%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:40:40 PM UTC 2026
% Result : Theorem 5.59s 1.30s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 217
% Syntax : Number of formulae : 792 ( 47 unt; 196 def)
% Number of atoms : 2731 ( 563 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 3385 (1446 ~;1601 |; 100 &)
% ( 200 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 197 ( 195 usr; 193 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 404 ( 389 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0) )
& sdtlseqdt0(W0,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& W0 = sdtsldt0(xm,xl) ) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0) )
& sdtlseqdt0(W0,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& W0 = sdtsldt0(xm,xl) ) )
=> doDivides0(xl,xn) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f41,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
sz10 != sz00,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f49,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f59,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f60,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f63,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f68,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(f69,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f71,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(f72,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)],[f71]) ).
fof(f73,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)],[f71]) ).
fof(f74,plain,
! [W0,W1] :
( ( W1 = sz00
& W0 = sz00 )
| sdtpldt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
! [X0,X1] :
( X1 = sz00
| sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f78,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,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(f80,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)],[f79]) ).
fof(f81,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))],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( aNaturalNumber0(sK0_skl(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0_skl(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f85,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(f86,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)],[f85]) ).
fof(f87,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)],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f100,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(f102,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)],[f100]) ).
fof(f103,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f104,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f105,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(f106,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)],[f105]) ).
fof(f107,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)],[f105]) ).
fof(f108,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)],[f105]) ).
fof(f109,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)],[f105]) ).
fof(f110,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f112,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [W0,W1] :
( sdtlseqdt0(W1,sdtasdt0(W1,W0))
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f114,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f119,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(f120,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)],[f119]) ).
fof(f121,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))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( aNaturalNumber0(sK1_skl(X1,X0))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sK1_skl(X1,X0))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,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(f126,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)],[f125]) ).
fof(f127,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)],[f126]) ).
fof(f128,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,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)],[f127]) ).
fof(f130,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)],[f127]) ).
fof(f131,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(f132,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [W0,W1,W2] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f134,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f136,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f137,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f138,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f139,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f140,plain,
( ~ doDivides0(xl,xn)
& ( ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0) )
& sdtlseqdt0(W0,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& W0 = sdtsldt0(xm,xl) )
| xl = sz00 ) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f141,plain,
( ~ doDivides0(xl,xn)
& ( ( xn = sdtasdt0(xl,sK4_skl)
& sdtpldt0(sdtasdt0(xl,sK2_skl),sdtasdt0(xl,sK4_skl)) = sdtpldt0(sdtasdt0(xl,sK2_skl),xn)
& sK4_skl = sdtmndt0(sK3_skl,sK2_skl)
& sdtlseqdt0(sK2_skl,sK3_skl)
& sK3_skl = sdtsldt0(sdtpldt0(xm,xn),xl)
& sK2_skl = sdtsldt0(xm,xl) )
| xl = sz00 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(W0,sK2_skl),skolemize(W1,sK3_skl),skolemize(W2,sK4_skl)],[f140]) ).
fof(f142,plain,
( sK2_skl = sdtsldt0(xm,xl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
( sK3_skl = sdtsldt0(sdtpldt0(xm,xn),xl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f144,plain,
( sdtlseqdt0(sK2_skl,sK3_skl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f145,plain,
( sK4_skl = sdtmndt0(sK3_skl,sK2_skl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f147,plain,
( xn = sdtasdt0(xl,sK4_skl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f148,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f149,definition,
( sQ0_spl
<=> xl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ0_spl
| xl = sz00 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ1_spl
<=> sK2_skl = sdtsldt0(xm,xl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ1_spl
| sK2_skl = sdtsldt0(xm,xl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f149,f152]) ).
fof(f156,definition,
( sQ2_spl
<=> sK3_skl = sdtsldt0(sdtpldt0(xm,xn),xl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ2_spl
| sK3_skl = sdtsldt0(sdtpldt0(xm,xn),xl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f143,f149,f156]) ).
fof(f160,definition,
( sQ3_spl
<=> sdtlseqdt0(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( ~ sQ3_spl
| sdtlseqdt0(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f144,f149,f160]) ).
fof(f164,definition,
( sQ4_spl
<=> sK4_skl = sdtmndt0(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ4_spl
| sK4_skl = sdtmndt0(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f145,f149,f164]) ).
fof(f172,definition,
( sQ6_spl
<=> xn = sdtasdt0(xl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ6_spl
| xn = sdtasdt0(xl,sK4_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f147,f149,f172]) ).
fof(f176,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f84]) ).
fof(f177,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f183,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f128]) ).
fof(f184,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f129]) ).
fof(f185,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X0 = sz00
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f186,plain,
( ~ sQ0_spl
| ~ doDivides0(sz00,xn) ),
inference(forward_demodulation,[status(thm)],[f150,f148]) ).
fof(f189,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[f53,f137]) ).
fof(f191,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[f53,f136]) ).
fof(f192,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(resolution,[status(thm)],[f53,f41]) ).
fof(f194,definition,
( sQ7_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ7_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,definition,
( sQ8_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ8_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f202,definition,
( sQ9_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ9_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f208,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[f54,f137]) ).
fof(f210,plain,
xm = sdtpldt0(sz00,xm),
inference(resolution,[status(thm)],[f54,f136]) ).
fof(f217,plain,
! [X0] :
( sdtpldt0(X0,xn) = sdtpldt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f49,f137]) ).
fof(f222,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f42,f54]) ).
fof(f223,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[f42,f53]) ).
fof(f227,definition,
( sQ10_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ10_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f233,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(resolution,[status(thm)],[f60,f42]) ).
fof(f235,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[f60,f137]) ).
fof(f237,plain,
sdtasdt0(xm,sz10) = xm,
inference(resolution,[status(thm)],[f60,f136]) ).
fof(f238,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(resolution,[status(thm)],[f60,f41]) ).
fof(f249,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[status(thm)],[f61,f137]) ).
fof(f252,plain,
sz00 = sdtasdt0(sz10,sz00),
inference(resolution,[status(thm)],[f61,f41]) ).
fof(f261,plain,
sdtasdt0(xn,sz00) = sz00,
inference(resolution,[status(thm)],[f63,f137]) ).
fof(f264,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(resolution,[status(thm)],[f63,f41]) ).
fof(f317,plain,
sz00 = sdtasdt0(sz00,xn),
inference(resolution,[status(thm)],[f64,f137]) ).
fof(f344,plain,
( ~ sQ0_spl
| doDivides0(sz00,sdtpldt0(xm,xn)) ),
inference(forward_demodulation,[status(thm)],[f150,f139]) ).
fof(f345,plain,
sdtpldt0(sz10,xn) = sdtpldt0(xn,sz10),
inference(resolution,[status(thm)],[f217,f42]) ).
fof(f349,plain,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(resolution,[status(thm)],[f217,f136]) ).
fof(f352,plain,
( aNaturalNumber0(sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f345,f45]) ).
fof(f353,definition,
( sQ11_spl
<=> aNaturalNumber0(sdtpldt0(sz10,xn)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ11_spl
| aNaturalNumber0(sdtpldt0(sz10,xn)) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f352,f194,f227,f353]) ).
fof(f378,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f349,f45]) ).
fof(f379,definition,
( sQ12_spl
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( ~ sQ12_spl
| aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f378,f194,f202,f379]) ).
fof(f383,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f137]) ).
fof(f384,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f385,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f42]) ).
fof(f386,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f136]) ).
fof(f388,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f460,plain,
! [X0] :
( sz10 = sz10
| sdtpldt0(X0,sz10) != sdtpldt0(X0,sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f42]) ).
fof(f464,plain,
! [X0] :
( xn = xn
| sdtpldt0(X0,xn) != sdtpldt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f137]) ).
fof(f466,plain,
! [X0] :
( ~ sQ12_spl
| sdtpldt0(xm,xn) = sdtpldt0(xm,xn)
| sdtpldt0(X0,sdtpldt0(xm,xn)) != sdtpldt0(X0,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f380]) ).
fof(f468,plain,
! [X0] :
( ~ sQ11_spl
| sdtpldt0(sz10,xn) = sdtpldt0(sz10,xn)
| sdtpldt0(X0,sdtpldt0(sz10,xn)) != sdtpldt0(X0,sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f354]) ).
fof(f472,plain,
! [X0] :
( xm = xm
| sdtpldt0(X0,xm) != sdtpldt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f136]) ).
fof(f474,plain,
! [X0] :
( sz00 = sz00
| sdtpldt0(X0,sz00) != sdtpldt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f41]) ).
fof(f484,definition,
! [X0] :
( sQ13_spl
<=> ( sdtpldt0(X0,sz10) != sdtpldt0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f485,plain,
! [X0] :
( ~ sQ13_spl
| sdtpldt0(X0,sz10) != sdtpldt0(X0,sz10)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,definition,
( sQ14_spl
<=> sz10 = sz10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f460,f484,f487]) ).
fof(f491,definition,
! [X0] :
( sQ15_spl
<=> ( sdtpldt0(X0,xn) != sdtpldt0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f492,plain,
! [X0] :
( ~ sQ15_spl
| sdtpldt0(X0,xn) != sdtpldt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
( sQ16_spl
<=> xn = xn ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f464,f491,f494]) ).
fof(f498,definition,
! [X0] :
( sQ17_spl
<=> ( sdtpldt0(X0,sdtpldt0(xm,xn)) != sdtpldt0(X0,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f499,plain,
! [X0] :
( ~ sQ17_spl
| sdtpldt0(X0,sdtpldt0(xm,xn)) != sdtpldt0(X0,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ18_spl
<=> sdtpldt0(xm,xn) = sdtpldt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ12_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f466,f498,f501,f379]) ).
fof(f505,definition,
! [X0] :
( sQ19_spl
<=> ( sdtpldt0(X0,sdtpldt0(sz10,xn)) != sdtpldt0(X0,sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f506,plain,
! [X0] :
( ~ sQ19_spl
| sdtpldt0(X0,sdtpldt0(sz10,xn)) != sdtpldt0(X0,sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,definition,
( sQ20_spl
<=> sdtpldt0(sz10,xn) = sdtpldt0(sz10,xn) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( ~ sQ11_spl
| sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f468,f505,f508,f353]) ).
fof(f512,definition,
! [X0] :
( sQ21_spl
<=> ( sdtpldt0(X0,xm) != sdtpldt0(X0,xm)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f513,plain,
! [X0] :
( ~ sQ21_spl
| sdtpldt0(X0,xm) != sdtpldt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,definition,
( sQ22_spl
<=> xm = xm ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f472,f512,f515]) ).
fof(f519,definition,
! [X0] :
( sQ23_spl
<=> ( sdtpldt0(X0,sz00) != sdtpldt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f520,plain,
! [X0] :
( ~ sQ23_spl
| sdtpldt0(X0,sz00) != sdtpldt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ24_spl
<=> sz00 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f474,f519,f522]) ).
fof(f526,plain,
! [X0] :
( ~ sQ17_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f499]) ).
fof(f527,plain,
! [X0] :
( ~ sQ19_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f506]) ).
fof(f528,plain,
! [X0] :
( ~ sQ23_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f520]) ).
fof(f529,plain,
! [X0] :
( ~ sQ21_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f513]) ).
fof(f530,plain,
! [X0] :
( ~ sQ15_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f492]) ).
fof(f531,plain,
! [X0] :
( ~ sQ13_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f485]) ).
fof(f532,plain,
( ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f526]) ).
fof(f538,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f539,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f527]) ).
fof(f540,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f531]) ).
fof(f542,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f543,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f528]) ).
fof(f544,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f530]) ).
fof(f546,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f529]) ).
fof(f548,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f597,definition,
( sQ33_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( ~ sQ33_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f599,plain,
( sQ33_spl
| xm != sz00 ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f626,plain,
! [X0] :
( sz10 = sz00
| X0 = sz00
| sdtasdt0(X0,sz10) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f42,f78]) ).
fof(f627,plain,
! [X0] :
( sz10 = sz00
| sdtpldt0(X0,sz10) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f42,f76]) ).
fof(f631,definition,
! [X0] :
( sQ39_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sz10) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f634,definition,
( sQ40_spl
<=> sz10 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( ~ sQ40_spl
| sz10 = sz00 ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,plain,
( sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f626,f631,f634]) ).
fof(f638,definition,
! [X0] :
( sQ41_spl
<=> ( sdtpldt0(X0,sz10) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( sQ40_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f627,f638,f634]) ).
fof(f642,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f43]) ).
fof(f643,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f647,plain,
( ~ sQ0_spl
| ~ sQ33_spl
| doDivides0(sz00,sdtpldt0(sz00,xn)) ),
inference(backward_demodulation,[status(thm)],[f598,f344]) ).
fof(f658,plain,
( ~ sQ0_spl
| ~ sQ33_spl
| doDivides0(sz00,xn) ),
inference(forward_demodulation,[status(thm)],[f208,f647]) ).
fof(f659,plain,
( ~ sQ0_spl
| ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f186]) ).
fof(f660,plain,
( ~ sQ0_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f685,plain,
xl = sdtpldt0(sz00,xl),
inference(resolution,[status(thm)],[f135,f54]) ).
fof(f704,plain,
( ~ sQ0_spl
| doDivides0(sz00,xm) ),
inference(forward_demodulation,[status(thm)],[f150,f138]) ).
fof(f723,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(sz10,sdtpldt0(sz10,sz00))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f223,f176]) ).
fof(f724,plain,
( ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sz00,sdtpldt0(sz00,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f222,f176]) ).
fof(f725,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(sz00,sdtpldt0(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f192,f176]) ).
fof(f726,definition,
( sQ44_spl
<=> sdtlseqdt0(sz10,sdtpldt0(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( ~ sQ44_spl
| sdtlseqdt0(sz10,sdtpldt0(sz10,sz00)) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( ~ sQ8_spl
| sQ44_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f723,f227,f726,f197]) ).
fof(f730,definition,
( sQ45_spl
<=> sdtlseqdt0(sz00,sdtpldt0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( ~ sQ45_spl
| sdtlseqdt0(sz00,sdtpldt0(sz00,sz10)) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f733,plain,
( sQ45_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f724,f197,f227,f730]) ).
fof(f734,definition,
( sQ46_spl
<=> sdtlseqdt0(sz00,sdtpldt0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f735,plain,
( ~ sQ46_spl
| sdtlseqdt0(sz00,sdtpldt0(sz00,sz00)) ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f737,plain,
( sQ46_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f725,f197,f734]) ).
fof(f738,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f41]) ).
fof(f739,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f740,plain,
( ~ sQ44_spl
| sdtlseqdt0(sz10,sz10) ),
inference(forward_demodulation,[status(thm)],[f223,f727]) ).
fof(f741,plain,
( ~ sQ45_spl
| sdtlseqdt0(sz00,sz10) ),
inference(forward_demodulation,[status(thm)],[f222,f731]) ).
fof(f742,plain,
( ~ sQ46_spl
| sdtlseqdt0(sz00,sz00) ),
inference(forward_demodulation,[status(thm)],[f192,f735]) ).
fof(f743,plain,
( ~ sQ44_spl
| sdtpldt0(sz10,sK0_skl(sz10,sz10)) = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f740,f83]) ).
fof(f744,plain,
( ~ sQ44_spl
| aNaturalNumber0(sK0_skl(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f740,f82]) ).
fof(f745,definition,
( sQ47_spl
<=> sdtpldt0(sz10,sK0_skl(sz10,sz10)) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( ~ sQ44_spl
| sQ47_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f743,f227,f745,f726]) ).
fof(f749,definition,
( sQ48_spl
<=> aNaturalNumber0(sK0_skl(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ44_spl
| sQ48_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f744,f227,f749,f726]) ).
fof(f753,plain,
( ~ sQ45_spl
| sdtpldt0(sz00,sK0_skl(sz10,sz00)) = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f741,f83]) ).
fof(f754,plain,
( ~ sQ45_spl
| aNaturalNumber0(sK0_skl(sz10,sz00))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f741,f82]) ).
fof(f755,definition,
( sQ49_spl
<=> sdtpldt0(sz00,sK0_skl(sz10,sz00)) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( ~ sQ45_spl
| sQ49_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f753,f197,f227,f755,f730]) ).
fof(f759,definition,
( sQ50_spl
<=> aNaturalNumber0(sK0_skl(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f762,plain,
( ~ sQ45_spl
| sQ50_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f754,f197,f227,f759,f730]) ).
fof(f763,plain,
( ~ sQ45_spl
| aNaturalNumber0(sdtmndt0(sz10,sz00))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f177,f741]) ).
fof(f764,plain,
( ~ sQ44_spl
| aNaturalNumber0(sdtmndt0(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f177,f740]) ).
fof(f766,definition,
( sQ51_spl
<=> aNaturalNumber0(sdtmndt0(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f769,plain,
( ~ sQ45_spl
| sQ51_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f763,f197,f227,f766,f730]) ).
fof(f770,definition,
( sQ52_spl
<=> aNaturalNumber0(sdtmndt0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f773,plain,
( ~ sQ44_spl
| sQ52_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f764,f227,f770,f726]) ).
fof(f775,plain,
( ~ sQ46_spl
| aNaturalNumber0(sdtmndt0(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f742,f177]) ).
fof(f776,plain,
( ~ sQ46_spl
| sdtpldt0(sz00,sK0_skl(sz00,sz00)) = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f742,f83]) ).
fof(f777,plain,
( ~ sQ46_spl
| aNaturalNumber0(sK0_skl(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f742,f82]) ).
fof(f778,definition,
( sQ53_spl
<=> aNaturalNumber0(sdtmndt0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f781,plain,
( ~ sQ46_spl
| sQ53_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f775,f197,f778,f734]) ).
fof(f782,definition,
( sQ54_spl
<=> sdtpldt0(sz00,sK0_skl(sz00,sz00)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ46_spl
| sQ54_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f776,f197,f782,f734]) ).
fof(f786,definition,
( sQ55_spl
<=> aNaturalNumber0(sK0_skl(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f789,plain,
( ~ sQ46_spl
| sQ55_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f777,f197,f786,f734]) ).
fof(f790,plain,
( ~ sQ12_spl
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f380,f176]) ).
fof(f796,definition,
( sQ56_spl
<=> sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( ~ sQ12_spl
| ~ sQ7_spl
| sQ56_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f790,f202,f796,f194,f379]) ).
fof(f802,plain,
( ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz00,sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f210,f176]) ).
fof(f803,definition,
( sQ57_spl
<=> sdtlseqdt0(sz00,sdtpldt0(sz00,xm)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f804,plain,
( ~ sQ57_spl
| sdtlseqdt0(sz00,sdtpldt0(sz00,xm)) ),
inference(component_clause,[status(thm)],[f803]) ).
fof(f806,plain,
( sQ57_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f802,f197,f202,f803]) ).
fof(f807,plain,
( ~ sQ57_spl
| sdtlseqdt0(sz00,xm) ),
inference(forward_demodulation,[status(thm)],[f210,f804]) ).
fof(f808,plain,
( ~ sQ57_spl
| aNaturalNumber0(sdtmndt0(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f807,f177]) ).
fof(f809,plain,
( ~ sQ57_spl
| sdtpldt0(sz00,sK0_skl(xm,sz00)) = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f807,f83]) ).
fof(f810,plain,
( ~ sQ57_spl
| aNaturalNumber0(sK0_skl(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f807,f82]) ).
fof(f811,definition,
( sQ58_spl
<=> aNaturalNumber0(sdtmndt0(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( ~ sQ57_spl
| sQ58_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f808,f197,f202,f811,f803]) ).
fof(f815,definition,
( sQ59_spl
<=> sdtpldt0(sz00,sK0_skl(xm,sz00)) = xm ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( ~ sQ57_spl
| sQ59_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f809,f197,f202,f815,f803]) ).
fof(f819,definition,
( sQ60_spl
<=> aNaturalNumber0(sK0_skl(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( ~ sQ57_spl
| sQ60_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f810,f197,f202,f819,f803]) ).
fof(f823,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(xm,sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f191,f176]) ).
fof(f824,definition,
( sQ61_spl
<=> sdtlseqdt0(xm,sdtpldt0(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ61_spl
| sdtlseqdt0(xm,sdtpldt0(xm,sz00)) ),
inference(component_clause,[status(thm)],[f824]) ).
fof(f827,plain,
( ~ sQ8_spl
| sQ61_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f823,f202,f824,f197]) ).
fof(f828,plain,
( ~ sQ61_spl
| sdtlseqdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f191,f825]) ).
fof(f829,plain,
( ~ sQ61_spl
| aNaturalNumber0(sdtmndt0(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f828,f177]) ).
fof(f830,plain,
( ~ sQ61_spl
| sdtpldt0(xm,sK0_skl(xm,xm)) = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f828,f83]) ).
fof(f831,plain,
( ~ sQ61_spl
| aNaturalNumber0(sK0_skl(xm,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f828,f82]) ).
fof(f832,definition,
( sQ62_spl
<=> aNaturalNumber0(sdtmndt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( ~ sQ61_spl
| sQ62_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f829,f202,f832,f824]) ).
fof(f836,definition,
( sQ63_spl
<=> sdtpldt0(xm,sK0_skl(xm,xm)) = xm ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( ~ sQ61_spl
| sQ63_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f830,f202,f836,f824]) ).
fof(f840,definition,
( sQ64_spl
<=> aNaturalNumber0(sK0_skl(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( ~ sQ61_spl
| sQ64_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f831,f202,f840,f824]) ).
fof(f864,plain,
( ~ sQ11_spl
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(sz10,sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f354,f176]) ).
fof(f872,definition,
( sQ65_spl
<=> sdtlseqdt0(sz10,sdtpldt0(sz10,xn)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f875,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| sQ65_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f864,f227,f872,f194,f353]) ).
fof(f878,plain,
( ~ aNaturalNumber0(xn)
| sdtlseqdt0(sz00,sdtpldt0(sz00,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f208,f176]) ).
fof(f879,definition,
( sQ66_spl
<=> sdtlseqdt0(sz00,sdtpldt0(sz00,xn)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f880,plain,
( ~ sQ66_spl
| sdtlseqdt0(sz00,sdtpldt0(sz00,xn)) ),
inference(component_clause,[status(thm)],[f879]) ).
fof(f882,plain,
( sQ66_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f878,f197,f194,f879]) ).
fof(f883,plain,
( ~ sQ66_spl
| sdtlseqdt0(sz00,xn) ),
inference(forward_demodulation,[status(thm)],[f208,f880]) ).
fof(f884,plain,
( ~ sQ66_spl
| aNaturalNumber0(sdtmndt0(xn,sz00))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f883,f177]) ).
fof(f885,plain,
( ~ sQ66_spl
| sdtpldt0(sz00,sK0_skl(xn,sz00)) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f883,f83]) ).
fof(f886,plain,
( ~ sQ66_spl
| aNaturalNumber0(sK0_skl(xn,sz00))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f883,f82]) ).
fof(f887,definition,
( sQ67_spl
<=> aNaturalNumber0(sdtmndt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f888,plain,
( ~ sQ67_spl
| aNaturalNumber0(sdtmndt0(xn,sz00)) ),
inference(component_clause,[status(thm)],[f887]) ).
fof(f890,plain,
( ~ sQ66_spl
| sQ67_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f884,f197,f194,f887,f879]) ).
fof(f891,definition,
( sQ68_spl
<=> sdtpldt0(sz00,sK0_skl(xn,sz00)) = xn ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f894,plain,
( ~ sQ66_spl
| sQ68_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f885,f197,f194,f891,f879]) ).
fof(f895,definition,
( sQ69_spl
<=> aNaturalNumber0(sK0_skl(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( ~ sQ69_spl
| aNaturalNumber0(sK0_skl(xn,sz00)) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f898,plain,
( ~ sQ66_spl
| sQ69_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f886,f197,f194,f895,f879]) ).
fof(f899,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(xn,sdtpldt0(xn,sz00))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f189,f176]) ).
fof(f900,definition,
( sQ70_spl
<=> sdtlseqdt0(xn,sdtpldt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f901,plain,
( ~ sQ70_spl
| sdtlseqdt0(xn,sdtpldt0(xn,sz00)) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,plain,
( ~ sQ8_spl
| sQ70_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f899,f194,f900,f197]) ).
fof(f904,plain,
( ~ sQ70_spl
| sdtlseqdt0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f189,f901]) ).
fof(f922,plain,
( ~ sQ70_spl
| aNaturalNumber0(sdtmndt0(xn,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f904,f177]) ).
fof(f923,plain,
( ~ sQ70_spl
| sdtpldt0(xn,sK0_skl(xn,xn)) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f904,f83]) ).
fof(f924,plain,
( ~ sQ70_spl
| aNaturalNumber0(sK0_skl(xn,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f904,f82]) ).
fof(f925,definition,
( sQ71_spl
<=> aNaturalNumber0(sdtmndt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( ~ sQ71_spl
| aNaturalNumber0(sdtmndt0(xn,xn)) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,plain,
( ~ sQ70_spl
| sQ71_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f922,f194,f925,f900]) ).
fof(f929,definition,
( sQ72_spl
<=> sdtpldt0(xn,sK0_skl(xn,xn)) = xn ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ70_spl
| sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f923,f194,f929,f900]) ).
fof(f933,definition,
( sQ73_spl
<=> aNaturalNumber0(sK0_skl(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f936,plain,
( ~ sQ70_spl
| sQ73_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f924,f194,f933,f900]) ).
fof(f1188,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(sdtpldt0(X0,sz00),sdtpldt0(X0,sz10))
| ~ aNaturalNumber0(X0)
| sz00 = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f102,f741]) ).
fof(f1213,definition,
! [X0] :
( sQ109_spl
<=> ( sdtlseqdt0(sdtpldt0(X0,sz00),sdtpldt0(X0,sz10))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
( ~ sQ45_spl
| sQ109_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1188,f197,f227,f634,f1213,f730]) ).
fof(f1232,plain,
! [X0] :
( ~ sQ45_spl
| sdtpldt0(sz00,X0) != sdtpldt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| sz00 = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f103,f741]) ).
fof(f1257,definition,
! [X0] :
( sQ116_spl
<=> ( sdtpldt0(sz00,X0) != sdtpldt0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1260,plain,
( ~ sQ45_spl
| sQ116_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1232,f197,f227,f634,f1257,f730]) ).
fof(f1320,plain,
( ~ sQ3_spl
| aNaturalNumber0(sdtmndt0(sK3_skl,sK2_skl))
| ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(sK2_skl) ),
inference(resolution,[status(thm)],[f161,f177]) ).
fof(f1323,definition,
( sQ118_spl
<=> aNaturalNumber0(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1325,plain,
( sQ118_spl
| ~ aNaturalNumber0(sK2_skl) ),
inference(component_clause,[status(thm)],[f1323]) ).
fof(f1326,definition,
( sQ119_spl
<=> aNaturalNumber0(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1328,plain,
( sQ119_spl
| ~ aNaturalNumber0(sK3_skl) ),
inference(component_clause,[status(thm)],[f1326]) ).
fof(f1340,definition,
( sQ123_spl
<=> aNaturalNumber0(sdtmndt0(sK3_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1341,plain,
( ~ sQ123_spl
| aNaturalNumber0(sdtmndt0(sK3_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f1340]) ).
fof(f1343,plain,
( ~ sQ3_spl
| sQ123_spl
| ~ sQ119_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f1320,f1323,f1326,f1340,f160]) ).
fof(f1372,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(sz10,X0))
| ~ aNaturalNumber0(X0)
| sz00 = sz10
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f104,f741]) ).
fof(f1385,definition,
! [X0] :
( sQ128_spl
<=> ( sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(sz10,X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1388,plain,
( ~ sQ45_spl
| sQ128_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1372,f197,f227,f634,f1385,f730]) ).
fof(f1397,plain,
! [X0] :
( ~ sQ45_spl
| sdtasdt0(X0,sz00) != sdtasdt0(X0,sz10)
| sz00 = sz10
| X0 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f106,f741]) ).
fof(f1410,definition,
! [X0] :
( sQ132_spl
<=> ( sdtasdt0(X0,sz00) != sdtasdt0(X0,sz10)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1413,plain,
( ~ sQ45_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1397,f1410,f197,f227,f634,f730]) ).
fof(f1423,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10))
| sz00 = sz10
| X0 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f107,f741]) ).
fof(f1436,definition,
! [X0] :
( sQ136_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1439,plain,
( ~ sQ45_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1423,f1436,f197,f227,f634,f730]) ).
fof(f1546,plain,
! [X0] :
( ~ sQ45_spl
| sdtasdt0(sz00,X0) != sdtasdt0(sz10,X0)
| sz00 = sz10
| X0 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f108,f741]) ).
fof(f1555,definition,
! [X0] :
( sQ148_spl
<=> ( sdtasdt0(sz00,X0) != sdtasdt0(sz10,X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1558,plain,
( ~ sQ45_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1546,f1555,f197,f227,f634,f730]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ45_spl
| sdtlseqdt0(sdtasdt0(sz00,X0),sdtasdt0(sz10,X0))
| sz00 = sz10
| X0 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f109,f741]) ).
fof(f1576,definition,
! [X0] :
( sQ151_spl
<=> ( sdtlseqdt0(sdtasdt0(sz00,X0),sdtasdt0(sz10,X0))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1579,plain,
( ~ sQ45_spl
| sQ40_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1567,f1576,f197,f227,f634,f730]) ).
fof(f1769,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(sz10,X1),sdtasdt0(X0,X1))
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f109]) ).
fof(f1770,plain,
! [X0,X1] :
( sdtasdt0(sz10,X1) != sdtasdt0(X0,X1)
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f108]) ).
fof(f1771,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,X0))
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f107]) ).
fof(f1772,plain,
! [X0,X1] :
( sdtasdt0(X1,sz10) != sdtasdt0(X1,X0)
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f106]) ).
fof(f1773,plain,
! [X0,X1] :
( sdtlseqdt0(sdtpldt0(sz10,X1),sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f104]) ).
fof(f1774,plain,
! [X0,X1] :
( sdtpldt0(sz10,X1) != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f103]) ).
fof(f1775,plain,
! [X0,X1] :
( sdtlseqdt0(sdtpldt0(X1,sz10),sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f102]) ).
fof(f1776,plain,
! [X0] :
( aNaturalNumber0(sdtmndt0(X0,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f177]) ).
fof(f1777,plain,
! [X0] :
( sdtpldt0(sz10,sK0_skl(X0,sz10)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f83]) ).
fof(f1778,plain,
! [X0] :
( aNaturalNumber0(sK0_skl(X0,sz10))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f112,f82]) ).
fof(f1779,definition,
! [X0,X1] :
( sQ169_spl
<=> ( sdtlseqdt0(sdtasdt0(sz10,X1),sdtasdt0(X0,X1))
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1782,plain,
( ~ sQ10_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f1769,f1779,f227]) ).
fof(f1783,definition,
! [X0,X1] :
( sQ170_spl
<=> ( sdtasdt0(sz10,X1) != sdtasdt0(X0,X1)
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1786,plain,
( ~ sQ10_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1770,f1783,f227]) ).
fof(f1787,definition,
! [X0,X1] :
( sQ171_spl
<=> ( sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,X0))
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( ~ sQ10_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1771,f1787,f227]) ).
fof(f1791,definition,
! [X0,X1] :
( sQ172_spl
<=> ( sdtasdt0(X1,sz10) != sdtasdt0(X1,X0)
| sz10 = X0
| X1 = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1794,plain,
( ~ sQ10_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f1772,f1791,f227]) ).
fof(f1795,definition,
! [X0,X1] :
( sQ173_spl
<=> ( sdtlseqdt0(sdtpldt0(sz10,X1),sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1798,plain,
( ~ sQ10_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f1773,f1795,f227]) ).
fof(f1799,definition,
! [X0,X1] :
( sQ174_spl
<=> ( sdtpldt0(sz10,X1) != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1802,plain,
( ~ sQ10_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f1774,f1799,f227]) ).
fof(f1803,definition,
! [X0,X1] :
( sQ175_spl
<=> ( sdtlseqdt0(sdtpldt0(X1,sz10),sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X1)
| sz10 = X0
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1806,plain,
( ~ sQ10_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f1775,f1803,f227]) ).
fof(f1807,definition,
! [X0] :
( sQ176_spl
<=> ( aNaturalNumber0(sdtmndt0(X0,sz10))
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1810,plain,
( ~ sQ10_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f1776,f1807,f227]) ).
fof(f1811,definition,
! [X0] :
( sQ177_spl
<=> ( sdtpldt0(sz10,sK0_skl(X0,sz10)) = X0
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1814,plain,
( ~ sQ10_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f1777,f1811,f227]) ).
fof(f1815,definition,
! [X0] :
( sQ178_spl
<=> ( aNaturalNumber0(sK0_skl(X0,sz10))
| ~ aNaturalNumber0(X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1818,plain,
( ~ sQ10_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1778,f1815,f227]) ).
fof(f1943,plain,
( ~ sQ6_spl
| ~ aNaturalNumber0(sK4_skl)
| doDivides0(xl,sdtasdt0(xl,sK4_skl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f173,f182]) ).
fof(f1944,plain,
( ~ aNaturalNumber0(sz00)
| doDivides0(sz00,sdtasdt0(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f264,f182]) ).
fof(f1945,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(sz00,sdtasdt0(sz00,sz10))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f238,f182]) ).
fof(f1946,plain,
( ~ aNaturalNumber0(sz00)
| doDivides0(sz10,sdtasdt0(sz10,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f252,f182]) ).
fof(f1947,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(sz10,sdtasdt0(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f233,f182]) ).
fof(f1948,definition,
( sQ191_spl
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1950,plain,
( sQ191_spl
| ~ aNaturalNumber0(xl) ),
inference(component_clause,[status(thm)],[f1948]) ).
fof(f1951,definition,
( sQ192_spl
<=> doDivides0(xl,sdtasdt0(xl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f1952,plain,
( ~ sQ192_spl
| doDivides0(xl,sdtasdt0(xl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1954,definition,
( sQ193_spl
<=> aNaturalNumber0(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1956,plain,
( sQ193_spl
| ~ aNaturalNumber0(sK4_skl) ),
inference(component_clause,[status(thm)],[f1954]) ).
fof(f1957,plain,
( ~ sQ6_spl
| ~ sQ193_spl
| sQ192_spl
| ~ sQ7_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f1943,f1948,f194,f1951,f1954,f172]) ).
fof(f1958,definition,
( sQ194_spl
<=> doDivides0(sz00,sdtasdt0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1961,plain,
( sQ194_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1944,f197,f1958]) ).
fof(f1962,definition,
( sQ195_spl
<=> doDivides0(sz00,sdtasdt0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1963,plain,
( ~ sQ195_spl
| doDivides0(sz00,sdtasdt0(sz00,sz10)) ),
inference(component_clause,[status(thm)],[f1962]) ).
fof(f1965,plain,
( ~ sQ10_spl
| sQ195_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1945,f197,f1962,f227]) ).
fof(f1966,definition,
( sQ196_spl
<=> doDivides0(sz10,sdtasdt0(sz10,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f1967,plain,
( ~ sQ196_spl
| doDivides0(sz10,sdtasdt0(sz10,sz00)) ),
inference(component_clause,[status(thm)],[f1966]) ).
fof(f1969,plain,
( sQ196_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1946,f227,f197,f1966]) ).
fof(f1970,definition,
( sQ197_spl
<=> doDivides0(sz10,sdtasdt0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1971,plain,
( ~ sQ197_spl
| doDivides0(sz10,sdtasdt0(sz10,sz10)) ),
inference(component_clause,[status(thm)],[f1970]) ).
fof(f1973,plain,
( sQ197_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1947,f227,f1970]) ).
fof(f1974,plain,
( ~ sQ195_spl
| doDivides0(sz00,sz00) ),
inference(forward_demodulation,[status(thm)],[f238,f1963]) ).
fof(f1975,plain,
( ~ sQ196_spl
| doDivides0(sz10,sz00) ),
inference(forward_demodulation,[status(thm)],[f252,f1967]) ).
fof(f1976,plain,
( ~ sQ197_spl
| doDivides0(sz10,sz10) ),
inference(forward_demodulation,[status(thm)],[f233,f1971]) ).
fof(f1983,plain,
( sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1950,f135]) ).
fof(f1984,plain,
sQ191_spl,
inference(contradiction_clause,[status(thm)],[f1983]) ).
fof(f1986,plain,
( ~ sQ192_spl
| ~ sQ6_spl
| doDivides0(xl,xn) ),
inference(forward_demodulation,[status(thm)],[f173,f1952]) ).
fof(f1987,plain,
( ~ sQ192_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1986,f148]) ).
fof(f1988,plain,
( ~ sQ192_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1987]) ).
fof(f2003,definition,
! [X0] :
( sQ199_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sK2_skl) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2006,definition,
( sQ200_spl
<=> sK2_skl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2007,plain,
( ~ sQ200_spl
| sK2_skl = sz00 ),
inference(component_clause,[status(thm)],[f2006]) ).
fof(f2010,definition,
! [X0] :
( sQ201_spl
<=> ( sdtpldt0(X0,sK2_skl) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2023,plain,
( ~ sQ196_spl
| aNaturalNumber0(sdtsldt0(sz00,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f1975,f183]) ).
fof(f2024,definition,
( sQ203_spl
<=> aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2027,plain,
( ~ sQ196_spl
| sQ203_spl
| sQ40_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2023,f227,f197,f634,f2024,f1966]) ).
fof(f2028,plain,
( ~ sQ197_spl
| aNaturalNumber0(sdtsldt0(sz10,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f1976,f183]) ).
fof(f2029,definition,
( sQ204_spl
<=> aNaturalNumber0(sdtsldt0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2032,plain,
( ~ sQ197_spl
| sQ204_spl
| sQ40_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2028,f227,f634,f2029,f1970]) ).
fof(f2092,plain,
( ~ aNaturalNumber0(xl)
| sdtlseqdt0(sz00,sdtpldt0(sz00,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f685,f176]) ).
fof(f2093,definition,
( sQ216_spl
<=> sdtlseqdt0(sz00,sdtpldt0(sz00,xl)) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2094,plain,
( ~ sQ216_spl
| sdtlseqdt0(sz00,sdtpldt0(sz00,xl)) ),
inference(component_clause,[status(thm)],[f2093]) ).
fof(f2096,plain,
( sQ216_spl
| ~ sQ191_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2092,f197,f1948,f2093]) ).
fof(f2097,plain,
( ~ sQ216_spl
| sdtlseqdt0(sz00,xl) ),
inference(forward_demodulation,[status(thm)],[f685,f2094]) ).
fof(f2105,plain,
( ~ sQ216_spl
| aNaturalNumber0(sdtmndt0(xl,sz00))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f2097,f177]) ).
fof(f2106,plain,
( ~ sQ216_spl
| sdtpldt0(sz00,sK0_skl(xl,sz00)) = xl
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f2097,f83]) ).
fof(f2107,plain,
( ~ sQ216_spl
| aNaturalNumber0(sK0_skl(xl,sz00))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f2097,f82]) ).
fof(f2136,definition,
( sQ224_spl
<=> aNaturalNumber0(sdtmndt0(xl,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( ~ sQ224_spl
| aNaturalNumber0(sdtmndt0(xl,sz00)) ),
inference(component_clause,[status(thm)],[f2136]) ).
fof(f2139,plain,
( ~ sQ216_spl
| sQ224_spl
| ~ sQ191_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2105,f197,f1948,f2136,f2093]) ).
fof(f2140,definition,
( sQ225_spl
<=> sdtpldt0(sz00,sK0_skl(xl,sz00)) = xl ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( ~ sQ216_spl
| sQ225_spl
| ~ sQ191_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2106,f197,f1948,f2140,f2093]) ).
fof(f2144,definition,
( sQ226_spl
<=> aNaturalNumber0(sK0_skl(xl,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2145,plain,
( ~ sQ226_spl
| aNaturalNumber0(sK0_skl(xl,sz00)) ),
inference(component_clause,[status(thm)],[f2144]) ).
fof(f2147,plain,
( ~ sQ216_spl
| sQ226_spl
| ~ sQ191_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2107,f197,f1948,f2144,f2093]) ).
fof(f2155,plain,
( ~ sQ197_spl
| aNaturalNumber0(sK1_skl(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f122,f1976]) ).
fof(f2156,plain,
( ~ sQ196_spl
| aNaturalNumber0(sK1_skl(sz00,sz10))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f122,f1975]) ).
fof(f2157,plain,
( ~ sQ195_spl
| aNaturalNumber0(sK1_skl(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f122,f1974]) ).
fof(f2158,definition,
( sQ227_spl
<=> aNaturalNumber0(sK1_skl(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2161,plain,
( ~ sQ197_spl
| sQ227_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2155,f227,f2158,f1970]) ).
fof(f2162,definition,
( sQ228_spl
<=> aNaturalNumber0(sK1_skl(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2165,plain,
( ~ sQ196_spl
| sQ228_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2156,f227,f197,f2162,f1966]) ).
fof(f2166,definition,
( sQ229_spl
<=> aNaturalNumber0(sK1_skl(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2169,plain,
( ~ sQ195_spl
| sQ229_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2157,f197,f2166,f1962]) ).
fof(f2170,plain,
( ~ sQ197_spl
| sz10 = sdtasdt0(sz10,sK1_skl(sz10,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f123,f1976]) ).
fof(f2171,plain,
( ~ sQ196_spl
| sz00 = sdtasdt0(sz10,sK1_skl(sz00,sz10))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f123,f1975]) ).
fof(f2172,plain,
( ~ sQ195_spl
| sz00 = sdtasdt0(sz00,sK1_skl(sz00,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f123,f1974]) ).
fof(f2173,definition,
( sQ230_spl
<=> sz10 = sdtasdt0(sz10,sK1_skl(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2176,plain,
( ~ sQ197_spl
| sQ230_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2170,f227,f2173,f1970]) ).
fof(f2177,definition,
( sQ231_spl
<=> sz00 = sdtasdt0(sz10,sK1_skl(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2180,plain,
( ~ sQ196_spl
| sQ231_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2171,f227,f197,f2177,f1966]) ).
fof(f2181,definition,
( sQ232_spl
<=> sz00 = sdtasdt0(sz00,sK1_skl(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2184,plain,
( ~ sQ195_spl
| sQ232_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2172,f197,f2181,f1962]) ).
fof(f2185,plain,
( ~ sQ197_spl
| sz10 = sdtasdt0(sz10,sdtsldt0(sz10,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f184,f1976]) ).
fof(f2186,plain,
( ~ sQ196_spl
| sz00 = sdtasdt0(sz10,sdtsldt0(sz00,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f184,f1975]) ).
fof(f2188,definition,
( sQ233_spl
<=> sz10 = sdtasdt0(sz10,sdtsldt0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2191,plain,
( ~ sQ197_spl
| sQ233_spl
| sQ40_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2185,f227,f634,f2188,f1970]) ).
fof(f2192,definition,
( sQ234_spl
<=> sz00 = sdtasdt0(sz10,sdtsldt0(sz00,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( ~ sQ196_spl
| sQ234_spl
| sQ40_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2186,f227,f197,f634,f2192,f1966]) ).
fof(f2201,plain,
( ~ sQ0_spl
| xm = sdtasdt0(sz00,sK1_skl(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f704,f123]) ).
fof(f2202,plain,
( ~ sQ0_spl
| aNaturalNumber0(sK1_skl(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f704,f122]) ).
fof(f2208,definition,
( sQ237_spl
<=> xm = sdtasdt0(sz00,sK1_skl(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2209,plain,
( ~ sQ237_spl
| xm = sdtasdt0(sz00,sK1_skl(xm,sz00)) ),
inference(component_clause,[status(thm)],[f2208]) ).
fof(f2211,plain,
( ~ sQ0_spl
| sQ237_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2201,f197,f202,f2208,f149]) ).
fof(f2212,definition,
( sQ238_spl
<=> aNaturalNumber0(sK1_skl(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2213,plain,
( ~ sQ238_spl
| aNaturalNumber0(sK1_skl(xm,sz00)) ),
inference(component_clause,[status(thm)],[f2212]) ).
fof(f2215,plain,
( ~ sQ0_spl
| sQ238_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2202,f197,f202,f2212,f149]) ).
fof(f2303,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| X0 = sz00
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f182]) ).
fof(f2306,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = sdtsldt0(sdtasdt0(sz10,sz00),sz10)
| sz10 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f252,f2303]) ).
fof(f2307,plain,
( ~ aNaturalNumber0(sz10)
| sz10 = sdtsldt0(sdtasdt0(sz10,sz10),sz10)
| sz10 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f233,f2303]) ).
fof(f2316,definition,
( sQ246_spl
<=> sz00 = sdtsldt0(sdtasdt0(sz10,sz00),sz10) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2319,plain,
( sQ246_spl
| sQ40_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2306,f227,f197,f634,f2316]) ).
fof(f2320,definition,
( sQ247_spl
<=> sz10 = sdtsldt0(sdtasdt0(sz10,sz10),sz10) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2323,plain,
( sQ247_spl
| sQ40_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2307,f227,f634,f2320]) ).
fof(f2326,plain,
! [X0] :
( ~ sQ197_spl
| doDivides0(X0,sz10)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f132,f1976]) ).
fof(f2327,plain,
! [X0] :
( ~ sQ196_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f132,f1975]) ).
fof(f2330,plain,
! [X0] :
( ~ sQ195_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f132,f1974]) ).
fof(f2338,definition,
! [X0] :
( sQ248_spl
<=> ( doDivides0(X0,sz10)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2341,plain,
( ~ sQ197_spl
| ~ sQ10_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f2326,f2338,f227,f1970]) ).
fof(f2342,definition,
! [X0] :
( sQ249_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2345,plain,
( ~ sQ196_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2327,f2342,f227,f197,f1966]) ).
fof(f2354,definition,
! [X0] :
( sQ252_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2357,plain,
( ~ sQ195_spl
| ~ sQ8_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f2330,f2354,f197,f1962]) ).
fof(f2375,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(xn,sdtasdt0(xn,sz10))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f235,f182]) ).
fof(f2380,definition,
( sQ255_spl
<=> doDivides0(xn,sdtasdt0(xn,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2381,plain,
( ~ sQ255_spl
| doDivides0(xn,sdtasdt0(xn,sz10)) ),
inference(component_clause,[status(thm)],[f2380]) ).
fof(f2383,plain,
( ~ sQ10_spl
| sQ255_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2375,f194,f2380,f227]) ).
fof(f2384,plain,
( ~ sQ255_spl
| doDivides0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f235,f2381]) ).
fof(f2386,plain,
! [X0] :
( ~ sQ255_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2384,f132]) ).
fof(f2388,plain,
( ~ sQ255_spl
| xn = sdtasdt0(xn,sK1_skl(xn,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2384,f123]) ).
fof(f2389,plain,
( ~ sQ255_spl
| aNaturalNumber0(sK1_skl(xn,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2384,f122]) ).
fof(f2391,definition,
! [X0] :
( sQ256_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2394,plain,
( ~ sQ255_spl
| ~ sQ7_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f2386,f2391,f194,f2380]) ).
fof(f2399,definition,
( sQ258_spl
<=> xn = sdtasdt0(xn,sK1_skl(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2402,plain,
( ~ sQ255_spl
| sQ258_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2388,f194,f2399,f2380]) ).
fof(f2403,definition,
( sQ259_spl
<=> aNaturalNumber0(sK1_skl(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2406,plain,
( ~ sQ255_spl
| sQ259_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2389,f194,f2403,f2380]) ).
fof(f2411,plain,
( ~ aNaturalNumber0(xn)
| xn = sdtsldt0(sdtasdt0(sz10,xn),sz10)
| sz10 = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f249,f2303]) ).
fof(f2412,plain,
( ~ aNaturalNumber0(xn)
| doDivides0(sz10,sdtasdt0(sz10,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f249,f182]) ).
fof(f2413,definition,
( sQ261_spl
<=> xn = sdtsldt0(sdtasdt0(sz10,xn),sz10) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2416,plain,
( sQ261_spl
| sQ40_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2411,f227,f194,f634,f2413]) ).
fof(f2417,definition,
( sQ262_spl
<=> doDivides0(sz10,sdtasdt0(sz10,xn)) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2418,plain,
( ~ sQ262_spl
| doDivides0(sz10,sdtasdt0(sz10,xn)) ),
inference(component_clause,[status(thm)],[f2417]) ).
fof(f2420,plain,
( sQ262_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2412,f227,f194,f2417]) ).
fof(f2422,plain,
( ~ sQ262_spl
| doDivides0(sz10,xn) ),
inference(forward_demodulation,[status(thm)],[f249,f2418]) ).
fof(f2423,plain,
! [X0] :
( ~ sQ262_spl
| doDivides0(X0,xn)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2422,f132]) ).
fof(f2424,plain,
( ~ sQ262_spl
| xn = sdtasdt0(sz10,sdtsldt0(xn,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f2422,f184]) ).
fof(f2425,plain,
( ~ sQ262_spl
| xn = sdtasdt0(sz10,sK1_skl(xn,sz10))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f2422,f123]) ).
fof(f2426,plain,
( ~ sQ262_spl
| aNaturalNumber0(sK1_skl(xn,sz10))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f2422,f122]) ).
fof(f2427,plain,
( ~ sQ262_spl
| aNaturalNumber0(sdtsldt0(xn,sz10))
| sz10 = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f2422,f183]) ).
fof(f2428,definition,
! [X0] :
( sQ263_spl
<=> ( doDivides0(X0,xn)
| ~ doDivides0(X0,sz10)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2431,plain,
( ~ sQ262_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f2423,f2428,f227,f194,f2417]) ).
fof(f2432,definition,
( sQ264_spl
<=> xn = sdtasdt0(sz10,sdtsldt0(xn,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
( ~ sQ262_spl
| sQ264_spl
| sQ40_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2424,f227,f194,f634,f2432,f2417]) ).
fof(f2436,definition,
( sQ265_spl
<=> xn = sdtasdt0(sz10,sK1_skl(xn,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2439,plain,
( ~ sQ262_spl
| sQ265_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2425,f227,f194,f2436,f2417]) ).
fof(f2440,definition,
( sQ266_spl
<=> aNaturalNumber0(sK1_skl(xn,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2443,plain,
( ~ sQ262_spl
| sQ266_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2426,f227,f194,f2440,f2417]) ).
fof(f2444,definition,
( sQ267_spl
<=> aNaturalNumber0(sdtsldt0(xn,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2447,plain,
( ~ sQ262_spl
| sQ267_spl
| sQ40_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2427,f227,f194,f634,f2444,f2417]) ).
fof(f2449,plain,
( ~ aNaturalNumber0(sz00)
| doDivides0(xn,sdtasdt0(xn,sz00))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f261,f182]) ).
fof(f2454,definition,
( sQ269_spl
<=> doDivides0(xn,sdtasdt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2455,plain,
( ~ sQ269_spl
| doDivides0(xn,sdtasdt0(xn,sz00)) ),
inference(component_clause,[status(thm)],[f2454]) ).
fof(f2457,plain,
( sQ269_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2449,f194,f197,f2454]) ).
fof(f2458,plain,
( ~ sQ269_spl
| doDivides0(xn,sz00) ),
inference(forward_demodulation,[status(thm)],[f261,f2455]) ).
fof(f2460,plain,
! [X0] :
( ~ sQ269_spl
| doDivides0(X0,sz00)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2458,f132]) ).
fof(f2462,plain,
( ~ sQ269_spl
| sz00 = sdtasdt0(xn,sK1_skl(sz00,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2458,f123]) ).
fof(f2463,plain,
( ~ sQ269_spl
| aNaturalNumber0(sK1_skl(sz00,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2458,f122]) ).
fof(f2465,definition,
! [X0] :
( sQ270_spl
<=> ( doDivides0(X0,sz00)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2468,plain,
( ~ sQ269_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2460,f2465,f194,f197,f2454]) ).
fof(f2473,definition,
( sQ272_spl
<=> sz00 = sdtasdt0(xn,sK1_skl(sz00,xn)) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2476,plain,
( ~ sQ269_spl
| sQ272_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2462,f194,f197,f2473,f2454]) ).
fof(f2477,definition,
( sQ273_spl
<=> aNaturalNumber0(sK1_skl(sz00,xn)) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2480,plain,
( ~ sQ269_spl
| sQ273_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2463,f194,f197,f2477,f2454]) ).
fof(f2486,plain,
( ~ aNaturalNumber0(xn)
| doDivides0(sz00,sdtasdt0(sz00,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(paramodulation,[status(thm)],[f317,f182]) ).
fof(f2491,definition,
( sQ276_spl
<=> doDivides0(sz00,sdtasdt0(sz00,xn)) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2494,plain,
( ~ sQ7_spl
| sQ276_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2486,f197,f2491,f194]) ).
fof(f2530,plain,
! [X0] :
( ~ sQ269_spl
| doDivides0(xn,sdtpldt0(X0,sz00))
| ~ doDivides0(xn,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f134,f2458]) ).
fof(f2531,plain,
! [X0] :
( ~ sQ255_spl
| doDivides0(xn,sdtpldt0(X0,xn))
| ~ doDivides0(xn,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f134,f2384]) ).
fof(f2532,plain,
! [X0] :
( ~ sQ262_spl
| doDivides0(sz10,sdtpldt0(X0,xn))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f134,f2422]) ).
fof(f2533,plain,
! [X0] :
( ~ sQ197_spl
| doDivides0(sz10,sdtpldt0(X0,sz10))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f134,f1976]) ).
fof(f2534,plain,
! [X0] :
( ~ sQ196_spl
| doDivides0(sz10,sdtpldt0(X0,sz00))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f134,f1975]) ).
fof(f2537,plain,
! [X0] :
( ~ sQ195_spl
| doDivides0(sz00,sdtpldt0(X0,sz00))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f134,f1974]) ).
fof(f2539,definition,
! [X0] :
( sQ277_spl
<=> ( doDivides0(xn,sdtpldt0(X0,sz00))
| ~ doDivides0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2542,plain,
( ~ sQ269_spl
| ~ sQ8_spl
| sQ277_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2530,f194,f2539,f197,f2454]) ).
fof(f2543,definition,
! [X0] :
( sQ278_spl
<=> ( doDivides0(xn,sdtpldt0(X0,xn))
| ~ doDivides0(xn,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2546,plain,
( ~ sQ255_spl
| sQ278_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2531,f194,f2543,f2380]) ).
fof(f2547,definition,
! [X0] :
( sQ279_spl
<=> ( doDivides0(sz10,sdtpldt0(X0,xn))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
( ~ sQ262_spl
| ~ sQ7_spl
| sQ279_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2532,f227,f2547,f194,f2417]) ).
fof(f2551,definition,
! [X0] :
( sQ280_spl
<=> ( doDivides0(sz10,sdtpldt0(X0,sz10))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2554,plain,
( ~ sQ197_spl
| sQ280_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2533,f227,f2551,f1970]) ).
fof(f2555,definition,
! [X0] :
( sQ281_spl
<=> ( doDivides0(sz10,sdtpldt0(X0,sz00))
| ~ doDivides0(sz10,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2558,plain,
( ~ sQ196_spl
| ~ sQ8_spl
| sQ281_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2534,f227,f2555,f197,f1966]) ).
fof(f2567,definition,
! [X0] :
( sQ284_spl
<=> ( doDivides0(sz00,sdtpldt0(X0,sz00))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2570,plain,
( ~ sQ195_spl
| sQ284_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2537,f197,f2567,f1962]) ).
fof(f2586,plain,
! [X0] :
( ~ sQ71_spl
| sdtmndt0(xn,xn) = sdtmndt0(xn,xn)
| sdtpldt0(X0,sdtmndt0(xn,xn)) != sdtpldt0(X0,sdtmndt0(xn,xn))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f926]) ).
fof(f2588,plain,
! [X0] :
( ~ sQ67_spl
| sdtmndt0(xn,sz00) = sdtmndt0(xn,sz00)
| sdtpldt0(X0,sdtmndt0(xn,sz00)) != sdtpldt0(X0,sdtmndt0(xn,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f888]) ).
fof(f2592,plain,
! [X0] :
( ~ sQ69_spl
| sK0_skl(xn,sz00) = sK0_skl(xn,sz00)
| sdtpldt0(X0,sK0_skl(xn,sz00)) != sdtpldt0(X0,sK0_skl(xn,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f896]) ).
fof(f2612,definition,
! [X0] :
( sQ285_spl
<=> ( sdtpldt0(X0,sdtmndt0(xn,xn)) != sdtpldt0(X0,sdtmndt0(xn,xn))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2613,plain,
! [X0] :
( ~ sQ285_spl
| sdtpldt0(X0,sdtmndt0(xn,xn)) != sdtpldt0(X0,sdtmndt0(xn,xn))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2612]) ).
fof(f2615,definition,
( sQ286_spl
<=> sdtmndt0(xn,xn) = sdtmndt0(xn,xn) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2618,plain,
( ~ sQ71_spl
| sQ286_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f2586,f2612,f2615,f925]) ).
fof(f2619,definition,
! [X0] :
( sQ287_spl
<=> ( sdtpldt0(X0,sdtmndt0(xn,sz00)) != sdtpldt0(X0,sdtmndt0(xn,sz00))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2620,plain,
! [X0] :
( ~ sQ287_spl
| sdtpldt0(X0,sdtmndt0(xn,sz00)) != sdtpldt0(X0,sdtmndt0(xn,sz00))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2619]) ).
fof(f2622,definition,
( sQ288_spl
<=> sdtmndt0(xn,sz00) = sdtmndt0(xn,sz00) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f2625,plain,
( ~ sQ67_spl
| sQ288_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f2588,f2619,f2622,f887]) ).
fof(f2633,definition,
! [X0] :
( sQ291_spl
<=> ( sdtpldt0(X0,sK0_skl(xn,sz00)) != sdtpldt0(X0,sK0_skl(xn,sz00))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2634,plain,
! [X0] :
( ~ sQ291_spl
| sdtpldt0(X0,sK0_skl(xn,sz00)) != sdtpldt0(X0,sK0_skl(xn,sz00))
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2633]) ).
fof(f2636,definition,
( sQ292_spl
<=> sK0_skl(xn,sz00) = sK0_skl(xn,sz00) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2639,plain,
( ~ sQ69_spl
| sQ292_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2592,f2633,f2636,f895]) ).
fof(f2643,plain,
! [X0] :
( ~ sQ285_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f2613]) ).
fof(f2644,plain,
! [X0] :
( ~ sQ291_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f2634]) ).
fof(f2645,plain,
! [X0] :
( ~ sQ287_spl
| ~ aNaturalNumber0(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f2620]) ).
fof(f2701,plain,
( ~ sQ238_spl
| sz00 = sdtasdt0(sz00,sK1_skl(xm,sz00)) ),
inference(resolution,[status(thm)],[f2213,f64]) ).
fof(f2727,plain,
( ~ sQ285_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f2643]) ).
fof(f2728,plain,
~ sQ285_spl,
inference(contradiction_clause,[status(thm)],[f2727]) ).
fof(f2729,plain,
( ~ sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f2645]) ).
fof(f2730,plain,
~ sQ287_spl,
inference(contradiction_clause,[status(thm)],[f2729]) ).
fof(f2731,plain,
( ~ sQ291_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f2644]) ).
fof(f2732,plain,
~ sQ291_spl,
inference(contradiction_clause,[status(thm)],[f2731]) ).
fof(f2872,plain,
( ~ sQ238_spl
| ~ sQ237_spl
| sz00 = xm ),
inference(forward_demodulation,[status(thm)],[f2209,f2701]) ).
fof(f2873,plain,
( ~ sQ238_spl
| ~ sQ237_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2872,f599]) ).
fof(f2874,plain,
( ~ sQ238_spl
| ~ sQ237_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f2873]) ).
fof(f3003,plain,
sdtasdt0(xl,sz00) = sz00,
inference(resolution,[status(thm)],[f63,f135]) ).
fof(f3027,plain,
sdtasdt0(xl,sz10) = xl,
inference(resolution,[status(thm)],[f60,f135]) ).
fof(f3116,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00)
| sdtasdt0(sdtmndt0(xl,sz00),X0) != sdtasdt0(sdtmndt0(xl,sz00),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f73,f2137]) ).
fof(f3118,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sK0_skl(xl,sz00)
| sdtasdt0(sK0_skl(xl,sz00),X0) != sdtasdt0(sK0_skl(xl,sz00),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f73,f2145]) ).
fof(f3179,definition,
! [X0] :
( sQ307_spl
<=> ( sdtasdt0(sdtmndt0(xl,sz00),X0) != sdtasdt0(sdtmndt0(xl,sz00),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3182,definition,
( sQ308_spl
<=> sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f3185,plain,
( ~ sQ224_spl
| sQ308_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3116,f3179,f3182,f2136]) ).
fof(f3186,definition,
! [X0] :
( sQ309_spl
<=> ( sdtasdt0(sK0_skl(xl,sz00),X0) != sdtasdt0(sK0_skl(xl,sz00),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f3189,definition,
( sQ310_spl
<=> sK0_skl(xl,sz00) = sK0_skl(xl,sz00) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f3192,plain,
( ~ sQ226_spl
| sQ310_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f3118,f3186,f3189,f2144]) ).
fof(f3216,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00)
| sdtasdt0(X0,sdtmndt0(xl,sz00)) != sdtasdt0(X0,sdtmndt0(xl,sz00))
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f72,f2137]) ).
fof(f3218,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sK0_skl(xl,sz00)
| sdtasdt0(X0,sK0_skl(xl,sz00)) != sdtasdt0(X0,sK0_skl(xl,sz00))
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f72,f2145]) ).
fof(f3261,definition,
! [X0] :
( sQ317_spl
<=> ( sdtasdt0(X0,sdtmndt0(xl,sz00)) != sdtasdt0(X0,sdtmndt0(xl,sz00))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f3264,plain,
( ~ sQ224_spl
| sQ308_spl
| sQ317_spl ),
inference(split_clause,[status(thm)],[f3216,f3261,f3182,f2136]) ).
fof(f3265,definition,
! [X0] :
( sQ318_spl
<=> ( sdtasdt0(X0,sK0_skl(xl,sz00)) != sdtasdt0(X0,sK0_skl(xl,sz00))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f3268,plain,
( ~ sQ226_spl
| sQ310_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f3218,f3265,f3189,f2144]) ).
fof(f3304,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00)
| sdtpldt0(sdtmndt0(xl,sz00),X0) != sdtpldt0(sdtmndt0(xl,sz00),X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f70,f2137]) ).
fof(f3306,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sK0_skl(xl,sz00)
| sdtpldt0(sK0_skl(xl,sz00),X0) != sdtpldt0(sK0_skl(xl,sz00),X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f70,f2145]) ).
fof(f3339,definition,
! [X0] :
( sQ323_spl
<=> ( sdtpldt0(sdtmndt0(xl,sz00),X0) != sdtpldt0(sdtmndt0(xl,sz00),X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3342,plain,
( ~ sQ224_spl
| sQ308_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f3304,f3339,f3182,f2136]) ).
fof(f3343,definition,
! [X0] :
( sQ324_spl
<=> ( sdtpldt0(sK0_skl(xl,sz00),X0) != sdtpldt0(sK0_skl(xl,sz00),X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f3346,plain,
( ~ sQ226_spl
| sQ310_spl
| sQ324_spl ),
inference(split_clause,[status(thm)],[f3306,f3343,f3189,f2144]) ).
fof(f3362,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2303,f47]) ).
fof(f3451,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| xl = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f184,f138]) ).
fof(f3455,definition,
( sQ329_spl
<=> xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3456,plain,
( ~ sQ329_spl
| xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
inference(component_clause,[status(thm)],[f3455]) ).
fof(f3458,plain,
( sQ329_spl
| sQ0_spl
| ~ sQ9_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f3451,f1948,f202,f149,f3455]) ).
fof(f3462,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| xm = sdtasdt0(xl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f153,f3456]) ).
fof(f3463,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f183,f138]) ).
fof(f3467,definition,
( sQ330_spl
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3468,plain,
( ~ sQ330_spl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(component_clause,[status(thm)],[f3467]) ).
fof(f3470,plain,
( sQ330_spl
| sQ0_spl
| ~ sQ9_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f3463,f1948,f202,f149,f3467]) ).
fof(f3474,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| aNaturalNumber0(sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f153,f3468]) ).
fof(f3478,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3474,f1325]) ).
fof(f3479,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ118_spl ),
inference(contradiction_clause,[status(thm)],[f3478]) ).
fof(f3523,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sdtsldt0(sdtasdt0(X0,sK2_skl),X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f3362]) ).
fof(f3525,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sK2_skl
| sdtpldt0(sK2_skl,X0) != sdtpldt0(sK2_skl,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f70]) ).
fof(f3529,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sK2_skl
| sdtasdt0(X0,sK2_skl) != sdtasdt0(X0,sK2_skl)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f72]) ).
fof(f3533,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sK2_skl
| sdtasdt0(sK2_skl,X0) != sdtasdt0(sK2_skl,X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f73]) ).
fof(f3537,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sdtasdt0(sK2_skl,sz10) = sK2_skl ),
inference(resolution,[status(thm)],[f3474,f60]) ).
fof(f3538,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sdtasdt0(sz10,sK2_skl) ),
inference(resolution,[status(thm)],[f3474,f61]) ).
fof(f3556,definition,
! [X0] :
( sQ331_spl
<=> ( sdtpldt0(sK2_skl,X0) != sdtpldt0(sK2_skl,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f3559,definition,
( sQ332_spl
<=> sK2_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f3562,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ332_spl
| sQ331_spl ),
inference(split_clause,[status(thm)],[f3525,f3556,f3559,f152,f3467]) ).
fof(f3564,definition,
! [X0] :
( sQ333_spl
<=> ( sdtasdt0(X0,sK2_skl) != sdtasdt0(X0,sK2_skl)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3567,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ332_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f3529,f3564,f3559,f152,f3467]) ).
fof(f3569,definition,
! [X0] :
( sQ334_spl
<=> ( sdtasdt0(sK2_skl,X0) != sdtasdt0(sK2_skl,X0)
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f3572,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ332_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f3533,f3569,f3559,f152,f3467]) ).
fof(f3639,plain,
( sdtlseqdt0(xl,xl)
| sz10 = sz00
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f3027,f114]) ).
fof(f3642,plain,
( sdtlseqdt0(xm,xm)
| sz10 = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f237,f114]) ).
fof(f3646,plain,
( sdtlseqdt0(sz00,sz00)
| sz10 = sz00
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f238,f114]) ).
fof(f3650,plain,
( sdtlseqdt0(sz10,sz10)
| sz10 = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f233,f114]) ).
fof(f3651,definition,
( sQ339_spl
<=> sdtlseqdt0(xl,xl) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f3654,plain,
( sQ339_spl
| sQ40_spl
| ~ sQ191_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3639,f227,f1948,f634,f3651]) ).
fof(f3663,definition,
( sQ342_spl
<=> sdtlseqdt0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f3666,plain,
( sQ342_spl
| sQ40_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3642,f227,f202,f634,f3663]) ).
fof(f3667,definition,
( sQ343_spl
<=> sdtlseqdt0(sz00,sz00) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f3673,plain,
( sQ343_spl
| sQ40_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3646,f227,f197,f634,f3667]) ).
fof(f3686,definition,
( sQ347_spl
<=> sdtlseqdt0(sz10,sz10) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f3689,plain,
( sQ347_spl
| sQ40_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3650,f227,f634,f3686]) ).
fof(f3714,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| sdtlseqdt0(xl,xm)
| sK2_skl = sz00
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK2_skl) ),
inference(paramodulation,[status(thm)],[f3462,f114]) ).
fof(f3715,definition,
( sQ348_spl
<=> sdtlseqdt0(xl,xm) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f3716,plain,
( ~ sQ348_spl
| sdtlseqdt0(xl,xm) ),
inference(component_clause,[status(thm)],[f3715]) ).
fof(f3718,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| sQ348_spl
| sQ200_spl
| ~ sQ191_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f3714,f1323,f1948,f2006,f3715,f152,f3455]) ).
fof(f3719,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| ~ sQ200_spl
| xm = sdtasdt0(xl,sz00) ),
inference(backward_demodulation,[status(thm)],[f2007,f3462]) ).
fof(f3723,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| ~ sQ200_spl
| xm = sz00 ),
inference(forward_demodulation,[status(thm)],[f3003,f3719]) ).
fof(f3724,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| ~ sQ200_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3723,f599]) ).
fof(f3725,plain,
( ~ sQ329_spl
| ~ sQ1_spl
| ~ sQ200_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f3724]) ).
fof(f3946,plain,
! [X0] :
( ~ sQ224_spl
| sdtlseqdt0(sdtasdt0(X0,sdtmndt0(xl,sz00)),sdtasdt0(X0,sdtmndt0(xl,sz00)))
| ~ sdtlseqdt0(sdtmndt0(xl,sz00),sdtmndt0(xl,sz00))
| sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f107,f2137]) ).
fof(f3952,plain,
! [X0] :
( ~ sQ226_spl
| sdtlseqdt0(sdtasdt0(X0,sK0_skl(xl,sz00)),sdtasdt0(X0,sK0_skl(xl,sz00)))
| ~ sdtlseqdt0(sK0_skl(xl,sz00),sK0_skl(xl,sz00))
| sK0_skl(xl,sz00) = sK0_skl(xl,sz00)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f107,f2145]) ).
fof(f3970,definition,
( sQ356_spl
<=> sdtlseqdt0(xn,xn) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4006,definition,
! [X0] :
( sQ366_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,sdtmndt0(xl,sz00)),sdtasdt0(X0,sdtmndt0(xl,sz00)))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f4009,definition,
( sQ367_spl
<=> sdtlseqdt0(sdtmndt0(xl,sz00),sdtmndt0(xl,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f4012,plain,
( ~ sQ224_spl
| ~ sQ367_spl
| sQ308_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f3946,f4006,f3182,f4009,f2136]) ).
fof(f4027,definition,
! [X0] :
( sQ372_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,sK0_skl(xl,sz00)),sdtasdt0(X0,sK0_skl(xl,sz00)))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f4030,definition,
( sQ373_spl
<=> sdtlseqdt0(sK0_skl(xl,sz00),sK0_skl(xl,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f4033,plain,
( ~ sQ226_spl
| ~ sQ373_spl
| sQ310_spl
| sQ372_spl ),
inference(split_clause,[status(thm)],[f3952,f4027,f3189,f4030,f2144]) ).
fof(f4636,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sz00
| X0 = sz00
| sdtasdt0(X0,sdtmndt0(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f78,f2137]) ).
fof(f4638,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sz00
| X0 = sz00
| sdtasdt0(X0,sK0_skl(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f78,f2145]) ).
fof(f4695,definition,
! [X0] :
( sQ440_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtmndt0(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f4698,definition,
( sQ441_spl
<=> sdtmndt0(xl,sz00) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f4701,plain,
( ~ sQ224_spl
| sQ441_spl
| sQ440_spl ),
inference(split_clause,[status(thm)],[f4636,f4695,f4698,f2136]) ).
fof(f4709,definition,
! [X0] :
( sQ444_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sK0_skl(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f4712,definition,
( sQ445_spl
<=> sK0_skl(xl,sz00) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f4715,plain,
( ~ sQ226_spl
| sQ445_spl
| sQ444_spl ),
inference(split_clause,[status(thm)],[f4638,f4709,f4712,f2144]) ).
fof(f4730,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sz00
| sdtpldt0(X0,sdtmndt0(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f76,f2137]) ).
fof(f4732,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sz00
| sdtpldt0(X0,sK0_skl(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f76,f2145]) ).
fof(f4768,definition,
! [X0] :
( sQ453_spl
<=> ( sdtpldt0(X0,sdtmndt0(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f4771,plain,
( ~ sQ224_spl
| sQ441_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f4730,f4768,f4698,f2136]) ).
fof(f4776,definition,
! [X0] :
( sQ455_spl
<=> ( sdtpldt0(X0,sK0_skl(xl,sz00)) != sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f4779,plain,
( ~ sQ226_spl
| sQ445_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f4732,f4776,f4712,f2144]) ).
fof(f4817,plain,
( sdtlseqdt0(xn,xn)
| sz10 = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f235,f114]) ).
fof(f4818,plain,
( sQ356_spl
| sQ40_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4817,f227,f194,f634,f3970]) ).
fof(f4949,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sz00
| sdtpldt0(X0,sK2_skl) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f76]) ).
fof(f4950,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sz00
| X0 = sz00
| sdtasdt0(X0,sK2_skl) != sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f78]) ).
fof(f4951,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sdtlseqdt0(sdtasdt0(X0,sK2_skl),sdtasdt0(X0,sK2_skl))
| ~ sdtlseqdt0(sK2_skl,sK2_skl)
| sK2_skl = sK2_skl
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3474,f107]) ).
fof(f4990,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ200_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f4949,f2010,f2006,f152,f3467]) ).
fof(f4991,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ200_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f4950,f2003,f2006,f152,f3467]) ).
fof(f4992,definition,
! [X0] :
( sQ460_spl
<=> ( sdtlseqdt0(sdtasdt0(X0,sK2_skl),sdtasdt0(X0,sK2_skl))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f4995,definition,
( sQ461_spl
<=> sdtlseqdt0(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f4996,plain,
( ~ sQ461_spl
| sdtlseqdt0(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f4995]) ).
fof(f4998,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| ~ sQ461_spl
| sQ332_spl
| sQ460_spl ),
inference(split_clause,[status(thm)],[f4951,f4992,f3559,f4995,f152,f3467]) ).
fof(f5014,plain,
! [X0] :
( ~ sQ348_spl
| sdtlseqdt0(sdtasdt0(xl,X0),sdtasdt0(xm,X0))
| xl = xm
| X0 = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f3716,f109]) ).
fof(f5015,definition,
! [X0] :
( sQ464_spl
<=> ( sdtlseqdt0(sdtasdt0(xl,X0),sdtasdt0(xm,X0))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f5018,definition,
( sQ465_spl
<=> xl = xm ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f5021,plain,
( ~ sQ348_spl
| sQ465_spl
| ~ sQ9_spl
| ~ sQ191_spl
| sQ464_spl ),
inference(split_clause,[status(thm)],[f5014,f5015,f1948,f202,f5018,f3715]) ).
fof(f5022,plain,
! [X0] :
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sK2_skl
| sdtpldt0(X0,sK2_skl) != sdtpldt0(X0,sK2_skl)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f3474]) ).
fof(f5046,plain,
! [X0] :
( ~ sQ224_spl
| sdtmndt0(xl,sz00) = sdtmndt0(xl,sz00)
| sdtpldt0(X0,sdtmndt0(xl,sz00)) != sdtpldt0(X0,sdtmndt0(xl,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f2137]) ).
fof(f5050,plain,
! [X0] :
( ~ sQ226_spl
| sK0_skl(xl,sz00) = sK0_skl(xl,sz00)
| sdtpldt0(X0,sK0_skl(xl,sz00)) != sdtpldt0(X0,sK0_skl(xl,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f2145]) ).
fof(f5073,definition,
! [X0] :
( sQ466_spl
<=> ( sdtpldt0(X0,sK2_skl) != sdtpldt0(X0,sK2_skl)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f5076,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ332_spl
| sQ466_spl ),
inference(split_clause,[status(thm)],[f5022,f5073,f3559,f152,f3467]) ).
fof(f5112,definition,
! [X0] :
( sQ475_spl
<=> ( sdtpldt0(X0,sdtmndt0(xl,sz00)) != sdtpldt0(X0,sdtmndt0(xl,sz00))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f5115,plain,
( ~ sQ224_spl
| sQ308_spl
| sQ475_spl ),
inference(split_clause,[status(thm)],[f5046,f5112,f3182,f2136]) ).
fof(f5120,definition,
! [X0] :
( sQ477_spl
<=> ( sdtpldt0(X0,sK0_skl(xl,sz00)) != sdtpldt0(X0,sK0_skl(xl,sz00))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f5123,plain,
( ~ sQ226_spl
| sQ310_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f5050,f5120,f3189,f2144]) ).
fof(f5138,plain,
! [X0] :
( ~ doDivides0(X0,xn)
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f132,f148]) ).
fof(f5142,definition,
! [X0] :
( sQ478_spl
<=> ( ~ doDivides0(X0,xn)
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f5143,plain,
! [X0] :
( ~ sQ478_spl
| ~ doDivides0(X0,xn)
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f5142]) ).
fof(f5145,plain,
( ~ sQ7_spl
| sQ478_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f5138,f1948,f5142,f194]) ).
fof(f5156,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sdtlseqdt0(sz10,sK2_skl)
| sK2_skl = sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sK2_skl) ),
inference(paramodulation,[status(thm)],[f3538,f114]) ).
fof(f5157,definition,
( sQ480_spl
<=> sdtlseqdt0(sz10,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f5158,plain,
( ~ sQ480_spl
| sdtlseqdt0(sz10,sK2_skl) ),
inference(component_clause,[status(thm)],[f5157]) ).
fof(f5160,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ480_spl
| sQ200_spl
| ~ sQ10_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f5156,f1323,f227,f2006,f5157,f152,f3467]) ).
fof(f5161,plain,
! [X0] :
( ~ sQ480_spl
| sdtlseqdt0(sdtasdt0(sz10,X0),sdtasdt0(sK2_skl,X0))
| sz10 = sK2_skl
| X0 = sz00
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5158,f109]) ).
fof(f5162,definition,
! [X0] :
( sQ481_spl
<=> ( sdtlseqdt0(sdtasdt0(sz10,X0),sdtasdt0(sK2_skl,X0))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f5165,definition,
( sQ482_spl
<=> sz10 = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f5168,plain,
( ~ sQ480_spl
| sQ482_spl
| ~ sQ118_spl
| ~ sQ10_spl
| sQ481_spl ),
inference(split_clause,[status(thm)],[f5161,f5162,f227,f1323,f5165,f5157]) ).
fof(f5169,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sdtlseqdt0(sK2_skl,sK2_skl)
| sz10 = sz00
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f3537,f114]) ).
fof(f5170,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ461_spl
| sQ40_spl
| ~ sQ118_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5169,f227,f1323,f634,f4995,f152,f3467]) ).
fof(f5171,plain,
! [X0] :
( doDivides0(xl,sdtpldt0(X0,xm))
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f138,f134]) ).
fof(f5174,definition,
! [X0] :
( sQ483_spl
<=> ( doDivides0(xl,sdtpldt0(X0,xm))
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f5177,plain,
( ~ sQ9_spl
| sQ483_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f5171,f1948,f5174,f202]) ).
fof(f5184,plain,
! [X0] :
( ~ sQ461_spl
| sdtlseqdt0(sdtasdt0(sK2_skl,X0),sdtasdt0(sK2_skl,X0))
| sK2_skl = sK2_skl
| X0 = sz00
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f4996,f109]) ).
fof(f5185,definition,
! [X0] :
( sQ484_spl
<=> ( sdtlseqdt0(sdtasdt0(sK2_skl,X0),sdtasdt0(sK2_skl,X0))
| X0 = sz00
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f5188,plain,
( ~ sQ461_spl
| sQ332_spl
| ~ sQ118_spl
| sQ484_spl ),
inference(split_clause,[status(thm)],[f5184,f5185,f1323,f3559,f4995]) ).
fof(f5525,plain,
( xm = sdtasdt0(xl,sK1_skl(xm,xl))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f123,f138]) ).
fof(f5533,definition,
( sQ510_spl
<=> xm = sdtasdt0(xl,sK1_skl(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f5536,plain,
( sQ510_spl
| ~ sQ9_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f5525,f1948,f202,f5533]) ).
fof(f5544,plain,
( aNaturalNumber0(sK1_skl(xm,xl))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f122,f138]) ).
fof(f5552,definition,
( sQ511_spl
<=> aNaturalNumber0(sK1_skl(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f5555,plain,
( sQ511_spl
| ~ sQ9_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f5544,f1948,f202,f5552]) ).
fof(f6177,plain,
( ~ sQ478_spl
| ~ doDivides0(xm,xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f5143,f138]) ).
fof(f6178,plain,
! [X0,X1] :
( ~ sQ478_spl
| ~ doDivides0(X1,X0)
| ~ doDivides0(xl,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f5143,f132]) ).
fof(f6179,definition,
( sQ562_spl
<=> doDivides0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f6181,plain,
( sQ562_spl
| ~ doDivides0(xm,xn) ),
inference(component_clause,[status(thm)],[f6179]) ).
fof(f6182,plain,
( ~ sQ478_spl
| ~ sQ562_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6177,f202,f6179,f5142]) ).
fof(f6183,definition,
! [X0,X1] :
( sQ563_spl
<=> ( ~ doDivides0(X1,X0)
| ~ doDivides0(xl,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X0,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f6186,plain,
( ~ sQ478_spl
| ~ sQ191_spl
| sQ563_spl ),
inference(split_clause,[status(thm)],[f6178,f6183,f1948,f5142]) ).
fof(f6188,plain,
! [X0] :
( sQ562_spl
| ~ doDivides0(X0,xn)
| ~ doDivides0(xm,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f6181,f132]) ).
fof(f6189,definition,
! [X0] :
( sQ564_spl
<=> ( ~ doDivides0(X0,xn)
| ~ doDivides0(xm,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f6192,plain,
( sQ562_spl
| ~ sQ7_spl
| sQ564_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6188,f202,f6189,f194,f6179]) ).
fof(f7300,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sdtsldt0(sdtasdt0(sK2_skl,sK2_skl),sK2_skl)
| sK2_skl = sz00 ),
inference(resolution,[status(thm)],[f3523,f3474]) ).
fof(f7307,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sK2_skl = sdtsldt0(sdtasdt0(sz10,sK2_skl),sz10)
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f3523,f42]) ).
fof(f7332,definition,
( sQ656_spl
<=> sK2_skl = sdtsldt0(sdtasdt0(sK2_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f7335,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ656_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f7300,f2006,f7332,f152,f3467]) ).
fof(f7360,definition,
( sQ663_spl
<=> sK2_skl = sdtsldt0(sdtasdt0(sz10,sK2_skl),sz10) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f7363,plain,
( ~ sQ330_spl
| ~ sQ1_spl
| sQ663_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f7307,f634,f7360,f152,f3467]) ).
fof(f7498,plain,
( ~ sQ478_spl
| ~ doDivides0(sdtpldt0(xm,xn),xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[f139,f5143]) ).
fof(f7499,plain,
( aNaturalNumber0(sK1_skl(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f139,f122]) ).
fof(f7500,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sK1_skl(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f139,f123]) ).
fof(f7501,plain,
! [X0] :
( doDivides0(xl,sdtpldt0(X0,sdtpldt0(xm,xn)))
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f139,f134]) ).
fof(f7502,plain,
( aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| xl = sz00
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f139,f183]) ).
fof(f7504,definition,
( sQ671_spl
<=> doDivides0(sdtpldt0(xm,xn),xn) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f7507,plain,
( ~ sQ478_spl
| ~ sQ671_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7498,f379,f7504,f5142]) ).
fof(f7508,definition,
( sQ672_spl
<=> aNaturalNumber0(sK1_skl(sdtpldt0(xm,xn),xl)) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f7511,plain,
( sQ672_spl
| ~ sQ12_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f7499,f1948,f379,f7508]) ).
fof(f7512,definition,
( sQ673_spl
<=> sdtpldt0(xm,xn) = sdtasdt0(xl,sK1_skl(sdtpldt0(xm,xn),xl)) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f7515,plain,
( sQ673_spl
| ~ sQ12_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f7500,f1948,f379,f7512]) ).
fof(f7516,definition,
! [X0] :
( sQ674_spl
<=> ( doDivides0(xl,sdtpldt0(X0,sdtpldt0(xm,xn)))
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f7519,plain,
( ~ sQ12_spl
| sQ674_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f7501,f1948,f7516,f379]) ).
fof(f7520,definition,
( sQ675_spl
<=> aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f7521,plain,
( ~ sQ675_spl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(component_clause,[status(thm)],[f7520]) ).
fof(f7523,plain,
( sQ675_spl
| sQ0_spl
| ~ sQ12_spl
| ~ sQ191_spl ),
inference(split_clause,[status(thm)],[f7502,f1948,f379,f149,f7520]) ).
fof(f7528,plain,
( ~ sQ675_spl
| ~ sQ2_spl
| aNaturalNumber0(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f157,f7521]) ).
fof(f7529,plain,
( ~ sQ675_spl
| ~ sQ2_spl
| sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7528,f1328]) ).
fof(f7530,plain,
( ~ sQ675_spl
| ~ sQ2_spl
| sQ119_spl ),
inference(contradiction_clause,[status(thm)],[f7529]) ).
fof(f7546,plain,
( ~ sQ123_spl
| ~ sQ4_spl
| aNaturalNumber0(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f165,f1341]) ).
fof(f7547,plain,
( ~ sQ123_spl
| ~ sQ4_spl
| sQ193_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7546,f1956]) ).
fof(f7548,plain,
( ~ sQ123_spl
| ~ sQ4_spl
| sQ193_spl ),
inference(contradiction_clause,[status(thm)],[f7547]) ).
fof(f7549,plain,
$false,
inference(sat_refutation,[status(thm)],[f155,f159,f163,f167,f175,f356,f382,f384,f386,f388,f490,f497,f504,f511,f518,f525,f538,f540,f542,f544,f546,f548,f637,f641,f643,f660,f729,f733,f737,f739,f748,f752,f758,f762,f769,f773,f781,f785,f789,f799,f806,f814,f818,f822,f827,f835,f839,f843,f875,f882,f890,f894,f898,f903,f928,f932,f936,f1216,f1260,f1343,f1388,f1413,f1439,f1558,f1579,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1957,f1961,f1965,f1969,f1973,f1984,f1988,f2027,f2032,f2096,f2139,f2143,f2147,f2161,f2165,f2169,f2176,f2180,f2184,f2191,f2195,f2211,f2215,f2319,f2323,f2341,f2345,f2357,f2383,f2394,f2402,f2406,f2416,f2420,f2431,f2435,f2439,f2443,f2447,f2457,f2468,f2476,f2480,f2494,f2542,f2546,f2550,f2554,f2558,f2570,f2618,f2625,f2639,f2728,f2730,f2732,f2874,f3185,f3192,f3264,f3268,f3342,f3346,f3458,f3470,f3479,f3562,f3567,f3572,f3654,f3666,f3673,f3689,f3718,f3725,f4012,f4033,f4701,f4715,f4771,f4779,f4818,f4990,f4991,f4998,f5021,f5076,f5115,f5123,f5145,f5160,f5168,f5170,f5177,f5188,f5536,f5555,f6182,f6186,f6192,f7335,f7363,f7507,f7511,f7515,f7519,f7523,f7530,f7548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:33:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 5.59/1.30 % Refutation found
% 5.59/1.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.59/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.04/1.32 % Elapsed time: 0.960486 seconds
% 1.04/1.32 % CPU time: 7.297159 seconds
% 1.04/1.32 % Total memory used: 156.977 MB
% 1.04/1.32 % Net memory used: 148.677 MB
%------------------------------------------------------------------------------