%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:40:46 PM UTC 2026
% Result : Theorem 7.10s 1.34s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 271
% Syntax : Number of formulae : 976 ( 44 unt; 238 def)
% Number of atoms : 4282 ( 504 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 6091 (2785 ~;2903 |; 117 &)
% ( 243 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 239 ( 237 usr; 234 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 814 ( 807 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( W1 != sz00
& doDivides0(W0,W1) )
=> sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
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(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(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(f77,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f78,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
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(f103,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
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(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(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(f121,plain,
! [X0,X1,X2] :
( 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(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(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(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(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(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,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f196,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f197,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,definition,
( sQ0_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ0_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( sQ0_spl
| sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ1_spl
<=> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ1_spl
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ2_spl
<=> sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ2_spl
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ2_spl
| sdtasdt0(xp,xm) != sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ3_spl
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ3_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f197,f198,f201,f204,f207]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f111]) ).
fof(f218,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f109]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X3)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f214]) ).
fof(f220,definition,
( sQ4_spl
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ4_spl
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f226,definition,
( sQ6_spl
<=> aNaturalNumber0(sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ6_spl
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f231,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f218]) ).
fof(f232,plain,
( sQ6_spl
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f228,f62]) ).
fof(f233,definition,
( sQ7_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( sQ7_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,definition,
( sQ8_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f232,f233,f236,f226]) ).
fof(f240,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f173]) ).
fof(f241,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f249,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f114,f111]) ).
fof(f251,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f249]) ).
fof(f254,definition,
( sQ10_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ10_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f269,definition,
( sQ13_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ13_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f282,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f172]) ).
fof(f283,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f284,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f178,f114]) ).
fof(f285,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f178,f111]) ).
fof(f286,definition,
( sQ16_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ16_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,definition,
( sQ17_spl
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ17_spl
| sdtlseqdt0(xn,xp) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f284,f286,f233,f289]) ).
fof(f293,definition,
! [X0] :
( sQ18_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f294,plain,
! [X0] :
( ~ sQ18_spl
| ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f285,f233,f293,f286]) ).
fof(f297,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f171]) ).
fof(f298,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f179,f114]) ).
fof(f300,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f179,f111]) ).
fof(f301,definition,
( sQ19_spl
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ19_spl
| sdtlseqdt0(xm,xp) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f299,f269,f233,f301]) ).
fof(f305,definition,
! [X0] :
( sQ20_spl
<=> ( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f306,plain,
! [X0] :
( ~ sQ20_spl
| ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ13_spl
| sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f300,f233,f305,f269]) ).
fof(f310,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ sdtlseqdt0(X0,sdtasdt0(sz10,X0))
| X0 = sdtasdt0(sz10,X0)
| sz10 = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f121,f76]) ).
fof(f312,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ sdtlseqdt0(sdtasdt0(sz10,X0),X0)
| sdtasdt0(sz10,X0) = X0
| sz10 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f121,f76]) ).
fof(f313,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X1)
| X1 = X1
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f121]) ).
fof(f314,definition,
( sQ21_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ21_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
! [X0] :
( sQ22_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ sdtlseqdt0(X0,sdtasdt0(sz10,X0))
| X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f320,definition,
( sQ23_spl
<=> sz10 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ23_spl
| sz10 = sz00 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( sQ23_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f310,f314,f317,f320]) ).
fof(f324,definition,
! [X0] :
( sQ24_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ sdtlseqdt0(sdtasdt0(sz10,X0),X0)
| sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ23_spl
| sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f312,f314,f324,f320]) ).
fof(f328,definition,
! [X0] :
( sQ25_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f329,plain,
! [X0] :
( ~ sQ25_spl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
! [X1] :
( sQ26_spl
<=> ( ~ sdtlseqdt0(X1,X1)
| X1 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f313,f328,f331]) ).
fof(f335,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f58]) ).
fof(f336,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f57]) ).
fof(f338,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f345,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f181,f111]) ).
fof(f347,definition,
! [X0] :
( sQ27_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f348,plain,
! [X0] :
( ~ sQ27_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f345,f347,f286,f233]) ).
fof(f351,definition,
( sQ28_spl
<=> sdtlseqdt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f354,definition,
( sQ29_spl
<=> xp = xn ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( ~ sQ29_spl
| xp = xn ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f358,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f180]) ).
fof(f359,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f183,f111]) ).
fof(f362,definition,
! [X0] :
( sQ30_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f363,plain,
! [X0] :
( ~ sQ30_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f360,f362,f269,f233]) ).
fof(f366,definition,
( sQ31_spl
<=> sdtlseqdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f369,definition,
( sQ32_spl
<=> xp = xm ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( ~ sQ32_spl
| xp = xm ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f373,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f182]) ).
fof(f374,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f376,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(f380,definition,
( sQ33_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ33_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,definition,
! [X0] :
( sQ34_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(sz00,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f376,f380,f383]) ).
fof(f388,definition,
! [X0] :
( sQ35_spl
<=> ~ aNaturalNumber0(X0) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f389,plain,
! [X0] :
( ~ sQ35_spl
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,definition,
! [X1] :
( sQ36_spl
<=> ( X1 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f382,f56]) ).
fof(f396,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( sQ10_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f256,f62]) ).
fof(f399,plain,
( sQ10_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f398,f286,f269,f254]) ).
fof(f400,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f195,f111]) ).
fof(f401,plain,
( xk = xp
| ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f195,f109]) ).
fof(f402,definition,
! [X0] :
( sQ37_spl
<=> ( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f400,f402,f233,f236]) ).
fof(f406,definition,
( sQ38_spl
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( sQ38_spl
| ~ sdtlseqdt0(xk,xp) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ39_spl
<=> xk = xp ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ39_spl
| xk = xp ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ39_spl
| ~ sQ38_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f401,f236,f233,f406,f409]) ).
fof(f413,plain,
( ~ sQ39_spl
| sdtlseqdt0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f410,f195]) ).
fof(f419,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ sdtlseqdt0(sdtasdt0(X0,sz10),X0)
| sdtasdt0(X0,sz10) = X0
| sz10 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f123,f75]) ).
fof(f421,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ sdtlseqdt0(X0,sdtasdt0(X0,sz10))
| X0 = sdtasdt0(X0,sz10)
| sz10 = sz00
| ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f123,f75]) ).
fof(f424,definition,
! [X0] :
( sQ40_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ sdtlseqdt0(sdtasdt0(X0,sz10),X0)
| sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10)) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ23_spl
| sQ40_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f419,f314,f424,f320]) ).
fof(f428,definition,
! [X0] :
( sQ41_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ sdtlseqdt0(X0,sdtasdt0(X0,sz10))
| X0 = sdtasdt0(X0,sz10)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ23_spl
| sQ41_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f421,f314,f428,f320]) ).
fof(f439,plain,
( ~ sQ35_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f190,f389]) ).
fof(f445,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f448,plain,
! [X0,X1] :
( X1 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f87]) ).
fof(f449,plain,
( sQ36_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f448,f328,f391]) ).
fof(f452,plain,
( ~ sQ2_spl
| xm = xk
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xm)
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f205,f87]) ).
fof(f460,definition,
( sQ42_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f463,definition,
( sQ43_spl
<=> xm = xk ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ43_spl
| xm = xk ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ2_spl
| sQ43_spl
| ~ sQ8_spl
| ~ sQ13_spl
| sQ42_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f452,f233,f460,f269,f236,f463,f204]) ).
fof(f471,definition,
( sQ45_spl
<=> xk = sz00 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ45_spl
| xk = sz00 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f489,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f186]) ).
fof(f490,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f507,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(f508,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(f509,definition,
! [X0] :
( sQ49_spl
<=> ( sK0_skl(sz00,X0) = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f510,plain,
! [X0] :
( ~ sQ49_spl
| sK0_skl(sz00,X0) = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( ~ sQ33_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f507,f509,f380]) ).
fof(f513,definition,
! [X0] :
( sQ50_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f514,plain,
! [X0] :
( ~ sQ50_spl
| X0 = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,plain,
( ~ sQ33_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f508,f513,f380]) ).
fof(f517,plain,
! [X0] :
( ~ sQ49_spl
| sK0_skl(sz00,X0) = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f510]) ).
fof(f518,plain,
! [X0] :
( ~ sQ50_spl
| X0 = sz00
| ~ aNaturalNumber0(sK0_skl(sz00,X0))
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f514]) ).
fof(f525,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f103]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(X2,sdtmndt0(X1,X0))
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtpldt0(X2,sK0_skl(sdtmndt0(X1,X0),X2))) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f104,f98]) ).
fof(f527,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f104]) ).
fof(f528,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f99]) ).
fof(f529,plain,
! [X0,X1,X2,X3] :
( ~ aNaturalNumber0(X3)
| sdtlseqdt0(X2,sdtmndt0(X1,X0))
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtpldt0(X2,X3)) != X1
| ~ aNaturalNumber0(sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f528,f99]) ).
fof(f532,plain,
! [X0,X1,X2,X3] :
( sdtpldt0(X3,sdtmndt0(X1,X0)) = X2
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X0,sdtmndt0(X2,X3)) != X1
| ~ aNaturalNumber0(sdtmndt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f528,f104]) ).
fof(f536,definition,
( sQ51_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ51_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f560,definition,
( sQ54_spl
<=> sdtlseqdt0(sz00,sz00) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ54_spl
| sdtlseqdt0(sz00,sz00) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f562,plain,
( sQ54_spl
| ~ sdtlseqdt0(sz00,sz00) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f569,definition,
( sQ55_spl
<=> sz00 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f573,definition,
( sQ56_spl
<=> aNaturalNumber0(sdtasdt0(xp,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( sQ56_spl
| ~ aNaturalNumber0(sdtasdt0(xp,sz00)) ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f576,definition,
( sQ57_spl
<=> aNaturalNumber0(sdtasdt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( sQ57_spl
| ~ aNaturalNumber0(sdtasdt0(xn,sz00)) ),
inference(component_clause,[status(thm)],[f576]) ).
fof(f583,plain,
! [X0,X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sdtpldt0(X1,X3))
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f111,f117]) ).
fof(f613,plain,
! [X0] :
( X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f127,f109]) ).
fof(f614,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(f615,definition,
! [X0] :
( sQ59_spl
<=> ( X0 = sz10
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ21_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f613,f615,f314]) ).
fof(f619,definition,
! [X0,X1] :
( sQ60_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ21_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f614,f619,f314]) ).
fof(f633,plain,
! [X0] :
( sK1_skl(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sK1_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f138,f93]) ).
fof(f639,definition,
! [X0] :
( sQ61_spl
<=> ( sK1_skl(sz00,X0) = sz00
| X0 = sz00
| ~ aNaturalNumber0(sK1_skl(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( ~ sQ33_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f633,f639,f380]) ).
fof(f671,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f139]) ).
fof(f682,plain,
! [X0] :
( ~ sQ54_spl
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f561,f111]) ).
fof(f684,definition,
! [X0] :
( sQ62_spl
<=> ( sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( ~ sQ54_spl
| ~ sQ33_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f682,f684,f380,f560]) ).
fof(f688,plain,
( sQ1_spl
| ~ sdtlseqdt0(xn,xp)
| xn = xp
| xm = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f203,f124]) ).
fof(f691,plain,
( sQ1_spl
| ~ sQ17_spl
| sQ29_spl
| sQ51_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f688,f269,f286,f233,f536,f354,f289,f201]) ).
fof(f703,plain,
! [X0] :
( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f193,f111]) ).
fof(f704,definition,
( sQ63_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( sQ63_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f710,definition,
( sQ65_spl
<=> xk = xr ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( ~ sQ65_spl
| xk = xr ),
inference(component_clause,[status(thm)],[f710]) ).
fof(f714,definition,
! [X0] :
( sQ66_spl
<=> ( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f717,plain,
( ~ sQ8_spl
| ~ sQ63_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f703,f714,f704,f236]) ).
fof(f718,plain,
( sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f706,f190]) ).
fof(f719,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f718]) ).
fof(f722,plain,
( ~ sQ65_spl
| isPrime0(xk) ),
inference(backward_demodulation,[status(thm)],[f711,f192]) ).
fof(f725,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(f728,definition,
! [X0] :
( sQ67_spl
<=> ( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f725,f728,f233,f254]) ).
fof(f739,plain,
( sQ54_spl
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f562,f107]) ).
fof(f742,plain,
( sQ54_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f739,f380,f560]) ).
fof(f808,plain,
! [X0] :
( doDivides0(X0,xk)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f191,f147]) ).
fof(f809,definition,
! [X0] :
( sQ76_spl
<=> ( doDivides0(X0,xk)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f812,plain,
( ~ sQ8_spl
| ~ sQ63_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f808,f809,f704,f236]) ).
fof(f817,plain,
( sdtlseqdt0(xr,xk)
| xk = sz00
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f153,f191]) ).
fof(f821,definition,
( sQ77_spl
<=> sdtlseqdt0(xr,xk) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f824,plain,
( sQ77_spl
| sQ45_spl
| ~ sQ8_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f817,f704,f236,f471,f821]) ).
fof(f825,definition,
( sQ78_spl
<=> sdtasdt0(xn,xm) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( ~ sQ78_spl
| sdtasdt0(xn,xm) = sz00 ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f827,plain,
( sQ78_spl
| sdtasdt0(xn,xm) != sz00 ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f847,plain,
( xr != sz00
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f159,f192]) ).
fof(f848,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f159,f176]) ).
fof(f849,definition,
( sQ81_spl
<=> xr = sz00 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ81_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f847,f704,f849]) ).
fof(f853,plain,
( ~ sQ42_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f848,f233,f460]) ).
fof(f871,plain,
( ~ sQ25_spl
| xp = sz00 ),
inference(resolution,[status(thm)],[f329,f173]) ).
fof(f879,plain,
( ~ sQ25_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f871,f460,f328]) ).
fof(f881,plain,
( sQ2_spl
| ~ sQ0_spl
| sdtasdt0(xn,xm) != sdtasdt0(xp,xk) ),
inference(backward_demodulation,[status(thm)],[f199,f206]) ).
fof(f890,definition,
( sQ83_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f892,plain,
( sQ83_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f890]) ).
fof(f910,plain,
( xr != sz10
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f160,f192]) ).
fof(f911,plain,
( xp != sz10
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f160,f176]) ).
fof(f912,definition,
( sQ86_spl
<=> xr = sz10 ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f915,plain,
( ~ sQ86_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f910,f704,f912]) ).
fof(f916,definition,
( sQ87_spl
<=> xp = sz10 ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( ~ sQ87_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f911,f233,f916]) ).
fof(f920,plain,
( xr = xk
| xr = sz10
| ~ aNaturalNumber0(xr)
| ~ isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f161,f191]) ).
fof(f921,plain,
( xp = sdtasdt0(xn,xm)
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f161,f177]) ).
fof(f924,definition,
( sQ88_spl
<=> isPrime0(xk) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( sQ88_spl
| ~ isPrime0(xk) ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f927,plain,
( sQ65_spl
| sQ86_spl
| ~ sQ63_spl
| ~ sQ88_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f920,f236,f924,f704,f912,f710]) ).
fof(f928,definition,
( sQ89_spl
<=> isPrime0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( sQ89_spl
| ~ isPrime0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f931,definition,
( sQ90_spl
<=> xp = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ90_spl
| xp = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,plain,
( sQ90_spl
| sQ87_spl
| ~ sQ7_spl
| ~ sQ89_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f921,f254,f928,f233,f916,f931]) ).
fof(f937,plain,
( sQ4_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f222,f62]) ).
fof(f938,plain,
( sQ4_spl
| ~ sQ13_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f937,f233,f269,f220]) ).
fof(f950,plain,
! [X0] :
( sQ38_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f408,f111]) ).
fof(f951,plain,
( sQ38_spl
| sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f408,f114]) ).
fof(f952,definition,
! [X0] :
( sQ92_spl
<=> ( ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f955,plain,
( sQ38_spl
| ~ sQ7_spl
| sQ92_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f950,f236,f952,f233,f406]) ).
fof(f956,definition,
( sQ93_spl
<=> sdtlseqdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f959,plain,
( sQ38_spl
| sQ93_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f951,f233,f236,f956,f406]) ).
fof(f976,plain,
( sQ57_spl
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f578,f62]) ).
fof(f977,plain,
( sQ57_spl
| ~ sQ33_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f976,f286,f380,f576]) ).
fof(f1017,plain,
( ~ sQ51_spl
| doDivides0(xp,sdtasdt0(xn,sz00)) ),
inference(backward_demodulation,[status(thm)],[f537,f177]) ).
fof(f1080,definition,
( sQ103_spl
<=> doDivides0(xp,sdtasdt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1082,plain,
( sQ103_spl
| ~ doDivides0(xp,sdtasdt0(xn,sz00)) ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1164,plain,
( xr = sdtasdt0(xn,xm)
| xr = sz10
| ~ aNaturalNumber0(xr)
| ~ isPrime0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f194,f161]) ).
fof(f1165,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(f1166,definition,
( sQ120_spl
<=> xr = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1167,plain,
( ~ sQ120_spl
| xr = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f1166]) ).
fof(f1169,plain,
( sQ120_spl
| sQ86_spl
| ~ sQ63_spl
| ~ sQ89_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1164,f254,f928,f704,f912,f1166]) ).
fof(f1170,definition,
! [X0] :
( sQ121_spl
<=> ( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
( ~ sQ10_spl
| ~ sQ63_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1165,f1170,f704,f254]) ).
fof(f1265,definition,
( sQ129_spl
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1268,definition,
( sQ130_spl
<=> xn = sz10 ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1269,plain,
( ~ sQ130_spl
| xn = sz10 ),
inference(component_clause,[status(thm)],[f1268]) ).
fof(f1292,plain,
( sQ56_spl
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f575,f62]) ).
fof(f1293,plain,
( sQ56_spl
| ~ sQ33_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1292,f233,f380,f573]) ).
fof(f1300,plain,
( ~ sQ130_spl
| ~ sdtlseqdt0(xp,sz10) ),
inference(backward_demodulation,[status(thm)],[f1269,f178]) ).
fof(f1301,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| sdtlseqdt0(sz10,xp) ),
inference(backward_demodulation,[status(thm)],[f1269,f290]) ).
fof(f1371,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| doDivides0(sz00,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f79,f139]) ).
fof(f1372,definition,
! [X0] :
( sQ140_spl
<=> ( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1373,plain,
! [X0] :
( ~ sQ140_spl
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1372]) ).
fof(f1375,definition,
( sQ141_spl
<=> doDivides0(sz00,sz00) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1376,plain,
( ~ sQ141_spl
| doDivides0(sz00,sz00) ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,plain,
( sQ141_spl
| ~ sQ33_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1371,f1372,f380,f1375]) ).
fof(f1379,plain,
! [X0] :
( ~ sQ140_spl
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1373]) ).
fof(f1380,plain,
! [X0] :
( ~ aNaturalNumber0(sz00)
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f78,f139]) ).
fof(f1381,definition,
! [X0] :
( sQ142_spl
<=> ( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1382,plain,
! [X0] :
( ~ sQ142_spl
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1381]) ).
fof(f1384,plain,
( ~ sQ33_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1380,f1381,f380]) ).
fof(f1385,plain,
! [X0] :
( ~ sQ142_spl
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1382]) ).
fof(f1387,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f76,f139]) ).
fof(f1391,definition,
! [X0] :
( sQ143_spl
<=> ( ~ aNaturalNumber0(X0)
| doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
! [X0] :
( ~ sQ143_spl
| ~ aNaturalNumber0(X0)
| doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1391]) ).
fof(f1394,plain,
( ~ sQ21_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1387,f1391,f314]) ).
fof(f1396,plain,
! [X0] :
( ~ sQ143_spl
| doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1392]) ).
fof(f1410,plain,
( ~ sQ140_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f171,f1379]) ).
fof(f1416,plain,
~ sQ140_spl,
inference(contradiction_clause,[status(thm)],[f1410]) ).
fof(f1426,plain,
( ~ sQ90_spl
| doDivides0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f932,f177]) ).
fof(f1427,plain,
( sQ89_spl
| ~ sQ90_spl
| ~ isPrime0(xp) ),
inference(backward_demodulation,[status(thm)],[f932,f930]) ).
fof(f1434,plain,
( sQ89_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1427,f176]) ).
fof(f1435,plain,
( sQ89_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f1434]) ).
fof(f1502,definition,
( sQ154_spl
<=> sdtlseqdt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1503,plain,
( ~ sQ154_spl
| sdtlseqdt0(xn,xr) ),
inference(component_clause,[status(thm)],[f1502]) ).
fof(f1504,plain,
( sQ154_spl
| ~ sdtlseqdt0(xn,xr) ),
inference(component_clause,[status(thm)],[f1502]) ).
fof(f1758,plain,
! [X0] :
( ~ sQ143_spl
| sdtlseqdt0(sz10,X0)
| X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1396,f153]) ).
fof(f1759,definition,
! [X0] :
( sQ180_spl
<=> ( sdtlseqdt0(sz10,X0)
| X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( ~ sQ143_spl
| ~ sQ21_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f1758,f1759,f314,f1391]) ).
fof(f1764,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(f1769,definition,
! [X0] :
( sQ181_spl
<=> ( ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10)) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1772,plain,
( sQ181_spl
| sQ23_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1764,f314,f320,f1769]) ).
fof(f1858,definition,
( sQ187_spl
<=> doDivides0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1859,plain,
( ~ sQ187_spl
| doDivides0(xp,sz00) ),
inference(component_clause,[status(thm)],[f1858]) ).
fof(f1860,plain,
( sQ187_spl
| ~ doDivides0(xp,sz00) ),
inference(component_clause,[status(thm)],[f1858]) ).
fof(f1865,definition,
! [X0] :
( sQ189_spl
<=> ( aNaturalNumber0(X0)
| X0 != xk ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1937,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0)
| sz10 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0)) ),
inference(resolution,[status(thm)],[f76,f87]) ).
fof(f1942,definition,
! [X0] :
( sQ202_spl
<=> ( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(sz10,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f1945,plain,
( sQ23_spl
| ~ sQ21_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f1937,f1942,f314,f320]) ).
fof(f1949,plain,
! [X0] :
( sz00 = sz00
| X0 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f78,f93]) ).
fof(f1950,definition,
! [X0] :
( sQ203_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1951,plain,
! [X0] :
( ~ sQ203_spl
| X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1950]) ).
fof(f1953,plain,
( sQ55_spl
| ~ sQ33_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f1949,f1950,f380,f569]) ).
fof(f1954,plain,
! [X0] :
( ~ sQ203_spl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1951]) ).
fof(f1957,plain,
( ~ sQ142_spl
| sQ187_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1860,f1385]) ).
fof(f1958,plain,
( ~ sQ142_spl
| sQ187_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1957,f233,f1858,f1381]) ).
fof(f2132,plain,
( ~ sQ203_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f1954,f328,f1950]) ).
fof(f2150,plain,
( ~ sQ0_spl
| xn = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f199,f88]) ).
fof(f2171,plain,
( ~ sQ0_spl
| sQ29_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sQ51_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2150,f269,f536,f286,f233,f354,f198]) ).
fof(f2201,plain,
! [X0] :
( ~ sQ154_spl
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1503,f111]) ).
fof(f2202,plain,
( ~ sQ154_spl
| xr = xn
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1503,f109]) ).
fof(f2203,definition,
! [X0] :
( sQ231_spl
<=> ( sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2206,plain,
( ~ sQ154_spl
| ~ sQ63_spl
| ~ sQ16_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2201,f2203,f286,f704,f1502]) ).
fof(f2207,definition,
( sQ232_spl
<=> sdtlseqdt0(xr,xn) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2209,plain,
( sQ232_spl
| ~ sdtlseqdt0(xr,xn) ),
inference(component_clause,[status(thm)],[f2207]) ).
fof(f2210,definition,
( sQ233_spl
<=> xr = xn ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2211,plain,
( ~ sQ233_spl
| xr = xn ),
inference(component_clause,[status(thm)],[f2210]) ).
fof(f2213,plain,
( ~ sQ154_spl
| sQ233_spl
| ~ sQ232_spl
| ~ sQ16_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f2202,f704,f286,f2207,f2210,f1502]) ).
fof(f2223,plain,
( ~ sQ233_spl
| isPrime0(xn) ),
inference(backward_demodulation,[status(thm)],[f2211,f192]) ).
fof(f2296,plain,
( ~ sQ187_spl
| xp = sz00
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f161,f1859]) ).
fof(f2297,plain,
! [X0] :
( ~ sQ143_spl
| ~ aNaturalNumber0(X0)
| sz10 = X0
| sz10 = sz10
| ~ aNaturalNumber0(sz10)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f161,f1396]) ).
fof(f2303,plain,
( ~ sQ187_spl
| sQ42_spl
| sQ87_spl
| ~ sQ7_spl
| ~ sQ129_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2296,f380,f1265,f233,f916,f460,f1858]) ).
fof(f2304,definition,
! [X0] :
( sQ238_spl
<=> ( ~ aNaturalNumber0(X0)
| sz10 = X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2305,plain,
! [X0] :
( ~ sQ238_spl
| ~ aNaturalNumber0(X0)
| sz10 = X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2304]) ).
fof(f2307,definition,
( sQ239_spl
<=> sz10 = sz10 ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2310,plain,
( ~ sQ143_spl
| sQ239_spl
| ~ sQ21_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2297,f2304,f314,f2307,f1391]) ).
fof(f2316,plain,
! [X0] :
( ~ sQ238_spl
| sz10 = X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2305]) ).
fof(f2346,plain,
! [X0] :
( sQ232_spl
| ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f2209,f111]) ).
fof(f2348,definition,
! [X0] :
( sQ245_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2351,plain,
( sQ232_spl
| ~ sQ16_spl
| sQ245_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f2346,f704,f2348,f286,f2207]) ).
fof(f2356,plain,
! [X0,X1] :
( sQ232_spl
| ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f219,f2209]) ).
fof(f2357,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f219,f178]) ).
fof(f2358,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f219,f179]) ).
fof(f2367,plain,
! [X0,X1] :
( ~ sQ154_spl
| ~ sdtlseqdt0(xr,X1)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f1503]) ).
fof(f2368,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f290]) ).
fof(f2369,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f302]) ).
fof(f2371,plain,
! [X0,X1,X2] :
( X2 = sz10
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f127]) ).
fof(f2379,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f561]) ).
fof(f2380,plain,
! [X0,X1] :
( ~ sdtlseqdt0(xk,X1)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f195]) ).
fof(f2390,plain,
! [X0,X1] :
( ~ sQ154_spl
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f1503]) ).
fof(f2391,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f290]) ).
fof(f2392,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f302]) ).
fof(f2393,plain,
! [X0,X1,X2] :
( X2 = sz10
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f127]) ).
fof(f2398,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f561]) ).
fof(f2399,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f219,f195]) ).
fof(f2406,definition,
! [X0,X1] :
( sQ246_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( sQ232_spl
| ~ sQ16_spl
| sQ246_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f2356,f704,f2406,f286,f2207]) ).
fof(f2410,definition,
! [X0,X1] :
( sQ247_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2413,plain,
( ~ sQ16_spl
| sQ247_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2357,f233,f2410,f286]) ).
fof(f2414,definition,
! [X0,X1] :
( sQ248_spl
<=> ( ~ sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2417,plain,
( ~ sQ13_spl
| sQ248_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2358,f233,f2414,f269]) ).
fof(f2430,definition,
! [X0,X1] :
( sQ251_spl
<=> ( ~ sdtlseqdt0(xr,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2433,plain,
( ~ sQ154_spl
| ~ sQ63_spl
| ~ sQ16_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f2367,f2430,f286,f704,f1502]) ).
fof(f2434,definition,
! [X0,X1] :
( sQ252_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2437,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f2368,f2434,f286,f233,f289]) ).
fof(f2438,definition,
! [X0,X1] :
( sQ253_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f2441,plain,
( ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f2369,f2438,f269,f233,f301]) ).
fof(f2442,definition,
! [X0] :
( sQ254_spl
<=> ( sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2446,definition,
! [X0,X1,X2] :
( sQ255_spl
<=> ( X2 = sz10
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2449,plain,
( ~ sQ21_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f2371,f2446,f314]) ).
fof(f2461,definition,
! [X0,X1] :
( sQ258_spl
<=> ( ~ sdtlseqdt0(sz00,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2464,plain,
( ~ sQ54_spl
| ~ sQ33_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f2379,f2461,f380,f560]) ).
fof(f2465,definition,
! [X0,X1] :
( sQ259_spl
<=> ( ~ sdtlseqdt0(xk,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2468,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f2380,f2465,f233,f236]) ).
fof(f2475,definition,
! [X0,X1] :
( sQ260_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X0,xr)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2478,plain,
( ~ sQ154_spl
| ~ sQ16_spl
| ~ sQ63_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f2390,f2475,f704,f286,f1502]) ).
fof(f2479,definition,
! [X0,X1] :
( sQ261_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2482,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ7_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f2391,f2479,f233,f286,f289]) ).
fof(f2483,definition,
! [X0,X1] :
( sQ262_spl
<=> ( ~ sdtlseqdt0(X1,xm)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2486,plain,
( ~ sQ19_spl
| ~ sQ13_spl
| ~ sQ7_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f2392,f2483,f233,f269,f301]) ).
fof(f2487,definition,
! [X0,X1,X2] :
( sQ263_spl
<=> ( X2 = sz10
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,sz10)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2490,plain,
( ~ sQ21_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f2393,f2487,f314]) ).
fof(f2501,definition,
! [X0,X1] :
( sQ266_spl
<=> ( ~ sdtlseqdt0(X1,sz00)
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2504,plain,
( ~ sQ54_spl
| ~ sQ33_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f2398,f2501,f380,f560]) ).
fof(f2505,definition,
! [X0,X1] :
( sQ267_spl
<=> ( ~ sdtlseqdt0(X1,xp)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2508,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f2399,f2505,f236,f233]) ).
fof(f2536,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f193,f219]) ).
fof(f2537,plain,
! [X0,X1] :
( ~ sdtlseqdt0(xk,X1)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f193,f219]) ).
fof(f2540,definition,
! [X0,X1] :
( sQ270_spl
<=> ( ~ sdtlseqdt0(X1,xr)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2543,plain,
( ~ sQ63_spl
| ~ sQ8_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2536,f2540,f236,f704]) ).
fof(f2544,definition,
! [X0,X1] :
( sQ271_spl
<=> ( ~ sdtlseqdt0(xk,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2547,plain,
( ~ sQ8_spl
| ~ sQ63_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f2537,f2544,f704,f236]) ).
fof(f2552,plain,
! [X0,X1] :
( ~ sQ143_spl
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| doDivides0(sz10,X1)
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f151,f1396]) ).
fof(f2555,definition,
! [X0,X1] :
( sQ272_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| doDivides0(sz10,X1)
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2558,plain,
( ~ sQ143_spl
| sQ272_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2552,f314,f2555,f1391]) ).
fof(f2569,plain,
! [X0] :
( ~ sQ187_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f1859]) ).
fof(f2570,plain,
! [X0,X1] :
( ~ sQ143_spl
| ~ aNaturalNumber0(X1)
| doDivides0(X0,X1)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f1396]) ).
fof(f2571,plain,
! [X0] :
( ~ sQ141_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f1376]) ).
fof(f2573,plain,
! [X0,X1] :
( ~ sQ142_spl
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sz00)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f147,f1385]) ).
fof(f2584,definition,
! [X0] :
( sQ273_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2587,plain,
( ~ sQ187_spl
| ~ sQ33_spl
| ~ sQ7_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f2569,f2584,f233,f380,f1858]) ).
fof(f2588,definition,
! [X0,X1] :
( sQ274_spl
<=> ( ~ aNaturalNumber0(X1)
| doDivides0(X0,X1)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2591,plain,
( ~ sQ143_spl
| ~ sQ21_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f2570,f2588,f314,f1391]) ).
fof(f2592,definition,
! [X0] :
( sQ275_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2595,plain,
( ~ sQ141_spl
| ~ sQ33_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2571,f2592,f380,f1375]) ).
fof(f2598,definition,
! [X0,X1] :
( sQ276_spl
<=> ( ~ aNaturalNumber0(X1)
| doDivides0(X0,sz00)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2601,plain,
( ~ sQ142_spl
| ~ sQ33_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f2573,f2598,f380,f1381]) ).
fof(f2647,plain,
! [X0] :
( xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f193]) ).
fof(f2648,plain,
! [X0] :
( ~ sQ154_spl
| xr = X0
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f1503]) ).
fof(f2649,plain,
! [X0] :
( ~ sQ17_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f290]) ).
fof(f2650,plain,
! [X0] :
( ~ sQ19_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f302]) ).
fof(f2652,plain,
! [X0,X1] :
( X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f127]) ).
fof(f2660,plain,
! [X0] :
( ~ sQ54_spl
| sz00 = X0
| ~ sdtlseqdt0(sz00,X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f561]) ).
fof(f2661,plain,
! [X0] :
( xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f195]) ).
fof(f2675,plain,
! [X0,X1] :
( X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0)
| sz10 = X0
| ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f231,f127]) ).
fof(f2688,definition,
! [X0] :
( sQ283_spl
<=> ( xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f2691,plain,
( ~ sQ8_spl
| ~ sQ63_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f2647,f2688,f704,f236]) ).
fof(f2692,definition,
! [X0] :
( sQ284_spl
<=> ( xr = X0
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2695,plain,
( ~ sQ154_spl
| ~ sQ63_spl
| ~ sQ16_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f2648,f2692,f286,f704,f1502]) ).
fof(f2696,definition,
! [X0] :
( sQ285_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2699,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f2649,f2696,f286,f233,f289]) ).
fof(f2700,definition,
! [X0] :
( sQ286_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2703,plain,
( ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f2650,f2700,f269,f233,f301]) ).
fof(f2704,definition,
( sQ287_spl
<=> sdtlseqdt0(sz10,sz10) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2705,plain,
( ~ sQ287_spl
| sdtlseqdt0(sz10,sz10) ),
inference(component_clause,[status(thm)],[f2704]) ).
fof(f2706,plain,
( sQ287_spl
| ~ sdtlseqdt0(sz10,sz10) ),
inference(component_clause,[status(thm)],[f2704]) ).
fof(f2708,definition,
! [X0,X1] :
( sQ288_spl
<=> ( X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f2711,plain,
( ~ sQ21_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f2652,f2708,f314]) ).
fof(f2723,definition,
! [X0] :
( sQ291_spl
<=> ( sz00 = X0
| ~ sdtlseqdt0(sz00,X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2726,plain,
( ~ sQ54_spl
| ~ sQ33_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2660,f2723,f380,f560]) ).
fof(f2727,definition,
! [X0] :
( sQ292_spl
<=> ( xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2730,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f2661,f2727,f233,f236]) ).
fof(f2741,definition,
! [X0,X1] :
( sQ293_spl
<=> ( X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0)
| sz10 = X0
| ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2744,plain,
( ~ sQ21_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f2675,f2741,f314]) ).
fof(f2761,plain,
! [X0] :
( sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f193]) ).
fof(f2762,plain,
! [X0] :
( ~ sQ154_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f1503]) ).
fof(f2763,plain,
! [X0] :
( ~ sQ17_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f290]) ).
fof(f2764,plain,
! [X0] :
( ~ sQ19_spl
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f302]) ).
fof(f2765,plain,
! [X0,X1] :
( X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f127]) ).
fof(f2769,plain,
! [X0] :
( ~ sQ54_spl
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f561]) ).
fof(f2770,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f251,f195]) ).
fof(f2778,plain,
! [X0] :
( sQ232_spl
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f251,f2209]) ).
fof(f2779,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f251,f178]) ).
fof(f2780,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f251,f179]) ).
fof(f2792,definition,
! [X0] :
( sQ295_spl
<=> ( sdtlseqdt0(xr,X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f2795,plain,
( ~ sQ63_spl
| ~ sQ8_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f2761,f2792,f236,f704]) ).
fof(f2796,definition,
! [X0] :
( sQ296_spl
<=> ( sdtlseqdt0(xn,X0)
| sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2799,plain,
( ~ sQ154_spl
| ~ sQ16_spl
| ~ sQ63_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f2762,f2796,f704,f286,f1502]) ).
fof(f2800,definition,
! [X0] :
( sQ297_spl
<=> ( sdtlseqdt0(xn,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2803,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ7_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2763,f2800,f233,f286,f289]) ).
fof(f2804,definition,
! [X0] :
( sQ298_spl
<=> ( sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2807,plain,
( ~ sQ19_spl
| ~ sQ13_spl
| ~ sQ7_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f2764,f2804,f233,f269,f301]) ).
fof(f2808,definition,
! [X0,X1] :
( sQ299_spl
<=> ( X1 = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2811,plain,
( ~ sQ21_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f2765,f2808,f314]) ).
fof(f2818,definition,
! [X0] :
( sQ301_spl
<=> ( sdtlseqdt0(sz00,X0)
| sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f2821,plain,
( ~ sQ54_spl
| ~ sQ33_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f2769,f2818,f380,f560]) ).
fof(f2822,definition,
! [X0] :
( sQ302_spl
<=> ( sdtlseqdt0(xp,X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f2825,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f2770,f2822,f236,f233]) ).
fof(f2837,definition,
! [X0] :
( sQ304_spl
<=> ( ~ sdtlseqdt0(xr,X0)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f2840,plain,
( sQ232_spl
| ~ sQ63_spl
| sQ304_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2778,f286,f2837,f704,f2207]) ).
fof(f2841,definition,
! [X0] :
( sQ305_spl
<=> ( ~ sdtlseqdt0(xp,X0)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f2844,plain,
( ~ sQ7_spl
| sQ305_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2779,f286,f2841,f233]) ).
fof(f2845,definition,
! [X0] :
( sQ306_spl
<=> ( ~ sdtlseqdt0(xp,X0)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f2848,plain,
( ~ sQ7_spl
| sQ306_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2780,f269,f2845,f233]) ).
fof(f2913,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f139,f75]) ).
fof(f2938,definition,
! [X0] :
( sQ312_spl
<=> ( ~ aNaturalNumber0(X0)
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f2941,plain,
( ~ sQ21_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f2913,f2938,f314]) ).
fof(f3035,plain,
( ~ sQ18_spl
| ~ sdtlseqdt0(xk,xn)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f294,f195]) ).
fof(f3036,plain,
! [X0] :
( ~ sQ18_spl
| X0 = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,X0),xn)
| ~ aNaturalNumber0(sdtasdt0(xp,X0)) ),
inference(resolution,[status(thm)],[f294,f129]) ).
fof(f3037,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f294,f251]) ).
fof(f3038,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f294,f219]) ).
fof(f3039,plain,
! [X0] :
( ~ sQ18_spl
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f294,f114]) ).
fof(f3040,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f294,f111]) ).
fof(f3041,plain,
( ~ sQ18_spl
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f294,f107]) ).
fof(f3042,definition,
( sQ323_spl
<=> sdtlseqdt0(xk,xn) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3044,plain,
( sQ323_spl
| ~ sdtlseqdt0(xk,xn) ),
inference(component_clause,[status(thm)],[f3042]) ).
fof(f3045,plain,
( ~ sQ18_spl
| ~ sQ323_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3035,f236,f3042,f293]) ).
fof(f3046,definition,
! [X0] :
( sQ324_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,X0),xn)
| ~ aNaturalNumber0(sdtasdt0(xp,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f3049,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| sQ324_spl ),
inference(split_clause,[status(thm)],[f3036,f3046,f233,f293]) ).
fof(f3050,definition,
! [X0,X1] :
( sQ325_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f3053,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f3037,f3050,f233,f293]) ).
fof(f3054,definition,
! [X0,X1,X2] :
( sQ326_spl
<=> ( ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f3057,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f3038,f3054,f233,f293]) ).
fof(f3058,definition,
! [X0] :
( sQ327_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f3061,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f3039,f3058,f233,f293]) ).
fof(f3062,definition,
! [X0,X1] :
( sQ328_spl
<=> ( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3065,plain,
( ~ sQ18_spl
| ~ sQ7_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f3040,f3062,f233,f293]) ).
fof(f3066,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3041,f233,f351,f293]) ).
fof(f3071,plain,
( ~ sQ20_spl
| ~ sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f306,f195]) ).
fof(f3072,plain,
! [X0] :
( ~ sQ20_spl
| X0 = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,X0),xm)
| ~ aNaturalNumber0(sdtasdt0(xp,X0)) ),
inference(resolution,[status(thm)],[f306,f129]) ).
fof(f3073,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f306,f251]) ).
fof(f3074,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f306,f219]) ).
fof(f3075,plain,
! [X0] :
( ~ sQ20_spl
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f306,f114]) ).
fof(f3076,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f306,f111]) ).
fof(f3077,plain,
( ~ sQ20_spl
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f306,f107]) ).
fof(f3078,definition,
( sQ329_spl
<=> sdtlseqdt0(xk,xm) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
( sQ329_spl
| ~ sdtlseqdt0(xk,xm) ),
inference(component_clause,[status(thm)],[f3078]) ).
fof(f3081,plain,
( ~ sQ20_spl
| ~ sQ329_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3071,f236,f3078,f305]) ).
fof(f3082,definition,
! [X0] :
( sQ330_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xp,X0),xm)
| ~ aNaturalNumber0(sdtasdt0(xp,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3085,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f3072,f3082,f233,f305]) ).
fof(f3086,definition,
! [X0,X1] :
( sQ331_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f3089,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ331_spl ),
inference(split_clause,[status(thm)],[f3073,f3086,f233,f305]) ).
fof(f3090,definition,
! [X0,X1,X2] :
( sQ332_spl
<=> ( ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f3093,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f3074,f3090,f233,f305]) ).
fof(f3094,definition,
! [X0] :
( sQ333_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3097,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f3075,f3094,f233,f305]) ).
fof(f3098,definition,
! [X0,X1] :
( sQ334_spl
<=> ( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f3076,f3098,f233,f305]) ).
fof(f3102,plain,
( ~ sQ20_spl
| ~ sQ31_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3077,f233,f366,f305]) ).
fof(f3114,plain,
( sQ89_spl
| ~ sQ120_spl
| ~ isPrime0(xr) ),
inference(backward_demodulation,[status(thm)],[f1167,f930]) ).
fof(f3118,plain,
( ~ sQ120_spl
| doDivides0(xp,xr) ),
inference(backward_demodulation,[status(thm)],[f1167,f177]) ).
fof(f3119,plain,
( ~ sQ120_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1167,f139]) ).
fof(f3138,plain,
( sQ89_spl
| ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3114,f192]) ).
fof(f3139,plain,
( sQ89_spl
| ~ sQ120_spl ),
inference(contradiction_clause,[status(thm)],[f3138]) ).
fof(f3140,definition,
( sQ335_spl
<=> doDivides0(xn,xr) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f3141,plain,
( ~ sQ335_spl
| doDivides0(xn,xr) ),
inference(component_clause,[status(thm)],[f3140]) ).
fof(f3143,plain,
( ~ sQ120_spl
| ~ sQ13_spl
| sQ335_spl
| ~ sQ63_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3119,f286,f704,f3140,f269,f1166]) ).
fof(f3204,plain,
! [X0] :
( ~ sQ238_spl
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2316,f160]) ).
fof(f3302,plain,
( ~ sQ120_spl
| xp = xr
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3118,f161]) ).
fof(f3308,definition,
( sQ354_spl
<=> isPrime0(xr) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3310,plain,
( sQ354_spl
| ~ isPrime0(xr) ),
inference(component_clause,[status(thm)],[f3308]) ).
fof(f3311,definition,
( sQ355_spl
<=> xp = xr ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f3312,plain,
( ~ sQ355_spl
| xp = xr ),
inference(component_clause,[status(thm)],[f3311]) ).
fof(f3314,plain,
( ~ sQ120_spl
| sQ355_spl
| sQ87_spl
| ~ sQ7_spl
| ~ sQ354_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f3302,f704,f3308,f233,f916,f3311,f1166]) ).
fof(f3319,plain,
( sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3310,f192]) ).
fof(f3320,plain,
sQ354_spl,
inference(contradiction_clause,[status(thm)],[f3319]) ).
fof(f3324,plain,
( ~ sQ355_spl
| doDivides0(xp,xk) ),
inference(backward_demodulation,[status(thm)],[f3312,f191]) ).
fof(f3333,plain,
( ~ sQ90_spl
| xp = xp
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1426,f161]) ).
fof(f3339,definition,
( sQ358_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f3341,plain,
( sQ358_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f3339]) ).
fof(f3342,definition,
( sQ359_spl
<=> xp = xp ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f3345,plain,
( ~ sQ90_spl
| sQ359_spl
| sQ87_spl
| ~ sQ358_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3333,f233,f3339,f916,f3342,f931]) ).
fof(f3346,definition,
( sQ360_spl
<=> sdtlseqdt0(xp,xp) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f3350,plain,
( sQ358_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3341,f176]) ).
fof(f3351,plain,
sQ358_spl,
inference(contradiction_clause,[status(thm)],[f3350]) ).
fof(f3367,definition,
! [X0] :
( sQ361_spl
<=> ( sdtlseqdt0(xp,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f3372,definition,
! [X0] :
( sQ362_spl
<=> ( ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f3377,definition,
! [X0] :
( sQ363_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f3381,definition,
! [X0] :
( sQ364_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f3385,definition,
! [X0,X1] :
( sQ365_spl
<=> ( ~ sdtlseqdt0(X1,xp)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f3390,definition,
! [X0,X1] :
( sQ366_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f3396,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| doDivides0(xn,xp) ),
inference(forward_demodulation,[status(thm)],[f3312,f3141]) ).
fof(f3397,plain,
! [X0] :
( ~ sQ335_spl
| ~ sQ355_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3396,f147]) ).
fof(f3398,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| xn = xp
| xn = sz10
| ~ aNaturalNumber0(xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3396,f161]) ).
fof(f3400,definition,
! [X0] :
( sQ367_spl
<=> ( doDivides0(X0,xp)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f3403,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f3397,f3400,f286,f233,f3311,f3140]) ).
fof(f3404,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| sQ29_spl
| sQ130_spl
| ~ sQ16_spl
| ~ sQ358_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3398,f233,f3339,f286,f1268,f354,f3311,f3140]) ).
fof(f3411,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| ~ sQ130_spl
| doDivides0(sz10,xp) ),
inference(backward_demodulation,[status(thm)],[f1269,f3396]) ).
fof(f3473,plain,
( sQ323_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(xk,sz10) ),
inference(forward_demodulation,[status(thm)],[f1269,f3044]) ).
fof(f3474,plain,
! [X0] :
( sQ323_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f3473,f251]) ).
fof(f3475,plain,
! [X0,X1] :
( sQ323_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3473,f219]) ).
fof(f3476,plain,
( sQ323_spl
| ~ sQ130_spl
| sdtlseqdt0(sz10,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f3473,f114]) ).
fof(f3477,plain,
! [X0] :
( sQ323_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3473,f111]) ).
fof(f3478,definition,
! [X0] :
( sQ372_spl
<=> ( ~ sdtlseqdt0(xk,X0)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f3481,plain,
( sQ323_spl
| ~ sQ130_spl
| ~ sQ8_spl
| sQ372_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3474,f314,f3478,f236,f1268,f3042]) ).
fof(f3482,definition,
! [X0,X1] :
( sQ373_spl
<=> ( ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3485,plain,
( sQ323_spl
| ~ sQ130_spl
| ~ sQ21_spl
| sQ373_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3475,f236,f3482,f314,f1268,f3042]) ).
fof(f3486,definition,
( sQ374_spl
<=> sdtlseqdt0(sz10,xk) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3489,plain,
( sQ323_spl
| ~ sQ130_spl
| sQ374_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3476,f314,f236,f3486,f1268,f3042]) ).
fof(f3490,definition,
! [X0] :
( sQ375_spl
<=> ( ~ sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f3493,plain,
( sQ323_spl
| ~ sQ130_spl
| ~ sQ21_spl
| sQ375_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3477,f236,f3490,f314,f1268,f3042]) ).
fof(f3600,plain,
( sQ287_spl
| sdtlseqdt0(sz10,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f2706,f114]) ).
fof(f3612,plain,
( sQ287_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3600,f314,f2704]) ).
fof(f3623,plain,
( ~ sQ238_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3204,f176]) ).
fof(f3625,plain,
( ~ sQ238_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3623,f233,f2304]) ).
fof(f3631,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f99,f68]) ).
fof(f3644,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f99,f69]) ).
fof(f3648,definition,
! [X0] :
( sQ394_spl
<=> ( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f3651,plain,
( ~ sQ33_spl
| sQ394_spl ),
inference(split_clause,[status(thm)],[f3631,f3648,f380]) ).
fof(f3667,definition,
! [X0] :
( sQ395_spl
<=> ( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f3668,plain,
! [X0] :
( ~ sQ395_spl
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f3667]) ).
fof(f3670,plain,
( sQ395_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3644,f380,f3667]) ).
fof(f3673,plain,
! [X0] :
( ~ sQ395_spl
| sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3668]) ).
fof(f3739,plain,
( sQ154_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(sz10,xr) ),
inference(forward_demodulation,[status(thm)],[f1269,f1504]) ).
fof(f3740,plain,
( sQ154_spl
| ~ sQ130_spl
| ~ sQ355_spl
| ~ sdtlseqdt0(sz10,xp) ),
inference(forward_demodulation,[status(thm)],[f3312,f3739]) ).
fof(f3741,plain,
( sQ154_spl
| ~ sQ130_spl
| ~ sQ355_spl
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3740,f127]) ).
fof(f3746,plain,
( sQ154_spl
| ~ sQ130_spl
| ~ sQ355_spl
| sQ87_spl
| sQ42_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3741,f233,f460,f916,f3311,f1268,f1502]) ).
fof(f3755,definition,
( sQ407_spl
<=> sdtlseqdt0(xp,sz10) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f3791,plain,
! [X0] :
( ~ sQ355_spl
| doDivides0(X0,xk)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3324,f147]) ).
fof(f3792,plain,
( ~ sQ355_spl
| sdtlseqdt0(xp,xk)
| xk = sz00
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f3324,f153]) ).
fof(f3793,definition,
! [X0] :
( sQ409_spl
<=> ( doDivides0(X0,xk)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f3796,plain,
( ~ sQ355_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ409_spl ),
inference(split_clause,[status(thm)],[f3791,f3793,f233,f236,f3311]) ).
fof(f3797,plain,
( ~ sQ355_spl
| sQ93_spl
| sQ45_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3792,f233,f236,f471,f956,f3311]) ).
fof(f3798,plain,
! [X0] :
( ~ sQ130_spl
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f1300,f251]) ).
fof(f3799,plain,
! [X0,X1] :
( ~ sQ130_spl
| ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1300,f219]) ).
fof(f3800,plain,
( ~ sQ130_spl
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f1300,f114]) ).
fof(f3801,plain,
! [X0] :
( ~ sQ130_spl
| ~ sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1300,f111]) ).
fof(f3802,definition,
! [X0] :
( sQ410_spl
<=> ( ~ sdtlseqdt0(xp,X0)
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f3805,plain,
( ~ sQ130_spl
| ~ sQ7_spl
| sQ410_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3798,f314,f3802,f233,f1268]) ).
fof(f3806,definition,
! [X0,X1] :
( sQ411_spl
<=> ( ~ sdtlseqdt0(X1,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f3809,plain,
( ~ sQ130_spl
| ~ sQ21_spl
| sQ411_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3799,f233,f3806,f314,f1268]) ).
fof(f3810,definition,
( sQ412_spl
<=> sdtlseqdt0(sz10,xp) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f3813,plain,
( ~ sQ130_spl
| sQ412_spl
| ~ sQ7_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3800,f314,f233,f3810,f1268]) ).
fof(f3814,definition,
! [X0] :
( sQ413_spl
<=> ( ~ sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f3817,plain,
( ~ sQ130_spl
| ~ sQ21_spl
| sQ413_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3801,f233,f3814,f314,f1268]) ).
fof(f3818,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(f3823,definition,
! [X0] :
( sQ414_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,sz00))
| sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sz00)) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3826,plain,
( sQ414_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3818,f380,f3823]) ).
fof(f3901,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ130_spl
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1301,f251]) ).
fof(f3903,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ130_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1301,f231]) ).
fof(f3904,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1301,f219]) ).
fof(f3905,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1301,f219]) ).
fof(f3906,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ130_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f1301,f111]) ).
fof(f3907,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| xp = sz10
| ~ sdtlseqdt0(xp,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1301,f109]) ).
fof(f3908,definition,
! [X0] :
( sQ427_spl
<=> ( sdtlseqdt0(sz10,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f3911,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sQ21_spl
| ~ sQ7_spl
| sQ427_spl ),
inference(split_clause,[status(thm)],[f3901,f3908,f233,f314,f1268,f289]) ).
fof(f3913,definition,
! [X0] :
( sQ428_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f3916,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sQ7_spl
| ~ sQ21_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f3903,f3913,f314,f233,f1268,f289]) ).
fof(f3917,definition,
! [X0,X1] :
( sQ429_spl
<=> ( ~ sdtlseqdt0(X1,sz10)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f3920,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sQ21_spl
| ~ sQ7_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f3904,f3917,f233,f314,f1268,f289]) ).
fof(f3921,definition,
! [X0,X1] :
( sQ430_spl
<=> ( ~ sdtlseqdt0(xp,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f3924,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sQ7_spl
| ~ sQ21_spl
| sQ430_spl ),
inference(split_clause,[status(thm)],[f3905,f3921,f314,f233,f1268,f289]) ).
fof(f3925,definition,
! [X0] :
( sQ431_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f3928,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| ~ sQ7_spl
| ~ sQ21_spl
| sQ431_spl ),
inference(split_clause,[status(thm)],[f3906,f3925,f314,f233,f1268,f289]) ).
fof(f3929,plain,
( ~ sQ17_spl
| ~ sQ130_spl
| sQ87_spl
| ~ sQ407_spl
| ~ sQ21_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3907,f233,f314,f3755,f916,f1268,f289]) ).
fof(f3930,plain,
! [X0] :
( ~ sQ335_spl
| ~ sQ355_spl
| ~ sQ130_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3411,f147]) ).
fof(f3932,definition,
! [X0] :
( sQ432_spl
<=> ( doDivides0(X0,xp)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f3935,plain,
( ~ sQ335_spl
| ~ sQ355_spl
| ~ sQ130_spl
| ~ sQ7_spl
| ~ sQ21_spl
| sQ432_spl ),
inference(split_clause,[status(thm)],[f3930,f3932,f314,f233,f1268,f3311,f3140]) ).
fof(f3958,plain,
( ~ sQ355_spl
| xp = xk
| xp = sz10
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f161,f3324]) ).
fof(f3977,plain,
( ~ sQ355_spl
| sQ39_spl
| sQ87_spl
| ~ sQ7_spl
| ~ sQ88_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3958,f236,f924,f233,f916,f409,f3311]) ).
fof(f4029,plain,
! [X0] :
( ~ sQ287_spl
| sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2705,f251]) ).
fof(f4033,plain,
! [X0] :
( ~ sQ287_spl
| sz10 = X0
| ~ sdtlseqdt0(sz10,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2705,f231]) ).
fof(f4034,plain,
! [X0] :
( ~ sQ287_spl
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2705,f219]) ).
fof(f4035,plain,
! [X0,X1] :
( ~ sQ287_spl
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2705,f219]) ).
fof(f4037,plain,
! [X0,X1] :
( ~ sQ287_spl
| ~ sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2705,f219]) ).
fof(f4040,definition,
! [X0] :
( sQ446_spl
<=> ( sdtlseqdt0(sz10,X0)
| sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f4043,plain,
( ~ sQ287_spl
| ~ sQ21_spl
| sQ446_spl ),
inference(split_clause,[status(thm)],[f4029,f4040,f314,f2704]) ).
fof(f4047,definition,
! [X0] :
( sQ447_spl
<=> ( sz10 = X0
| ~ sdtlseqdt0(sz10,X0)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f4050,plain,
( ~ sQ287_spl
| ~ sQ21_spl
| sQ447_spl ),
inference(split_clause,[status(thm)],[f4033,f4047,f314,f2704]) ).
fof(f4051,plain,
( ~ sQ287_spl
| ~ sQ21_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f4034,f2442,f314,f2704]) ).
fof(f4052,definition,
! [X0,X1] :
( sQ448_spl
<=> ( ~ sdtlseqdt0(X1,sz10)
| sdtlseqdt0(X0,sz10)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4055,plain,
( ~ sQ287_spl
| ~ sQ21_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f4035,f4052,f314,f2704]) ).
fof(f4057,definition,
! [X0,X1] :
( sQ449_spl
<=> ( ~ sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,sz10)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4060,plain,
( ~ sQ287_spl
| ~ sQ21_spl
| sQ449_spl ),
inference(split_clause,[status(thm)],[f4037,f4057,f314,f2704]) ).
fof(f4208,plain,
( ~ sQ90_spl
| ~ sQ130_spl
| xp = sdtasdt0(sz10,xm) ),
inference(forward_demodulation,[status(thm)],[f1269,f932]) ).
fof(f4210,plain,
( ~ sQ90_spl
| ~ sQ130_spl
| xm = xp
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f4208,f76]) ).
fof(f4236,plain,
( ~ sQ90_spl
| ~ sQ130_spl
| sQ32_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4210,f269,f369,f1268,f931]) ).
fof(f4342,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f184,f143]) ).
fof(f4343,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f184,f144]) ).
fof(f4345,plain,
! [X0] :
( aNaturalNumber0(X0)
| X0 != xk
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f184,f143]) ).
fof(f4346,plain,
! [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
| X0 != xk
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f184,f144]) ).
fof(f4347,plain,
! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| X0 = xk
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f184,f671]) ).
fof(f4348,plain,
( sQ8_spl
| ~ sQ83_spl
| sQ42_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4342,f233,f254,f460,f890,f236]) ).
fof(f4349,definition,
( sQ472_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f4352,plain,
( sQ472_spl
| ~ sQ83_spl
| sQ42_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4343,f233,f254,f460,f890,f4349]) ).
fof(f4357,plain,
( sQ189_spl
| ~ sQ83_spl
| sQ42_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4345,f233,f254,f460,f890,f1865]) ).
fof(f4358,definition,
! [X0] :
( sQ474_spl
<=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
| X0 != xk ) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f4361,plain,
( sQ474_spl
| ~ sQ83_spl
| sQ42_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4346,f233,f254,f460,f890,f4358]) ).
fof(f4362,definition,
! [X0] :
( sQ475_spl
<=> ( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| X0 = xk ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f4365,plain,
( sQ475_spl
| sQ42_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4347,f233,f254,f460,f4362]) ).
fof(f4366,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f892,f177]) ).
fof(f4367,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f4366]) ).
fof(f4394,definition,
! [X0] :
( sQ477_spl
<=> ( sdtlseqdt0(xn,X0)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f4398,definition,
! [X0] :
( sQ478_spl
<=> ( ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f4405,definition,
! [X0] :
( sQ480_spl
<=> ( xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f4409,definition,
! [X0,X1] :
( sQ481_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f4413,definition,
! [X0,X1] :
( sQ482_spl
<=> ( ~ sdtlseqdt0(xk,X1)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f4417,definition,
! [X0] :
( sQ483_spl
<=> ( sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f4422,plain,
! [X0] :
( ~ sQ39_spl
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f413,f251]) ).
fof(f4423,plain,
( ~ sQ39_spl
| xp = xp
| ~ sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f413,f231]) ).
fof(f4424,plain,
! [X0] :
( ~ sQ39_spl
| xp = xp
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f413,f231]) ).
fof(f4426,plain,
! [X0] :
( ~ sQ39_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f413,f231]) ).
fof(f4427,plain,
! [X0] :
( ~ sQ39_spl
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f413,f219]) ).
fof(f4428,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f413,f219]) ).
fof(f4430,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f413,f219]) ).
fof(f4433,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f4422,f3367,f233,f409]) ).
fof(f4434,plain,
( ~ sQ39_spl
| sQ359_spl
| ~ sQ360_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4423,f233,f3346,f3342,f409]) ).
fof(f4435,plain,
( ~ sQ39_spl
| sQ359_spl
| sQ362_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4424,f233,f3372,f3342,f409]) ).
fof(f4437,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| sQ363_spl ),
inference(split_clause,[status(thm)],[f4426,f3377,f233,f409]) ).
fof(f4438,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f4427,f3381,f233,f409]) ).
fof(f4439,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f4428,f3385,f233,f409]) ).
fof(f4441,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f4430,f3390,f233,f409]) ).
fof(f4444,plain,
( sQ88_spl
| ~ sQ39_spl
| ~ isPrime0(xp) ),
inference(backward_demodulation,[status(thm)],[f410,f926]) ).
fof(f4451,plain,
( sQ88_spl
| ~ sQ39_spl
| ~ sQ358_spl ),
inference(split_clause,[status(thm)],[f4444,f3339,f409,f924]) ).
fof(f4453,plain,
( ~ sQ39_spl
| doDivides0(xr,xp) ),
inference(forward_demodulation,[status(thm)],[f410,f191]) ).
fof(f4454,plain,
( ~ sQ39_spl
| xr = xp
| xr = sz10
| ~ aNaturalNumber0(xr)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f4453,f161]) ).
fof(f4455,plain,
! [X0] :
( ~ sQ39_spl
| doDivides0(X0,xp)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4453,f147]) ).
fof(f4456,plain,
( ~ sQ39_spl
| sdtlseqdt0(xr,xp)
| xp = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f4453,f153]) ).
fof(f4457,plain,
( ~ sQ39_spl
| sQ355_spl
| sQ86_spl
| ~ sQ63_spl
| ~ sQ358_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4454,f233,f3339,f704,f912,f3311,f409]) ).
fof(f4458,definition,
! [X0] :
( sQ484_spl
<=> ( doDivides0(X0,xp)
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f4461,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ63_spl
| sQ484_spl ),
inference(split_clause,[status(thm)],[f4455,f4458,f704,f233,f409]) ).
fof(f4462,definition,
( sQ485_spl
<=> sdtlseqdt0(xr,xp) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f4465,plain,
( ~ sQ39_spl
| sQ485_spl
| sQ42_spl
| ~ sQ7_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f4456,f704,f233,f460,f4462,f409]) ).
fof(f4481,plain,
( ~ sQ65_spl
| xk != sz10
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f722,f160]) ).
fof(f4483,definition,
( sQ486_spl
<=> xk = sz10 ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f4486,plain,
( ~ sQ65_spl
| ~ sQ486_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4481,f236,f4483,f710]) ).
fof(f4539,plain,
( ~ sQ43_spl
| sdtlseqdt0(xp,xm) ),
inference(forward_demodulation,[status(thm)],[f464,f195]) ).
fof(f4540,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4539,f179]) ).
fof(f4541,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f4540]) ).
fof(f4570,plain,
( sQ3_spl
| ~ sdtlseqdt0(xm,xk)
| xm = xk
| xp = sz00
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f209,f122]) ).
fof(f4576,definition,
( sQ496_spl
<=> sdtlseqdt0(xm,xk) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f4579,plain,
( sQ3_spl
| ~ sQ496_spl
| sQ43_spl
| sQ42_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4570,f233,f269,f236,f460,f463,f4576,f207]) ).
fof(f4625,plain,
! [X0,X1] :
( ~ sQ27_spl
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f251]) ).
fof(f4627,plain,
! [X0,X1] :
( ~ sQ27_spl
| X0 = xp
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f231]) ).
fof(f4629,plain,
! [X0,X1] :
( ~ sQ27_spl
| xp = X1
| ~ sdtlseqdt0(xp,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f231]) ).
fof(f4631,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f219]) ).
fof(f4633,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sdtlseqdt0(xp,X2)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f219]) ).
fof(f4634,plain,
! [X0,X1] :
( ~ sQ27_spl
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f111]) ).
fof(f4635,plain,
! [X0] :
( ~ sQ27_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f348,f109]) ).
fof(f4636,definition,
! [X0,X1] :
( sQ501_spl
<=> ( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f4639,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ501_spl ),
inference(split_clause,[status(thm)],[f4625,f4636,f233,f347]) ).
fof(f4641,definition,
! [X0,X1] :
( sQ502_spl
<=> ( X0 = xp
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f4644,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ502_spl ),
inference(split_clause,[status(thm)],[f4627,f4641,f233,f347]) ).
fof(f4646,definition,
! [X0,X1] :
( sQ503_spl
<=> ( xp = X1
| ~ sdtlseqdt0(xp,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f4649,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ503_spl ),
inference(split_clause,[status(thm)],[f4629,f4646,f233,f347]) ).
fof(f4651,definition,
! [X0,X1,X2] :
( sQ504_spl
<=> ( ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f4654,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ504_spl ),
inference(split_clause,[status(thm)],[f4631,f4651,f233,f347]) ).
fof(f4656,definition,
! [X0,X1,X2] :
( sQ505_spl
<=> ( ~ sdtlseqdt0(xp,X2)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f4659,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f4633,f4656,f233,f347]) ).
fof(f4660,definition,
! [X0,X1] :
( sQ506_spl
<=> ( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f4663,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ506_spl ),
inference(split_clause,[status(thm)],[f4634,f4660,f233,f347]) ).
fof(f4664,definition,
! [X0] :
( sQ507_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f4667,plain,
( ~ sQ27_spl
| ~ sQ7_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f4635,f4664,f233,f347]) ).
fof(f4675,plain,
! [X0,X1] :
( ~ sQ30_spl
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f251]) ).
fof(f4677,plain,
! [X0,X1] :
( ~ sQ30_spl
| X0 = xp
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f231]) ).
fof(f4679,plain,
! [X0,X1] :
( ~ sQ30_spl
| xp = X1
| ~ sdtlseqdt0(xp,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f231]) ).
fof(f4681,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f219]) ).
fof(f4683,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| ~ sdtlseqdt0(xp,X2)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f219]) ).
fof(f4684,plain,
! [X0,X1] :
( ~ sQ30_spl
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f111]) ).
fof(f4685,plain,
! [X0] :
( ~ sQ30_spl
| xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f363,f109]) ).
fof(f4686,definition,
! [X0,X1] :
( sQ508_spl
<=> ( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f4689,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ508_spl ),
inference(split_clause,[status(thm)],[f4675,f4686,f233,f362]) ).
fof(f4691,definition,
! [X0,X1] :
( sQ509_spl
<=> ( X0 = xp
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f4694,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ509_spl ),
inference(split_clause,[status(thm)],[f4677,f4691,f233,f362]) ).
fof(f4696,definition,
! [X0,X1] :
( sQ510_spl
<=> ( xp = X1
| ~ sdtlseqdt0(xp,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f4699,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ510_spl ),
inference(split_clause,[status(thm)],[f4679,f4696,f233,f362]) ).
fof(f4701,definition,
! [X0,X1,X2] :
( sQ511_spl
<=> ( ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f4704,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ511_spl ),
inference(split_clause,[status(thm)],[f4681,f4701,f233,f362]) ).
fof(f4706,definition,
! [X0,X1,X2] :
( sQ512_spl
<=> ( ~ sdtlseqdt0(xp,X2)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f4709,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ512_spl ),
inference(split_clause,[status(thm)],[f4683,f4706,f233,f362]) ).
fof(f4710,definition,
! [X0,X1] :
( sQ513_spl
<=> ( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f4713,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ513_spl ),
inference(split_clause,[status(thm)],[f4684,f4710,f233,f362]) ).
fof(f4714,definition,
! [X0] :
( sQ514_spl
<=> ( xp = X0
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f4717,plain,
( ~ sQ30_spl
| ~ sQ7_spl
| sQ514_spl ),
inference(split_clause,[status(thm)],[f4685,f4714,f233,f362]) ).
fof(f4894,plain,
! [X0] :
( ~ sQ49_spl
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sK0_skl(sz00,X0) = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f517,f97]) ).
fof(f4895,definition,
! [X0] :
( sQ525_spl
<=> ( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| sK0_skl(sz00,X0) = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f4898,plain,
( ~ sQ49_spl
| ~ sQ33_spl
| sQ525_spl ),
inference(split_clause,[status(thm)],[f4894,f4895,f380,f509]) ).
fof(f4900,plain,
! [X0] :
( ~ sQ50_spl
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f518,f97]) ).
fof(f4901,definition,
! [X0] :
( sQ526_spl
<=> ( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f4904,plain,
( ~ sQ50_spl
| ~ sQ33_spl
| sQ526_spl ),
inference(split_clause,[status(thm)],[f4900,f4901,f380,f513]) ).
fof(f4952,plain,
! [X0] :
( sQ323_spl
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f3044,f251]) ).
fof(f4953,plain,
! [X0,X1] :
( sQ323_spl
| ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3044,f219]) ).
fof(f4954,plain,
( sQ323_spl
| sdtlseqdt0(xn,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f3044,f114]) ).
fof(f4955,plain,
! [X0] :
( sQ323_spl
| ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3044,f111]) ).
fof(f4956,definition,
! [X0] :
( sQ532_spl
<=> ( ~ sdtlseqdt0(xk,X0)
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f4959,plain,
( sQ323_spl
| ~ sQ8_spl
| sQ532_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4952,f286,f4956,f236,f3042]) ).
fof(f4960,definition,
! [X0,X1] :
( sQ533_spl
<=> ( ~ sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f4963,plain,
( sQ323_spl
| ~ sQ16_spl
| sQ533_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4953,f236,f4960,f286,f3042]) ).
fof(f4964,definition,
( sQ534_spl
<=> sdtlseqdt0(xn,xk) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f4965,plain,
( ~ sQ534_spl
| sdtlseqdt0(xn,xk) ),
inference(component_clause,[status(thm)],[f4964]) ).
fof(f4967,plain,
( sQ323_spl
| sQ534_spl
| ~ sQ8_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4954,f286,f236,f4964,f3042]) ).
fof(f4968,plain,
( sQ323_spl
| ~ sQ16_spl
| sQ478_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4955,f236,f4398,f286,f3042]) ).
fof(f4969,plain,
! [X0,X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X3,X2)
| X3 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(X0,sdtpldt0(X1,X3))
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f60]) ).
fof(f4972,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) = sz10
| sdtpldt0(X0,X2) = sz00
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sz10,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f4969,f127]) ).
fof(f4983,definition,
! [X0,X1,X2] :
( sQ535_spl
<=> ( sdtpldt0(X0,X2) = sz10
| sdtpldt0(X0,X2) = sz00
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sz10,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f4986,plain,
( sQ535_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4972,f314,f4983]) ).
fof(f4999,plain,
! [X0] :
( sQ329_spl
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f3080,f251]) ).
fof(f5000,plain,
! [X0,X1] :
( sQ329_spl
| ~ sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3080,f219]) ).
fof(f5001,plain,
( sQ329_spl
| sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f3080,f114]) ).
fof(f5002,plain,
! [X0] :
( sQ329_spl
| ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f3080,f111]) ).
fof(f5003,definition,
! [X0] :
( sQ536_spl
<=> ( ~ sdtlseqdt0(xk,X0)
| sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f5006,plain,
( sQ329_spl
| ~ sQ8_spl
| sQ536_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4999,f269,f5003,f236,f3078]) ).
fof(f5007,definition,
! [X0,X1] :
( sQ537_spl
<=> ( ~ sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f5010,plain,
( sQ329_spl
| ~ sQ13_spl
| sQ537_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5000,f236,f5007,f269,f3078]) ).
fof(f5011,plain,
( sQ329_spl
| sQ496_spl
| ~ sQ8_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5001,f269,f236,f4576,f3078]) ).
fof(f5012,definition,
! [X0] :
( sQ538_spl
<=> ( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f5015,plain,
( sQ329_spl
| ~ sQ13_spl
| sQ538_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5002,f236,f5012,f269,f3078]) ).
fof(f5022,plain,
( ~ sQ51_spl
| xk = sdtsldt0(sdtasdt0(xn,sz00),xp) ),
inference(backward_demodulation,[status(thm)],[f537,f184]) ).
fof(f5231,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ51_spl
| sdtasdt0(xn,sz00) != sdtasdt0(xp,xk) ),
inference(forward_demodulation,[status(thm)],[f537,f881]) ).
fof(f5235,plain,
! [X0] :
( sQ38_spl
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f408,f251]) ).
fof(f5236,plain,
! [X0,X1] :
( sQ38_spl
| ~ sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f408,f219]) ).
fof(f5240,definition,
! [X0] :
( sQ563_spl
<=> ( ~ sdtlseqdt0(xk,X0)
| sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f5243,plain,
( sQ38_spl
| ~ sQ8_spl
| sQ563_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5235,f233,f5240,f236,f406]) ).
fof(f5244,definition,
! [X0,X1] :
( sQ564_spl
<=> ( ~ sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f5247,plain,
( sQ38_spl
| ~ sQ7_spl
| sQ564_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5236,f236,f5244,f233,f406]) ).
fof(f5264,plain,
! [X0] :
( ~ sQ534_spl
| sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4965,f251]) ).
fof(f5266,plain,
! [X0] :
( ~ sQ534_spl
| xk = X0
| ~ sdtlseqdt0(xk,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4965,f231]) ).
fof(f5267,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4965,f219]) ).
fof(f5268,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ sdtlseqdt0(xk,X1)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4965,f219]) ).
fof(f5269,plain,
! [X0] :
( ~ sQ534_spl
| sdtlseqdt0(X0,xk)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4965,f111]) ).
fof(f5271,plain,
( ~ sQ534_spl
| ~ sQ16_spl
| ~ sQ8_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f5264,f4394,f236,f286,f4964]) ).
fof(f5273,plain,
( ~ sQ534_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ480_spl ),
inference(split_clause,[status(thm)],[f5266,f4405,f286,f236,f4964]) ).
fof(f5274,plain,
( ~ sQ534_spl
| ~ sQ16_spl
| ~ sQ8_spl
| sQ481_spl ),
inference(split_clause,[status(thm)],[f5267,f4409,f236,f286,f4964]) ).
fof(f5275,plain,
( ~ sQ534_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ482_spl ),
inference(split_clause,[status(thm)],[f5268,f4413,f286,f236,f4964]) ).
fof(f5276,plain,
( ~ sQ534_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ483_spl ),
inference(split_clause,[status(thm)],[f5269,f4417,f286,f236,f4964]) ).
fof(f5295,plain,
( ~ sQ233_spl
| xn != sz10
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2223,f160]) ).
fof(f5297,plain,
( ~ sQ233_spl
| ~ sQ130_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5295,f286,f1268,f2210]) ).
fof(f5338,definition,
( sQ569_spl
<=> sdtasdt0(xn,sz00) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f5339,plain,
( ~ sQ569_spl
| sdtasdt0(xn,sz00) = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f5338]) ).
fof(f5362,plain,
( ~ sQ569_spl
| sQ2_spl
| ~ sQ0_spl
| ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5339,f5231]) ).
fof(f5363,plain,
( ~ sQ569_spl
| sQ2_spl
| ~ sQ0_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f5362]) ).
fof(f5366,plain,
( ~ sQ51_spl
| sdtasdt0(xn,sz00) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xn,sz00))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,sz00))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f5022,f144]) ).
fof(f5372,plain,
( ~ sQ51_spl
| sQ569_spl
| ~ sQ103_spl
| sQ42_spl
| ~ sQ57_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5366,f233,f576,f460,f1080,f5338,f536]) ).
fof(f5388,plain,
( sQ0_spl
| ~ sQ51_spl
| sdtasdt0(xn,sz00) != sdtasdt0(xp,xm) ),
inference(forward_demodulation,[status(thm)],[f537,f200]) ).
fof(f5389,plain,
( sQ0_spl
| ~ sQ51_spl
| sdtasdt0(xn,sz00) != sdtasdt0(xp,sz00) ),
inference(forward_demodulation,[status(thm)],[f537,f5388]) ).
fof(f5392,plain,
( sQ103_spl
| ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1082,f1017]) ).
fof(f5393,plain,
( sQ103_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f5392]) ).
fof(f5649,plain,
! [X0,X1,X2] :
( ~ sQ395_spl
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f3673,f4969]) ).
fof(f5650,plain,
! [X0,X1] :
( ~ sQ395_spl
| sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f251]) ).
fof(f5652,plain,
! [X0,X1] :
( ~ sQ395_spl
| sz00 = X0
| ~ sdtlseqdt0(X1,sz00)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f231]) ).
fof(f5654,plain,
! [X0,X1] :
( ~ sQ395_spl
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f231]) ).
fof(f5656,plain,
! [X0,X1,X2] :
( ~ sQ395_spl
| ~ sdtlseqdt0(X2,sz00)
| ~ aNaturalNumber0(sz00)
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f219]) ).
fof(f5658,plain,
! [X0,X1,X2] :
( ~ sQ395_spl
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f219]) ).
fof(f5659,plain,
! [X0,X1] :
( ~ sQ395_spl
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f111]) ).
fof(f5660,plain,
! [X0] :
( ~ sQ395_spl
| X0 = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3673,f109]) ).
fof(f5661,definition,
! [X0,X1,X2] :
( sQ600_spl
<=> ( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f5664,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ600_spl ),
inference(split_clause,[status(thm)],[f5649,f5661,f380,f3667]) ).
fof(f5665,definition,
! [X0,X1] :
( sQ601_spl
<=> ( sdtlseqdt0(sz00,X1)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f5668,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ601_spl ),
inference(split_clause,[status(thm)],[f5650,f5665,f380,f3667]) ).
fof(f5670,definition,
! [X0,X1] :
( sQ602_spl
<=> ( sz00 = X0
| ~ sdtlseqdt0(X1,sz00)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f5673,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ602_spl ),
inference(split_clause,[status(thm)],[f5652,f5670,f380,f3667]) ).
fof(f5675,definition,
! [X0,X1] :
( sQ603_spl
<=> ( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f5678,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ603_spl ),
inference(split_clause,[status(thm)],[f5654,f5675,f380,f3667]) ).
fof(f5680,definition,
! [X0,X1,X2] :
( sQ604_spl
<=> ( ~ sdtlseqdt0(X2,sz00)
| sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f5683,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ604_spl ),
inference(split_clause,[status(thm)],[f5656,f5680,f380,f3667]) ).
fof(f5685,definition,
! [X0,X1,X2] :
( sQ605_spl
<=> ( ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ605_spl])],[split_symbol_definition]) ).
fof(f5688,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ605_spl ),
inference(split_clause,[status(thm)],[f5658,f5685,f380,f3667]) ).
fof(f5689,definition,
! [X0,X1] :
( sQ606_spl
<=> ( sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ606_spl])],[split_symbol_definition]) ).
fof(f5692,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ606_spl ),
inference(split_clause,[status(thm)],[f5659,f5689,f380,f3667]) ).
fof(f5693,definition,
! [X0] :
( sQ607_spl
<=> ( X0 = sz00
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f5696,plain,
( ~ sQ395_spl
| ~ sQ33_spl
| sQ607_spl ),
inference(split_clause,[status(thm)],[f5660,f5693,f380,f3667]) ).
fof(f5705,plain,
( sQ78_spl
| ~ sQ51_spl
| sdtasdt0(xn,sz00) != sz00 ),
inference(forward_demodulation,[status(thm)],[f537,f827]) ).
fof(f5706,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f5705,f78]) ).
fof(f5707,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5706,f286,f536,f825]) ).
fof(f5715,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| sdtasdt0(xn,sz00) = sz00 ),
inference(forward_demodulation,[status(thm)],[f537,f826]) ).
fof(f6127,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(X2,sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtpldt0(X2,sK0_skl(sdtmndt0(X1,X0),X2))) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f525]) ).
fof(f6129,plain,
! [X0,X1] :
( X0 = sz00
| ~ aNaturalNumber0(sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6127,f90]) ).
fof(f6130,plain,
! [X0,X1] :
( sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)) = sz00
| ~ aNaturalNumber0(sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6127,f91]) ).
fof(f6141,definition,
! [X0,X1] :
( sQ645_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f6144,plain,
( ~ sQ33_spl
| sQ645_spl ),
inference(split_clause,[status(thm)],[f6129,f6141,f380]) ).
fof(f6145,definition,
! [X0,X1] :
( sQ646_spl
<=> ( sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)) = sz00
| ~ aNaturalNumber0(sdtpldt0(X1,sK0_skl(sdtmndt0(sz00,X0),X1)))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f6148,plain,
( ~ sQ33_spl
| sQ646_spl ),
inference(split_clause,[status(thm)],[f6130,f6145,f380]) ).
fof(f6251,plain,
! [X0] :
( X0 = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f527,f90]) ).
fof(f6252,plain,
! [X0] :
( sdtmndt0(sz00,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f527,f91]) ).
fof(f6263,definition,
! [X0] :
( sQ650_spl
<=> ( X0 = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f6266,plain,
( ~ sQ33_spl
| sQ650_spl ),
inference(split_clause,[status(thm)],[f6251,f6263,f380]) ).
fof(f6267,definition,
! [X0] :
( sQ651_spl
<=> ( sdtmndt0(sz00,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(sz00,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f6270,plain,
( ~ sQ33_spl
| sQ651_spl ),
inference(split_clause,[status(thm)],[f6252,f6267,f380]) ).
fof(f6279,plain,
! [X0,X1,X2,X3] :
( ~ aNaturalNumber0(X3)
| sdtlseqdt0(X2,sdtmndt0(X1,X0))
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtpldt0(X2,X3)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f60]) ).
fof(f6295,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtmndt0(sdtpldt0(X0,X1),sz00))
| ~ aNaturalNumber0(sdtmndt0(sdtpldt0(X0,X1),sz00))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f6279,f69]) ).
fof(f6303,definition,
! [X0,X1] :
( sQ652_spl
<=> ( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtmndt0(sdtpldt0(X0,X1),sz00))
| ~ aNaturalNumber0(sdtmndt0(sdtpldt0(X0,X1),sz00))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f6306,plain,
( sQ652_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f6295,f380,f6303]) ).
fof(f6309,plain,
! [X0,X1,X2,X3] :
( sdtpldt0(X3,sdtmndt0(X1,X0)) = X2
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X0,sdtmndt0(X2,X3)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f525]) ).
fof(f6312,plain,
! [X0,X1,X2] :
( X2 = sz00
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtmndt0(sz00,X2)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6309,f90]) ).
fof(f6313,plain,
! [X0,X1,X2] :
( sdtmndt0(X1,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtmndt0(sz00,X2)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f6309,f91]) ).
fof(f6329,definition,
! [X0,X1,X2] :
( sQ653_spl
<=> ( X2 = sz00
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,sz00)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtmndt0(sz00,X2)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f6332,plain,
( ~ sQ33_spl
| sQ653_spl ),
inference(split_clause,[status(thm)],[f6312,f6329,f380]) ).
fof(f6333,definition,
! [X0,X1,X2] :
( sQ654_spl
<=> ( sdtmndt0(X1,X0) = sz00
| ~ aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,sz00)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,sdtmndt0(sz00,X2)) != X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f6336,plain,
( ~ sQ33_spl
| sQ654_spl ),
inference(split_clause,[status(thm)],[f6313,f6333,f380]) ).
fof(f6352,plain,
( sQ0_spl
| ~ sQ51_spl
| ~ sQ78_spl
| sz00 != sdtasdt0(xp,sz00) ),
inference(backward_demodulation,[status(thm)],[f5715,f5389]) ).
fof(f6480,plain,
( sQ0_spl
| ~ sQ51_spl
| ~ sQ78_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f6352,f78]) ).
fof(f6481,plain,
( sQ0_spl
| ~ sQ51_spl
| ~ sQ78_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6480,f233,f825,f536,f198]) ).
fof(f6482,plain,
$false,
inference(sat_refutation,[status(thm)],[f210,f239,f241,f283,f292,f296,f298,f304,f308,f323,f327,f334,f336,f338,f350,f359,f365,f374,f386,f396,f399,f405,f412,f427,f431,f445,f449,f466,f490,f512,f516,f618,f622,f642,f687,f691,f717,f719,f731,f742,f812,f824,f852,f853,f879,f915,f919,f927,f934,f938,f955,f959,f977,f1169,f1173,f1293,f1378,f1384,f1394,f1416,f1435,f1762,f1772,f1945,f1953,f1958,f2132,f2171,f2206,f2213,f2303,f2310,f2351,f2409,f2413,f2417,f2433,f2437,f2441,f2449,f2464,f2468,f2478,f2482,f2486,f2490,f2504,f2508,f2543,f2547,f2558,f2587,f2591,f2595,f2601,f2691,f2695,f2699,f2703,f2711,f2726,f2730,f2744,f2795,f2799,f2803,f2807,f2811,f2821,f2825,f2840,f2844,f2848,f2941,f3045,f3049,f3053,f3057,f3061,f3065,f3066,f3081,f3085,f3089,f3093,f3097,f3101,f3102,f3139,f3143,f3314,f3320,f3345,f3351,f3403,f3404,f3481,f3485,f3489,f3493,f3612,f3625,f3651,f3670,f3746,f3796,f3797,f3805,f3809,f3813,f3817,f3826,f3911,f3916,f3920,f3924,f3928,f3929,f3935,f3977,f4043,f4050,f4051,f4055,f4060,f4236,f4348,f4352,f4357,f4361,f4365,f4367,f4433,f4434,f4435,f4437,f4438,f4439,f4441,f4451,f4457,f4461,f4465,f4486,f4541,f4579,f4639,f4644,f4649,f4654,f4659,f4663,f4667,f4689,f4694,f4699,f4704,f4709,f4713,f4717,f4898,f4904,f4959,f4963,f4967,f4968,f4986,f5006,f5010,f5011,f5015,f5243,f5247,f5271,f5273,f5274,f5275,f5276,f5297,f5363,f5372,f5393,f5664,f5668,f5673,f5678,f5683,f5688,f5692,f5696,f5707,f6144,f6148,f6266,f6270,f6306,f6332,f6336,f6481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:36:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 7.10/1.34 % Refutation found
% 7.10/1.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.10/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.10/1.38 % Elapsed time: 1.008342 seconds
% 7.10/1.38 % CPU time: 7.463062 seconds
% 7.10/1.38 % Total memory used: 150.694 MB
% 7.10/1.38 % Net memory used: 145.864 MB
%------------------------------------------------------------------------------