sQ190_spl
| iLess0(xn,xm)
| xn = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1990,f133]) ).
fof(f1994,plain,
! [X0] :
( ~ sQ190_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1990,f111]) ).
fof(f1995,plain,
( ~ sQ190_spl
| xm = xn
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f1990,f109]) ).
fof(f1996,definition,
( sQ191_spl
<=> xn = xm ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1997,plain,
( ~ sQ191_spl
| xn = xm ),
inference(component_clause,[status(thm)],[f1996]) ).
fof(f1999,definition,
( sQ192_spl
<=> iLess0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2002,plain,
( ~ sQ190_spl
| sQ192_spl
| sQ191_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1993,f248,f241,f1996,f1999,f1989]) ).
fof(f2003,definition,
! [X0] :
( sQ193_spl
<=> ( sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2004,plain,
! [X0] :
( ~ sQ193_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2003]) ).
fof(f2006,plain,
( ~ sQ190_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f1994,f2003,f248,f241,f1989]) ).
fof(f2007,definition,
( sQ194_spl
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2008,plain,
( ~ sQ194_spl
| sdtlseqdt0(xm,xn) ),
inference(component_clause,[status(thm)],[f2007]) ).
fof(f2009,plain,
( sQ194_spl
| ~ sdtlseqdt0(xm,xn) ),
inference(component_clause,[status(thm)],[f2007]) ).
fof(f2010,plain,
( ~ sQ190_spl
| sQ191_spl
| ~ sQ194_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1995,f241,f248,f2007,f1996,f1989]) ).
fof(f2050,plain,
( sQ133_spl
| ~ sQ191_spl
| ~ sdtlseqdt0(sz00,xm) ),
inference(forward_demodulation,[status(thm)],[f1997,f1195]) ).
fof(f2051,plain,
( sQ133_spl
| ~ sQ191_spl
| sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2050,f114]) ).
fof(f2052,plain,
( sQ133_spl
| ~ sQ191_spl
| sQ144_spl
| ~ sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2051,f241,f355,f1311,f1996,f1193]) ).
fof(f2054,plain,
( sQ130_spl
| ~ sQ191_spl
| ~ sdtlseqdt0(xm,sz00) ),
inference(forward_demodulation,[status(thm)],[f1997,f1179]) ).
fof(f2055,plain,
( ~ sQ133_spl
| ~ sQ191_spl
| sdtlseqdt0(sz00,xm) ),
inference(forward_demodulation,[status(thm)],[f1997,f1194]) ).
fof(f2064,plain,
( sQ194_spl
| ~ sQ191_spl
| ~ sdtlseqdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f1997,f2009]) ).
fof(f2066,plain,
( sQ194_spl
| ~ sQ191_spl
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2064,f107]) ).
fof(f2067,definition,
( sQ195_spl
<=> sdtlseqdt0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2068,plain,
( ~ sQ195_spl
| sdtlseqdt0(xm,xm) ),
inference(component_clause,[status(thm)],[f2067]) ).
fof(f2069,plain,
( sQ195_spl
| ~ sdtlseqdt0(xm,xm) ),
inference(component_clause,[status(thm)],[f2067]) ).
fof(f2071,plain,
( sQ194_spl
| ~ sQ191_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2066,f241,f1996,f2007]) ).
fof(f2074,plain,
( sQ190_spl
| sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f1991,f114]) ).
fof(f2075,plain,
( sQ190_spl
| sQ194_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2074,f241,f248,f2007,f1989]) ).
fof(f2076,plain,
( sQ130_spl
| ~ sQ191_spl
| ~ sQ144_spl ),
inference(split_clause,[status(thm)],[f2054,f1311,f1996,f1177]) ).
fof(f2077,plain,
( ~ sQ133_spl
| ~ sQ191_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f2055,f1322,f1996,f1193]) ).
fof(f2079,plain,
! [X0] :
( ~ sQ195_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2068,f111]) ).
fof(f2080,plain,
( ~ sQ195_spl
| xm = xm
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2068,f109]) ).
fof(f2081,definition,
( sQ196_spl
<=> xm = xm ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2088,definition,
! [X0] :
( sQ198_spl
<=> ( sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( ~ sQ195_spl
| ~ sQ7_spl
| sQ198_spl ),
inference(split_clause,[status(thm)],[f2079,f2088,f241,f2067]) ).
fof(f2092,plain,
( sQ196_spl
| ~ sQ195_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2080,f241,f2067,f2081]) ).
fof(f2137,plain,
( sQ195_spl
| sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2069,f114]) ).
fof(f2139,plain,
( sQ195_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2137,f241,f2067]) ).
fof(f2147,plain,
( sQ159_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f1425,f60]) ).
fof(f2148,plain,
( sQ159_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2147,f241,f1423]) ).
fof(f2149,plain,
( sQ166_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1543,f62]) ).
fof(f2150,plain,
( sQ166_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2149,f248,f241,f1541]) ).
fof(f2151,plain,
! [X0] :
( ~ sQ170_spl
| sdtlseqdt0(sdtasdt0(X0,xm),sz00)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f124]) ).
fof(f2152,plain,
! [X0] :
( ~ sQ170_spl
| sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f124]) ).
fof(f2153,plain,
! [X0] :
( ~ sQ170_spl
| sdtlseqdt0(sdtasdt0(xn,X0),sz00)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f122]) ).
fof(f2154,plain,
! [X0] :
( ~ sQ170_spl
| sdtlseqdt0(sz00,sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f122]) ).
fof(f2155,plain,
( ~ sQ170_spl
| sdtasdt0(xm,xn) = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f71]) ).
fof(f2157,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(sz00,X0) = sdtasdt0(xn,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f73]) ).
fof(f2158,plain,
( ~ sQ170_spl
| sdtlseqdt0(xn,sz00)
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f129]) ).
fof(f2159,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(X0,xm) != sz00
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f123]) ).
fof(f2160,plain,
! [X0] :
( ~ sQ170_spl
| sz00 != sdtasdt0(X0,xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f123]) ).
fof(f2161,plain,
( ~ sQ170_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xn,sz00)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f1482]) ).
fof(f2162,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(sdtpldt0(X0,xn),xm) = sdtpldt0(sdtasdt0(X0,xm),sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f82]) ).
fof(f2163,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(sdtpldt0(xn,X0),xm) = sdtpldt0(sz00,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1651,f82]) ).
fof(f2164,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(xn,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xn,X0),sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f81]) ).
fof(f2165,plain,
! [X0] :
( ~ sQ170_spl
| sdtasdt0(xn,sdtpldt0(xm,X0)) = sdtpldt0(sz00,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1651,f81]) ).
fof(f2167,definition,
! [X0] :
( sQ199_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xm),sz00)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2170,plain,
( ~ sQ170_spl
| sQ147_spl
| ~ sQ9_spl
| sQ199_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2151,f241,f2167,f248,f1325,f1650]) ).
fof(f2171,definition,
! [X0] :
( sQ200_spl
<=> ( sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2174,plain,
( ~ sQ170_spl
| sQ147_spl
| sQ200_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2152,f241,f248,f2171,f1325,f1650]) ).
fof(f2175,definition,
! [X0] :
( sQ201_spl
<=> ( sdtlseqdt0(sdtasdt0(xn,X0),sz00)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2178,plain,
( ~ sQ170_spl
| sQ134_spl
| ~ sQ7_spl
| sQ201_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2153,f248,f2175,f241,f1196,f1650]) ).
fof(f2179,definition,
! [X0] :
( sQ202_spl
<=> ( sdtlseqdt0(sz00,sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2182,plain,
( ~ sQ170_spl
| sQ134_spl
| sQ202_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2154,f248,f241,f2179,f1196,f1650]) ).
fof(f2183,definition,
( sQ203_spl
<=> sdtasdt0(xm,xn) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2184,plain,
( ~ sQ203_spl
| sdtasdt0(xm,xn) = sz00 ),
inference(component_clause,[status(thm)],[f2183]) ).
fof(f2186,plain,
( ~ sQ170_spl
| sQ203_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2155,f241,f248,f2183,f1650]) ).
fof(f2188,definition,
! [X0] :
( sQ204_spl
<=> ( sdtasdt0(sz00,X0) = sdtasdt0(xn,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2191,plain,
( ~ sQ170_spl
| sQ204_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2157,f248,f241,f2188,f1650]) ).
fof(f2192,plain,
( ~ sQ170_spl
| sQ130_spl
| sQ147_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2158,f241,f248,f1325,f1177,f1650]) ).
fof(f2193,definition,
! [X0] :
( sQ205_spl
<=> ( sdtasdt0(X0,xm) != sz00
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2196,plain,
( ~ sQ170_spl
| sQ147_spl
| ~ sQ9_spl
| sQ205_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2159,f241,f2193,f248,f1325,f1650]) ).
fof(f2197,definition,
! [X0] :
( sQ206_spl
<=> ( sz00 != sdtasdt0(X0,xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2200,plain,
( ~ sQ170_spl
| sQ147_spl
| sQ206_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2160,f241,f248,f2197,f1325,f1650]) ).
fof(f2201,definition,
( sQ207_spl
<=> doDivides0(xn,sz00) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ207_spl
| doDivides0(xn,sz00) ),
inference(component_clause,[status(thm)],[f2201]) ).
fof(f2204,plain,
( ~ sQ170_spl
| ~ sQ7_spl
| sQ207_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2161,f248,f2201,f241,f1650]) ).
fof(f2205,definition,
! [X0] :
( sQ208_spl
<=> ( sdtasdt0(sdtpldt0(X0,xn),xm) = sdtpldt0(sdtasdt0(X0,xm),sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2208,plain,
( ~ sQ170_spl
| ~ sQ9_spl
| sQ208_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2162,f241,f2205,f248,f1650]) ).
fof(f2209,definition,
! [X0] :
( sQ209_spl
<=> ( sdtasdt0(sdtpldt0(xn,X0),xm) = sdtpldt0(sz00,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2212,plain,
( ~ sQ170_spl
| sQ209_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2163,f241,f248,f2209,f1650]) ).
fof(f2213,definition,
! [X0] :
( sQ210_spl
<=> ( sdtasdt0(xn,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xn,X0),sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2216,plain,
( ~ sQ170_spl
| ~ sQ7_spl
| sQ210_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2164,f248,f2213,f241,f1650]) ).
fof(f2217,definition,
! [X0] :
( sQ211_spl
<=> ( sdtasdt0(xn,sdtpldt0(xm,X0)) = sdtpldt0(sz00,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2220,plain,
( ~ sQ170_spl
| sQ211_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2165,f248,f241,f2217,f1650]) ).
fof(f2225,plain,
( sQ144_spl
| ~ sQ134_spl
| ~ sQ194_spl ),
inference(split_clause,[status(thm)],[f1987,f2007,f1196,f1311]) ).
fof(f2226,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| sdtasdt0(xn,xm) = xn ),
inference(backward_demodulation,[status(thm)],[f1197,f1651]) ).
fof(f2242,plain,
! [X0,X1] :
( ~ sQ134_spl
| X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f93]) ).
fof(f2243,plain,
! [X0,X1] :
( ~ sQ134_spl
| X1 = sz00
| X0 = xn
| sdtasdt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f2242]) ).
fof(f2244,plain,
! [X0,X1] :
( ~ sQ134_spl
| X1 = xn
| X0 = xn
| sdtasdt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f2243]) ).
fof(f2245,plain,
! [X0] :
( ~ sQ134_spl
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sK1_skl(xn,X0) = xn
| X0 = xn
| ~ aNaturalNumber0(sK1_skl(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2244,f138]) ).
fof(f2246,definition,
! [X0] :
( sQ212_spl
<=> ( ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0)
| sK1_skl(xn,X0) = xn
| X0 = xn
| ~ aNaturalNumber0(sK1_skl(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2249,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f2245,f2246,f248,f1196]) ).
fof(f2251,plain,
! [X0,X1] :
( ~ sQ134_spl
| X1 = sz00
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f91]) ).
fof(f2252,plain,
! [X0,X1] :
( ~ sQ134_spl
| X1 = xn
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f2251]) ).
fof(f2253,plain,
! [X0] :
( ~ sQ134_spl
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtmndt0(xn,X0) = xn
| ~ aNaturalNumber0(sdtmndt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2252,f208]) ).
fof(f2254,plain,
! [X0] :
( ~ sQ134_spl
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sK0_skl(xn,X0) = xn
| ~ aNaturalNumber0(sK0_skl(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2252,f98]) ).
fof(f2255,definition,
! [X0] :
( sQ213_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| sdtmndt0(xn,X0) = xn
| ~ aNaturalNumber0(sdtmndt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2258,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f2253,f2255,f248,f1196]) ).
fof(f2259,definition,
! [X0] :
( sQ214_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| sK0_skl(xn,X0) = xn
| ~ aNaturalNumber0(sK0_skl(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2262,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f2254,f2259,f248,f1196]) ).
fof(f2265,plain,
! [X0,X1] :
( ~ sQ134_spl
| X0 = sz00
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f90]) ).
fof(f2266,plain,
! [X0,X1] :
( ~ sQ134_spl
| X0 = xn
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f2265]) ).
fof(f2267,plain,
! [X0] :
( ~ sQ134_spl
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| X0 = xn
| ~ aNaturalNumber0(sdtmndt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2266,f208]) ).
fof(f2268,plain,
! [X0] :
( ~ sQ134_spl
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| X0 = xn
| ~ aNaturalNumber0(sK0_skl(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2266,f98]) ).
fof(f2269,definition,
! [X0] :
( sQ215_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| X0 = xn
| ~ aNaturalNumber0(sdtmndt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2272,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f2267,f2269,f248,f1196]) ).
fof(f2273,definition,
! [X0] :
( sQ216_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| X0 = xn
| ~ aNaturalNumber0(sK0_skl(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f2268,f2273,f248,f1196]) ).
fof(f2284,plain,
( ~ sQ134_spl
| ~ sQ191_spl
| sz00 = xm ),
inference(backward_demodulation,[status(thm)],[f1997,f1197]) ).
fof(f2285,plain,
( ~ sQ134_spl
| ~ sQ191_spl
| sz10 != xm ),
inference(backward_demodulation,[status(thm)],[f1997,f1200]) ).
fof(f2307,plain,
( sQ1_spl
| ~ sQ191_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_demodulation,[status(thm)],[f1997,f204]) ).
fof(f2308,plain,
( sQ1_spl
| ~ sQ191_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xm),xr),sdtpldt0(sdtpldt0(xm,xm),xp)) ),
inference(forward_demodulation,[status(thm)],[f1997,f2307]) ).
fof(f2309,plain,
( sQ1_spl
| ~ sQ191_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xm))
| ~ sdtlseqdt0(xr,xp)
| xr = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f2308,f117]) ).
fof(f2311,plain,
( sQ1_spl
| ~ sQ191_spl
| ~ sQ159_spl
| ~ sQ43_spl
| sQ47_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2309,f298,f222,f522,f503,f1423,f1996,f202]) ).
fof(f2313,plain,
( ~ sQ207_spl
| ~ sQ191_spl
| doDivides0(xm,sz00) ),
inference(forward_demodulation,[status(thm)],[f1997,f2202]) ).
fof(f2314,plain,
( ~ sQ207_spl
| ~ sQ191_spl
| ~ sQ134_spl
| doDivides0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f2284,f2313]) ).
fof(f2315,plain,
! [X0] :
( ~ sQ207_spl
| ~ sQ191_spl
| ~ sQ134_spl
| doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2314,f147]) ).
fof(f2316,definition,
! [X0] :
( sQ217_spl
<=> ( doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2319,plain,
( ~ sQ207_spl
| ~ sQ191_spl
| ~ sQ134_spl
| ~ sQ7_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f2315,f2316,f241,f1196,f1996,f2201]) ).
fof(f2329,plain,
( ~ sQ191_spl
| doDivides0(xr,sdtasdt0(xm,xm)) ),
inference(forward_demodulation,[status(thm)],[f1997,f194]) ).
fof(f2330,plain,
! [X0] :
( ~ sQ191_spl
| doDivides0(X0,sdtasdt0(xm,xm))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2329,f147]) ).
fof(f2331,definition,
! [X0] :
( sQ218_spl
<=> ( doDivides0(X0,sdtasdt0(xm,xm))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2334,definition,
( sQ219_spl
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2336,plain,
( sQ219_spl
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(component_clause,[status(thm)],[f2334]) ).
fof(f2337,plain,
( ~ sQ191_spl
| ~ sQ219_spl
| ~ sQ17_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2330,f2331,f298,f2334,f1996]) ).
fof(f2338,plain,
( ~ sQ191_spl
| doDivides0(xp,sdtasdt0(xm,xm)) ),
inference(forward_demodulation,[status(thm)],[f1997,f177]) ).
fof(f2339,plain,
! [X0] :
( ~ sQ191_spl
| doDivides0(X0,sdtasdt0(xm,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2338,f147]) ).
fof(f2340,definition,
! [X0] :
( sQ220_spl
<=> ( doDivides0(X0,sdtasdt0(xm,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2343,plain,
( ~ sQ191_spl
| ~ sQ219_spl
| ~ sQ3_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f2339,f2340,f222,f2334,f1996]) ).
fof(f2349,plain,
( sQ133_spl
| ~ sQ147_spl
| ~ sQ194_spl ),
inference(split_clause,[status(thm)],[f1612,f2007,f1325,f1193]) ).
fof(f2363,plain,
( sQ180_spl
| ~ sQ191_spl
| ~ isPrime0(sdtasdt0(xm,xm)) ),
inference(forward_demodulation,[status(thm)],[f1997,f1794]) ).
fof(f2364,plain,
( sQ180_spl
| ~ sQ191_spl
| ~ sQ183_spl
| ~ isPrime0(xr) ),
inference(backward_demodulation,[status(thm)],[f2367,f2363]) ).
fof(f2367,plain,
( ~ sQ183_spl
| ~ sQ191_spl
| xr = sdtasdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f1997,f1803]) ).
fof(f2375,plain,
( sQ180_spl
| ~ sQ191_spl
| ~ sQ183_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2364,f192]) ).
fof(f2376,plain,
( sQ180_spl
| ~ sQ191_spl
| ~ sQ183_spl ),
inference(contradiction_clause,[status(thm)],[f2375]) ).
fof(f2381,definition,
( sQ222_spl
<=> doDivides0(xm,xr) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( ~ sQ222_spl
| doDivides0(xm,xr) ),
inference(component_clause,[status(thm)],[f2381]) ).
fof(f2405,plain,
! [X0] :
( ~ sQ222_spl
| doDivides0(X0,xr)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2382,f147]) ).
fof(f2406,definition,
! [X0] :
( sQ227_spl
<=> ( doDivides0(X0,xr)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( ~ sQ222_spl
| ~ sQ17_spl
| ~ sQ7_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2405,f2406,f241,f298,f2381]) ).
fof(f2422,definition,
( sQ229_spl
<=> doDivides0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( ~ sQ229_spl
| doDivides0(xm,xp) ),
inference(component_clause,[status(thm)],[f2422]) ).
fof(f2444,plain,
! [X0] :
( ~ sQ229_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2423,f147]) ).
fof(f2445,definition,
! [X0] :
( sQ234_spl
<=> ( doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2448,plain,
( ~ sQ229_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2444,f2445,f241,f222,f2422]) ).
fof(f2457,definition,
! [X0] :
( sQ235_spl
<=> ( X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2458,plain,
! [X0] :
( ~ sQ235_spl
| X0 = xm
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2457]) ).
fof(f2474,plain,
( ~ sQ235_spl
| sz10 = xm ),
inference(resolution,[status(thm)],[f2458,f57]) ).
fof(f2484,plain,
( ~ sQ235_spl
| ~ sQ134_spl
| ~ sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2474,f2285]) ).
fof(f2485,plain,
( ~ sQ235_spl
| ~ sQ134_spl
| ~ sQ191_spl ),
inference(contradiction_clause,[status(thm)],[f2484]) ).
fof(f2486,plain,
( ~ sQ83_spl
| ~ sQ191_spl
| sdtpldt0(xm,xm) = sz00 ),
inference(forward_demodulation,[status(thm)],[f1997,f832]) ).
fof(f2489,plain,
( ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| sdtpldt0(xm,xm) = xm ),
inference(forward_demodulation,[status(thm)],[f2284,f2486]) ).
fof(f2497,plain,
( ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| ~ aNaturalNumber0(xm)
| xm = sdtmndt0(xm,xm)
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xm))
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2489,f1109]) ).
fof(f2505,definition,
! [X0] :
( sQ236_spl
<=> ( doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2510,definition,
! [X0] :
( sQ237_spl
<=> ( sdtpldt0(xm,X0) = sdtpldt0(xm,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2514,definition,
! [X0] :
( sQ238_spl
<=> ( X0 = xm
| sdtpldt0(xm,X0) != xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2515,plain,
! [X0] :
( ~ sQ238_spl
| X0 = xm
| sdtpldt0(xm,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2514]) ).
fof(f2519,definition,
! [X0] :
( sQ239_spl
<=> ( X0 = xm
| sdtpldt0(X0,xm) != xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2524,definition,
( sQ240_spl
<=> sdtlseqdt0(xm,sdtpldt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2526,plain,
( sQ240_spl
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xm)) ),
inference(component_clause,[status(thm)],[f2524]) ).
fof(f2527,definition,
( sQ241_spl
<=> xm = sdtmndt0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2528,plain,
( ~ sQ241_spl
| xm = sdtmndt0(xm,xm) ),
inference(component_clause,[status(thm)],[f2527]) ).
fof(f2530,plain,
( ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| sQ241_spl
| ~ sQ240_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2497,f241,f2524,f2527,f1196,f1996,f831]) ).
fof(f2531,definition,
! [X0] :
( sQ242_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,xm),xm)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2535,definition,
! [X0] :
( sQ243_spl
<=> ( sdtlseqdt0(xm,sdtpldt0(X0,xm))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2539,definition,
! [X0] :
( sQ244_spl
<=> ( sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2543,definition,
! [X0] :
( sQ245_spl
<=> ( sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
( sQ240_spl
| ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| ~ sdtlseqdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f2489,f2526]) ).
fof(f2550,plain,
( sQ240_spl
| ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| ~ sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2549,f2068]) ).
fof(f2551,plain,
( sQ240_spl
| ~ sQ83_spl
| ~ sQ191_spl
| ~ sQ134_spl
| ~ sQ195_spl ),
inference(contradiction_clause,[status(thm)],[f2550]) ).
fof(f2559,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(xm,xm) = xn ),
inference(forward_demodulation,[status(thm)],[f1997,f2226]) ).
fof(f2560,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(xm,xm) = xm ),
inference(forward_demodulation,[status(thm)],[f1997,f2559]) ).
fof(f2562,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(xm,X0) = sdtasdt0(xm,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f73]) ).
fof(f2563,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xm,xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f1482]) ).
fof(f2564,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(sdtpldt0(X0,xm),xm) = sdtpldt0(sdtasdt0(X0,xm),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f82]) ).
fof(f2565,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(sdtpldt0(xm,X0),xm) = sdtpldt0(xm,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f82]) ).
fof(f2566,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(xm,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xm,X0),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f81]) ).
fof(f2567,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sdtasdt0(xm,sdtpldt0(xm,X0)) = sdtpldt0(xm,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2560,f81]) ).
fof(f2570,definition,
! [X0] :
( sQ246_spl
<=> ( sdtasdt0(xm,X0) = sdtasdt0(xm,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2573,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ246_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2562,f241,f2570,f1996,f1196,f1650]) ).
fof(f2574,definition,
( sQ247_spl
<=> doDivides0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2575,plain,
( ~ sQ247_spl
| doDivides0(xm,xm) ),
inference(component_clause,[status(thm)],[f2574]) ).
fof(f2577,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ247_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2563,f241,f2574,f1996,f1196,f1650]) ).
fof(f2578,definition,
! [X0] :
( sQ248_spl
<=> ( sdtasdt0(sdtpldt0(X0,xm),xm) = sdtpldt0(sdtasdt0(X0,xm),xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2581,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ248_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2564,f241,f2578,f1996,f1196,f1650]) ).
fof(f2582,definition,
! [X0] :
( sQ249_spl
<=> ( sdtasdt0(sdtpldt0(xm,X0),xm) = sdtpldt0(xm,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2585,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ249_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2565,f241,f2582,f1996,f1196,f1650]) ).
fof(f2586,definition,
! [X0] :
( sQ250_spl
<=> ( sdtasdt0(xm,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xm,X0),xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2589,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ250_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2566,f241,f2586,f1996,f1196,f1650]) ).
fof(f2590,definition,
! [X0] :
( sQ251_spl
<=> ( sdtasdt0(xm,sdtpldt0(xm,X0)) = sdtpldt0(xm,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2593,plain,
( ~ sQ170_spl
| ~ sQ134_spl
| ~ sQ191_spl
| sQ251_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2567,f241,f2590,f1996,f1196,f1650]) ).
fof(f2609,plain,
( ~ sQ241_spl
| sdtpldt0(xm,xm) = xm
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2528,f208]) ).
fof(f2611,definition,
( sQ252_spl
<=> sdtpldt0(xm,xm) = xm ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2612,plain,
( ~ sQ252_spl
| sdtpldt0(xm,xm) = xm ),
inference(component_clause,[status(thm)],[f2611]) ).
fof(f2614,plain,
( ~ sQ241_spl
| sQ252_spl
| ~ sQ195_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2609,f241,f2067,f2611,f2527]) ).
fof(f2653,plain,
! [X0] :
( ~ sQ252_spl
| doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f2612,f151]) ).
fof(f2655,plain,
! [X0] :
( ~ sQ252_spl
| sdtpldt0(xm,X0) = sdtpldt0(xm,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f66]) ).
fof(f2656,plain,
! [X0] :
( ~ sQ252_spl
| X0 = xm
| sdtpldt0(xm,X0) != xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f84]) ).
fof(f2658,plain,
! [X0] :
( ~ sQ252_spl
| X0 = xm
| sdtpldt0(X0,xm) != xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f85]) ).
fof(f2660,plain,
( ~ sQ252_spl
| ~ aNaturalNumber0(xm)
| xm = sdtmndt0(xm,xm)
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xm))
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f1109]) ).
fof(f2661,plain,
! [X0] :
( ~ sQ252_spl
| sdtlseqdt0(sdtpldt0(X0,xm),xm)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f2612,f119]) ).
fof(f2662,plain,
! [X0] :
( ~ sQ252_spl
| sdtlseqdt0(xm,sdtpldt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f119]) ).
fof(f2663,plain,
! [X0] :
( ~ sQ252_spl
| sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f2612,f117]) ).
fof(f2664,plain,
! [X0] :
( ~ sQ252_spl
| sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f117]) ).
fof(f2667,plain,
( ~ sQ252_spl
| ~ sQ7_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2653,f2505,f241,f2611]) ).
fof(f2669,plain,
( ~ sQ252_spl
| sQ237_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2655,f241,f2510,f2611]) ).
fof(f2670,plain,
( ~ sQ252_spl
| sQ238_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2656,f241,f2514,f2611]) ).
fof(f2672,plain,
( ~ sQ252_spl
| sQ239_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2658,f241,f2519,f2611]) ).
fof(f2674,plain,
( ~ sQ252_spl
| sQ241_spl
| ~ sQ240_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2660,f241,f2524,f2527,f2611]) ).
fof(f2675,plain,
( ~ sQ252_spl
| ~ sQ7_spl
| sQ242_spl ),
inference(split_clause,[status(thm)],[f2661,f2531,f241,f2611]) ).
fof(f2676,plain,
( ~ sQ252_spl
| sQ243_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2662,f241,f2535,f2611]) ).
fof(f2677,plain,
( ~ sQ252_spl
| ~ sQ7_spl
| sQ244_spl ),
inference(split_clause,[status(thm)],[f2663,f2539,f241,f2611]) ).
fof(f2678,plain,
( ~ sQ252_spl
| sQ245_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2664,f241,f2543,f2611]) ).
fof(f2682,plain,
( sQ240_spl
| ~ sQ252_spl
| ~ sdtlseqdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f2612,f2526]) ).
fof(f2683,plain,
( sQ240_spl
| ~ sQ252_spl
| ~ sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2682,f2068]) ).
fof(f2684,plain,
( sQ240_spl
| ~ sQ252_spl
| ~ sQ195_spl ),
inference(contradiction_clause,[status(thm)],[f2683]) ).
fof(f2695,plain,
! [X0] :
( ~ sQ134_spl
| ~ sQ191_spl
| sdtpldt0(X0,xm) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f2284,f68]) ).
fof(f2696,plain,
! [X0] :
( ~ sQ134_spl
| ~ sQ191_spl
| sdtpldt0(X0,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(X0,xm)) ),
inference(resolution,[status(thm)],[f2695,f85]) ).
fof(f2699,definition,
! [X0] :
( sQ255_spl
<=> ( sdtpldt0(X0,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,xm)) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2702,plain,
( ~ sQ134_spl
| ~ sQ191_spl
| ~ sQ7_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f2696,f2699,f241,f1996,f1196]) ).
fof(f2706,plain,
! [X0] :
( ~ sQ134_spl
| ~ sQ191_spl
| X0 = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f2284,f69]) ).
fof(f2707,plain,
! [X0] :
( ~ sQ134_spl
| ~ sQ191_spl
| X0 = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,X0)) ),
inference(resolution,[status(thm)],[f2706,f84]) ).
fof(f2710,definition,
! [X0] :
( sQ256_spl
<=> ( X0 = sdtpldt0(xm,X0)
| ~ aNaturalNumber0(sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2713,plain,
( ~ sQ134_spl
| ~ sQ191_spl
| ~ sQ7_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f2707,f2710,f241,f1996,f1196]) ).
fof(f2717,plain,
( ~ sQ104_spl
| ~ sQ191_spl
| sdtlseqdt0(xp,sdtpldt0(xm,xm)) ),
inference(forward_demodulation,[status(thm)],[f1997,f938]) ).
fof(f2718,plain,
( ~ sQ104_spl
| ~ sQ191_spl
| ~ sQ252_spl
| sdtlseqdt0(xp,xm) ),
inference(forward_demodulation,[status(thm)],[f2612,f2717]) ).
fof(f2719,plain,
( ~ sQ104_spl
| ~ sQ191_spl
| ~ sQ252_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2718,f179]) ).
fof(f2720,plain,
( ~ sQ104_spl
| ~ sQ191_spl
| ~ sQ252_spl ),
inference(contradiction_clause,[status(thm)],[f2719]) ).
fof(f2731,plain,
! [X0] :
( ~ sQ247_spl
| doDivides0(X0,xm)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2575,f147]) ).
fof(f2732,plain,
( ~ sQ247_spl
| ~ sQ7_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f2731,f2316,f241,f2574]) ).
fof(f2747,plain,
( ~ sQ194_spl
| iLess0(xm,xn)
| xm = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2008,f133]) ).
fof(f2748,plain,
! [X0] :
( ~ sQ194_spl
| sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2008,f111]) ).
fof(f2750,definition,
( sQ257_spl
<=> iLess0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f2753,plain,
( ~ sQ194_spl
| sQ257_spl
| sQ191_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2747,f241,f248,f1996,f2750,f2007]) ).
fof(f2754,definition,
! [X0] :
( sQ258_spl
<=> ( sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2757,plain,
( ~ sQ194_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f2748,f2754,f241,f248,f2007]) ).
fof(f2763,plain,
( ~ sQ134_spl
| ~ sQ147_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f1414,f1996,f1325,f1196]) ).
fof(f2800,definition,
( sQ259_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2802,plain,
( sQ259_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f2800]) ).
fof(f2804,plain,
( sQ259_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2802,f177]) ).
fof(f2805,plain,
sQ259_spl,
inference(contradiction_clause,[status(thm)],[f2804]) ).
fof(f2806,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f184,f214]) ).
fof(f2807,definition,
( sQ260_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2808,plain,
( ~ sQ260_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f2807]) ).
fof(f2810,plain,
( sQ260_spl
| ~ sQ259_spl
| sQ97_spl
| ~ sQ166_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2806,f222,f1541,f909,f2800,f2807]) ).
fof(f2863,plain,
( sQ219_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2336,f62]) ).
fof(f2864,plain,
( sQ219_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2863,f241,f2334]) ).
fof(f2865,plain,
! [X0] :
( ~ sQ203_spl
| sdtlseqdt0(sdtasdt0(xm,X0),sz00)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f122]) ).
fof(f2866,plain,
! [X0] :
( ~ sQ203_spl
| sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f122]) ).
fof(f2867,plain,
! [X0] :
( ~ sQ203_spl
| sdtlseqdt0(sdtasdt0(X0,xn),sz00)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2184,f124]) ).
fof(f2868,plain,
! [X0] :
( ~ sQ203_spl
| sdtlseqdt0(sz00,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2184,f124]) ).
fof(f2869,plain,
( ~ sQ203_spl
| ~ aNaturalNumber0(xn)
| xn = sdtsldt0(sz00,xm)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f1640]) ).
fof(f2870,plain,
! [X0] :
( ~ sQ203_spl
| sdtasdt0(sz00,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f73]) ).
fof(f2871,plain,
( ~ sQ203_spl
| ~ aNaturalNumber0(xn)
| doDivides0(xm,sz00)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f1482]) ).
fof(f2872,plain,
! [X0] :
( ~ sQ203_spl
| sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2184,f82]) ).
fof(f2873,plain,
! [X0] :
( ~ sQ203_spl
| sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(sz00,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2184,f82]) ).
fof(f2874,plain,
! [X0] :
( ~ sQ203_spl
| sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f81]) ).
fof(f2875,plain,
! [X0] :
( ~ sQ203_spl
| sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(sz00,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2184,f81]) ).
fof(f2877,definition,
! [X0] :
( sQ261_spl
<=> ( sdtlseqdt0(sdtasdt0(xm,X0),sz00)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2880,plain,
( ~ sQ203_spl
| sQ147_spl
| ~ sQ9_spl
| sQ261_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2865,f241,f2877,f248,f1325,f2183]) ).
fof(f2881,definition,
! [X0] :
( sQ262_spl
<=> ( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2884,plain,
( ~ sQ203_spl
| sQ147_spl
| sQ262_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2866,f241,f248,f2881,f1325,f2183]) ).
fof(f2885,definition,
! [X0] :
( sQ263_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xn),sz00)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2888,plain,
( ~ sQ203_spl
| sQ134_spl
| ~ sQ7_spl
| sQ263_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2867,f248,f2885,f241,f1196,f2183]) ).
fof(f2889,definition,
! [X0] :
( sQ264_spl
<=> ( sdtlseqdt0(sz00,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2892,plain,
( ~ sQ203_spl
| sQ134_spl
| sQ264_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2868,f248,f241,f2889,f1196,f2183]) ).
fof(f2893,definition,
( sQ265_spl
<=> xn = sdtsldt0(sz00,xm) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2894,plain,
( ~ sQ265_spl
| xn = sdtsldt0(sz00,xm) ),
inference(component_clause,[status(thm)],[f2893]) ).
fof(f2896,plain,
( ~ sQ203_spl
| ~ sQ9_spl
| sQ265_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2869,f241,f1325,f2893,f248,f2183]) ).
fof(f2897,definition,
! [X0] :
( sQ266_spl
<=> ( sdtasdt0(sz00,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2900,plain,
( ~ sQ203_spl
| sQ266_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2870,f241,f248,f2897,f2183]) ).
fof(f2901,definition,
( sQ267_spl
<=> doDivides0(xm,sz00) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2902,plain,
( ~ sQ267_spl
| doDivides0(xm,sz00) ),
inference(component_clause,[status(thm)],[f2901]) ).
fof(f2904,plain,
( ~ sQ203_spl
| ~ sQ9_spl
| sQ267_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2871,f241,f2901,f248,f2183]) ).
fof(f2905,definition,
! [X0] :
( sQ268_spl
<=> ( sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f2908,plain,
( ~ sQ203_spl
| ~ sQ7_spl
| sQ268_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2872,f248,f2905,f241,f2183]) ).
fof(f2909,definition,
! [X0] :
( sQ269_spl
<=> ( sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(sz00,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2912,plain,
( ~ sQ203_spl
| sQ269_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2873,f248,f241,f2909,f2183]) ).
fof(f2913,definition,
! [X0] :
( sQ270_spl
<=> ( sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2916,plain,
( ~ sQ203_spl
| ~ sQ9_spl
| sQ270_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2874,f241,f2913,f248,f2183]) ).
fof(f2917,definition,
! [X0] :
( sQ271_spl
<=> ( sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(sz00,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2920,plain,
( ~ sQ203_spl
| sQ271_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2875,f241,f248,f2917,f2183]) ).
fof(f2922,plain,
! [X0] :
( ~ sQ267_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2902,f147]) ).
fof(f2923,definition,
! [X0] :
( sQ272_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2926,plain,
( ~ sQ267_spl
| ~ sQ26_spl
| ~ sQ7_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f2922,f2923,f241,f355,f2901]) ).
fof(f2984,definition,
! [X0] :
( sQ274_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3011,plain,
! [X0] :
( ~ sQ131_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,sz00)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f1182,f151]) ).
fof(f3012,plain,
! [X0] :
( ~ sQ131_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xn)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f1182,f149]) ).
fof(f3013,plain,
! [X0] :
( ~ sQ131_spl
| sdtpldt0(sz00,X0) = sdtpldt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1182,f66]) ).
fof(f3014,plain,
! [X0] :
( ~ sQ131_spl
| X0 = xn
| sdtpldt0(xm,X0) != sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1182,f84]) ).
fof(f3025,definition,
! [X0] :
( sQ278_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,sz00)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3028,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f3011,f3025,f241,f248,f1181]) ).
fof(f3029,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f3012,f2984,f241,f248,f1181]) ).
fof(f3030,definition,
! [X0] :
( sQ279_spl
<=> ( sdtpldt0(sz00,X0) = sdtpldt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3033,plain,
( ~ sQ131_spl
| sQ279_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3013,f241,f248,f3030,f1181]) ).
fof(f3034,definition,
! [X0] :
( sQ280_spl
<=> ( X0 = xn
| sdtpldt0(xm,X0) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3037,plain,
( ~ sQ131_spl
| ~ sQ9_spl
| sQ280_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3014,f241,f3034,f248,f1181]) ).
fof(f3064,plain,
( ~ sQ182_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xn,xp)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f1799,f1482]) ).
fof(f3090,definition,
( sQ286_spl
<=> sdtasdt0(xm,xn) = xp ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3091,plain,
( ~ sQ286_spl
| sdtasdt0(xm,xn) = xp ),
inference(component_clause,[status(thm)],[f3090]) ).
fof(f3099,definition,
( sQ288_spl
<=> doDivides0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3100,plain,
( ~ sQ288_spl
| doDivides0(xn,xp) ),
inference(component_clause,[status(thm)],[f3099]) ).
fof(f3102,plain,
( ~ sQ182_spl
| ~ sQ7_spl
| sQ288_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3064,f248,f3099,f241,f1798]) ).
fof(f3120,plain,
( ~ sQ288_spl
| xn = xp
| xn = sz10
| ~ aNaturalNumber0(xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3100,f161]) ).
fof(f3123,definition,
( sQ293_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3125,plain,
( sQ293_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f3123]) ).
fof(f3126,definition,
( sQ294_spl
<=> xn = sz10 ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3127,plain,
( ~ sQ294_spl
| xn = sz10 ),
inference(component_clause,[status(thm)],[f3126]) ).
fof(f3129,plain,
( ~ sQ288_spl
| sQ23_spl
| sQ294_spl
| ~ sQ9_spl
| ~ sQ293_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3120,f222,f3123,f248,f3126,f318,f3099]) ).
fof(f3135,plain,
( sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3125,f176]) ).
fof(f3136,plain,
sQ293_spl,
inference(contradiction_clause,[status(thm)],[f3135]) ).
fof(f3139,plain,
( ~ sQ294_spl
| xn != sz00 ),
inference(backward_demodulation,[status(thm)],[f3127,f58]) ).
fof(f3140,plain,
! [X0] :
( ~ sQ294_spl
| sdtasdt0(X0,xn) = X0
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f3127,f75]) ).
fof(f3147,plain,
( ~ sQ265_spl
| sz00 = sdtasdt0(xm,xn)
| ~ doDivides0(xm,sz00)
| xm = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2894,f214]) ).
fof(f3148,plain,
( ~ sQ265_spl
| sQ203_spl
| ~ sQ267_spl
| sQ147_spl
| ~ sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3147,f241,f355,f1325,f2901,f2183,f2893]) ).
fof(f3175,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(X0,xn) != xp
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f123]) ).
fof(f3176,plain,
! [X0] :
( ~ sQ286_spl
| xp != sdtasdt0(X0,xn)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f123]) ).
fof(f3178,plain,
! [X0] :
( ~ sQ286_spl
| sdtlseqdt0(sdtasdt0(xm,X0),xp)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f122]) ).
fof(f3179,plain,
! [X0] :
( ~ sQ286_spl
| sdtlseqdt0(xp,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f122]) ).
fof(f3180,plain,
! [X0] :
( ~ sQ286_spl
| sdtlseqdt0(sdtasdt0(X0,xn),xp)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f124]) ).
fof(f3181,plain,
! [X0] :
( ~ sQ286_spl
| sdtlseqdt0(xp,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f124]) ).
fof(f3182,plain,
( ~ sQ286_spl
| ~ aNaturalNumber0(xn)
| xn = sdtsldt0(xp,xm)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f1640]) ).
fof(f3183,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(xp,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f73]) ).
fof(f3184,plain,
( ~ sQ286_spl
| ~ aNaturalNumber0(xn)
| doDivides0(xm,xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f1482]) ).
fof(f3185,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f82]) ).
fof(f3186,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(xp,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3091,f82]) ).
fof(f3187,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f81]) ).
fof(f3188,plain,
! [X0] :
( ~ sQ286_spl
| sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(xp,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3091,f81]) ).
fof(f3190,definition,
! [X0] :
( sQ296_spl
<=> ( sdtasdt0(X0,xn) != xp
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f3193,plain,
( ~ sQ286_spl
| sQ134_spl
| ~ sQ7_spl
| sQ296_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3175,f248,f3190,f241,f1196,f3090]) ).
fof(f3194,definition,
! [X0] :
( sQ297_spl
<=> ( xp != sdtasdt0(X0,xn)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f3197,plain,
( ~ sQ286_spl
| sQ134_spl
| sQ297_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3176,f248,f241,f3194,f1196,f3090]) ).
fof(f3199,definition,
! [X0] :
( sQ298_spl
<=> ( sdtlseqdt0(sdtasdt0(xm,X0),xp)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( ~ sQ286_spl
| sQ147_spl
| ~ sQ9_spl
| sQ298_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3178,f241,f3199,f248,f1325,f3090]) ).
fof(f3203,definition,
! [X0] :
( sQ299_spl
<=> ( sdtlseqdt0(xp,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3206,plain,
( ~ sQ286_spl
| sQ147_spl
| sQ299_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3179,f241,f248,f3203,f1325,f3090]) ).
fof(f3207,definition,
! [X0] :
( sQ300_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xn),xp)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f3210,plain,
( ~ sQ286_spl
| sQ134_spl
| ~ sQ7_spl
| sQ300_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3180,f248,f3207,f241,f1196,f3090]) ).
fof(f3211,definition,
! [X0] :
( sQ301_spl
<=> ( sdtlseqdt0(xp,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f3214,plain,
( ~ sQ286_spl
| sQ134_spl
| sQ301_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3181,f248,f241,f3211,f1196,f3090]) ).
fof(f3215,definition,
( sQ302_spl
<=> xn = sdtsldt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3216,plain,
( ~ sQ302_spl
| xn = sdtsldt0(xp,xm) ),
inference(component_clause,[status(thm)],[f3215]) ).
fof(f3218,plain,
( ~ sQ286_spl
| ~ sQ9_spl
| sQ302_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3182,f241,f1325,f3215,f248,f3090]) ).
fof(f3219,definition,
! [X0] :
( sQ303_spl
<=> ( sdtasdt0(xp,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3222,plain,
( ~ sQ286_spl
| sQ303_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3183,f241,f248,f3219,f3090]) ).
fof(f3223,plain,
( ~ sQ286_spl
| ~ sQ9_spl
| sQ229_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3184,f241,f2422,f248,f3090]) ).
fof(f3224,definition,
! [X0] :
( sQ304_spl
<=> ( sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3227,plain,
( ~ sQ286_spl
| ~ sQ7_spl
| sQ304_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3185,f248,f3224,f241,f3090]) ).
fof(f3228,definition,
! [X0] :
( sQ305_spl
<=> ( sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(xp,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f3231,plain,
( ~ sQ286_spl
| sQ305_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3186,f248,f241,f3228,f3090]) ).
fof(f3232,definition,
! [X0] :
( sQ306_spl
<=> ( sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f3235,plain,
( ~ sQ286_spl
| ~ sQ9_spl
| sQ306_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3187,f241,f3232,f248,f3090]) ).
fof(f3236,definition,
! [X0] :
( sQ307_spl
<=> ( sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(xp,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3239,plain,
( ~ sQ286_spl
| sQ307_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3188,f241,f248,f3236,f3090]) ).
fof(f3262,plain,
( ~ sQ47_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f625,f304,f522]) ).
fof(f3327,plain,
( sQ182_spl
| ~ sQ47_spl
| xr != sdtasdt0(xn,xm) ),
inference(forward_demodulation,[status(thm)],[f523,f1800]) ).
fof(f3356,plain,
( sQ136_spl
| ~ sQ131_spl
| ~ sdtlseqdt0(xm,sz00) ),
inference(forward_demodulation,[status(thm)],[f1182,f1282]) ).
fof(f3357,plain,
( sQ136_spl
| ~ sQ131_spl
| ~ sQ144_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3356,f1312]) ).
fof(f3358,plain,
( sQ136_spl
| ~ sQ131_spl
| ~ sQ144_spl ),
inference(contradiction_clause,[status(thm)],[f3357]) ).
fof(f3364,plain,
( ~ sQ172_spl
| iLess0(xr,sdtasdt0(xn,xm))
| xr = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1658,f133]) ).
fof(f3365,plain,
! [X0] :
( ~ sQ172_spl
| sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1658,f111]) ).
fof(f3366,plain,
( ~ sQ172_spl
| sdtasdt0(xn,xm) = xr
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f1658,f109]) ).
fof(f3367,definition,
( sQ312_spl
<=> iLess0(xr,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f3370,plain,
( ~ sQ172_spl
| sQ312_spl
| sQ183_spl
| ~ sQ166_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3364,f298,f1541,f1802,f3367,f1657]) ).
fof(f3371,definition,
! [X0] :
( sQ313_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f3374,plain,
( ~ sQ172_spl
| ~ sQ166_spl
| ~ sQ17_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f3365,f3371,f298,f1541,f1657]) ).
fof(f3375,definition,
( sQ314_spl
<=> sdtlseqdt0(sdtasdt0(xn,xm),xr) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f3377,plain,
( sQ314_spl
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xr) ),
inference(component_clause,[status(thm)],[f3375]) ).
fof(f3378,plain,
( ~ sQ172_spl
| sQ183_spl
| ~ sQ314_spl
| ~ sQ17_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f3366,f1541,f298,f3375,f1802,f1657]) ).
fof(f3379,plain,
( ~ sQ183_spl
| sQ182_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1803,f3327]) ).
fof(f3380,plain,
( ~ sQ183_spl
| sQ182_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f3379]) ).
fof(f3421,plain,
( sQ161_spl
| ~ sQ252_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xr)) ),
inference(forward_demodulation,[status(thm)],[f2612,f1432]) ).
fof(f3422,plain,
( sQ160_spl
| ~ sQ252_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(forward_demodulation,[status(thm)],[f2612,f1429]) ).
fof(f3471,definition,
( sQ316_spl
<=> sdtlseqdt0(xp,xp) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f3472,plain,
( ~ sQ316_spl
| sdtlseqdt0(xp,xp) ),
inference(component_clause,[status(thm)],[f3471]) ).
fof(f3473,plain,
( sQ316_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(component_clause,[status(thm)],[f3471]) ).
fof(f3496,definition,
( sQ319_spl
<=> xp = xp ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f3500,definition,
( sQ320_spl
<=> xn = xn ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f3513,plain,
( sQ160_spl
| ~ sQ252_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f3422,f399,f2611,f1427]) ).
fof(f3556,plain,
! [X0] :
( ~ sQ48_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f546,f111]) ).
fof(f3557,plain,
( ~ sQ48_spl
| xr = xr
| ~ sdtlseqdt0(xr,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f546,f109]) ).
fof(f3559,plain,
( ~ sQ48_spl
| ~ sQ17_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f3556,f664,f298,f545]) ).
fof(f3560,plain,
( sQ66_spl
| ~ sQ48_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3557,f298,f545,f668]) ).
fof(f3562,plain,
! [X0] :
( ~ sQ316_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3472,f111]) ).
fof(f3563,plain,
( ~ sQ316_spl
| xp = xp
| ~ sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3472,f109]) ).
fof(f3568,definition,
! [X0] :
( sQ322_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3571,plain,
( ~ sQ316_spl
| ~ sQ3_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f3562,f3568,f222,f3471]) ).
fof(f3572,plain,
( sQ319_spl
| ~ sQ316_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3563,f222,f3471,f3496]) ).
fof(f3576,definition,
( sQ323_spl
<=> aNaturalNumber0(sdtpldt0(sz00,xp)) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3578,plain,
( sQ323_spl
| ~ aNaturalNumber0(sdtpldt0(sz00,xp)) ),
inference(component_clause,[status(thm)],[f3576]) ).
fof(f3579,definition,
( sQ324_spl
<=> aNaturalNumber0(sdtpldt0(sz00,xr)) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f3581,plain,
( sQ324_spl
| ~ aNaturalNumber0(sdtpldt0(sz00,xr)) ),
inference(component_clause,[status(thm)],[f3579]) ).
fof(f3586,plain,
! [X0,X1] :
( X1 = sz00
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = X0
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f62]) ).
fof(f3611,plain,
( sQ48_spl
| sdtlseqdt0(xr,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f547,f114]) ).
fof(f3613,plain,
( sQ48_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3611,f298,f545]) ).
fof(f3615,plain,
( sQ316_spl
| sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3473,f114]) ).
fof(f3617,plain,
( sQ316_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3615,f222,f3471]) ).
fof(f3631,plain,
( ~ sQ183_spl
| doDivides0(xp,xr) ),
inference(backward_demodulation,[status(thm)],[f1803,f177]) ).
fof(f3647,plain,
( ~ sQ183_spl
| sdtasdt0(xm,xn) = xr
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f1803,f71]) ).
fof(f3690,definition,
( sQ336_spl
<=> xm = sdtsldt0(xr,xn) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f3691,plain,
( ~ sQ336_spl
| xm = sdtsldt0(xr,xn) ),
inference(component_clause,[status(thm)],[f3690]) ).
fof(f3694,definition,
( sQ337_spl
<=> sdtasdt0(xm,xn) = xr ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f3695,plain,
( ~ sQ337_spl
| sdtasdt0(xm,xn) = xr ),
inference(component_clause,[status(thm)],[f3694]) ).
fof(f3697,plain,
( ~ sQ183_spl
| sQ337_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3647,f241,f248,f3694,f1802]) ).
fof(f3703,definition,
( sQ339_spl
<=> doDivides0(xn,xr) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f3704,plain,
( ~ sQ339_spl
| doDivides0(xn,xr) ),
inference(component_clause,[status(thm)],[f3703]) ).
fof(f3728,plain,
( ~ sQ183_spl
| sdtlseqdt0(xp,xr)
| xr = sz00
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3631,f153]) ).
fof(f3730,plain,
( ~ sQ183_spl
| sQ46_spl
| sQ82_spl
| ~ sQ17_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3728,f222,f298,f827,f519,f1802]) ).
fof(f3739,plain,
( ~ sQ339_spl
| sdtlseqdt0(xn,xr)
| xr = sz00
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f3704,f153]) ).
fof(f3740,plain,
! [X0] :
( ~ sQ339_spl
| doDivides0(X0,xr)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3704,f147]) ).
fof(f3741,plain,
( ~ sQ339_spl
| sQ64_spl
| sQ82_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3739,f248,f298,f827,f657,f3703]) ).
fof(f3742,definition,
! [X0] :
( sQ345_spl
<=> ( doDivides0(X0,xr)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f3745,plain,
( ~ sQ339_spl
| ~ sQ17_spl
| ~ sQ9_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f3740,f3742,f248,f298,f3703]) ).
fof(f3746,plain,
! [X0] :
( ~ sQ302_spl
| sdtasdt0(X0,xn) = sdtsldt0(sdtasdt0(X0,xp),xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xm,xp)
| xm = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3216,f155]) ).
fof(f3747,plain,
( ~ sQ302_spl
| xp = sdtasdt0(xm,xn)
| ~ doDivides0(xm,xp)
| xm = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3216,f214]) ).
fof(f3748,definition,
! [X0] :
( sQ346_spl
<=> ( sdtasdt0(X0,xn) = sdtsldt0(sdtasdt0(X0,xp),xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f3751,plain,
( ~ sQ302_spl
| sQ346_spl
| ~ sQ229_spl
| sQ147_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3746,f241,f222,f1325,f2422,f3748,f3215]) ).
fof(f3752,plain,
( ~ sQ302_spl
| sQ286_spl
| ~ sQ229_spl
| sQ147_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3747,f241,f222,f1325,f2422,f3090,f3215]) ).
fof(f3782,plain,
( ~ sQ83_spl
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f90,f832]) ).
fof(f3783,plain,
( ~ sQ131_spl
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f90,f1182]) ).
fof(f3785,plain,
! [X0] :
( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f90,f208]) ).
fof(f3790,plain,
( ~ sQ83_spl
| sQ134_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3782,f248,f241,f1196,f831]) ).
fof(f3791,plain,
( ~ sQ131_spl
| sQ147_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3783,f241,f248,f1325,f1181]) ).
fof(f3793,definition,
! [X0] :
( sQ351_spl
<=> ( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f3796,plain,
( ~ sQ26_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f3785,f3793,f355]) ).
fof(f3802,plain,
( ~ sQ146_spl
| iLess0(sz00,xm)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1323,f133]) ).
fof(f3803,plain,
! [X0] :
( ~ sQ146_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1323,f111]) ).
fof(f3805,definition,
( sQ352_spl
<=> iLess0(sz00,xm) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f3808,plain,
( ~ sQ146_spl
| sQ352_spl
| sQ147_spl
| ~ sQ7_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3802,f355,f241,f1325,f3805,f1322]) ).
fof(f3809,definition,
! [X0] :
( sQ353_spl
<=> ( sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f3810,plain,
! [X0] :
( ~ sQ353_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f3809]) ).
fof(f3812,plain,
( ~ sQ146_spl
| ~ sQ7_spl
| ~ sQ26_spl
| sQ353_spl ),
inference(split_clause,[status(thm)],[f3803,f3809,f355,f241,f1322]) ).
fof(f3816,plain,
( sQ324_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f3581,f60]) ).
fof(f3817,plain,
( sQ324_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3816,f355,f298,f3579]) ).
fof(f3823,plain,
! [X0] :
( ~ sQ207_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2202,f147]) ).
fof(f3825,definition,
! [X0] :
( sQ354_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3828,plain,
( ~ sQ207_spl
| ~ sQ26_spl
| ~ sQ9_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f3823,f3825,f248,f355,f2201]) ).
fof(f3836,plain,
( sQ323_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f3578,f60]) ).
fof(f3837,plain,
( sQ323_spl
| ~ sQ3_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3836,f355,f222,f3576]) ).
fof(f3839,plain,
( ~ sQ336_spl
| xr = sdtasdt0(xn,xm)
| ~ doDivides0(xn,xr)
| xn = sz00
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3691,f214]) ).
fof(f3844,plain,
( ~ sQ336_spl
| sQ183_spl
| ~ sQ339_spl
| sQ134_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3839,f248,f298,f1196,f3703,f1802,f3690]) ).
fof(f3866,plain,
! [X0] :
( ~ sQ337_spl
| X0 = xm
| sdtasdt0(X0,xn) != xr
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f88]) ).
fof(f3868,plain,
( ~ sQ337_spl
| xn = sz00
| ~ aNaturalNumber0(xn)
| sdtasdt0(xm,xn) = xm
| ~ sdtlseqdt0(xr,xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f3586]) ).
fof(f3869,plain,
! [X0] :
( ~ sQ337_spl
| X0 = xn
| sdtasdt0(xm,X0) != xr
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f87]) ).
fof(f3871,plain,
( ~ sQ337_spl
| sdtlseqdt0(xm,xr)
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f129]) ).
fof(f3872,plain,
! [X0] :
( ~ sQ337_spl
| sdtlseqdt0(sdtasdt0(xm,X0),xr)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f122]) ).
fof(f3873,plain,
! [X0] :
( ~ sQ337_spl
| sdtlseqdt0(xr,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f122]) ).
fof(f3874,plain,
! [X0] :
( ~ sQ337_spl
| sdtlseqdt0(sdtasdt0(X0,xn),xr)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f124]) ).
fof(f3875,plain,
! [X0] :
( ~ sQ337_spl
| sdtlseqdt0(xr,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f124]) ).
fof(f3876,plain,
( ~ sQ337_spl
| ~ aNaturalNumber0(xn)
| xn = sdtsldt0(xr,xm)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f1640]) ).
fof(f3877,plain,
! [X0] :
( ~ sQ337_spl
| sdtasdt0(xr,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f73]) ).
fof(f3878,plain,
( ~ sQ337_spl
| ~ aNaturalNumber0(xn)
| doDivides0(xm,xr)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f1482]) ).
fof(f3879,plain,
! [X0] :
( ~ sQ337_spl
| sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f82]) ).
fof(f3880,plain,
! [X0] :
( ~ sQ337_spl
| sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(xr,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f3695,f82]) ).
fof(f3881,plain,
! [X0] :
( ~ sQ337_spl
| sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f81]) ).
fof(f3882,plain,
! [X0] :
( ~ sQ337_spl
| sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(xr,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f3695,f81]) ).
fof(f3884,definition,
! [X0] :
( sQ357_spl
<=> ( X0 = xm
| sdtasdt0(X0,xn) != xr
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f3887,plain,
( ~ sQ337_spl
| ~ sQ7_spl
| sQ357_spl
| sQ134_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3866,f248,f1196,f3884,f241,f3694]) ).
fof(f3889,definition,
( sQ358_spl
<=> sdtasdt0(xm,xn) = xm ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f3890,plain,
( ~ sQ358_spl
| sdtasdt0(xm,xn) = xm ),
inference(component_clause,[status(thm)],[f3889]) ).
fof(f3892,plain,
( ~ sQ337_spl
| sQ134_spl
| ~ sQ9_spl
| sQ358_spl
| ~ sQ55_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3868,f241,f598,f3889,f248,f1196,f3694]) ).
fof(f3893,definition,
! [X0] :
( sQ359_spl
<=> ( X0 = xn
| sdtasdt0(xm,X0) != xr
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f3896,plain,
( ~ sQ337_spl
| ~ sQ9_spl
| sQ359_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3869,f241,f1325,f3893,f248,f3694]) ).
fof(f3898,plain,
( ~ sQ337_spl
| sQ63_spl
| sQ134_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3871,f248,f241,f1196,f651,f3694]) ).
fof(f3899,definition,
! [X0] :
( sQ360_spl
<=> ( sdtlseqdt0(sdtasdt0(xm,X0),xr)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f3902,plain,
( ~ sQ337_spl
| sQ147_spl
| ~ sQ9_spl
| sQ360_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3872,f241,f3899,f248,f1325,f3694]) ).
fof(f3903,definition,
! [X0] :
( sQ361_spl
<=> ( sdtlseqdt0(xr,sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f3906,plain,
( ~ sQ337_spl
| sQ147_spl
| sQ361_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3873,f241,f248,f3903,f1325,f3694]) ).
fof(f3907,definition,
! [X0] :
( sQ362_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xn),xr)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f3910,plain,
( ~ sQ337_spl
| sQ134_spl
| ~ sQ7_spl
| sQ362_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3874,f248,f3907,f241,f1196,f3694]) ).
fof(f3911,definition,
! [X0] :
( sQ363_spl
<=> ( sdtlseqdt0(xr,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f3914,plain,
( ~ sQ337_spl
| sQ134_spl
| sQ363_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3875,f248,f241,f3911,f1196,f3694]) ).
fof(f3915,definition,
( sQ364_spl
<=> xn = sdtsldt0(xr,xm) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f3918,plain,
( ~ sQ337_spl
| ~ sQ9_spl
| sQ364_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3876,f241,f1325,f3915,f248,f3694]) ).
fof(f3919,definition,
! [X0] :
( sQ365_spl
<=> ( sdtasdt0(xr,X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f3922,plain,
( ~ sQ337_spl
| sQ365_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3877,f241,f248,f3919,f3694]) ).
fof(f3923,plain,
( ~ sQ337_spl
| ~ sQ9_spl
| sQ222_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3878,f241,f2381,f248,f3694]) ).
fof(f3924,definition,
! [X0] :
( sQ366_spl
<=> ( sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f3927,plain,
( ~ sQ337_spl
| ~ sQ7_spl
| sQ366_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3879,f248,f3924,f241,f3694]) ).
fof(f3928,definition,
! [X0] :
( sQ367_spl
<=> ( sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(xr,sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f3931,plain,
( ~ sQ337_spl
| sQ367_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3880,f248,f241,f3928,f3694]) ).
fof(f3932,definition,
! [X0] :
( sQ368_spl
<=> ( sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f3935,plain,
( ~ sQ337_spl
| ~ sQ9_spl
| sQ368_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3881,f241,f3932,f248,f3694]) ).
fof(f3936,definition,
! [X0] :
( sQ369_spl
<=> ( sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(xr,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3939,plain,
( ~ sQ337_spl
| sQ369_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3882,f241,f248,f3936,f3694]) ).
fof(f3941,plain,
( ~ sQ358_spl
| ~ sQ337_spl
| xr = xm ),
inference(forward_demodulation,[status(thm)],[f3695,f3890]) ).
fof(f3942,plain,
( ~ sQ358_spl
| ~ sQ337_spl
| sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3941,f603]) ).
fof(f3943,plain,
( ~ sQ358_spl
| ~ sQ337_spl
| sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f3942]) ).
fof(f3944,plain,
( ~ sQ294_spl
| ~ sQ134_spl ),
inference(split_clause,[status(thm)],[f3139,f1196,f3126]) ).
fof(f3960,plain,
! [X0] :
( ~ sQ134_spl
| sdtpldt0(X0,xn) = X0
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f1197,f68]) ).
fof(f3961,plain,
! [X0] :
( ~ sQ134_spl
| X0 = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f1197,f69]) ).
fof(f3974,plain,
( sQ133_spl
| ~ sQ134_spl
| ~ sdtlseqdt0(xn,xn) ),
inference(backward_demodulation,[status(thm)],[f1197,f1195]) ).
fof(f4002,plain,
( ~ sQ267_spl
| ~ sQ134_spl
| doDivides0(xm,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f2902]) ).
fof(f4003,plain,
! [X0] :
( ~ sQ267_spl
| ~ sQ134_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4002,f147]) ).
fof(f4004,definition,
! [X0] :
( sQ370_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f4007,plain,
( ~ sQ267_spl
| ~ sQ134_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ370_spl ),
inference(split_clause,[status(thm)],[f4003,f4004,f241,f248,f1196,f2901]) ).
fof(f4008,plain,
( ~ sQ207_spl
| ~ sQ134_spl
| doDivides0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f2202]) ).
fof(f4009,plain,
! [X0] :
( ~ sQ207_spl
| ~ sQ134_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4008,f147]) ).
fof(f4010,definition,
! [X0] :
( sQ371_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f4013,plain,
( ~ sQ207_spl
| ~ sQ134_spl
| ~ sQ9_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f4009,f4010,f248,f1196,f2201]) ).
fof(f4088,plain,
( sQ161_spl
| ~ sQ252_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f3421,f60]) ).
fof(f4089,plain,
( sQ161_spl
| ~ sQ252_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4088,f241,f298,f2611,f1430]) ).
fof(f4110,plain,
( ~ sQ170_spl
| doDivides0(xr,sz00) ),
inference(backward_demodulation,[status(thm)],[f1651,f194]) ).
fof(f4111,plain,
( ~ sQ170_spl
| doDivides0(xp,sz00) ),
inference(backward_demodulation,[status(thm)],[f1651,f177]) ).
fof(f4142,plain,
! [X0] :
( ~ sQ170_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4110,f147]) ).
fof(f4143,definition,
! [X0] :
( sQ372_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f4146,plain,
( ~ sQ170_spl
| ~ sQ26_spl
| ~ sQ17_spl
| sQ372_spl ),
inference(split_clause,[status(thm)],[f4142,f4143,f298,f355,f1650]) ).
fof(f4147,plain,
! [X0] :
( ~ sQ170_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4111,f147]) ).
fof(f4148,definition,
! [X0] :
( sQ373_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f4151,plain,
( ~ sQ170_spl
| ~ sQ26_spl
| ~ sQ3_spl
| sQ373_spl ),
inference(split_clause,[status(thm)],[f4147,f4148,f222,f355,f1650]) ).
fof(f4158,plain,
( ~ sQ203_spl
| sdtlseqdt0(xm,sz00)
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2184,f129]) ).
fof(f4170,plain,
( ~ sQ203_spl
| sQ144_spl
| sQ134_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4158,f248,f241,f1196,f1311,f2183]) ).
fof(f4195,plain,
( sQ32_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f404,f60]) ).
fof(f4196,plain,
( sQ32_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4195,f222,f219,f402]) ).
fof(f4197,plain,
( ~ sQ104_spl
| iLess0(xp,sdtpldt0(xn,xm))
| xp = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f938,f133]) ).
fof(f4198,plain,
! [X0] :
( ~ sQ104_spl
| sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f938,f111]) ).
fof(f4199,plain,
( ~ sQ104_spl
| sdtpldt0(xn,xm) = xp
| ~ sdtlseqdt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f938,f109]) ).
fof(f4200,definition,
( sQ374_spl
<=> xp = sdtpldt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f4201,plain,
( ~ sQ374_spl
| xp = sdtpldt0(xn,xm) ),
inference(component_clause,[status(thm)],[f4200]) ).
fof(f4203,definition,
( sQ375_spl
<=> iLess0(xp,sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f4206,plain,
( ~ sQ104_spl
| sQ375_spl
| sQ374_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4197,f222,f219,f4200,f4203,f937]) ).
fof(f4207,definition,
! [X0] :
( sQ376_spl
<=> ( sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f4210,plain,
( ~ sQ104_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f4198,f4207,f222,f219,f937]) ).
fof(f4211,definition,
( sQ377_spl
<=> sdtlseqdt0(sdtpldt0(xn,xm),xp) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f4212,plain,
( ~ sQ377_spl
| sdtlseqdt0(sdtpldt0(xn,xm),xp) ),
inference(component_clause,[status(thm)],[f4211]) ).
fof(f4213,plain,
( sQ377_spl
| ~ sdtlseqdt0(sdtpldt0(xn,xm),xp) ),
inference(component_clause,[status(thm)],[f4211]) ).
fof(f4214,plain,
( ~ sQ104_spl
| sQ374_spl
| ~ sQ377_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4199,f219,f222,f4211,f4200,f937]) ).
fof(f4215,plain,
( sQ4_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f227,f60]) ).
fof(f4216,plain,
( sQ4_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4215,f219,f298,f225]) ).
fof(f4227,plain,
( sQ0_spl
| ~ sQ47_spl
| sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(backward_demodulation,[status(thm)],[f523,f201]) ).
fof(f4246,plain,
( sQ0_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4227]) ).
fof(f4247,plain,
( sQ0_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f4246]) ).
fof(f4290,plain,
( sQ1_spl
| ~ sQ374_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xp,xp)) ),
inference(backward_demodulation,[status(thm)],[f4201,f204]) ).
fof(f4293,plain,
! [X0] :
( ~ sQ374_spl
| doDivides0(X0,xm)
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4201,f151]) ).
fof(f4294,plain,
! [X0] :
( ~ sQ374_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4201,f149]) ).
fof(f4295,plain,
! [X0] :
( ~ sQ374_spl
| sdtpldt0(xp,X0) = sdtpldt0(xn,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4201,f66]) ).
fof(f4296,plain,
! [X0] :
( ~ sQ374_spl
| X0 = xm
| sdtpldt0(xn,X0) != xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4201,f84]) ).
fof(f4298,plain,
! [X0] :
( ~ sQ374_spl
| X0 = xn
| sdtpldt0(X0,xm) != xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4201,f85]) ).
fof(f4300,plain,
( ~ sQ374_spl
| ~ aNaturalNumber0(xm)
| xm = sdtmndt0(xp,xn)
| ~ sdtlseqdt0(xn,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4201,f1109]) ).
fof(f4301,plain,
! [X0] :
( ~ sQ374_spl
| sdtlseqdt0(sdtpldt0(X0,xm),xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4201,f119]) ).
fof(f4302,plain,
! [X0] :
( ~ sQ374_spl
| sdtlseqdt0(xp,sdtpldt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4201,f119]) ).
fof(f4303,plain,
! [X0] :
( ~ sQ374_spl
| sdtlseqdt0(sdtpldt0(xn,X0),xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4201,f117]) ).
fof(f4304,plain,
! [X0] :
( ~ sQ374_spl
| sdtlseqdt0(xp,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4201,f117]) ).
fof(f4306,plain,
( ~ sQ374_spl
| sdtpldt0(xm,xn) = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4201,f64]) ).
fof(f4309,plain,
( sQ1_spl
| ~ sQ374_spl
| ~ sdtlseqdt0(sdtpldt0(xp,xr),sdtpldt0(xp,xp)) ),
inference(forward_demodulation,[status(thm)],[f4201,f4290]) ).
fof(f4310,definition,
! [X0] :
( sQ378_spl
<=> ( doDivides0(X0,xm)
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f4313,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f4293,f4310,f248,f241,f4200]) ).
fof(f4314,definition,
! [X0] :
( sQ379_spl
<=> ( doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f4317,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f4294,f4314,f248,f241,f4200]) ).
fof(f4318,definition,
! [X0] :
( sQ380_spl
<=> ( sdtpldt0(xp,X0) = sdtpldt0(xn,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f4321,plain,
( ~ sQ374_spl
| sQ380_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4295,f248,f241,f4318,f4200]) ).
fof(f4322,definition,
! [X0] :
( sQ381_spl
<=> ( X0 = xm
| sdtpldt0(xn,X0) != xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f4325,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| sQ381_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4296,f248,f4322,f241,f4200]) ).
fof(f4327,definition,
! [X0] :
( sQ382_spl
<=> ( X0 = xn
| sdtpldt0(X0,xm) != xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f4330,plain,
( ~ sQ374_spl
| ~ sQ9_spl
| sQ382_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4298,f241,f4327,f248,f4200]) ).
fof(f4332,definition,
( sQ383_spl
<=> xm = sdtmndt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f4333,plain,
( ~ sQ383_spl
| xm = sdtmndt0(xp,xn) ),
inference(component_clause,[status(thm)],[f4332]) ).
fof(f4335,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| sQ383_spl
| ~ sQ120_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4300,f248,f1138,f4332,f241,f4200]) ).
fof(f4336,definition,
! [X0] :
( sQ384_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,xm),xp)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f4339,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f4301,f4336,f248,f241,f4200]) ).
fof(f4340,definition,
! [X0] :
( sQ385_spl
<=> ( sdtlseqdt0(xp,sdtpldt0(X0,xm))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f4343,plain,
( ~ sQ374_spl
| ~ sQ7_spl
| sQ385_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4302,f248,f4340,f241,f4200]) ).
fof(f4344,definition,
! [X0] :
( sQ386_spl
<=> ( sdtlseqdt0(sdtpldt0(xn,X0),xp)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f4347,plain,
( ~ sQ374_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f4303,f4344,f241,f248,f4200]) ).
fof(f4348,definition,
! [X0] :
( sQ387_spl
<=> ( sdtlseqdt0(xp,sdtpldt0(xn,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f4351,plain,
( ~ sQ374_spl
| ~ sQ9_spl
| sQ387_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4304,f241,f4348,f248,f4200]) ).
fof(f4353,definition,
( sQ388_spl
<=> sdtpldt0(xm,xn) = xp ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f4354,plain,
( ~ sQ388_spl
| sdtpldt0(xm,xn) = xp ),
inference(component_clause,[status(thm)],[f4353]) ).
fof(f4356,plain,
( ~ sQ374_spl
| sQ388_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4306,f241,f248,f4353,f4200]) ).
fof(f4359,plain,
( sQ120_spl
| ~ sQ374_spl
| ~ sdtlseqdt0(xn,xp) ),
inference(forward_demodulation,[status(thm)],[f4201,f1140]) ).
fof(f4360,plain,
( sQ120_spl
| ~ sQ374_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4359,f181]) ).
fof(f4361,plain,
( sQ120_spl
| ~ sQ374_spl ),
inference(contradiction_clause,[status(thm)],[f4360]) ).
fof(f4363,plain,
( ~ sQ170_spl
| xp = sz00
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f161,f4111]) ).
fof(f4366,plain,
( ~ sQ207_spl
| xn = sz00
| xn = sz10
| ~ aNaturalNumber0(xn)
| ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f161,f2202]) ).
fof(f4367,plain,
( ~ sQ267_spl
| xm = sz00
| xm = sz10
| ~ aNaturalNumber0(xm)
| ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f161,f2902]) ).
fof(f4372,definition,
( sQ389_spl
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f4375,plain,
( ~ sQ170_spl
| sQ97_spl
| sQ181_spl
| ~ sQ3_spl
| ~ sQ389_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4363,f355,f4372,f222,f1795,f909,f1650]) ).
fof(f4377,plain,
( ~ sQ207_spl
| sQ134_spl
| sQ294_spl
| ~ sQ9_spl
| ~ sQ389_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4366,f355,f4372,f248,f3126,f1196,f2201]) ).
fof(f4378,definition,
( sQ390_spl
<=> xm = sz10 ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f4379,plain,
( ~ sQ390_spl
| xm = sz10 ),
inference(component_clause,[status(thm)],[f4378]) ).
fof(f4381,plain,
( ~ sQ267_spl
| sQ147_spl
| sQ390_spl
| ~ sQ7_spl
| ~ sQ389_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4367,f355,f4372,f241,f4378,f1325,f2901]) ).
fof(f4389,plain,
! [X0] :
( ~ sQ388_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4354,f151]) ).
fof(f4390,plain,
! [X0] :
( ~ sQ388_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,xn)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4354,f149]) ).
fof(f4391,plain,
! [X0] :
( ~ sQ388_spl
| sdtpldt0(xp,X0) = sdtpldt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f66]) ).
fof(f4392,plain,
! [X0] :
( ~ sQ388_spl
| X0 = xn
| sdtpldt0(xm,X0) != xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f84]) ).
fof(f4394,plain,
! [X0] :
( ~ sQ388_spl
| X0 = xm
| sdtpldt0(X0,xn) != xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4354,f85]) ).
fof(f4396,plain,
( ~ sQ388_spl
| ~ aNaturalNumber0(xn)
| xn = sdtmndt0(xp,xm)
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f1109]) ).
fof(f4397,plain,
! [X0] :
( ~ sQ388_spl
| sdtlseqdt0(sdtpldt0(X0,xn),xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4354,f119]) ).
fof(f4398,plain,
! [X0] :
( ~ sQ388_spl
| sdtlseqdt0(xp,sdtpldt0(X0,xn))
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f119]) ).
fof(f4399,plain,
! [X0] :
( ~ sQ388_spl
| sdtlseqdt0(sdtpldt0(xm,X0),xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f4354,f117]) ).
fof(f4400,plain,
! [X0] :
( ~ sQ388_spl
| sdtlseqdt0(xp,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4354,f117]) ).
fof(f4403,definition,
! [X0] :
( sQ391_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f4406,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f4389,f4403,f241,f248,f4353]) ).
fof(f4407,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f4390,f4314,f241,f248,f4353]) ).
fof(f4408,definition,
! [X0] :
( sQ392_spl
<=> ( sdtpldt0(xp,X0) = sdtpldt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f4411,plain,
( ~ sQ388_spl
| sQ392_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4391,f241,f248,f4408,f4353]) ).
fof(f4412,definition,
! [X0] :
( sQ393_spl
<=> ( X0 = xn
| sdtpldt0(xm,X0) != xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f4413,plain,
! [X0] :
( ~ sQ393_spl
| X0 = xn
| sdtpldt0(xm,X0) != xp
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f4412]) ).
fof(f4415,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| sQ393_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4392,f241,f4412,f248,f4353]) ).
fof(f4417,definition,
! [X0] :
( sQ394_spl
<=> ( X0 = xm
| sdtpldt0(X0,xn) != xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f4420,plain,
( ~ sQ388_spl
| ~ sQ7_spl
| sQ394_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4394,f248,f4417,f241,f4353]) ).
fof(f4422,definition,
( sQ395_spl
<=> xn = sdtmndt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f4423,plain,
( ~ sQ395_spl
| xn = sdtmndt0(xp,xm) ),
inference(component_clause,[status(thm)],[f4422]) ).
fof(f4425,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| sQ395_spl
| ~ sQ136_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4396,f241,f1280,f4422,f248,f4353]) ).
fof(f4426,definition,
! [X0] :
( sQ396_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,xn),xp)
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f4429,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f4397,f4426,f241,f248,f4353]) ).
fof(f4430,definition,
! [X0] :
( sQ397_spl
<=> ( sdtlseqdt0(xp,sdtpldt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f4433,plain,
( ~ sQ388_spl
| ~ sQ9_spl
| sQ397_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4398,f241,f4430,f248,f4353]) ).
fof(f4434,definition,
! [X0] :
( sQ398_spl
<=> ( sdtlseqdt0(sdtpldt0(xm,X0),xp)
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f4437,plain,
( ~ sQ388_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sQ398_spl ),
inference(split_clause,[status(thm)],[f4399,f4434,f248,f241,f4353]) ).
fof(f4438,definition,
! [X0] :
( sQ399_spl
<=> ( sdtlseqdt0(xp,sdtpldt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f4441,plain,
( ~ sQ388_spl
| ~ sQ7_spl
| sQ399_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4400,f248,f4438,f241,f4353]) ).
fof(f4444,plain,
( sQ136_spl
| ~ sQ388_spl
| ~ sdtlseqdt0(xm,xp) ),
inference(forward_demodulation,[status(thm)],[f4354,f1282]) ).
fof(f4445,plain,
( sQ136_spl
| ~ sQ388_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4444,f183]) ).
fof(f4446,plain,
( sQ136_spl
| ~ sQ388_spl ),
inference(contradiction_clause,[status(thm)],[f4445]) ).
fof(f4448,plain,
( ~ sQ383_spl
| sdtpldt0(xn,xm) = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4333,f208]) ).
fof(f4450,plain,
( ~ sQ383_spl
| sQ374_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4448,f248,f222,f251,f4200,f4332]) ).
fof(f4452,plain,
( ~ sQ395_spl
| sdtpldt0(xm,xn) = xp
| ~ sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4423,f208]) ).
fof(f4454,plain,
( ~ sQ395_spl
| sQ388_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4452,f241,f222,f244,f4353,f4422]) ).
fof(f4459,plain,
( sQ172_spl
| ~ sQ170_spl
| ~ sdtlseqdt0(xr,sz00) ),
inference(forward_demodulation,[status(thm)],[f1651,f1659]) ).
fof(f4460,plain,
( sQ172_spl
| ~ sQ170_spl
| ~ sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4459,f1457]) ).
fof(f4461,plain,
( sQ172_spl
| ~ sQ170_spl
| ~ sQ163_spl ),
inference(contradiction_clause,[status(thm)],[f4460]) ).
fof(f4470,plain,
( sQ1_spl
| ~ sQ374_spl
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xr,xp)
| xr = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f4309,f117]) ).
fof(f4472,plain,
( sQ1_spl
| ~ sQ374_spl
| ~ sQ43_spl
| sQ47_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f4470,f298,f222,f522,f503,f4200,f202]) ).
fof(f4476,definition,
( sQ401_spl
<=> aNaturalNumber0(sdtpldt0(xp,xr)) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f4478,plain,
( sQ401_spl
| ~ aNaturalNumber0(sdtpldt0(xp,xr)) ),
inference(component_clause,[status(thm)],[f4476]) ).
fof(f4500,plain,
( sQ314_spl
| sdtlseqdt0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3377,f114]) ).
fof(f4501,plain,
( sQ314_spl
| sQ172_spl
| ~ sQ166_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f4500,f298,f1541,f1657,f3375]) ).
fof(f4502,plain,
( ~ sQ171_spl
| iLess0(xp,sdtasdt0(xn,xm))
| xp = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1654,f133]) ).
fof(f4503,plain,
! [X0] :
( ~ sQ171_spl
| sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1654,f111]) ).
fof(f4504,plain,
( ~ sQ171_spl
| sdtasdt0(xn,xm) = xp
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f1654,f109]) ).
fof(f4505,definition,
( sQ403_spl
<=> iLess0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f4508,plain,
( ~ sQ171_spl
| sQ403_spl
| sQ182_spl
| ~ sQ166_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4502,f222,f1541,f1798,f4505,f1653]) ).
fof(f4509,definition,
! [X0] :
( sQ404_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f4512,plain,
( ~ sQ171_spl
| ~ sQ166_spl
| ~ sQ3_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4503,f4509,f222,f1541,f1653]) ).
fof(f4513,definition,
( sQ405_spl
<=> sdtlseqdt0(sdtasdt0(xn,xm),xp) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f4515,plain,
( sQ405_spl
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xp) ),
inference(component_clause,[status(thm)],[f4513]) ).
fof(f4516,plain,
( ~ sQ171_spl
| sQ182_spl
| ~ sQ405_spl
| ~ sQ3_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f4504,f1541,f222,f4513,f1798,f1653]) ).
fof(f4517,plain,
! [X0,X1,X2] :
( ~ sQ374_spl
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(xp,xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f4201,f175]) ).
fof(f4518,plain,
! [X0] :
( ~ sQ374_spl
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ iLess0(sdtpldt0(xp,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4201,f4517]) ).
fof(f4519,plain,
! [X0] :
( ~ sQ388_spl
| ~ sQ374_spl
| doDivides0(X0,xn)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xp,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xm,xn))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f4517]) ).
fof(f4520,plain,
! [X0] :
( ~ sQ252_spl
| ~ sQ374_spl
| doDivides0(X0,xm)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xm,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xm,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f4517]) ).
fof(f4521,definition,
! [X0] :
( sQ406_spl
<=> ( doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ iLess0(sdtpldt0(xp,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f4524,plain,
( ~ sQ374_spl
| sQ406_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4518,f248,f241,f4521,f4200]) ).
fof(f4525,definition,
! [X0] :
( sQ407_spl
<=> ( doDivides0(X0,xn)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xp,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xm,xn))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f4528,plain,
( ~ sQ388_spl
| ~ sQ374_spl
| sQ407_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4519,f241,f248,f4525,f4200,f4353]) ).
fof(f4529,definition,
! [X0] :
( sQ408_spl
<=> ( doDivides0(X0,xm)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xm,X0),sdtpldt0(xp,xp))
| ~ doDivides0(X0,sdtasdt0(xm,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f4532,plain,
( ~ sQ252_spl
| ~ sQ374_spl
| sQ408_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4520,f241,f4529,f4200,f2611]) ).
fof(f4593,definition,
( sQ409_spl
<=> doDivides0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f4595,plain,
( sQ409_spl
| ~ doDivides0(xp,sz00) ),
inference(component_clause,[status(thm)],[f4593]) ).
fof(f4597,plain,
( sQ409_spl
| ~ sQ170_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4595,f4111]) ).
fof(f4598,plain,
( sQ409_spl
| ~ sQ170_spl ),
inference(contradiction_clause,[status(thm)],[f4597]) ).
fof(f4639,plain,
( ~ sQ183_spl
| xp = xr
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3631,f161]) ).
fof(f4641,definition,
( sQ410_spl
<=> isPrime0(xr) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f4643,plain,
( sQ410_spl
| ~ isPrime0(xr) ),
inference(component_clause,[status(thm)],[f4641]) ).
fof(f4644,plain,
( ~ sQ183_spl
| sQ47_spl
| sQ181_spl
| ~ sQ3_spl
| ~ sQ410_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f4639,f298,f4641,f222,f1795,f522,f1802]) ).
fof(f4646,plain,
( sQ410_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4643,f192]) ).
fof(f4647,plain,
sQ410_spl,
inference(contradiction_clause,[status(thm)],[f4646]) ).
fof(f4652,plain,
( ~ sQ133_spl
| ~ sQ134_spl
| sdtlseqdt0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f1194]) ).
fof(f4654,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ134_spl
| sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4652,f111]) ).
fof(f4660,definition,
! [X0] :
( sQ412_spl
<=> ( sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f4663,plain,
( ~ sQ133_spl
| ~ sQ134_spl
| ~ sQ9_spl
| sQ412_spl ),
inference(split_clause,[status(thm)],[f4654,f4660,f248,f1196,f1193]) ).
fof(f4670,plain,
( sQ130_spl
| ~ sQ134_spl
| ~ sdtlseqdt0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f1197,f1179]) ).
fof(f4671,plain,
( sQ130_spl
| ~ sQ134_spl
| ~ sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4670,f4652]) ).
fof(f4672,plain,
( sQ130_spl
| ~ sQ134_spl
| ~ sQ133_spl ),
inference(contradiction_clause,[status(thm)],[f4671]) ).
fof(f4694,plain,
! [X0,X1] :
( ~ sQ134_spl
| X0 = sz00
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f90]) ).
fof(f4695,plain,
! [X0,X1] :
( ~ sQ134_spl
| X0 = xn
| sdtpldt0(X0,X1) != xn
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f1197,f4694]) ).
fof(f4704,plain,
( ~ sQ134_spl
| xn = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f3960,f4695]) ).
fof(f4706,plain,
! [X0] :
( ~ sQ134_spl
| sdtpldt0(X0,xn) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(X0,xn)) ),
inference(resolution,[status(thm)],[f3960,f85]) ).
fof(f4708,plain,
( ~ sQ388_spl
| ~ sQ134_spl
| xp = xm
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4354,f3960]) ).
fof(f4709,plain,
( ~ sQ134_spl
| sQ320_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4704,f248,f3500,f1196]) ).
fof(f4711,definition,
! [X0] :
( sQ414_spl
<=> ( sdtpldt0(X0,xn) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,xn))
| ~ aNaturalNumber0(sdtpldt0(X0,xn)) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f4714,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ414_spl ),
inference(split_clause,[status(thm)],[f4706,f4711,f248,f1196]) ).
fof(f4716,plain,
( ~ sQ388_spl
| ~ sQ134_spl
| sQ21_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4708,f241,f311,f1196,f4353]) ).
fof(f4721,plain,
! [X0] :
( ~ sQ134_spl
| X0 = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[f3961,f84]) ).
fof(f4725,definition,
! [X0] :
( sQ415_spl
<=> ( X0 = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f4728,plain,
( ~ sQ134_spl
| ~ sQ9_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f4721,f4725,f248,f1196]) ).
fof(f4850,plain,
( sQ104_spl
| sdtlseqdt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f939,f114]) ).
fof(f4851,plain,
( sQ104_spl
| sQ377_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4850,f219,f222,f4211,f937]) ).
fof(f4852,plain,
( sQ405_spl
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f4515,f114]) ).
fof(f4853,plain,
( sQ405_spl
| sQ171_spl
| ~ sQ166_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4852,f222,f1541,f1653,f4513]) ).
fof(f4863,plain,
( ~ sQ377_spl
| iLess0(sdtpldt0(xn,xm),xp)
| sdtpldt0(xn,xm) = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f4212,f133]) ).
fof(f4864,plain,
! [X0] :
( ~ sQ377_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4212,f111]) ).
fof(f4866,definition,
( sQ416_spl
<=> iLess0(sdtpldt0(xn,xm),xp) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f4869,plain,
( ~ sQ377_spl
| sQ416_spl
| sQ374_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4863,f219,f222,f4200,f4866,f4211]) ).
fof(f4870,definition,
! [X0] :
( sQ417_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f4873,plain,
( ~ sQ377_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f4864,f4870,f219,f222,f4211]) ).
fof(f4875,plain,
( sQ314_spl
| ~ sQ260_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xr) ),
inference(backward_demodulation,[status(thm)],[f2808,f3377]) ).
fof(f4877,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| sdtlseqdt0(xp,sdtasdt0(xp,xk)) ),
inference(backward_demodulation,[status(thm)],[f2808,f1654]) ).
fof(f4878,plain,
( sQ405_spl
| ~ sQ260_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xp) ),
inference(backward_demodulation,[status(thm)],[f2808,f4515]) ).
fof(f4880,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| sdtlseqdt0(xr,sdtasdt0(xp,xk)) ),
inference(backward_demodulation,[status(thm)],[f2808,f1658]) ).
fof(f4882,plain,
( ~ sQ260_spl
| doDivides0(xr,sdtasdt0(xp,xk)) ),
inference(backward_demodulation,[status(thm)],[f2808,f194]) ).
fof(f4883,plain,
( sQ183_spl
| ~ sQ260_spl
| xr != sdtasdt0(xp,xk) ),
inference(backward_demodulation,[status(thm)],[f2808,f1804]) ).
fof(f4886,plain,
( sQ182_spl
| ~ sQ260_spl
| xp != sdtasdt0(xp,xk) ),
inference(backward_demodulation,[status(thm)],[f2808,f1800]) ).
fof(f4887,plain,
( ~ sQ260_spl
| doDivides0(xp,sdtasdt0(xp,xk)) ),
inference(backward_demodulation,[status(thm)],[f2808,f177]) ).
fof(f4888,plain,
( ~ sQ260_spl
| sdtlseqdt0(xn,sdtasdt0(xp,xk))
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f129]) ).
fof(f4889,plain,
! [X0] :
( ~ sQ260_spl
| sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f122]) ).
fof(f4890,plain,
! [X0] :
( ~ sQ260_spl
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f122]) ).
fof(f4891,plain,
! [X0] :
( ~ sQ260_spl
| X0 = xm
| sdtasdt0(xn,X0) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f87]) ).
fof(f4893,plain,
! [X0] :
( ~ sQ260_spl
| X0 = xn
| sdtasdt0(X0,xm) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f88]) ).
fof(f4895,plain,
! [X0] :
( ~ sQ260_spl
| sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f124]) ).
fof(f4896,plain,
! [X0] :
( ~ sQ260_spl
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f124]) ).
fof(f4897,plain,
( ~ sQ260_spl
| sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f71]) ).
fof(f4899,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(sdtasdt0(xp,xk),X0) = sdtasdt0(xn,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f73]) ).
fof(f4900,plain,
( ~ sQ260_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xn,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f1482]) ).
fof(f4901,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(sdtpldt0(X0,xn),xm) = sdtpldt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f82]) ).
fof(f4902,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(sdtpldt0(xn,X0),xm) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2808,f82]) ).
fof(f4903,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(xn,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xn,X0),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f81]) ).
fof(f4904,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(xn,sdtpldt0(xm,X0)) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f81]) ).
fof(f4906,definition,
( sQ418_spl
<=> sdtlseqdt0(xn,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f4907,plain,
( ~ sQ418_spl
| sdtlseqdt0(xn,sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f4906]) ).
fof(f4909,plain,
( ~ sQ260_spl
| sQ418_spl
| sQ147_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4888,f241,f248,f1325,f4906,f2807]) ).
fof(f4910,definition,
! [X0] :
( sQ419_spl
<=> ( sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f4913,plain,
( ~ sQ260_spl
| sQ134_spl
| ~ sQ7_spl
| sQ419_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4889,f248,f4910,f241,f1196,f2807]) ).
fof(f4914,definition,
! [X0] :
( sQ420_spl
<=> ( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f4917,plain,
( ~ sQ260_spl
| sQ134_spl
| sQ420_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4890,f248,f241,f4914,f1196,f2807]) ).
fof(f4918,definition,
! [X0] :
( sQ421_spl
<=> ( X0 = xm
| sdtasdt0(xn,X0) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4921,plain,
( ~ sQ260_spl
| ~ sQ7_spl
| sQ421_spl
| sQ134_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4891,f248,f1196,f4918,f241,f2807]) ).
fof(f4923,definition,
! [X0] :
( sQ422_spl
<=> ( X0 = xn
| sdtasdt0(X0,xm) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f4926,plain,
( ~ sQ260_spl
| ~ sQ9_spl
| sQ422_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4893,f241,f1325,f4923,f248,f2807]) ).
fof(f4928,definition,
! [X0] :
( sQ423_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f4931,plain,
( ~ sQ260_spl
| sQ147_spl
| ~ sQ9_spl
| sQ423_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4895,f241,f4928,f248,f1325,f2807]) ).
fof(f4932,definition,
! [X0] :
( sQ424_spl
<=> ( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f4935,plain,
( ~ sQ260_spl
| sQ147_spl
| sQ424_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4896,f241,f248,f4932,f1325,f2807]) ).
fof(f4936,definition,
( sQ425_spl
<=> sdtasdt0(xm,xn) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f4937,plain,
( ~ sQ425_spl
| sdtasdt0(xm,xn) = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f4936]) ).
fof(f4939,plain,
( ~ sQ260_spl
| sQ425_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4897,f241,f248,f4936,f2807]) ).
fof(f4941,definition,
! [X0] :
( sQ426_spl
<=> ( sdtasdt0(sdtasdt0(xp,xk),X0) = sdtasdt0(xn,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f4944,plain,
( ~ sQ260_spl
| sQ426_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4899,f248,f241,f4941,f2807]) ).
fof(f4945,definition,
( sQ427_spl
<=> doDivides0(xn,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f4946,plain,
( ~ sQ427_spl
| doDivides0(xn,sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f4945]) ).
fof(f4948,plain,
( ~ sQ260_spl
| ~ sQ7_spl
| sQ427_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4900,f248,f4945,f241,f2807]) ).
fof(f4949,definition,
! [X0] :
( sQ428_spl
<=> ( sdtasdt0(sdtpldt0(X0,xn),xm) = sdtpldt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f4952,plain,
( ~ sQ260_spl
| ~ sQ9_spl
| sQ428_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4901,f241,f4949,f248,f2807]) ).
fof(f4953,definition,
! [X0] :
( sQ429_spl
<=> ( sdtasdt0(sdtpldt0(xn,X0),xm) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f4956,plain,
( ~ sQ260_spl
| sQ429_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4902,f241,f248,f4953,f2807]) ).
fof(f4957,definition,
! [X0] :
( sQ430_spl
<=> ( sdtasdt0(xn,sdtpldt0(X0,xm)) = sdtpldt0(sdtasdt0(xn,X0),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f4960,plain,
( ~ sQ260_spl
| ~ sQ7_spl
| sQ430_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4903,f248,f4957,f241,f2807]) ).
fof(f4961,definition,
! [X0] :
( sQ431_spl
<=> ( sdtasdt0(xn,sdtpldt0(xm,X0)) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f4964,plain,
( ~ sQ260_spl
| sQ431_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4904,f248,f241,f4961,f2807]) ).
fof(f4965,definition,
( sQ432_spl
<=> aNaturalNumber0(sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f5004,plain,
( ~ sQ130_spl
| ~ sQ134_spl
| sdtlseqdt0(xn,xn) ),
inference(backward_demodulation,[status(thm)],[f1197,f1178]) ).
fof(f5034,plain,
( ~ sQ260_spl
| xr = sdtasdt0(xp,xk)
| xr = sz10
| ~ aNaturalNumber0(xr)
| ~ isPrime0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f4882,f161]) ).
fof(f5035,plain,
! [X0] :
( ~ sQ260_spl
| doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4882,f147]) ).
fof(f5036,definition,
( sQ433_spl
<=> isPrime0(sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f5039,definition,
( sQ434_spl
<=> xr = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f5040,plain,
( ~ sQ434_spl
| xr = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f5039]) ).
fof(f5042,plain,
( ~ sQ260_spl
| sQ434_spl
| sQ116_spl
| ~ sQ17_spl
| ~ sQ433_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5034,f4965,f5036,f298,f1062,f5039,f2807]) ).
fof(f5043,definition,
! [X0] :
( sQ435_spl
<=> ( doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f5046,plain,
( ~ sQ260_spl
| ~ sQ432_spl
| ~ sQ17_spl
| sQ435_spl ),
inference(split_clause,[status(thm)],[f5035,f5043,f298,f4965,f2807]) ).
fof(f5047,plain,
( ~ sQ260_spl
| xp = sdtasdt0(xp,xk)
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f4887,f161]) ).
fof(f5048,plain,
! [X0] :
( ~ sQ260_spl
| doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4887,f147]) ).
fof(f5049,definition,
( sQ436_spl
<=> xp = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f5050,plain,
( ~ sQ436_spl
| xp = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f5049]) ).
fof(f5052,plain,
( ~ sQ260_spl
| sQ436_spl
| sQ181_spl
| ~ sQ3_spl
| ~ sQ433_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5047,f4965,f5036,f222,f1795,f5049,f2807]) ).
fof(f5053,definition,
! [X0] :
( sQ437_spl
<=> ( doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f5056,plain,
( ~ sQ260_spl
| ~ sQ432_spl
| ~ sQ3_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f5048,f5053,f222,f4965,f2807]) ).
fof(f5060,definition,
( sQ438_spl
<=> xm = sdtsldt0(sdtasdt0(xp,xk),xn) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f5064,plain,
( ~ sQ260_spl
| xk = sdtsldt0(sdtasdt0(xp,xk),xp) ),
inference(forward_demodulation,[status(thm)],[f2808,f184]) ).
fof(f5066,definition,
( sQ439_spl
<=> xk = xk ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f5070,plain,
! [X0] :
( ~ sQ252_spl
| doDivides0(X0,xm)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xm,X0),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X0,sdtasdt0(xm,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f2612,f175]) ).
fof(f5071,definition,
! [X0] :
( sQ440_spl
<=> ( doDivides0(X0,xm)
| doDivides0(X0,xm)
| ~ iLess0(sdtpldt0(xm,X0),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X0,sdtasdt0(xm,xm))
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f5074,plain,
( ~ sQ252_spl
| sQ440_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5070,f241,f5071,f2611]) ).
fof(f5095,plain,
( sQ314_spl
| ~ sQ260_spl
| sdtlseqdt0(xr,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f4875,f114]) ).
fof(f5096,definition,
( sQ441_spl
<=> sdtlseqdt0(xr,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f5099,plain,
( sQ314_spl
| ~ sQ260_spl
| sQ441_spl
| ~ sQ432_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5095,f298,f4965,f5096,f2807,f3375]) ).
fof(f5100,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| iLess0(xp,sdtasdt0(xp,xk))
| xp = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f4877,f133]) ).
fof(f5101,plain,
! [X0] :
( ~ sQ171_spl
| ~ sQ260_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4877,f111]) ).
fof(f5102,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| sdtasdt0(xp,xk) = xp
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f4877,f109]) ).
fof(f5103,definition,
( sQ442_spl
<=> iLess0(xp,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f5106,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| sQ442_spl
| sQ436_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5100,f222,f4965,f5049,f5103,f2807,f1653]) ).
fof(f5107,definition,
! [X0] :
( sQ443_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f5110,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| ~ sQ432_spl
| ~ sQ3_spl
| sQ443_spl ),
inference(split_clause,[status(thm)],[f5101,f5107,f222,f4965,f2807,f1653]) ).
fof(f5111,definition,
( sQ444_spl
<=> sdtlseqdt0(sdtasdt0(xp,xk),xp) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f5114,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| sQ436_spl
| ~ sQ444_spl
| ~ sQ3_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5102,f4965,f222,f5111,f5049,f2807,f1653]) ).
fof(f5115,plain,
( ~ sQ436_spl
| sQ182_spl
| ~ sQ260_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5050,f4886]) ).
fof(f5116,plain,
( ~ sQ436_spl
| sQ182_spl
| ~ sQ260_spl ),
inference(contradiction_clause,[status(thm)],[f5115]) ).
fof(f5117,plain,
( sQ405_spl
| ~ sQ260_spl
| sdtlseqdt0(xp,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f4878,f114]) ).
fof(f5118,definition,
( sQ445_spl
<=> sdtlseqdt0(xp,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f5121,plain,
( sQ405_spl
| ~ sQ260_spl
| sQ445_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5117,f222,f4965,f5118,f2807,f4513]) ).
fof(f5122,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| iLess0(xr,sdtasdt0(xp,xk))
| xr = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f4880,f133]) ).
fof(f5123,plain,
! [X0] :
( ~ sQ172_spl
| ~ sQ260_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4880,f111]) ).
fof(f5124,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| sdtasdt0(xp,xk) = xr
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f4880,f109]) ).
fof(f5125,definition,
( sQ446_spl
<=> iLess0(xr,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f5128,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| sQ446_spl
| sQ434_spl
| ~ sQ432_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5122,f298,f4965,f5039,f5125,f2807,f1657]) ).
fof(f5129,definition,
! [X0] :
( sQ447_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f5132,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| ~ sQ432_spl
| ~ sQ17_spl
| sQ447_spl ),
inference(split_clause,[status(thm)],[f5123,f5129,f298,f4965,f2807,f1657]) ).
fof(f5133,definition,
( sQ448_spl
<=> sdtlseqdt0(sdtasdt0(xp,xk),xr) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f5136,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| sQ434_spl
| ~ sQ448_spl
| ~ sQ17_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5124,f4965,f298,f5133,f5039,f2807,f1657]) ).
fof(f5137,plain,
( ~ sQ434_spl
| sQ183_spl
| ~ sQ260_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5040,f4883]) ).
fof(f5138,plain,
( ~ sQ434_spl
| sQ183_spl
| ~ sQ260_spl ),
inference(contradiction_clause,[status(thm)],[f5137]) ).
fof(f5140,plain,
! [X0] :
( ~ sQ427_spl
| doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4946,f147]) ).
fof(f5141,definition,
( sQ449_spl
<=> xn = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f5142,plain,
( ~ sQ449_spl
| xn = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f5141]) ).
fof(f5145,definition,
! [X0] :
( sQ450_spl
<=> ( doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f5148,plain,
( ~ sQ427_spl
| ~ sQ432_spl
| ~ sQ9_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f5140,f5145,f248,f4965,f4945]) ).
fof(f5149,plain,
( ~ sQ418_spl
| iLess0(xn,sdtasdt0(xp,xk))
| xn = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f4907,f133]) ).
fof(f5150,plain,
! [X0] :
( ~ sQ418_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4907,f111]) ).
fof(f5151,plain,
( ~ sQ418_spl
| sdtasdt0(xp,xk) = xn
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f4907,f109]) ).
fof(f5152,definition,
( sQ451_spl
<=> iLess0(xn,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f5155,plain,
( ~ sQ418_spl
| sQ451_spl
| sQ449_spl
| ~ sQ432_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5149,f248,f4965,f5141,f5152,f4906]) ).
fof(f5156,definition,
! [X0] :
( sQ452_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f5159,plain,
( ~ sQ418_spl
| ~ sQ432_spl
| ~ sQ9_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f5150,f5156,f248,f4965,f4906]) ).
fof(f5160,definition,
( sQ453_spl
<=> sdtlseqdt0(sdtasdt0(xp,xk),xn) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f5162,plain,
( sQ453_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xn) ),
inference(component_clause,[status(thm)],[f5160]) ).
fof(f5163,plain,
( ~ sQ418_spl
| sQ449_spl
| ~ sQ453_spl
| ~ sQ9_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5151,f4965,f248,f5160,f5141,f4906]) ).
fof(f5173,plain,
! [X0] :
( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sdtmndt0(sz00,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f91,f208]) ).
fof(f5175,definition,
! [X0] :
( sQ454_spl
<=> ( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| sdtmndt0(sz00,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f5178,plain,
( ~ sQ26_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f5173,f5175,f355]) ).
fof(f5183,plain,
! [X0] :
( ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sK1_skl(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sK1_skl(sz00,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f93,f138]) ).
fof(f5184,plain,
( ~ sQ260_spl
| xm = sz00
| xn = sz00
| sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f93]) ).
fof(f5187,definition,
! [X0] :
( sQ455_spl
<=> ( ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| sK1_skl(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sK1_skl(sz00,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f5190,plain,
( ~ sQ26_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f5183,f5187,f355]) ).
fof(f5191,definition,
( sQ456_spl
<=> sdtasdt0(xp,xk) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f5194,plain,
( ~ sQ260_spl
| sQ147_spl
| sQ134_spl
| ~ sQ456_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5184,f248,f241,f5191,f1196,f1325,f2807]) ).
fof(f5587,plain,
( ~ sQ449_spl
| sdtlseqdt0(xp,xn)
| xk = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(paramodulation,[status(thm)],[f5142,f129]) ).
fof(f5614,plain,
( ~ sQ449_spl
| sQ22_spl
| sQ173_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5587,f288,f222,f1661,f315,f5141]) ).
fof(f5777,plain,
! [X0] :
( sdtsldt0(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| X0 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f214,f93]) ).
fof(f5778,definition,
! [X0] :
( sQ494_spl
<=> ( sdtsldt0(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f5781,plain,
( ~ sQ26_spl
| sQ494_spl ),
inference(split_clause,[status(thm)],[f5777,f5778,f355]) ).
fof(f5783,plain,
( ~ sQ427_spl
| sdtlseqdt0(xn,sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f153,f4946]) ).
fof(f5784,plain,
( ~ sQ260_spl
| sdtlseqdt0(xp,sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f153,f4887]) ).
fof(f5785,plain,
( ~ sQ260_spl
| sdtlseqdt0(xr,sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f153,f4882]) ).
fof(f5789,plain,
( ~ sQ427_spl
| sQ418_spl
| sQ456_spl
| ~ sQ432_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5783,f248,f4965,f5191,f4906,f4945]) ).
fof(f5790,plain,
( ~ sQ260_spl
| sQ445_spl
| sQ456_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5784,f222,f4965,f5191,f5118,f2807]) ).
fof(f5791,plain,
( ~ sQ260_spl
| sQ441_spl
| sQ456_spl
| ~ sQ432_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5785,f298,f4965,f5191,f5096,f2807]) ).
fof(f5799,plain,
! [X0] :
( ~ sQ132_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1190,f114]) ).
fof(f5800,plain,
( ~ sQ132_spl
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1190,f107]) ).
fof(f5801,definition,
! [X0] :
( sQ495_spl
<=> ( sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f5804,plain,
( ~ sQ132_spl
| ~ sQ9_spl
| sQ495_spl ),
inference(split_clause,[status(thm)],[f5799,f5801,f248,f1189]) ).
fof(f5805,plain,
( ~ sQ132_spl
| sQ130_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5800,f248,f1177,f1189]) ).
fof(f5817,plain,
( sQ453_spl
| sdtlseqdt0(xn,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f5162,f114]) ).
fof(f5818,plain,
( sQ453_spl
| sQ418_spl
| ~ sQ432_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5817,f248,f4965,f4906,f5160]) ).
fof(f5826,plain,
( ~ sQ425_spl
| ~ sQ294_spl
| sdtasdt0(xp,xk) = xm
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f3140]) ).
fof(f5827,plain,
( ~ sQ425_spl
| ~ aNaturalNumber0(xn)
| xn = sdtsldt0(sdtasdt0(xp,xk),xm)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f1640]) ).
fof(f5828,plain,
! [X0] :
( ~ sQ425_spl
| sdtlseqdt0(sdtasdt0(X0,xn),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4937,f124]) ).
fof(f5829,plain,
! [X0] :
( ~ sQ425_spl
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4937,f124]) ).
fof(f5830,plain,
! [X0] :
( ~ sQ425_spl
| sdtlseqdt0(sdtasdt0(xm,X0),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| xm = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f122]) ).
fof(f5831,plain,
! [X0] :
( ~ sQ425_spl
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xm = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f122]) ).
fof(f5832,plain,
( ~ sQ425_spl
| sdtlseqdt0(xm,sdtasdt0(xp,xk))
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4937,f129]) ).
fof(f5834,plain,
! [X0] :
( ~ sQ425_spl
| sdtasdt0(sdtasdt0(xp,xk),X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f73]) ).
fof(f5835,plain,
( ~ sQ425_spl
| ~ aNaturalNumber0(xn)
| doDivides0(xm,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f1482]) ).
fof(f5836,plain,
! [X0] :
( ~ sQ425_spl
| sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4937,f82]) ).
fof(f5837,plain,
! [X0] :
( ~ sQ425_spl
| sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f4937,f82]) ).
fof(f5838,plain,
! [X0] :
( ~ sQ425_spl
| sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f81]) ).
fof(f5839,plain,
! [X0] :
( ~ sQ425_spl
| sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f81]) ).
fof(f5840,plain,
( ~ sQ425_spl
| aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4937,f62]) ).
fof(f5841,definition,
( sQ496_spl
<=> sdtasdt0(xp,xk) = xm ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f5842,plain,
( ~ sQ496_spl
| sdtasdt0(xp,xk) = xm ),
inference(component_clause,[status(thm)],[f5841]) ).
fof(f5844,plain,
( ~ sQ425_spl
| ~ sQ294_spl
| sQ496_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5826,f241,f5841,f3126,f4936]) ).
fof(f5845,definition,
( sQ497_spl
<=> xn = sdtsldt0(sdtasdt0(xp,xk),xm) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f5848,plain,
( ~ sQ425_spl
| ~ sQ9_spl
| sQ497_spl
| sQ147_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5827,f241,f1325,f5845,f248,f4936]) ).
fof(f5849,definition,
! [X0] :
( sQ498_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,xn),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| X0 = xm
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f5852,plain,
( ~ sQ425_spl
| sQ134_spl
| ~ sQ7_spl
| sQ498_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5828,f248,f5849,f241,f1196,f4936]) ).
fof(f5853,definition,
! [X0] :
( sQ499_spl
<=> ( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xn))
| ~ sdtlseqdt0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f5856,plain,
( ~ sQ425_spl
| sQ134_spl
| sQ499_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5829,f248,f241,f5853,f1196,f4936]) ).
fof(f5857,definition,
! [X0] :
( sQ500_spl
<=> ( sdtlseqdt0(sdtasdt0(xm,X0),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xn)
| X0 = xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f5860,plain,
( ~ sQ425_spl
| sQ147_spl
| ~ sQ9_spl
| sQ500_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5830,f241,f5857,f248,f1325,f4936]) ).
fof(f5861,definition,
! [X0] :
( sQ501_spl
<=> ( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,X0))
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f5864,plain,
( ~ sQ425_spl
| sQ147_spl
| sQ501_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5831,f241,f248,f5861,f1325,f4936]) ).
fof(f5865,definition,
( sQ502_spl
<=> sdtlseqdt0(xm,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f5866,plain,
( ~ sQ502_spl
| sdtlseqdt0(xm,sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f5865]) ).
fof(f5868,plain,
( ~ sQ425_spl
| sQ502_spl
| sQ134_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5832,f248,f241,f1196,f5865,f4936]) ).
fof(f5870,definition,
! [X0] :
( sQ503_spl
<=> ( sdtasdt0(sdtasdt0(xp,xk),X0) = sdtasdt0(xm,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f5873,plain,
( ~ sQ425_spl
| sQ503_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5834,f241,f248,f5870,f4936]) ).
fof(f5874,definition,
( sQ504_spl
<=> doDivides0(xm,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f5875,plain,
( ~ sQ504_spl
| doDivides0(xm,sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f5874]) ).
fof(f5877,plain,
( ~ sQ425_spl
| ~ sQ9_spl
| sQ504_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5835,f241,f5874,f248,f4936]) ).
fof(f5878,definition,
! [X0] :
( sQ505_spl
<=> ( sdtasdt0(sdtpldt0(X0,xm),xn) = sdtpldt0(sdtasdt0(X0,xn),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f5881,plain,
( ~ sQ425_spl
| ~ sQ7_spl
| sQ505_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5836,f248,f5878,f241,f4936]) ).
fof(f5882,definition,
! [X0] :
( sQ506_spl
<=> ( sdtasdt0(sdtpldt0(xm,X0),xn) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(X0,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f5885,plain,
( ~ sQ425_spl
| sQ506_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5837,f248,f241,f5882,f4936]) ).
fof(f5886,definition,
! [X0] :
( sQ507_spl
<=> ( sdtasdt0(xm,sdtpldt0(X0,xn)) = sdtpldt0(sdtasdt0(xm,X0),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f5889,plain,
( ~ sQ425_spl
| ~ sQ9_spl
| sQ507_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5838,f241,f5886,f248,f4936]) ).
fof(f5890,definition,
! [X0] :
( sQ508_spl
<=> ( sdtasdt0(xm,sdtpldt0(xn,X0)) = sdtpldt0(sdtasdt0(xp,xk),sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f5893,plain,
( ~ sQ425_spl
| sQ508_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5839,f241,f248,f5890,f4936]) ).
fof(f5894,plain,
( ~ sQ425_spl
| sQ432_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5840,f241,f248,f4965,f4936]) ).
fof(f5898,plain,
( sQ314_spl
| ~ sQ260_spl
| ~ sQ496_spl
| ~ sdtlseqdt0(xm,xr) ),
inference(backward_demodulation,[status(thm)],[f5842,f4875]) ).
fof(f5900,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| ~ sQ496_spl
| sdtlseqdt0(xp,xm) ),
inference(backward_demodulation,[status(thm)],[f5842,f4877]) ).
fof(f5930,plain,
( sQ314_spl
| ~ sQ260_spl
| ~ sQ496_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f5898,f651,f5841,f2807,f3375]) ).
fof(f5931,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| ~ sQ496_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5900,f179]) ).
fof(f5932,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| ~ sQ496_spl ),
inference(contradiction_clause,[status(thm)],[f5931]) ).
fof(f5959,plain,
! [X0] :
( ~ sQ193_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2004,f114]) ).
fof(f5960,plain,
( ~ sQ193_spl
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2004,f107]) ).
fof(f5961,definition,
! [X0] :
( sQ509_spl
<=> ( sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f5962,plain,
! [X0] :
( ~ sQ509_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f5961]) ).
fof(f5964,plain,
( ~ sQ193_spl
| ~ sQ9_spl
| sQ509_spl ),
inference(split_clause,[status(thm)],[f5959,f5961,f248,f2003]) ).
fof(f5965,plain,
( ~ sQ193_spl
| sQ190_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5960,f248,f1989,f2003]) ).
fof(f5966,plain,
! [X0] :
( ~ sQ509_spl
| sdtlseqdt0(xn,X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5962]) ).
fof(f5967,plain,
( ~ sQ388_spl
| ~ sQ393_spl
| xn = xn
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f4413,f4354]) ).
fof(f5969,plain,
( ~ sQ393_spl
| ~ sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sK0_skl(xp,xm) = xn
| ~ aNaturalNumber0(sK0_skl(xp,xm)) ),
inference(resolution,[status(thm)],[f4413,f98]) ).
fof(f5972,plain,
( ~ sQ388_spl
| ~ sQ393_spl
| sQ320_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5967,f248,f3500,f4412,f4353]) ).
fof(f5977,definition,
( sQ511_spl
<=> aNaturalNumber0(sK0_skl(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f5979,plain,
( sQ511_spl
| ~ aNaturalNumber0(sK0_skl(xp,xm)) ),
inference(component_clause,[status(thm)],[f5977]) ).
fof(f5980,definition,
( sQ512_spl
<=> sK0_skl(xp,xm) = xn ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f5981,plain,
( ~ sQ512_spl
| sK0_skl(xp,xm) = xn ),
inference(component_clause,[status(thm)],[f5980]) ).
fof(f5983,plain,
( ~ sQ393_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sQ512_spl
| ~ sQ511_spl ),
inference(split_clause,[status(thm)],[f5969,f5977,f5980,f241,f222,f244,f4412]) ).
fof(f5986,plain,
( sQ511_spl
| ~ sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f5979,f97]) ).
fof(f5987,plain,
( sQ511_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5986,f241,f222,f244,f5977]) ).
fof(f5997,plain,
( ~ sQ502_spl
| iLess0(xm,sdtasdt0(xp,xk))
| xm = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f5866,f133]) ).
fof(f5998,plain,
! [X0] :
( ~ sQ502_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5866,f111]) ).
fof(f5999,plain,
( ~ sQ502_spl
| sdtasdt0(xp,xk) = xm
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[f5866,f109]) ).
fof(f6000,definition,
( sQ514_spl
<=> iLess0(xm,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f6003,plain,
( ~ sQ502_spl
| sQ514_spl
| sQ496_spl
| ~ sQ432_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5997,f241,f4965,f5841,f6000,f5865]) ).
fof(f6004,definition,
! [X0] :
( sQ515_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f6007,plain,
( ~ sQ502_spl
| ~ sQ432_spl
| ~ sQ7_spl
| sQ515_spl ),
inference(split_clause,[status(thm)],[f5998,f6004,f241,f4965,f5865]) ).
fof(f6008,definition,
( sQ516_spl
<=> sdtlseqdt0(sdtasdt0(xp,xk),xm) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f6010,plain,
( sQ516_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xk),xm) ),
inference(component_clause,[status(thm)],[f6008]) ).
fof(f6011,plain,
( ~ sQ502_spl
| sQ496_spl
| ~ sQ516_spl
| ~ sQ7_spl
| ~ sQ432_spl ),
inference(split_clause,[status(thm)],[f5999,f4965,f241,f6008,f5841,f5865]) ).
fof(f6073,plain,
( ~ sQ193_spl
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| xn = sz10
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f127,f2004]) ).
fof(f6074,plain,
( ~ sQ36_spl
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sz10)
| xn = sz10
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f127,f450]) ).
fof(f6078,definition,
( sQ517_spl
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f6079,plain,
( ~ sQ517_spl
| sdtlseqdt0(sz10,xm) ),
inference(component_clause,[status(thm)],[f6078]) ).
fof(f6081,plain,
( ~ sQ193_spl
| sQ517_spl
| ~ sQ49_spl
| sQ294_spl
| sQ134_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6073,f248,f1196,f3126,f553,f6078,f2003]) ).
fof(f6082,definition,
( sQ518_spl
<=> sdtlseqdt0(sz10,xp) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f6083,plain,
( ~ sQ518_spl
| sdtlseqdt0(sz10,xp) ),
inference(component_clause,[status(thm)],[f6082]) ).
fof(f6085,plain,
( ~ sQ36_spl
| sQ518_spl
| ~ sQ49_spl
| sQ294_spl
| sQ134_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6074,f248,f1196,f3126,f553,f6082,f449]) ).
fof(f6089,plain,
( ~ sQ193_spl
| ~ sQ133_spl
| sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1194,f2004]) ).
fof(f6090,plain,
( ~ sQ36_spl
| ~ sQ133_spl
| sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1194,f450]) ).
fof(f6094,plain,
( ~ sQ193_spl
| ~ sQ133_spl
| sQ146_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6089,f355,f1322,f1193,f2003]) ).
fof(f6095,definition,
( sQ519_spl
<=> sdtlseqdt0(sz00,xp) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f6096,plain,
( ~ sQ519_spl
| sdtlseqdt0(sz00,xp) ),
inference(component_clause,[status(thm)],[f6095]) ).
fof(f6097,plain,
( sQ519_spl
| ~ sdtlseqdt0(sz00,xp) ),
inference(component_clause,[status(thm)],[f6095]) ).
fof(f6098,plain,
( ~ sQ36_spl
| ~ sQ133_spl
| sQ519_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6090,f355,f6095,f1193,f449]) ).
fof(f6125,plain,
! [X0] :
( ~ sQ130_spl
| ~ sQ134_spl
| sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5004,f111]) ).
fof(f6130,plain,
( ~ sQ130_spl
| ~ sQ134_spl
| ~ sQ9_spl
| sQ412_spl ),
inference(split_clause,[status(thm)],[f6125,f4660,f248,f1196,f1177]) ).
fof(f6132,plain,
( sQ133_spl
| ~ sQ134_spl
| ~ sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3974,f5004]) ).
fof(f6133,plain,
( sQ133_spl
| ~ sQ134_spl
| ~ sQ130_spl ),
inference(contradiction_clause,[status(thm)],[f6132]) ).
fof(f6154,plain,
( ~ sQ517_spl
| iLess0(sz10,xm)
| sz10 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f6079,f133]) ).
fof(f6155,plain,
! [X0] :
( ~ sQ517_spl
| sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6079,f111]) ).
fof(f6156,plain,
( ~ sQ517_spl
| xm = sz10
| ~ sdtlseqdt0(xm,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f6079,f109]) ).
fof(f6157,definition,
( sQ520_spl
<=> iLess0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f6160,plain,
( ~ sQ517_spl
| sQ520_spl
| sQ390_spl
| ~ sQ7_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6154,f553,f241,f4378,f6157,f6078]) ).
fof(f6161,definition,
! [X0] :
( sQ521_spl
<=> ( sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f6164,plain,
( ~ sQ517_spl
| ~ sQ7_spl
| ~ sQ49_spl
| sQ521_spl ),
inference(split_clause,[status(thm)],[f6155,f6161,f553,f241,f6078]) ).
fof(f6165,definition,
( sQ522_spl
<=> sdtlseqdt0(xm,sz10) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f6166,plain,
( ~ sQ522_spl
| sdtlseqdt0(xm,sz10) ),
inference(component_clause,[status(thm)],[f6165]) ).
fof(f6167,plain,
( sQ522_spl
| ~ sdtlseqdt0(xm,sz10) ),
inference(component_clause,[status(thm)],[f6165]) ).
fof(f6168,plain,
( ~ sQ517_spl
| sQ390_spl
| ~ sQ522_spl
| ~ sQ49_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6156,f241,f553,f6165,f4378,f6078]) ).
fof(f6245,plain,
! [X0] :
( ~ sQ390_spl
| sdtasdt0(X0,xm) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f4379,f75]) ).
fof(f6254,plain,
! [X0] :
( ~ sQ504_spl
| doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5875,f147]) ).
fof(f6255,definition,
! [X0] :
( sQ526_spl
<=> ( doDivides0(X0,sdtasdt0(xp,xk))
| ~ doDivides0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f6258,plain,
( ~ sQ504_spl
| ~ sQ432_spl
| ~ sQ7_spl
| sQ526_spl ),
inference(split_clause,[status(thm)],[f6254,f6255,f241,f4965,f5874]) ).
fof(f6296,plain,
( ~ sQ238_spl
| ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f2515,f68]) ).
fof(f6297,plain,
( ~ sQ238_spl
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| sdtmndt0(xm,xm) = xm
| ~ aNaturalNumber0(sdtmndt0(xm,xm)) ),
inference(resolution,[status(thm)],[f2515,f208]) ).
fof(f6298,plain,
( ~ sQ238_spl
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| sK0_skl(xm,xm) = xm
| ~ aNaturalNumber0(sK0_skl(xm,xm)) ),
inference(resolution,[status(thm)],[f2515,f98]) ).
fof(f6301,plain,
( ~ sQ238_spl
| ~ sQ7_spl
| sQ147_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6296,f355,f1325,f241,f2514]) ).
fof(f6302,definition,
( sQ527_spl
<=> aNaturalNumber0(sdtmndt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f6305,plain,
( ~ sQ238_spl
| ~ sQ195_spl
| ~ sQ7_spl
| sQ241_spl
| ~ sQ527_spl ),
inference(split_clause,[status(thm)],[f6297,f6302,f2527,f241,f2067,f2514]) ).
fof(f6306,definition,
( sQ528_spl
<=> aNaturalNumber0(sK0_skl(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f6309,definition,
( sQ529_spl
<=> sK0_skl(xm,xm) = xm ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f6312,plain,
( ~ sQ238_spl
| ~ sQ195_spl
| ~ sQ7_spl
| sQ529_spl
| ~ sQ528_spl ),
inference(split_clause,[status(thm)],[f6298,f6306,f6309,f241,f2067,f2514]) ).
fof(f6329,plain,
( ~ sQ519_spl
| iLess0(sz00,xp)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f6096,f133]) ).
fof(f6330,plain,
! [X0] :
( ~ sQ519_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6096,f111]) ).
fof(f6331,plain,
( ~ sQ519_spl
| xp = sz00
| ~ sdtlseqdt0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f6096,f109]) ).
fof(f6332,definition,
( sQ530_spl
<=> iLess0(sz00,xp) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f6335,plain,
( ~ sQ519_spl
| sQ530_spl
| sQ97_spl
| ~ sQ3_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6329,f355,f222,f909,f6332,f6095]) ).
fof(f6336,definition,
! [X0] :
( sQ531_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f6339,plain,
( ~ sQ519_spl
| ~ sQ3_spl
| ~ sQ26_spl
| sQ531_spl ),
inference(split_clause,[status(thm)],[f6330,f6336,f355,f222,f6095]) ).
fof(f6340,definition,
( sQ532_spl
<=> sdtlseqdt0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f6341,plain,
( ~ sQ532_spl
| sdtlseqdt0(xp,sz00) ),
inference(component_clause,[status(thm)],[f6340]) ).
fof(f6343,plain,
( ~ sQ519_spl
| sQ97_spl
| ~ sQ532_spl
| ~ sQ26_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6331,f222,f355,f6340,f909,f6095]) ).
fof(f6355,plain,
( sQ519_spl
| sdtlseqdt0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f6097,f114]) ).
fof(f6356,plain,
( sQ519_spl
| sQ532_spl
| ~ sQ26_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6355,f222,f355,f6340,f6095]) ).
fof(f6357,plain,
( ~ sQ532_spl
| iLess0(xp,sz00)
| xp = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f6341,f133]) ).
fof(f6358,plain,
! [X0] :
( ~ sQ532_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6341,f111]) ).
fof(f6360,definition,
( sQ534_spl
<=> iLess0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f6363,plain,
( ~ sQ532_spl
| sQ534_spl
| sQ97_spl
| ~ sQ26_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6357,f222,f355,f909,f6360,f6340]) ).
fof(f6364,definition,
! [X0] :
( sQ535_spl
<=> ( sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f6367,plain,
( ~ sQ532_spl
| ~ sQ26_spl
| ~ sQ3_spl
| sQ535_spl ),
inference(split_clause,[status(thm)],[f6358,f6364,f222,f355,f6340]) ).
fof(f6378,plain,
( ~ sQ512_spl
| sdtpldt0(xm,xn) = xp
| ~ sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f5981,f98]) ).
fof(f6380,plain,
( ~ sQ512_spl
| sQ388_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6378,f241,f222,f244,f4353,f5980]) ).
fof(f6383,plain,
( sQ377_spl
| ~ sQ374_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f4201,f4213]) ).
fof(f6413,plain,
( sQ377_spl
| ~ sQ374_spl
| ~ sQ316_spl ),
inference(split_clause,[status(thm)],[f6383,f3471,f4200,f4211]) ).
fof(f6484,plain,
( sQ401_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f4478,f60]) ).
fof(f6485,plain,
( sQ401_spl
| ~ sQ17_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6484,f222,f298,f4476]) ).
fof(f6542,plain,
( sQ516_spl
| sdtlseqdt0(xm,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f6010,f114]) ).
fof(f6543,plain,
( sQ516_spl
| sQ502_spl
| ~ sQ432_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6542,f241,f4965,f5865,f6008]) ).
fof(f6570,plain,
( ~ sQ260_spl
| ~ sQ390_spl
| sdtasdt0(xp,xk) = xn
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f6245]) ).
fof(f6590,plain,
( ~ sQ260_spl
| ~ sQ390_spl
| sQ449_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6570,f248,f5141,f4378,f2807]) ).
fof(f6610,plain,
( sQ522_spl
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f6167,f114]) ).
fof(f6611,plain,
( sQ522_spl
| sQ517_spl
| ~ sQ7_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6610,f553,f241,f6078,f6165]) ).
fof(f6612,plain,
( ~ sQ518_spl
| iLess0(sz10,xp)
| sz10 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f6083,f133]) ).
fof(f6613,plain,
! [X0] :
( ~ sQ518_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6083,f111]) ).
fof(f6614,plain,
( ~ sQ518_spl
| xp = sz10
| ~ sdtlseqdt0(xp,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f6083,f109]) ).
fof(f6615,definition,
( sQ539_spl
<=> iLess0(sz10,xp) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f6618,plain,
( ~ sQ518_spl
| sQ539_spl
| sQ181_spl
| ~ sQ3_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6612,f553,f222,f1795,f6615,f6082]) ).
fof(f6619,definition,
! [X0] :
( sQ540_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f6622,plain,
( ~ sQ518_spl
| ~ sQ3_spl
| ~ sQ49_spl
| sQ540_spl ),
inference(split_clause,[status(thm)],[f6613,f6619,f553,f222,f6082]) ).
fof(f6623,definition,
( sQ541_spl
<=> sdtlseqdt0(xp,sz10) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f6626,plain,
( ~ sQ518_spl
| sQ181_spl
| ~ sQ541_spl
| ~ sQ49_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6614,f222,f553,f6623,f1795,f6082]) ).
fof(f6635,plain,
! [X0] :
( ~ sQ260_spl
| sdtasdt0(X0,xk) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xp,xk)),xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(xp,xk))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f5064,f155]) ).
fof(f6636,definition,
( sQ542_spl
<=> doDivides0(xp,sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f6638,plain,
( sQ542_spl
| ~ doDivides0(xp,sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f6636]) ).
fof(f6639,definition,
! [X0] :
( sQ543_spl
<=> ( sdtasdt0(X0,xk) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xp,xk)),xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f6642,plain,
( ~ sQ260_spl
| sQ543_spl
| ~ sQ542_spl
| sQ97_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6635,f222,f4965,f909,f6636,f6639,f2807]) ).
fof(f6643,plain,
( sQ542_spl
| ~ sQ260_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6638,f4887]) ).
fof(f6644,plain,
( sQ542_spl
| ~ sQ260_spl ),
inference(contradiction_clause,[status(thm)],[f6643]) ).
fof(f6646,plain,
( ~ sQ504_spl
| sdtlseqdt0(xm,sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f153,f5875]) ).
fof(f6653,plain,
( ~ sQ504_spl
| sQ502_spl
| sQ456_spl
| ~ sQ432_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6646,f241,f4965,f5191,f5865,f5874]) ).
fof(f6663,plain,
! [X0] :
( ~ sQ509_spl
| iLess0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5966,f133]) ).
fof(f6664,plain,
! [X0,X1] :
( ~ sQ509_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5966,f111]) ).
fof(f6665,plain,
! [X0] :
( ~ sQ509_spl
| X0 = xn
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5966,f109]) ).
fof(f6668,definition,
! [X0] :
( sQ544_spl
<=> ( iLess0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f6671,plain,
( ~ sQ509_spl
| ~ sQ9_spl
| sQ544_spl ),
inference(split_clause,[status(thm)],[f6663,f6668,f248,f5961]) ).
fof(f6672,definition,
! [X0,X1] :
( sQ545_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f6675,plain,
( ~ sQ509_spl
| ~ sQ9_spl
| sQ545_spl ),
inference(split_clause,[status(thm)],[f6664,f6672,f248,f5961]) ).
fof(f6676,definition,
! [X0] :
( sQ546_spl
<=> ( X0 = xn
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f6679,plain,
( ~ sQ509_spl
| ~ sQ9_spl
| sQ546_spl ),
inference(split_clause,[status(thm)],[f6665,f6676,f248,f5961]) ).
fof(f6683,plain,
( ~ sQ130_spl
| ~ sQ353_spl
| sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f3810,f1178]) ).
fof(f6685,plain,
( ~ sQ163_spl
| ~ sQ353_spl
| sdtlseqdt0(xr,xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3810,f1457]) ).
fof(f6686,plain,
! [X0] :
( ~ sQ353_spl
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3810,f114]) ).
fof(f6687,plain,
( ~ sQ353_spl
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f3810,f107]) ).
fof(f6688,plain,
( ~ sQ130_spl
| ~ sQ353_spl
| sQ190_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6683,f248,f1989,f3809,f1177]) ).
fof(f6690,plain,
( ~ sQ163_spl
| ~ sQ353_spl
| sQ55_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f6685,f298,f598,f3809,f1456]) ).
fof(f6691,definition,
! [X0] :
( sQ547_spl
<=> ( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f6694,plain,
( ~ sQ353_spl
| ~ sQ26_spl
| sQ547_spl ),
inference(split_clause,[status(thm)],[f6686,f6691,f355,f3809]) ).
fof(f6695,plain,
( ~ sQ353_spl
| sQ146_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6687,f355,f1322,f3809]) ).
fof(f6712,plain,
( ~ sQ146_spl
| ~ sQ35_spl
| sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f446,f1323]) ).
fof(f6719,plain,
( ~ sQ146_spl
| ~ sQ35_spl
| sQ519_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6712,f355,f6095,f445,f1322]) ).
fof(f6725,plain,
( sQ522_spl
| ~ sQ40_spl
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f483,f6167]) ).
fof(f6732,plain,
! [X0] :
( ~ sQ40_spl
| iLess0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f483,f133]) ).
fof(f6733,plain,
! [X0,X1] :
( ~ sQ40_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f483,f111]) ).
fof(f6734,plain,
! [X0] :
( ~ sQ40_spl
| X0 = xm
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f483,f109]) ).
fof(f6735,plain,
( sQ522_spl
| ~ sQ40_spl
| sQ518_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6725,f553,f6082,f478,f6165]) ).
fof(f6742,definition,
! [X0] :
( sQ548_spl
<=> ( iLess0(xm,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f6745,plain,
( ~ sQ40_spl
| ~ sQ7_spl
| sQ548_spl ),
inference(split_clause,[status(thm)],[f6732,f6742,f241,f478]) ).
fof(f6746,definition,
! [X0,X1] :
( sQ549_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f6749,plain,
( ~ sQ40_spl
| ~ sQ7_spl
| sQ549_spl ),
inference(split_clause,[status(thm)],[f6733,f6746,f241,f478]) ).
fof(f6750,definition,
! [X0] :
( sQ550_spl
<=> ( X0 = xm
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f6753,plain,
( ~ sQ40_spl
| ~ sQ7_spl
| sQ550_spl ),
inference(split_clause,[status(thm)],[f6734,f6750,f241,f478]) ).
fof(f6757,plain,
( ~ sQ517_spl
| ~ sQ54_spl
| sdtlseqdt0(sz10,xr)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f595,f6079]) ).
fof(f6758,plain,
( ~ sQ146_spl
| ~ sQ54_spl
| sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f595,f1323]) ).
fof(f6759,plain,
( ~ sQ190_spl
| ~ sQ54_spl
| sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f595,f1990]) ).
fof(f6763,plain,
! [X0] :
( ~ sQ54_spl
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f595,f114]) ).
fof(f6764,plain,
( ~ sQ54_spl
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f595,f107]) ).
fof(f6765,definition,
( sQ551_spl
<=> sdtlseqdt0(sz10,xr) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f6768,plain,
( ~ sQ517_spl
| ~ sQ54_spl
| sQ551_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6757,f553,f6765,f594,f6078]) ).
fof(f6769,plain,
( ~ sQ146_spl
| ~ sQ54_spl
| sQ164_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6758,f355,f1476,f594,f1322]) ).
fof(f6770,plain,
( ~ sQ190_spl
| ~ sQ54_spl
| sQ64_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6759,f248,f657,f594,f1989]) ).
fof(f6774,definition,
! [X0] :
( sQ552_spl
<=> ( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ552_spl])],[split_symbol_definition]) ).
fof(f6777,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ552_spl ),
inference(split_clause,[status(thm)],[f6763,f6774,f241,f594]) ).
fof(f6778,plain,
( ~ sQ54_spl
| sQ63_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6764,f241,f651,f594]) ).
fof(f6780,plain,
! [X0] :
( ~ sQ518_spl
| sdtlseqdt0(X0,xp)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f456,f6083]) ).
fof(f6783,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f456,f196]) ).
fof(f6784,plain,
! [X0] :
( ~ sQ104_spl
| sdtlseqdt0(X0,sdtpldt0(xn,xm))
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f456,f938]) ).
fof(f6785,plain,
! [X0] :
( ~ sQ171_spl
| ~ sQ260_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f456,f4877]) ).
fof(f6786,plain,
! [X0] :
( ~ sQ316_spl
| sdtlseqdt0(X0,xp)
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f456,f3472]) ).
fof(f6788,plain,
! [X0] :
( ~ sQ418_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f456,f4907]) ).
fof(f6789,plain,
! [X0] :
( ~ sQ130_spl
| sdtlseqdt0(X0,sz00)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f456,f1178]) ).
fof(f6790,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f456,f181]) ).
fof(f6791,plain,
! [X0] :
( ~ sQ502_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f456,f5866]) ).
fof(f6792,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f456,f183]) ).
fof(f6793,plain,
! [X0] :
( ~ sQ63_spl
| sdtlseqdt0(X0,xr)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f456,f652]) ).
fof(f6794,plain,
! [X0] :
( ~ sQ195_spl
| sdtlseqdt0(X0,xm)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f456,f2068]) ).
fof(f6795,plain,
! [X0,X1] :
( ~ sQ40_spl
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f456,f483]) ).
fof(f6799,plain,
! [X0] :
( ~ sQ172_spl
| ~ sQ260_spl
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f456,f4880]) ).
fof(f6800,plain,
! [X0] :
( ~ sQ48_spl
| sdtlseqdt0(X0,xr)
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f456,f546]) ).
fof(f6801,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f456,f193]) ).
fof(f6808,definition,
! [X0] :
( sQ553_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f6811,plain,
( ~ sQ518_spl
| sQ553_spl
| ~ sQ3_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f6780,f553,f222,f6808,f6082]) ).
fof(f6814,definition,
! [X0] :
( sQ554_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f6817,plain,
( sQ554_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f6783,f288,f222,f6814]) ).
fof(f6818,definition,
! [X0] :
( sQ555_spl
<=> ( sdtlseqdt0(X0,sdtpldt0(xn,xm))
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f6821,plain,
( ~ sQ104_spl
| sQ555_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6784,f222,f219,f6818,f937]) ).
fof(f6822,definition,
! [X0] :
( sQ556_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f6825,plain,
( ~ sQ171_spl
| ~ sQ260_spl
| sQ556_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6785,f222,f4965,f6822,f2807,f1653]) ).
fof(f6826,definition,
! [X0] :
( sQ557_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f6829,plain,
( ~ sQ316_spl
| sQ557_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6786,f222,f6826,f3471]) ).
fof(f6834,definition,
! [X0] :
( sQ559_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f6837,plain,
( ~ sQ418_spl
| sQ559_spl
| ~ sQ432_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6788,f248,f4965,f6834,f4906]) ).
fof(f6838,definition,
! [X0] :
( sQ560_spl
<=> ( sdtlseqdt0(X0,sz00)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f6841,plain,
( ~ sQ130_spl
| sQ560_spl
| ~ sQ26_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6789,f248,f355,f6838,f1177]) ).
fof(f6842,definition,
! [X0] :
( sQ561_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f6845,plain,
( sQ561_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6790,f248,f222,f6842]) ).
fof(f6846,definition,
! [X0] :
( sQ562_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f6849,plain,
( ~ sQ502_spl
| sQ562_spl
| ~ sQ432_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6791,f241,f4965,f6846,f5865]) ).
fof(f6850,definition,
! [X0] :
( sQ563_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f6853,plain,
( sQ563_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6792,f241,f222,f6850]) ).
fof(f6854,definition,
! [X0] :
( sQ564_spl
<=> ( sdtlseqdt0(X0,xr)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f6857,plain,
( ~ sQ63_spl
| sQ564_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6793,f241,f298,f6854,f651]) ).
fof(f6858,definition,
! [X0] :
( sQ565_spl
<=> ( sdtlseqdt0(X0,xm)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f6861,plain,
( ~ sQ195_spl
| sQ565_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6794,f241,f6858,f2067]) ).
fof(f6862,definition,
! [X0,X1] :
( sQ566_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f6865,plain,
( ~ sQ40_spl
| sQ566_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6795,f241,f6862,f478]) ).
fof(f6872,definition,
! [X0] :
( sQ568_spl
<=> ( sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f6875,plain,
( ~ sQ172_spl
| ~ sQ260_spl
| sQ568_spl
| ~ sQ432_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f6799,f298,f4965,f6872,f2807,f1657]) ).
fof(f6876,definition,
! [X0] :
( sQ569_spl
<=> ( sdtlseqdt0(X0,xr)
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f6879,plain,
( ~ sQ48_spl
| sQ569_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f6800,f298,f6876,f545]) ).
fof(f6880,definition,
! [X0] :
( sQ570_spl
<=> ( sdtlseqdt0(X0,xk)
| sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f6883,plain,
( sQ570_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f6801,f298,f288,f6880]) ).
fof(f6895,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X3,sdtpldt0(X2,X1))
| ~ sdtlseqdt0(X3,sdtpldt0(X2,X0))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f60]) ).
fof(f6896,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| sdtlseqdt0(sdtpldt0(X2,X0),xp)
| ~ aNaturalNumber0(sdtpldt0(X2,X0))
| sdtlseqdt0(xm,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6895,f483]) ).
fof(f6904,definition,
! [X0,X1,X2] :
( sQ571_spl
<=> ( sdtlseqdt0(sdtpldt0(X2,X0),xp)
| ~ aNaturalNumber0(sdtpldt0(X2,X0))
| sdtlseqdt0(xm,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f6907,plain,
( ~ sQ40_spl
| ~ sQ7_spl
| sQ571_spl ),
inference(split_clause,[status(thm)],[f6896,f6904,f241,f478]) ).
fof(f6926,plain,
! [X0] :
( ~ sQ522_spl
| sdtlseqdt0(X0,sz10)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f6166,f456]) ).
fof(f6927,plain,
( ~ sQ522_spl
| iLess0(xm,sz10)
| xm = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f6166,f133]) ).
fof(f6928,plain,
! [X0] :
( ~ sQ522_spl
| sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6166,f111]) ).
fof(f6930,definition,
! [X0] :
( sQ573_spl
<=> ( sdtlseqdt0(X0,sz10)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f6933,plain,
( ~ sQ522_spl
| sQ573_spl
| ~ sQ49_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6926,f241,f553,f6930,f6165]) ).
fof(f6934,definition,
( sQ574_spl
<=> iLess0(xm,sz10) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f6937,plain,
( ~ sQ522_spl
| sQ574_spl
| sQ390_spl
| ~ sQ49_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6927,f241,f553,f4378,f6934,f6165]) ).
fof(f6938,definition,
! [X0] :
( sQ575_spl
<=> ( sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f6941,plain,
( ~ sQ522_spl
| ~ sQ49_spl
| ~ sQ7_spl
| sQ575_spl ),
inference(split_clause,[status(thm)],[f6928,f6938,f241,f553,f6165]) ).
fof(f6959,plain,
! [X0] :
( ~ sQ194_spl
| sdtlseqdt0(X0,xn)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2008,f456]) ).
fof(f6964,definition,
! [X0] :
( sQ577_spl
<=> ( sdtlseqdt0(X0,xn)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f6967,plain,
( ~ sQ194_spl
| sQ577_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6959,f241,f248,f6964,f2007]) ).
fof(f6975,plain,
! [X0] :
( ~ sQ146_spl
| sdtlseqdt0(X0,xm)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1323,f456]) ).
fof(f6981,definition,
! [X0] :
( sQ578_spl
<=> ( sdtlseqdt0(X0,xm)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ578_spl])],[split_symbol_definition]) ).
fof(f6984,plain,
( ~ sQ146_spl
| sQ578_spl
| ~ sQ7_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6975,f355,f241,f6981,f1322]) ).
fof(f6988,plain,
! [X0] :
( ~ sQ519_spl
| sdtlseqdt0(X0,xp)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f6096,f456]) ).
fof(f6992,definition,
! [X0] :
( sQ579_spl
<=> ( sdtlseqdt0(X0,xp)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f6995,plain,
( ~ sQ519_spl
| sQ579_spl
| ~ sQ3_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6988,f355,f222,f6992,f6095]) ).
fof(f7001,plain,
! [X0] :
( ~ sQ164_spl
| sdtlseqdt0(X0,xr)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1477,f456]) ).
fof(f7005,definition,
! [X0] :
( sQ580_spl
<=> ( sdtlseqdt0(X0,xr)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ580_spl])],[split_symbol_definition]) ).
fof(f7008,plain,
( ~ sQ164_spl
| sQ580_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f7001,f355,f298,f7005,f1476]) ).
fof(f7018,plain,
( ~ sQ260_spl
| sdtasdt0(xp,xk) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xp,xk))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f5064,f214]) ).
fof(f7023,definition,
( sQ581_spl
<=> sdtasdt0(xp,xk) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ581_spl])],[split_symbol_definition]) ).
fof(f7026,plain,
( ~ sQ260_spl
| sQ581_spl
| ~ sQ542_spl
| sQ97_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7018,f222,f4965,f909,f6636,f7023,f2807]) ).
fof(f7027,plain,
( ~ sQ260_spl
| ~ aNaturalNumber0(xk)
| xk = xk
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f5064,f1640]) ).
fof(f7028,plain,
( ~ sQ260_spl
| ~ aNaturalNumber0(xm)
| xm = sdtsldt0(sdtasdt0(xp,xk),xn)
| xn = sz00
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f2808,f1640]) ).
fof(f7029,plain,
( ~ sQ260_spl
| ~ sQ14_spl
| sQ439_spl
| sQ97_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7027,f222,f909,f5066,f288,f2807]) ).
fof(f7030,plain,
( ~ sQ260_spl
| ~ sQ7_spl
| sQ438_spl
| sQ134_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f7028,f248,f1196,f5060,f241,f2807]) ).
fof(f7031,plain,
( ~ sQ260_spl
| aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xp,xk))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f5064,f213]) ).
fof(f7032,plain,
( ~ sQ260_spl
| sQ14_spl
| ~ sQ542_spl
| sQ97_spl
| ~ sQ432_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7031,f222,f4965,f909,f6636,f288,f2807]) ).
fof(f7033,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f247,f254,f256,f258,f260,f277,f281,f297,f314,f321,f323,f325,f327,f329,f347,f361,f369,f371,f381,f392,f408,f440,f444,f448,f452,f463,f469,f473,f481,f489,f497,f498,f506,f510,f518,f525,f549,f562,f570,f572,f583,f597,f604,f617,f621,f634,f648,f654,f679,f688,f738,f742,f750,f754,f766,f790,f794,f819,f823,f830,f838,f842,f846,f850,f854,f858,f862,f866,f874,f881,f883,f903,f907,f916,f920,f924,f928,f932,f936,f940,f959,f1030,f1041,f1048,f1083,f1100,f1120,f1180,f1184,f1192,f1199,f1207,f1208,f1211,f1212,f1216,f1249,f1251,f1278,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1321,f1328,f1334,f1338,f1358,f1362,f1366,f1370,f1374,f1378,f1386,f1426,f1447,f1459,f1479,f1495,f1526,f1531,f1532,f1533,f1544,f1548,f1552,f1560,f1599,f1608,f1626,f1639,f1656,f1660,f1670,f1677,f1681,f1682,f1712,f1758,f1762,f1786,f1801,f1805,f1821,f1859,f1869,f1873,f1905,f1909,f1913,f1955,f1992,f2002,f2006,f2010,f2052,f2071,f2075,f2076,f2077,f2091,f2092,f2139,f2148,f2150,f2170,f2174,f2178,f2182,f2186,f2191,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2225,f2249,f2258,f2262,f2272,f2276,f2311,f2319,f2337,f2343,f2349,f2376,f2409,f2448,f2485,f2530,f2551,f2573,f2577,f2581,f2585,f2589,f2593,f2614,f2667,f2669,f2670,f2672,f2674,f2675,f2676,f2677,f2678,f2684,f2702,f2713,f2720,f2732,f2753,f2757,f2763,f2805,f2810,f2864,f2880,f2884,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2920,f2926,f3028,f3029,f3033,f3037,f3102,f3129,f3136,f3148,f3193,f3197,f3202,f3206,f3210,f3214,f3218,f3222,f3223,f3227,f3231,f3235,f3239,f3262,f3358,f3370,f3374,f3378,f3380,f3513,f3559,f3560,f3571,f3572,f3613,f3617,f3697,f3730,f3741,f3745,f3751,f3752,f3790,f3791,f3796,f3808,f3812,f3817,f3828,f3837,f3844,f3887,f3892,f3896,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3923,f3927,f3931,f3935,f3939,f3943,f3944,f4007,f4013,f4089,f4146,f4151,f4170,f4196,f4206,f4210,f4214,f4216,f4247,f4313,f4317,f4321,f4325,f4330,f4335,f4339,f4343,f4347,f4351,f4356,f4361,f4375,f4377,f4381,f4406,f4407,f4411,f4415,f4420,f4425,f4429,f4433,f4437,f4441,f4446,f4450,f4454,f4461,f4472,f4501,f4508,f4512,f4516,f4524,f4528,f4532,f4598,f4644,f4647,f4663,f4672,f4709,f4714,f4716,f4728,f4851,f4853,f4869,f4873,f4909,f4913,f4917,f4921,f4926,f4931,f4935,f4939,f4944,f4948,f4952,f4956,f4960,f4964,f5042,f5046,f5052,f5056,f5074,f5099,f5106,f5110,f5114,f5116,f5121,f5128,f5132,f5136,f5138,f5148,f5155,f5159,f5163,f5178,f5190,f5194,f5614,f5781,f5789,f5790,f5791,f5804,f5805,f5818,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5873,f5877,f5881,f5885,f5889,f5893,f5894,f5930,f5932,f5964,f5965,f5972,f5983,f5987,f6003,f6007,f6011,f6081,f6085,f6094,f6098,f6130,f6133,f6160,f6164,f6168,f6258,f6301,f6305,f6312,f6335,f6339,f6343,f6356,f6363,f6367,f6380,f6413,f6485,f6543,f6590,f6611,f6618,f6622,f6626,f6642,f6644,f6653,f6671,f6675,f6679,f6688,f6690,f6694,f6695,f6719,f6735,f6745,f6749,f6753,f6768,f6769,f6770,f6777,f6778,f6811,f6817,f6821,f6825,f6829,f6837,f6841,f6845,f6849,f6853,f6857,f6861,f6865,f6875,f6879,f6883,f6907,f6933,f6937,f6941,f6967,f6984,f6995,f7008,f7026,f7029,f7030,f7032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM507+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n019.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:35:49 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 29.31/4.31 % Refutation found
% 29.31/4.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 29.31/4.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 29.31/4.38 % Elapsed time: 3.995759 seconds
% 29.31/4.38 % CPU time: 30.987059 seconds
% 29.31/4.38 % Total memory used: 215.490 MB
% 29.31/4.38 % Net memory used: 202.275 MB
%------------------------------------------------------------------------------