%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:25:09 PM UTC 2026
% Result : Theorem 3.69s 6.42s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 36
% Syntax : Number of formulae : 1040 ( 191 unt; 0 def)
% Number of atoms : 3729 (1145 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 5009 (2320 ~;2526 |; 109 &)
% ( 12 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 1158 ( 0 sgn1148 !; 10 ?; 820 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& X0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
fof(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f39,axiom,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1395) ).
fof(f40,axiom,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(f41,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1459) ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
xn != sdtasdt0(xl,xr),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f106,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f107,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f108,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f109,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f110,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f111,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f112,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f113,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f39]) ).
fof(f114,plain,
xr = sdtmndt0(xq,xp),
inference(cnf_transformation,[],[f40]) ).
fof(f115,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f41]) ).
fof(f116,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[],[f44]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f122,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f125,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f53]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f53]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f130,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f131,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f134,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f148,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f149,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f77]) ).
fof(f150,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtsldt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f157,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f85]) ).
fof(f158,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtmndt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f104]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f164,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f165,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f123]) ).
fof(f166,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f139]) ).
fof(f167,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(X2)
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f153]) ).
fof(f168,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f152]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f151]) ).
fof(f171,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f161]) ).
fof(f172,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f160]) ).
fof(f173,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f159]) ).
tcf(c_49,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f107]) ).
tcf(c_50,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f106]) ).
tcf(c_51,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f105]) ).
tcf(c_52,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f109]) ).
tcf(c_53,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_54,plain,
xl != sz00,
inference(cnf_transformation,[],[f110]) ).
tcf(c_55,plain,
sdtsldt0(xm,xl) = xp,
inference(cnf_transformation,[],[f111]) ).
tcf(c_56,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnf_transformation,[],[f112]) ).
tcf(c_57,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f113]) ).
tcf(c_58,plain,
sdtmndt0(xq,xp) = xr,
inference(cnf_transformation,[],[f114]) ).
tcf(c_59,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f115]) ).
tcf(c_60,negated_conjecture,
sdtasdt0(xl,xr) != xn,
inference(cnf_transformation,[],[f116]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X0)) = sdtasdt0(X1,sdtpldt0(X2,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(X2,X0),X1) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_74,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_75,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X1,X2),X0) = sdtpldt0(X1,sdtpldt0(X2,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1) ) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_92,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_93,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_94,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f150]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_102,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(sdtpldt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X1,X2),X0) = sdtasdt0(X1,sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_81,c_108,c_81]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_78,c_65]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(sdtpldt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_78,c_103,c_144]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_108,c_95,c_141]) ).
tcf(c_2537,plain,
sdtpldt0(xl,sz00) = xl,
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_2538,plain,
sdtpldt0(xm,sz00) = xm,
inference(superposition,[status(thm)],[c_50,c_74]) ).
tcf(c_2539,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_51,c_74]) ).
tcf(c_2540,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(superposition,[status(thm)],[c_94,c_74]) ).
tcf(c_2545,plain,
sdtpldt0(sz00,xl) = xl,
inference(superposition,[status(thm)],[c_49,c_75]) ).
tcf(c_2546,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_50,c_75]) ).
tcf(c_2547,plain,
sdtpldt0(sz00,xn) = xn,
inference(superposition,[status(thm)],[c_51,c_75]) ).
tcf(c_2553,plain,
sdtasdt0(xl,sz00) = sz00,
inference(superposition,[status(thm)],[c_49,c_92]) ).
tcf(c_2554,plain,
sdtasdt0(xm,sz00) = sz00,
inference(superposition,[status(thm)],[c_50,c_92]) ).
tcf(c_2555,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_51,c_92]) ).
tcf(c_2556,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(superposition,[status(thm)],[c_94,c_92]) ).
tcf(c_2561,plain,
sdtasdt0(sz00,xl) = sz00,
inference(superposition,[status(thm)],[c_49,c_93]) ).
tcf(c_2562,plain,
sdtasdt0(sz00,xm) = sz00,
inference(superposition,[status(thm)],[c_50,c_93]) ).
tcf(c_2563,plain,
sdtasdt0(sz00,xn) = sz00,
inference(superposition,[status(thm)],[c_51,c_93]) ).
tcf(c_2578,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sdtpldt0(X0,X1)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_93]) ).
tcf(c_2579,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtpldt0(X0,X1),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_92]) ).
tcf(c_2580,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz00,sdtpldt0(X0,X1)) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_75]) ).
tcf(c_2581,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sz00) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_74]) ).
tcf(c_2607,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sdtasdt0(X0,X1)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_93]) ).
tcf(c_2608,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_92]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz00,sdtasdt0(X0,X1)) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_75]) ).
tcf(c_2610,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sz00) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_74]) ).
tcf(c_2633,plain,
( doDivides0(xl,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2553,c_141]) ).
tcf(c_2634,plain,
( doDivides0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2554,c_141]) ).
tcf(c_2635,plain,
( doDivides0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2555,c_141]) ).
tcf(c_2636,plain,
doDivides0(xn,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_2635,c_94,c_51]) ).
tcf(c_2637,plain,
doDivides0(xm,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_2634,c_94,c_50]) ).
tcf(c_2638,plain,
doDivides0(xl,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_2633,c_94,c_49]) ).
tcf(c_2639,plain,
( doDivides0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2556,c_141]) ).
tcf(c_2641,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_2639,c_94]) ).
tcf(c_2654,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2540,c_144]) ).
tcf(c_2655,plain,
( sdtlseqdt0(xl,xl)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2537,c_144]) ).
tcf(c_2656,plain,
( sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2538,c_144]) ).
tcf(c_2657,plain,
( sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2539,c_144]) ).
tcf(c_2658,plain,
( sdtlseqdt0(sz00,xl)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2545,c_144]) ).
tcf(c_2659,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2546,c_144]) ).
tcf(c_2660,plain,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2547,c_144]) ).
tcf(c_2661,plain,
sdtlseqdt0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_2654,c_94]) ).
tcf(c_2662,plain,
sdtlseqdt0(sz00,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_2660,c_94,c_51]) ).
tcf(c_2663,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_2659,c_94,c_50]) ).
tcf(c_2664,plain,
sdtlseqdt0(sz00,xl),
inference(forward_subsumption_resolution,[status(thm)],[c_2658,c_94,c_49]) ).
tcf(c_2665,plain,
sdtlseqdt0(xn,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_2657,c_94,c_51]) ).
tcf(c_2666,plain,
sdtlseqdt0(xm,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_2656,c_94,c_50]) ).
tcf(c_2667,plain,
sdtlseqdt0(xl,xl),
inference(forward_subsumption_resolution,[status(thm)],[c_2655,c_94,c_49]) ).
tcf(c_2668,plain,
( sdtlseqdt0(sdtasdt0(xl,xp),sdtpldt0(sdtasdt0(xl,xp),xn))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(superposition,[status(thm)],[c_59,c_144]) ).
tcf(c_2669,plain,
( aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xp),xn))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(superposition,[status(thm)],[c_59,c_78]) ).
tcf(c_2694,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sK0(X0,X1)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_93]) ).
tcf(c_2695,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sK0(X0,X1),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_92]) ).
tcf(c_2696,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz00,sK0(X0,X1)) = sK0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_75]) ).
tcf(c_2697,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK0(X0,X1),sz00) = sK0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_74]) ).
tcf(c_2724,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xl) = sdtpldt0(xl,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_77]) ).
tcf(c_2725,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xm) = sdtpldt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_77]) ).
tcf(c_2726,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xn) = sdtpldt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_77]) ).
tcf(c_2727,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X2,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_77]) ).
tcf(c_2728,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sK0(X0,X1),X2) = sdtpldt0(X2,sK0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_77]) ).
tcf(c_2729,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),X2) = sdtpldt0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_77]) ).
tcf(c_2730,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_77]) ).
tcf(c_2765,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sK1(X0,X1),X2) = sdtpldt0(X2,sK1(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_77]) ).
tcf(c_2766,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sK1(X0,X1)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_93]) ).
tcf(c_2767,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sK1(X0,X1),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_92]) ).
tcf(c_2768,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz00,sK1(X0,X1)) = sK1(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_75]) ).
tcf(c_2769,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK1(X0,X1),sz00) = sK1(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_74]) ).
tcf(c_2800,plain,
sdtpldt0(xl,xm) = sdtpldt0(xm,xl),
inference(superposition,[status(thm)],[c_50,c_2724]) ).
tcf(c_2801,plain,
sdtpldt0(xl,xn) = sdtpldt0(xn,xl),
inference(superposition,[status(thm)],[c_51,c_2724]) ).
tcf(c_2802,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xl) = sdtpldt0(xl,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_2724]) ).
tcf(c_2803,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK0(X0,X1),xl) = sdtpldt0(xl,sK0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_2724]) ).
tcf(c_2804,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),xl) = sdtpldt0(xl,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_2724]) ).
tcf(c_2805,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK1(X0,X1),xl) = sdtpldt0(xl,sK1(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_2724]) ).
tcf(c_2806,plain,
sdtpldt0(xl,sz00) = sdtpldt0(sz00,xl),
inference(superposition,[status(thm)],[c_94,c_2724]) ).
tcf(c_2830,plain,
( sdtlseqdt0(xm,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2800,c_144]) ).
tcf(c_2831,plain,
( aNaturalNumber0(sdtpldt0(xl,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2800,c_78]) ).
tcf(c_2832,plain,
aNaturalNumber0(sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_2831,c_50,c_49]) ).
tcf(c_2833,plain,
sdtlseqdt0(xm,sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_2830,c_50,c_49]) ).
tcf(c_2836,plain,
sdtpldt0(sdtpldt0(xl,xm),xl) = sdtpldt0(xl,sdtpldt0(xl,xm)),
inference(superposition,[status(thm)],[c_2832,c_2724]) ).
tcf(c_2837,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(X0,sdtpldt0(xl,xm)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_77]) ).
tcf(c_2838,plain,
sdtasdt0(sz00,sdtpldt0(xl,xm)) = sz00,
inference(superposition,[status(thm)],[c_2832,c_93]) ).
tcf(c_2839,plain,
sdtasdt0(sdtpldt0(xl,xm),sz00) = sz00,
inference(superposition,[status(thm)],[c_2832,c_92]) ).
tcf(c_2840,plain,
sdtpldt0(sz00,sdtpldt0(xl,xm)) = sdtpldt0(xl,xm),
inference(superposition,[status(thm)],[c_2832,c_75]) ).
tcf(c_2841,plain,
sdtpldt0(sdtpldt0(xl,xm),sz00) = sdtpldt0(xl,xm),
inference(superposition,[status(thm)],[c_2832,c_74]) ).
tcf(c_2853,plain,
( sdtlseqdt0(xn,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2801,c_144]) ).
tcf(c_2854,plain,
( aNaturalNumber0(sdtpldt0(xl,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2801,c_78]) ).
tcf(c_2855,plain,
aNaturalNumber0(sdtpldt0(xl,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_2854,c_51,c_49]) ).
tcf(c_2856,plain,
sdtlseqdt0(xn,sdtpldt0(xl,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_2853,c_51,c_49]) ).
tcf(c_2859,plain,
sdtpldt0(sdtpldt0(xl,xn),xl) = sdtpldt0(xl,sdtpldt0(xl,xn)),
inference(superposition,[status(thm)],[c_2855,c_2724]) ).
tcf(c_2860,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xl,xn),X0) = sdtpldt0(X0,sdtpldt0(xl,xn)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_77]) ).
tcf(c_2861,plain,
sdtasdt0(sz00,sdtpldt0(xl,xn)) = sz00,
inference(superposition,[status(thm)],[c_2855,c_93]) ).
tcf(c_2862,plain,
sdtasdt0(sdtpldt0(xl,xn),sz00) = sz00,
inference(superposition,[status(thm)],[c_2855,c_92]) ).
tcf(c_2863,plain,
sdtpldt0(sz00,sdtpldt0(xl,xn)) = sdtpldt0(xl,xn),
inference(superposition,[status(thm)],[c_2855,c_75]) ).
tcf(c_2864,plain,
sdtpldt0(sdtpldt0(xl,xn),sz00) = sdtpldt0(xl,xn),
inference(superposition,[status(thm)],[c_2855,c_74]) ).
tcf(c_2878,plain,
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2836,c_144]) ).
tcf(c_2879,plain,
( aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2836,c_78]) ).
tcf(c_2880,plain,
aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))),
inference(forward_subsumption_resolution,[status(thm)],[c_2879,c_49,c_2832]) ).
tcf(c_2881,plain,
sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xl,sdtpldt0(xl,xm))),
inference(forward_subsumption_resolution,[status(thm)],[c_2878,c_49,c_2832]) ).
tcf(c_2890,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xq) ),
inference(superposition,[status(thm)],[c_58,c_104]) ).
tcf(c_2891,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),xl) = sdtpldt0(xl,sdtmndt0(X1,X0)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_2724]) ).
tcf(c_2892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),X2) = sdtpldt0(X2,sdtmndt0(X1,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_77]) ).
tcf(c_2893,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sdtmndt0(X1,X0)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_93]) ).
tcf(c_2894,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtmndt0(X1,X0),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_92]) ).
tcf(c_2895,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz00,sdtmndt0(X1,X0)) = sdtmndt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_75]) ).
tcf(c_2896,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),sz00) = sdtmndt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_74]) ).
tcf(c_2897,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2890,c_57]) ).
tcf(c_2946,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xl) = sdtasdt0(xl,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_107]) ).
tcf(c_2947,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_107]) ).
tcf(c_2948,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_107]) ).
tcf(c_2949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtasdt0(X2,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_107]) ).
tcf(c_2950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sK0(X0,X1),X2) = sdtasdt0(X2,sK0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_107]) ).
tcf(c_2951,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_107]) ).
tcf(c_2952,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sK1(X0,X1),X2) = sdtasdt0(X2,sK1(X0,X1)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_107]) ).
tcf(c_2953,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_107]) ).
tcf(c_2954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtmndt0(X1,X0),X2) = sdtasdt0(X2,sdtmndt0(X1,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_107]) ).
tcf(c_2955,plain,
! [X0: $i] :
( ( sdtasdt0(sdtpldt0(xl,xm),X0) = sdtasdt0(X0,sdtpldt0(xl,xm)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_107]) ).
tcf(c_2956,plain,
! [X0: $i] :
( ( sdtasdt0(sdtpldt0(xl,xn),X0) = sdtasdt0(X0,sdtpldt0(xl,xn)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_107]) ).
tcf(c_3043,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xl,X0),xl) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_147]) ).
tcf(c_3044,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xm,X0),xm) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_147]) ).
tcf(c_3045,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xn,X0),xn) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_147]) ).
tcf(c_3046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_147]) ).
tcf(c_3047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(sdtpldt0(sK0(X0,X1),X2),sK0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_147]) ).
tcf(c_3048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(sdtpldt0(sdtasdt0(X0,X1),X2),sdtasdt0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_147]) ).
tcf(c_3049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(sdtpldt0(sK1(X0,X1),X2),sK1(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_147]) ).
tcf(c_3050,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(sz00,X0),sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_147]) ).
tcf(c_3051,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(sdtpldt0(sdtmndt0(X1,X0),X2),sdtmndt0(X1,X0)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_147]) ).
tcf(c_3052,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,xm)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_147]) ).
tcf(c_3053,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,xn)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_147]) ).
tcf(c_3115,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0),sdtpldt0(xl,sdtpldt0(xl,xm))) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_147]) ).
tcf(c_3116,plain,
! [X0: $i] :
( ( sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0) = sdtasdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xm))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_107]) ).
tcf(c_3117,plain,
sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),xl) = sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))),
inference(superposition,[status(thm)],[c_2880,c_2724]) ).
tcf(c_3118,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0) = sdtpldt0(X0,sdtpldt0(xl,sdtpldt0(xl,xm))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_77]) ).
tcf(c_3119,plain,
sdtasdt0(sz00,sdtpldt0(xl,sdtpldt0(xl,xm))) = sz00,
inference(superposition,[status(thm)],[c_2880,c_93]) ).
tcf(c_3120,plain,
sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sz00) = sz00,
inference(superposition,[status(thm)],[c_2880,c_92]) ).
tcf(c_3121,plain,
sdtpldt0(sz00,sdtpldt0(xl,sdtpldt0(xl,xm))) = sdtpldt0(xl,sdtpldt0(xl,xm)),
inference(superposition,[status(thm)],[c_2880,c_75]) ).
tcf(c_3122,plain,
sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sz00) = sdtpldt0(xl,sdtpldt0(xl,xm)),
inference(superposition,[status(thm)],[c_2880,c_74]) ).
tcf(c_3133,plain,
( doDivides0(sdtpldt0(xl,xm),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2839,c_141]) ).
tcf(c_3135,plain,
doDivides0(sdtpldt0(xl,xm),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3133,c_94,c_2832]) ).
tcf(c_3144,plain,
( doDivides0(sdtpldt0(xl,xn),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2862,c_141]) ).
tcf(c_3146,plain,
doDivides0(sdtpldt0(xl,xn),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3144,c_94,c_2855]) ).
tcf(c_3160,plain,
( sdtlseqdt0(sz00,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2840,c_144]) ).
tcf(c_3162,plain,
sdtlseqdt0(sz00,sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_3160,c_94,c_2832]) ).
tcf(c_3163,plain,
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2841,c_144]) ).
tcf(c_3165,plain,
sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_3163,c_94,c_2832]) ).
tcf(c_3166,plain,
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xl,sdtpldt0(xl,xn)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2859,c_144]) ).
tcf(c_3167,plain,
( aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xn)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2859,c_78]) ).
tcf(c_3168,plain,
aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xn))),
inference(forward_subsumption_resolution,[status(thm)],[c_3167,c_49,c_2855]) ).
tcf(c_3169,plain,
sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xl,sdtpldt0(xl,xn))),
inference(forward_subsumption_resolution,[status(thm)],[c_3166,c_49,c_2855]) ).
tcf(c_3178,plain,
( ( sdtasdt0(xl,xp) = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ( sdtpldt0(sdtasdt0(xl,xp),xn) != sz00 ) ),
inference(superposition,[status(thm)],[c_59,c_68]) ).
tcf(c_3186,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xl,xm) != sz00 ) ),
inference(superposition,[status(thm)],[c_2800,c_68]) ).
tcf(c_3187,plain,
( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xl,xn) != sz00 ) ),
inference(superposition,[status(thm)],[c_2801,c_68]) ).
tcf(c_3188,plain,
( ( sdtpldt0(xl,xm) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(xl,sdtpldt0(xl,xm)) != sz00 ) ),
inference(superposition,[status(thm)],[c_2836,c_68]) ).
tcf(c_3191,plain,
( ( sdtpldt0(xl,xn) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(xl,sdtpldt0(xl,xn)) != sz00 ) ),
inference(superposition,[status(thm)],[c_2859,c_68]) ).
tcf(c_3192,plain,
( ( xn = sz00 )
| ( sdtpldt0(xl,xn) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3187,c_51,c_49]) ).
tcf(c_3195,plain,
( ( xm = sz00 )
| ( sdtpldt0(xl,xm) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3186,c_50,c_49]) ).
tcf(c_3198,plain,
( ( sdtpldt0(xl,xn) = sz00 )
| ( sdtpldt0(xl,sdtpldt0(xl,xn)) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3191,c_49,c_2855]) ).
tcf(c_3201,plain,
( ( sdtpldt0(xl,xm) = sz00 )
| ( sdtpldt0(xl,sdtpldt0(xl,xm)) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3188,c_49,c_2832]) ).
tcf(c_3248,plain,
( ( sdtasdt0(xl,xr) = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ( sdtpldt0(sdtasdt0(xl,xp),xn) != sz00 ) ),
inference(superposition,[status(thm)],[c_59,c_69]) ).
tcf(c_3256,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xl,xm) != sz00 ) ),
inference(superposition,[status(thm)],[c_2800,c_69]) ).
tcf(c_3257,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xl,xn) != sz00 ) ),
inference(superposition,[status(thm)],[c_2801,c_69]) ).
tcf(c_3258,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(xl,sdtpldt0(xl,xm)) != sz00 ) ),
inference(superposition,[status(thm)],[c_2836,c_69]) ).
tcf(c_3261,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(xl,sdtpldt0(xl,xn)) != sz00 ) ),
inference(superposition,[status(thm)],[c_2859,c_69]) ).
tcf(c_3262,plain,
sdtpldt0(xl,xn) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3257,c_54,c_51,c_49]) ).
tcf(c_3263,plain,
sdtpldt0(xl,xm) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3256,c_54,c_50,c_49]) ).
tcf(c_3264,plain,
sdtpldt0(xl,sdtpldt0(xl,xn)) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3261,c_54,c_49,c_2855]) ).
tcf(c_3265,plain,
sdtpldt0(xl,sdtpldt0(xl,xm)) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3258,c_54,c_49,c_2832]) ).
tcf(c_3278,plain,
( ( sdtpldt0(xp,sK0(xp,xq)) = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_57,c_67]) ).
tcf(c_3279,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_99,c_67]) ).
tcf(c_3280,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK0(X0,sdtpldt0(X0,X1))) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_144,c_67]) ).
tcf(c_3281,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( sdtpldt0(X0,sK0(X0,sdtasdt0(X0,X1))) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_84,c_67]) ).
tcf(c_3282,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK0(X0,X0)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_102,c_67]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( sdtpldt0(X1,sK0(X1,X0)) = X0 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_99,c_67]) ).
tcf(c_3284,plain,
( ( sdtpldt0(sz00,sK0(sz00,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2661,c_67]) ).
tcf(c_3285,plain,
( ( sdtpldt0(xl,sK0(xl,xl)) = xl )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2667,c_67]) ).
tcf(c_3286,plain,
( ( sdtpldt0(xm,sK0(xm,xm)) = xm )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2666,c_67]) ).
tcf(c_3287,plain,
( ( sdtpldt0(xn,sK0(xn,xn)) = xn )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2665,c_67]) ).
tcf(c_3288,plain,
( ( sdtpldt0(sz00,sK0(sz00,xl)) = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2664,c_67]) ).
tcf(c_3289,plain,
( ( sdtpldt0(sz00,sK0(sz00,xm)) = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2663,c_67]) ).
tcf(c_3290,plain,
( ( sdtpldt0(sz00,sK0(sz00,xn)) = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2662,c_67]) ).
tcf(c_3291,plain,
( ( sdtpldt0(xm,sK0(xm,sdtpldt0(xl,xm))) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2833,c_67]) ).
tcf(c_3292,plain,
( ( sdtpldt0(xn,sK0(xn,sdtpldt0(xl,xn))) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2856,c_67]) ).
tcf(c_3293,plain,
( ( sdtpldt0(sdtpldt0(xl,xm),sK0(sdtpldt0(xl,xm),sdtpldt0(xl,sdtpldt0(xl,xm)))) = sdtpldt0(xl,sdtpldt0(xl,xm)) )
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_2881,c_67]) ).
tcf(c_3294,plain,
( ( sdtpldt0(sz00,sK0(sz00,sdtpldt0(xl,xm))) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3162,c_67]) ).
tcf(c_3295,plain,
( ( sdtpldt0(sdtpldt0(xl,xm),sK0(sdtpldt0(xl,xm),sdtpldt0(xl,xm))) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3165,c_67]) ).
tcf(c_3296,plain,
sdtpldt0(xn,sK0(xn,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_3287,c_51]) ).
tcf(c_3297,plain,
sdtpldt0(xm,sK0(xm,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_3286,c_50]) ).
tcf(c_3298,plain,
sdtpldt0(xl,sK0(xl,xl)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_3285,c_49]) ).
tcf(c_3299,plain,
sdtpldt0(sz00,sK0(sz00,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3284,c_94]) ).
tcf(c_3302,plain,
sdtpldt0(sz00,sK0(sz00,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_3290,c_94,c_51]) ).
tcf(c_3303,plain,
sdtpldt0(sz00,sK0(sz00,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_3289,c_94,c_50]) ).
tcf(c_3304,plain,
sdtpldt0(sz00,sK0(sz00,xl)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_3288,c_94,c_49]) ).
tcf(c_3316,plain,
sdtpldt0(sz00,sK0(sz00,sdtpldt0(xl,xm))) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3294,c_94,c_2832]) ).
tcf(c_3317,plain,
sdtpldt0(xn,sK0(xn,sdtpldt0(xl,xn))) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_3292,c_51,c_2855]) ).
tcf(c_3318,plain,
sdtpldt0(xm,sK0(xm,sdtpldt0(xl,xm))) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3291,c_50,c_2832]) ).
tcf(c_3319,plain,
sdtpldt0(sdtpldt0(xl,xm),sK0(sdtpldt0(xl,xm),sdtpldt0(xl,xm))) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3295,c_2832]) ).
tcf(c_3329,plain,
sdtpldt0(sdtpldt0(xl,xm),sK0(sdtpldt0(xl,xm),sdtpldt0(xl,sdtpldt0(xl,xm)))) = sdtpldt0(xl,sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_3293,c_2832,c_2880]) ).
tcf(c_3339,plain,
( ( sdtasdt0(xl,sK1(xl,xm)) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_52,c_83]) ).
tcf(c_3340,plain,
( ( sdtasdt0(xl,sK1(xl,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_53,c_83]) ).
tcf(c_3341,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK1(X0,sdtasdt0(X0,X1))) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_141,c_83]) ).
tcf(c_3342,plain,
( ( sdtasdt0(sz00,sK1(sz00,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2641,c_83]) ).
tcf(c_3343,plain,
( ( sdtasdt0(xl,sK1(xl,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2638,c_83]) ).
tcf(c_3344,plain,
( ( sdtasdt0(xm,sK1(xm,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2637,c_83]) ).
tcf(c_3345,plain,
( ( sdtasdt0(xn,sK1(xn,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2636,c_83]) ).
tcf(c_3346,plain,
( ( sdtasdt0(sdtpldt0(xl,xm),sK1(sdtpldt0(xl,xm),sz00)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3135,c_83]) ).
tcf(c_3347,plain,
( ( sdtasdt0(sdtpldt0(xl,xn),sK1(sdtpldt0(xl,xn),sz00)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3146,c_83]) ).
tcf(c_3348,plain,
sdtasdt0(sz00,sK1(sz00,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3342,c_94]) ).
tcf(c_3349,plain,
sdtasdt0(xn,sK1(xn,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3345,c_94,c_51]) ).
tcf(c_3350,plain,
sdtasdt0(xm,sK1(xm,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3344,c_94,c_50]) ).
tcf(c_3351,plain,
sdtasdt0(xl,sK1(xl,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3343,c_94,c_49]) ).
tcf(c_3352,plain,
sdtasdt0(xl,sK1(xl,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_3339,c_50,c_49]) ).
tcf(c_3353,plain,
sdtasdt0(sdtpldt0(xl,xn),sK1(sdtpldt0(xl,xn),sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3347,c_94,c_2855]) ).
tcf(c_3354,plain,
sdtasdt0(sdtpldt0(xl,xm),sK1(sdtpldt0(xl,xm),sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3346,c_94,c_2832]) ).
tcf(c_3355,plain,
( ( sdtasdt0(xl,sK1(xl,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3340,c_49]) ).
tcf(c_3391,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xn)),X0),sdtpldt0(xl,sdtpldt0(xl,xn))) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_147]) ).
tcf(c_3392,plain,
! [X0: $i] :
( ( sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),X0) = sdtasdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xn))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_107]) ).
tcf(c_3393,plain,
sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xn)),xl) = sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xn))),
inference(superposition,[status(thm)],[c_3168,c_2724]) ).
tcf(c_3394,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xn)),X0) = sdtpldt0(X0,sdtpldt0(xl,sdtpldt0(xl,xn))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_77]) ).
tcf(c_3395,plain,
sdtasdt0(sz00,sdtpldt0(xl,sdtpldt0(xl,xn))) = sz00,
inference(superposition,[status(thm)],[c_3168,c_93]) ).
tcf(c_3396,plain,
sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),sz00) = sz00,
inference(superposition,[status(thm)],[c_3168,c_92]) ).
tcf(c_3397,plain,
sdtpldt0(sz00,sdtpldt0(xl,sdtpldt0(xl,xn))) = sdtpldt0(xl,sdtpldt0(xl,xn)),
inference(superposition,[status(thm)],[c_3168,c_75]) ).
tcf(c_3398,plain,
sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xn)),sz00) = sdtpldt0(xl,sdtpldt0(xl,xn)),
inference(superposition,[status(thm)],[c_3168,c_74]) ).
tcf(c_3408,plain,
( ( sK0(xn,xn) = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK0(xn,xn))
| ( xn != sz00 ) ),
inference(superposition,[status(thm)],[c_3296,c_69]) ).
tcf(c_3412,plain,
( ( sK0(xn,xn) = sz00 )
| ~ aNaturalNumber0(sK0(xn,xn))
| ( xn != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3408,c_51]) ).
tcf(c_3416,plain,
( ( sK0(xm,xm) = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK0(xm,xm))
| ( xm != sz00 ) ),
inference(superposition,[status(thm)],[c_3297,c_69]) ).
tcf(c_3420,plain,
( ( sK0(xm,xm) = sz00 )
| ~ aNaturalNumber0(sK0(xm,xm))
| ( xm != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3416,c_50]) ).
tcf(c_3428,plain,
( ( sK0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK0(sz00,sz00)) ),
inference(superposition,[status(thm)],[c_3299,c_69]) ).
tcf(c_3432,plain,
( ( sK0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sK0(sz00,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3428,c_94]) ).
tcf(c_3435,plain,
( ( sK0(sz00,xn) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( xn != sz00 ) ),
inference(superposition,[status(thm)],[c_3302,c_69]) ).
tcf(c_3439,plain,
( ( sK0(sz00,xn) = sz00 )
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( xn != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3435,c_94]) ).
tcf(c_3443,plain,
( ( sK0(sz00,xm) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( xm != sz00 ) ),
inference(superposition,[status(thm)],[c_3303,c_69]) ).
tcf(c_3447,plain,
( ( sK0(sz00,xm) = sz00 )
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( xm != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3443,c_94]) ).
tcf(c_3458,plain,
( sdtlseqdt0(xn,sz00)
| ( sK1(xn,sz00) = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK1(xn,sz00)) ),
inference(superposition,[status(thm)],[c_3349,c_84]) ).
tcf(c_3461,plain,
( sdtlseqdt0(xn,sz00)
| ( sK1(xn,sz00) = sz00 )
| ~ aNaturalNumber0(sK1(xn,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3458,c_51]) ).
tcf(c_3467,plain,
( sdtlseqdt0(sz00,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2863,c_144]) ).
tcf(c_3469,plain,
sdtlseqdt0(sz00,sdtpldt0(xl,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_3467,c_94,c_2855]) ).
tcf(c_3480,plain,
( aNaturalNumber0(xp)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_3481,plain,
( aNaturalNumber0(xq)
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_56,c_96]) ).
tcf(c_3482,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtmndt0(sdtpldt0(sdtsldt0(X1,X0),X2),sdtsldt0(X1,X0)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_147]) ).
tcf(c_3483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(sdtsldt0(X1,X0),X2) = sdtasdt0(X2,sdtsldt0(X1,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_107]) ).
tcf(c_3484,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtsldt0(X1,X0),xl) = sdtpldt0(xl,sdtsldt0(X1,X0)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_2724]) ).
tcf(c_3485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtsldt0(X1,X0),X2) = sdtpldt0(X2,sdtsldt0(X1,X0)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_77]) ).
tcf(c_3486,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(sz00,sdtsldt0(X1,X0)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_93]) ).
tcf(c_3487,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(sdtsldt0(X1,X0),sz00) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_92]) ).
tcf(c_3488,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtsldt0(X1,X0)) = sdtsldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_75]) ).
tcf(c_3489,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtsldt0(X1,X0),sz00) = sdtsldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_74]) ).
tcf(c_3490,plain,
aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[status(thm)],[c_3480,c_54,c_50,c_49,c_52]) ).
tcf(c_3491,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3481,c_54,c_49,c_53]) ).
tcf(c_3537,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2897,c_3490]) ).
tcf(c_3560,plain,
( ( xp = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xq,xp) ),
inference(superposition,[status(thm)],[c_57,c_101]) ).
tcf(c_3562,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = X0 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_144,c_101]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( sdtasdt0(X0,X1) = X0 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_84,c_101]) ).
tcf(c_3570,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xl,sz00) ),
inference(superposition,[status(thm)],[c_2664,c_101]) ).
tcf(c_3571,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,sz00) ),
inference(superposition,[status(thm)],[c_2663,c_101]) ).
tcf(c_3572,plain,
( ( xn = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,sz00) ),
inference(superposition,[status(thm)],[c_2662,c_101]) ).
tcf(c_3573,plain,
( ( sdtpldt0(xl,xm) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ sdtlseqdt0(sdtpldt0(xl,xm),xm) ),
inference(superposition,[status(thm)],[c_2833,c_101]) ).
tcf(c_3574,plain,
( ( sdtpldt0(xl,xn) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ sdtlseqdt0(sdtpldt0(xl,xn),xn) ),
inference(superposition,[status(thm)],[c_2856,c_101]) ).
tcf(c_3575,plain,
( ( sdtpldt0(xl,sdtpldt0(xl,xm)) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2881,c_101]) ).
tcf(c_3576,plain,
( ( sdtpldt0(xl,xm) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sz00) ),
inference(superposition,[status(thm)],[c_3162,c_101]) ).
tcf(c_3578,plain,
( ( xn = sz00 )
| ~ sdtlseqdt0(xn,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3572,c_94,c_51]) ).
tcf(c_3581,plain,
( ( xm = sz00 )
| ~ sdtlseqdt0(xm,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3571,c_94,c_50]) ).
tcf(c_3584,plain,
~ sdtlseqdt0(xl,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3570,c_54,c_94,c_49]) ).
tcf(c_3589,plain,
~ sdtlseqdt0(sdtpldt0(xl,xm),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3576,c_3263,c_94,c_2832]) ).
tcf(c_3590,plain,
( ( sdtpldt0(xl,xn) = xn )
| ~ sdtlseqdt0(sdtpldt0(xl,xn),xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3574,c_51,c_2855]) ).
tcf(c_3593,plain,
( ( sdtpldt0(xl,xm) = xm )
| ~ sdtlseqdt0(sdtpldt0(xl,xm),xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3573,c_50,c_2832]) ).
tcf(c_3607,plain,
( ( sdtpldt0(xl,sdtpldt0(xl,xm)) = sdtpldt0(xl,xm) )
| ~ sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3575,c_2832,c_2880]) ).
tcf(c_3637,plain,
( ( sdtpldt0(xp,sdtmndt0(xq,xp)) = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_57,c_105]) ).
tcf(c_3638,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_99,c_105]) ).
tcf(c_3639,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(sdtpldt0(X0,X1),X0)) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_144,c_105]) ).
tcf(c_3640,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( sdtpldt0(X0,sdtmndt0(sdtasdt0(X0,X1),X0)) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_84,c_105]) ).
tcf(c_3641,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_102,c_105]) ).
tcf(c_3642,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( sdtpldt0(X1,sdtmndt0(X0,X1)) = X0 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_99,c_105]) ).
tcf(c_3643,plain,
( ( sdtpldt0(sz00,sdtmndt0(sz00,sz00)) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2661,c_105]) ).
tcf(c_3644,plain,
( ( sdtpldt0(xl,sdtmndt0(xl,xl)) = xl )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2667,c_105]) ).
tcf(c_3645,plain,
( ( sdtpldt0(xm,sdtmndt0(xm,xm)) = xm )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2666,c_105]) ).
tcf(c_3646,plain,
( ( sdtpldt0(xn,sdtmndt0(xn,xn)) = xn )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2665,c_105]) ).
tcf(c_3647,plain,
( ( sdtpldt0(sz00,sdtmndt0(xl,sz00)) = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2664,c_105]) ).
tcf(c_3648,plain,
( ( sdtpldt0(sz00,sdtmndt0(xm,sz00)) = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2663,c_105]) ).
tcf(c_3649,plain,
( ( sdtpldt0(sz00,sdtmndt0(xn,sz00)) = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2662,c_105]) ).
tcf(c_3650,plain,
( ( sdtpldt0(xm,sdtmndt0(sdtpldt0(xl,xm),xm)) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2833,c_105]) ).
tcf(c_3651,plain,
( ( sdtpldt0(xn,sdtmndt0(sdtpldt0(xl,xn),xn)) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2856,c_105]) ).
tcf(c_3652,plain,
( ( sdtpldt0(sdtpldt0(xl,xm),sdtmndt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,xm))) = sdtpldt0(xl,sdtpldt0(xl,xm)) )
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_2881,c_105]) ).
tcf(c_3653,plain,
( ( sdtpldt0(sz00,sdtmndt0(sdtpldt0(xl,xm),sz00)) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3162,c_105]) ).
tcf(c_3654,plain,
( ( sdtpldt0(sdtpldt0(xl,xm),sdtmndt0(sdtpldt0(xl,xm),sdtpldt0(xl,xm))) = sdtpldt0(xl,xm) )
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3165,c_105]) ).
tcf(c_3655,plain,
sdtpldt0(xn,sdtmndt0(xn,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_3646,c_51]) ).
tcf(c_3656,plain,
sdtpldt0(xm,sdtmndt0(xm,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_3645,c_50]) ).
tcf(c_3657,plain,
sdtpldt0(xl,sdtmndt0(xl,xl)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_3644,c_49]) ).
tcf(c_3658,plain,
sdtpldt0(sz00,sdtmndt0(sz00,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3643,c_94]) ).
tcf(c_3661,plain,
sdtpldt0(sz00,sdtmndt0(xn,sz00)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_3649,c_94,c_51]) ).
tcf(c_3662,plain,
sdtpldt0(sz00,sdtmndt0(xm,sz00)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_3648,c_94,c_50]) ).
tcf(c_3663,plain,
sdtpldt0(sz00,sdtmndt0(xl,sz00)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_3647,c_94,c_49]) ).
tcf(c_3664,plain,
( ( sdtpldt0(xp,xr) = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(light_normalisation,[status(thm)],[c_3637,c_58]) ).
tcf(c_3676,plain,
sdtpldt0(sz00,sdtmndt0(sdtpldt0(xl,xm),sz00)) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3653,c_94,c_2832]) ).
tcf(c_3677,plain,
sdtpldt0(xn,sdtmndt0(sdtpldt0(xl,xn),xn)) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_3651,c_51,c_2855]) ).
tcf(c_3678,plain,
sdtpldt0(xm,sdtmndt0(sdtpldt0(xl,xm),xm)) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3650,c_50,c_2832]) ).
tcf(c_3679,plain,
sdtpldt0(sdtpldt0(xl,xm),sdtmndt0(sdtpldt0(xl,xm),sdtpldt0(xl,xm))) = sdtpldt0(xl,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_3654,c_2832]) ).
tcf(c_3689,plain,
sdtpldt0(sdtpldt0(xl,xm),sdtmndt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,xm))) = sdtpldt0(xl,sdtpldt0(xl,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_3652,c_2832,c_2880]) ).
tcf(c_3734,plain,
! [X0: $i] :
( ( xl = sz00 )
| ( sdtsldt0(sdtasdt0(xl,X0),xl) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_154]) ).
tcf(c_3735,plain,
! [X0: $i] :
( ( xm = sz00 )
| ( sdtsldt0(sdtasdt0(xm,X0),xm) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_154]) ).
tcf(c_3736,plain,
! [X0: $i] :
( ( xn = sz00 )
| ( sdtsldt0(sdtasdt0(xn,X0),xn) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_154]) ).
tcf(c_3737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X0,X1) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtpldt0(X0,X1),X2),sdtpldt0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_154]) ).
tcf(c_3738,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK0(X0,X1) = sz00 )
| ( sdtsldt0(sdtasdt0(sK0(X0,X1),X2),sK0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_154]) ).
tcf(c_3739,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X0,X1) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtasdt0(X0,X1),X2),sdtasdt0(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_154]) ).
tcf(c_3740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(X0,X1) = sz00 )
| ( sdtsldt0(sdtasdt0(sK1(X0,X1),X2),sK1(X0,X1)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_154]) ).
tcf(c_3742,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(X1,X0) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtsldt0(X1,X0),X2),sdtsldt0(X1,X0)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_154]) ).
tcf(c_3743,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(X1,X0) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtmndt0(X1,X0),X2),sdtmndt0(X1,X0)) = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_154]) ).
tcf(c_3744,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,xm)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_154]) ).
tcf(c_3745,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,xn)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_154]) ).
tcf(c_3746,plain,
! [X0: $i] :
( ( sdtpldt0(xl,sdtpldt0(xl,xm)) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0),sdtpldt0(xl,sdtpldt0(xl,xm))) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_154]) ).
tcf(c_3747,plain,
! [X0: $i] :
( ( sdtpldt0(xl,sdtpldt0(xl,xn)) = sz00 )
| ( sdtsldt0(sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),X0),sdtpldt0(xl,sdtpldt0(xl,xn))) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_154]) ).
tcf(c_3754,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(xl,X0),xl) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3734,c_54]) ).
tcf(c_3757,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,xn)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3745,c_3262]) ).
tcf(c_3760,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,xm)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3744,c_3263]) ).
tcf(c_3835,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( sdtsldt0(sdtasdt0(xp,X0),xp) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_154]) ).
tcf(c_3836,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xp,X0),xp) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_147]) ).
tcf(c_3837,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_107]) ).
tcf(c_3838,plain,
sdtpldt0(xl,xp) = sdtpldt0(xp,xl),
inference(superposition,[status(thm)],[c_3490,c_2724]) ).
tcf(c_3839,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xp) = sdtpldt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_77]) ).
tcf(c_3840,plain,
sdtasdt0(sz00,xp) = sz00,
inference(superposition,[status(thm)],[c_3490,c_93]) ).
tcf(c_3841,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_3490,c_92]) ).
tcf(c_3842,plain,
sdtpldt0(sz00,xp) = xp,
inference(superposition,[status(thm)],[c_3490,c_75]) ).
tcf(c_3843,plain,
sdtpldt0(xp,sz00) = xp,
inference(superposition,[status(thm)],[c_3490,c_74]) ).
tcf(c_3901,plain,
( ( sdtpldt0(sz00,sdtmndt0(sdtpldt0(xl,xn),sz00)) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3469,c_105]) ).
tcf(c_3902,plain,
( ( sdtpldt0(xl,xn) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ sdtlseqdt0(sdtpldt0(xl,xn),sz00) ),
inference(superposition,[status(thm)],[c_3469,c_101]) ).
tcf(c_3903,plain,
( ( sdtpldt0(sz00,sK0(sz00,sdtpldt0(xl,xn))) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3469,c_67]) ).
tcf(c_3904,plain,
sdtpldt0(sz00,sK0(sz00,sdtpldt0(xl,xn))) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_3903,c_94,c_2855]) ).
tcf(c_3905,plain,
~ sdtlseqdt0(sdtpldt0(xl,xn),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3902,c_3262,c_94,c_2855]) ).
tcf(c_3906,plain,
sdtpldt0(sz00,sdtmndt0(sdtpldt0(xl,xn),sz00)) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_3901,c_94,c_2855]) ).
tcf(c_3917,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3841,c_141]) ).
tcf(c_3919,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3917,c_3490,c_94]) ).
tcf(c_3920,plain,
( ( sdtasdt0(xp,sK1(xp,sz00)) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3919,c_83]) ).
tcf(c_3921,plain,
sdtasdt0(xp,sK1(xp,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_3920,c_3490,c_94]) ).
tcf(c_3924,plain,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3842,c_144]) ).
tcf(c_3926,plain,
sdtlseqdt0(sz00,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_3924,c_3490,c_94]) ).
tcf(c_3930,plain,
( ( sdtpldt0(sz00,sdtmndt0(xp,sz00)) = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3926,c_105]) ).
tcf(c_3931,plain,
( ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xp,sz00) ),
inference(superposition,[status(thm)],[c_3926,c_101]) ).
tcf(c_3932,plain,
( ( sdtpldt0(sz00,sK0(sz00,xp)) = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3926,c_67]) ).
tcf(c_3933,plain,
sdtpldt0(sz00,sK0(sz00,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_3932,c_3490,c_94]) ).
tcf(c_3934,plain,
( ( sz00 = xp )
| ~ sdtlseqdt0(xp,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3931,c_3490,c_94]) ).
tcf(c_3937,plain,
sdtpldt0(sz00,sdtmndt0(xp,sz00)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_3930,c_3490,c_94]) ).
tcf(c_3956,plain,
( sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3843,c_144]) ).
tcf(c_3958,plain,
sdtlseqdt0(xp,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_3956,c_3490,c_94]) ).
tcf(c_3959,plain,
( ( sdtpldt0(xp,sdtmndt0(xp,xp)) = xp )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_3958,c_105]) ).
tcf(c_3961,plain,
( ( sdtpldt0(xp,sK0(xp,xp)) = xp )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_3958,c_67]) ).
tcf(c_3962,plain,
sdtpldt0(xp,sK0(xp,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_3961,c_3490]) ).
tcf(c_3963,plain,
sdtpldt0(xp,sdtmndt0(xp,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_3959,c_3490]) ).
tcf(c_3966,plain,
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xl,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2864,c_144]) ).
tcf(c_3968,plain,
sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xl,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_3966,c_94,c_2855]) ).
tcf(c_3981,plain,
! [X0: $i] :
( doDivides0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl) ),
inference(superposition,[status(thm)],[c_52,c_80]) ).
tcf(c_3982,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_53,c_80]) ).
tcf(c_3983,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_141,c_80]) ).
tcf(c_3985,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl) ),
inference(superposition,[status(thm)],[c_2638,c_80]) ).
tcf(c_3986,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xm) ),
inference(superposition,[status(thm)],[c_2637,c_80]) ).
tcf(c_3987,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xn) ),
inference(superposition,[status(thm)],[c_2636,c_80]) ).
tcf(c_3988,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ doDivides0(X0,sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3135,c_80]) ).
tcf(c_3989,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ doDivides0(X0,sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3146,c_80]) ).
tcf(c_3990,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ),
inference(superposition,[status(thm)],[c_3919,c_80]) ).
tcf(c_3991,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3990,c_3490,c_94]) ).
tcf(c_3995,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3987,c_94,c_51]) ).
tcf(c_3999,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3986,c_94,c_50]) ).
tcf(c_4003,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3985,c_94,c_49]) ).
tcf(c_4007,plain,
! [X0: $i] :
( doDivides0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3981,c_50,c_49]) ).
tcf(c_4011,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(xl,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3989,c_94,c_2855]) ).
tcf(c_4015,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3988,c_94,c_2832]) ).
tcf(c_4019,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3982,c_49]) ).
tcf(c_4083,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(superposition,[status(thm)],[c_57,c_100]) ).
tcf(c_4085,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_144,c_100]) ).
tcf(c_4086,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,sdtasdt0(X0,X1))
| ( X1 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_84,c_100]) ).
tcf(c_4088,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_99,c_100]) ).
tcf(c_4093,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xl)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2664,c_100]) ).
tcf(c_4094,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2663,c_100]) ).
tcf(c_4095,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2662,c_100]) ).
tcf(c_4096,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2833,c_100]) ).
tcf(c_4097,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2856,c_100]) ).
tcf(c_4098,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_2881,c_100]) ).
tcf(c_4099,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3162,c_100]) ).
tcf(c_4101,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3469,c_100]) ).
tcf(c_4102,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_3926,c_100]) ).
tcf(c_4104,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4102,c_3490,c_94]) ).
tcf(c_4108,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4095,c_94,c_51]) ).
tcf(c_4112,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4094,c_94,c_50]) ).
tcf(c_4116,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4093,c_94,c_49]) ).
tcf(c_4120,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4083,c_3490]) ).
tcf(c_4131,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4101,c_94,c_2855]) ).
tcf(c_4135,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4099,c_94,c_2832]) ).
tcf(c_4139,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4097,c_51,c_2855]) ).
tcf(c_4143,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4096,c_50,c_2832]) ).
tcf(c_4160,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4098,c_2832,c_2880]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xl) = sdtpldt0(X0,sdtpldt0(X1,xl)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_76]) ).
tcf(c_4201,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xm) = sdtpldt0(X0,sdtpldt0(X1,xm)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_76]) ).
tcf(c_4202,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xn) = sdtpldt0(X0,sdtpldt0(X1,xn)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_76]) ).
tcf(c_4203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(X2,X3),sdtpldt0(X0,X1)) = sdtpldt0(X2,sdtpldt0(X3,sdtpldt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_76]) ).
tcf(c_4204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(X2,X3),sK0(X0,X1)) = sdtpldt0(X2,sdtpldt0(X3,sK0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_76]) ).
tcf(c_4205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(X2,X3),sdtasdt0(X0,X1)) = sdtpldt0(X2,sdtpldt0(X3,sdtasdt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_76]) ).
tcf(c_4206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(X2,X3),sK1(X0,X1)) = sdtpldt0(X2,sdtpldt0(X3,sK1(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_76]) ).
tcf(c_4207,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sz00) = sdtpldt0(X0,sdtpldt0(X1,sz00)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_76]) ).
tcf(c_4208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtpldt0(X2,X3),sdtsldt0(X1,X0)) = sdtpldt0(X2,sdtpldt0(X3,sdtsldt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_76]) ).
tcf(c_4209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(X2,X3),sdtmndt0(X1,X0)) = sdtpldt0(X2,sdtpldt0(X3,sdtmndt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_76]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(xl,xm)) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(xl,xm))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_76]) ).
tcf(c_4211,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(xl,xn)) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(xl,xn))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_76]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(xl,sdtpldt0(xl,xm))) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xm)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_76]) ).
tcf(c_4213,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xp) = sdtpldt0(X0,sdtpldt0(X1,xp)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_76]) ).
tcf(c_4214,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(xl,sdtpldt0(xl,xn))) = sdtpldt0(X0,sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xn)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_76]) ).
tcf(c_4354,plain,
( ( xn = sz00 )
| ( sK1(xn,sz00) = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK1(xn,sz00)) ),
inference(superposition,[status(thm)],[c_3349,c_89]) ).
tcf(c_4357,plain,
( ( xn = sz00 )
| ( sK1(xn,sz00) = sz00 )
| ~ aNaturalNumber0(sK1(xn,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4354,c_51]) ).
tcf(c_4367,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_78,c_3491]) ).
tcf(c_4368,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[status(thm)],[c_4367,c_51,c_50]) ).
tcf(c_4369,plain,
aNaturalNumber0(xr),
inference(backward_subsumption_resolution,[status(thm)],[c_3537,c_4368]) ).
tcf(c_4370,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xq) = sdtpldt0(X0,sdtpldt0(X1,xq)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_76]) ).
tcf(c_4371,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( sdtsldt0(sdtasdt0(xq,X0),xq) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_154]) ).
tcf(c_4372,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xq,X0),xq) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_147]) ).
tcf(c_4373,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xq) = sdtasdt0(xq,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_107]) ).
tcf(c_4374,plain,
sdtpldt0(xl,xq) = sdtpldt0(xq,xl),
inference(superposition,[status(thm)],[c_4368,c_2724]) ).
tcf(c_4375,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xq) = sdtpldt0(xq,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_77]) ).
tcf(c_4376,plain,
sdtasdt0(sz00,xq) = sz00,
inference(superposition,[status(thm)],[c_4368,c_93]) ).
tcf(c_4377,plain,
sdtasdt0(xq,sz00) = sz00,
inference(superposition,[status(thm)],[c_4368,c_92]) ).
tcf(c_4378,plain,
sdtpldt0(sz00,xq) = xq,
inference(superposition,[status(thm)],[c_4368,c_75]) ).
tcf(c_4379,plain,
sdtpldt0(xq,sz00) = xq,
inference(superposition,[status(thm)],[c_4368,c_74]) ).
tcf(c_4430,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),xr) = sdtpldt0(X0,sdtpldt0(X1,xr)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_76]) ).
tcf(c_4431,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(xr,X0),xr) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_154]) ).
tcf(c_4432,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(xr,X0),xr) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_147]) ).
tcf(c_4433,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xr) = sdtasdt0(xr,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_107]) ).
tcf(c_4434,plain,
sdtpldt0(xl,xr) = sdtpldt0(xr,xl),
inference(superposition,[status(thm)],[c_4369,c_2724]) ).
tcf(c_4435,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xr) = sdtpldt0(xr,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_77]) ).
tcf(c_4436,plain,
sdtasdt0(sz00,xr) = sz00,
inference(superposition,[status(thm)],[c_4369,c_93]) ).
tcf(c_4437,plain,
sdtasdt0(xr,sz00) = sz00,
inference(superposition,[status(thm)],[c_4369,c_92]) ).
tcf(c_4438,plain,
sdtpldt0(sz00,xr) = xr,
inference(superposition,[status(thm)],[c_4369,c_75]) ).
tcf(c_4439,plain,
sdtpldt0(xr,sz00) = xr,
inference(superposition,[status(thm)],[c_4369,c_74]) ).
tcf(c_4463,plain,
( doDivides0(xq,sz00)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4377,c_141]) ).
tcf(c_4465,plain,
doDivides0(xq,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4463,c_4368,c_94]) ).
tcf(c_4466,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xq) ),
inference(superposition,[status(thm)],[c_4465,c_80]) ).
tcf(c_4467,plain,
( ( sdtasdt0(xq,sK1(xq,sz00)) = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4465,c_83]) ).
tcf(c_4468,plain,
sdtasdt0(xq,sK1(xq,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_4467,c_4368,c_94]) ).
tcf(c_4469,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xq) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4466,c_4368,c_94]) ).
tcf(c_4475,plain,
( sdtlseqdt0(sz00,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4378,c_144]) ).
tcf(c_4477,plain,
sdtlseqdt0(sz00,xq),
inference(forward_subsumption_resolution,[status(thm)],[c_4475,c_4368,c_94]) ).
tcf(c_4486,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_4477,c_100]) ).
tcf(c_4487,plain,
( ( sdtpldt0(sz00,sdtmndt0(xq,sz00)) = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4477,c_105]) ).
tcf(c_4488,plain,
( ( sz00 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xq,sz00) ),
inference(superposition,[status(thm)],[c_4477,c_101]) ).
tcf(c_4489,plain,
( ( sdtpldt0(sz00,sK0(sz00,xq)) = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4477,c_67]) ).
tcf(c_4490,plain,
sdtpldt0(sz00,sK0(sz00,xq)) = xq,
inference(forward_subsumption_resolution,[status(thm)],[c_4489,c_4368,c_94]) ).
tcf(c_4491,plain,
( ( sz00 = xq )
| ~ sdtlseqdt0(xq,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4488,c_4368,c_94]) ).
tcf(c_4494,plain,
sdtpldt0(sz00,sdtmndt0(xq,sz00)) = xq,
inference(forward_subsumption_resolution,[status(thm)],[c_4487,c_4368,c_94]) ).
tcf(c_4495,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4486,c_4368,c_94]) ).
tcf(c_4511,plain,
( sdtlseqdt0(xq,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4379,c_144]) ).
tcf(c_4513,plain,
sdtlseqdt0(xq,xq),
inference(forward_subsumption_resolution,[status(thm)],[c_4511,c_4368,c_94]) ).
tcf(c_4515,plain,
( ( sdtpldt0(xq,sdtmndt0(xq,xq)) = xq )
| ~ aNaturalNumber0(xq) ),
inference(superposition,[status(thm)],[c_4513,c_105]) ).
tcf(c_4517,plain,
( ( sdtpldt0(xq,sK0(xq,xq)) = xq )
| ~ aNaturalNumber0(xq) ),
inference(superposition,[status(thm)],[c_4513,c_67]) ).
tcf(c_4518,plain,
sdtpldt0(xq,sK0(xq,xq)) = xq,
inference(forward_subsumption_resolution,[status(thm)],[c_4517,c_4368]) ).
tcf(c_4519,plain,
sdtpldt0(xq,sdtmndt0(xq,xq)) = xq,
inference(forward_subsumption_resolution,[status(thm)],[c_4515,c_4368]) ).
tcf(c_4562,plain,
( ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ( sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) != sz00 ) ),
inference(superposition,[status(thm)],[c_3117,c_69]) ).
tcf(c_4564,plain,
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_3117,c_144]) ).
tcf(c_4565,plain,
( aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_3117,c_78]) ).
tcf(c_4566,plain,
aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm)))),
inference(forward_subsumption_resolution,[status(thm)],[c_4565,c_49,c_2880]) ).
tcf(c_4567,plain,
sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm)))),
inference(forward_subsumption_resolution,[status(thm)],[c_4564,c_49,c_2880]) ).
tcf(c_4568,plain,
sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_4562,c_54,c_49,c_2880]) ).
tcf(c_4593,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xl) = sdtasdt0(X0,sdtasdt0(X1,xl)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_106]) ).
tcf(c_4594,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xm) = sdtasdt0(X0,sdtasdt0(X1,xm)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_106]) ).
tcf(c_4595,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xn) = sdtasdt0(X0,sdtasdt0(X1,xn)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_106]) ).
tcf(c_4596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(X2,X3),sdtpldt0(X0,X1)) = sdtasdt0(X2,sdtasdt0(X3,sdtpldt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_106]) ).
tcf(c_4597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(X2,X3),sK0(X0,X1)) = sdtasdt0(X2,sdtasdt0(X3,sK0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_106]) ).
tcf(c_4598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(X2,X3),sdtasdt0(X0,X1)) = sdtasdt0(X2,sdtasdt0(X3,sdtasdt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_106]) ).
tcf(c_4599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(X2,X3),sK1(X0,X1)) = sdtasdt0(X2,sdtasdt0(X3,sK1(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_106]) ).
tcf(c_4600,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sz00) = sdtasdt0(X0,sdtasdt0(X1,sz00)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_106]) ).
tcf(c_4601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(sdtasdt0(X2,X3),sdtsldt0(X1,X0)) = sdtasdt0(X2,sdtasdt0(X3,sdtsldt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_106]) ).
tcf(c_4602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(X2,X3),sdtmndt0(X1,X0)) = sdtasdt0(X2,sdtasdt0(X3,sdtmndt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_106]) ).
tcf(c_4603,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(xl,xm)) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(xl,xm))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_106]) ).
tcf(c_4604,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(xl,xn)) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(xl,xn))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_106]) ).
tcf(c_4605,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(xl,sdtpldt0(xl,xm))) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(xl,sdtpldt0(xl,xm)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_106]) ).
tcf(c_4606,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xr) = sdtasdt0(X0,sdtasdt0(X1,xr)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_106]) ).
tcf(c_4607,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xp) = sdtasdt0(X0,sdtasdt0(X1,xp)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_106]) ).
tcf(c_4608,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),xq) = sdtasdt0(X0,sdtasdt0(X1,xq)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_106]) ).
tcf(c_4609,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(xl,sdtpldt0(xl,xn))) = sdtasdt0(X0,sdtasdt0(X1,sdtpldt0(xl,sdtpldt0(xl,xn)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_106]) ).
tcf(c_4796,plain,
! [X0: $i] :
( ( sdtasdt0(xl,xr) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ( sdtpldt0(sdtasdt0(xl,xp),X0) != sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(superposition,[status(thm)],[c_59,c_70]) ).
tcf(c_4797,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != sz00 ) ),
inference(superposition,[status(thm)],[c_2540,c_70]) ).
tcf(c_4798,plain,
! [X0: $i] :
( ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ( sdtpldt0(sz00,X0) != sz00 ) ),
inference(superposition,[status(thm)],[c_3299,c_70]) ).
tcf(c_4799,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,X0) != xl ) ),
inference(superposition,[status(thm)],[c_2537,c_70]) ).
tcf(c_4800,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != xm ) ),
inference(superposition,[status(thm)],[c_2538,c_70]) ).
tcf(c_4801,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != xn ) ),
inference(superposition,[status(thm)],[c_2539,c_70]) ).
tcf(c_4802,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xl ) ),
inference(superposition,[status(thm)],[c_2545,c_70]) ).
tcf(c_4803,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xm ) ),
inference(superposition,[status(thm)],[c_2546,c_70]) ).
tcf(c_4804,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xn ) ),
inference(superposition,[status(thm)],[c_2547,c_70]) ).
tcf(c_4805,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2800,c_70]) ).
tcf(c_4806,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2801,c_70]) ).
tcf(c_4807,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xl,sdtpldt0(xl,xm)) ) ),
inference(superposition,[status(thm)],[c_2836,c_70]) ).
tcf(c_4808,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(sz00,X0) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2840,c_70]) ).
tcf(c_4809,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2841,c_70]) ).
tcf(c_4810,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(sdtpldt0(xl,xn),X0) != sdtpldt0(xl,sdtpldt0(xl,xn)) ) ),
inference(superposition,[status(thm)],[c_2859,c_70]) ).
tcf(c_4811,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(sz00,X0) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2863,c_70]) ).
tcf(c_4812,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(sdtpldt0(xl,xn),X0) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2864,c_70]) ).
tcf(c_4813,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ( sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0) != sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) ) ),
inference(superposition,[status(thm)],[c_3117,c_70]) ).
tcf(c_4814,plain,
! [X0: $i] :
( ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ( sdtpldt0(xl,X0) != xl ) ),
inference(superposition,[status(thm)],[c_3298,c_70]) ).
tcf(c_4815,plain,
! [X0: $i] :
( ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ( sdtpldt0(xm,X0) != xm ) ),
inference(superposition,[status(thm)],[c_3297,c_70]) ).
tcf(c_4816,plain,
! [X0: $i] :
( ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ( sdtpldt0(xn,X0) != xn ) ),
inference(superposition,[status(thm)],[c_3296,c_70]) ).
tcf(c_4817,plain,
! [X0: $i] :
( ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ( sdtpldt0(sz00,X0) != xl ) ),
inference(superposition,[status(thm)],[c_3304,c_70]) ).
tcf(c_4818,plain,
! [X0: $i] :
( ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( sdtpldt0(sz00,X0) != xm ) ),
inference(superposition,[status(thm)],[c_3303,c_70]) ).
tcf(c_4819,plain,
! [X0: $i] :
( ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( sdtpldt0(sz00,X0) != xn ) ),
inference(superposition,[status(thm)],[c_3302,c_70]) ).
tcf(c_4820,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xp ) ),
inference(superposition,[status(thm)],[c_3842,c_70]) ).
tcf(c_4821,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xp,X0) != xp ) ),
inference(superposition,[status(thm)],[c_3843,c_70]) ).
tcf(c_4822,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xq ) ),
inference(superposition,[status(thm)],[c_4378,c_70]) ).
tcf(c_4823,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xq,X0) != xq ) ),
inference(superposition,[status(thm)],[c_4379,c_70]) ).
tcf(c_4825,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4797,c_94]) ).
tcf(c_4829,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xq,X0) != xq ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4823,c_4368,c_94]) ).
tcf(c_4833,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xq ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4822,c_4368,c_94]) ).
tcf(c_4837,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xp,X0) != xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4821,c_3490,c_94]) ).
tcf(c_4841,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4820,c_3490,c_94]) ).
tcf(c_4845,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4804,c_94,c_51]) ).
tcf(c_4849,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4803,c_94,c_50]) ).
tcf(c_4853,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4802,c_94,c_49]) ).
tcf(c_4857,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4801,c_94,c_51]) ).
tcf(c_4861,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4800,c_94,c_50]) ).
tcf(c_4865,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,X0) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4799,c_94,c_49]) ).
tcf(c_4869,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4806,c_51,c_49]) ).
tcf(c_4873,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xm,X0) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4805,c_50,c_49]) ).
tcf(c_4877,plain,
! [X0: $i] :
( ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( sdtpldt0(sz00,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4819,c_94]) ).
tcf(c_4882,plain,
! [X0: $i] :
( ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( sdtpldt0(sz00,X0) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4818,c_94]) ).
tcf(c_4887,plain,
! [X0: $i] :
( ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ( sdtpldt0(sz00,X0) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4817,c_94]) ).
tcf(c_4892,plain,
! [X0: $i] :
( ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ( sdtpldt0(xn,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4816,c_51]) ).
tcf(c_4897,plain,
! [X0: $i] :
( ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ( sdtpldt0(xm,X0) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4815,c_50]) ).
tcf(c_4902,plain,
! [X0: $i] :
( ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ( sdtpldt0(xl,X0) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4814,c_49]) ).
tcf(c_4907,plain,
! [X0: $i] :
( ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ( sdtpldt0(sz00,X0) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4798,c_94]) ).
tcf(c_4912,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xl,xn),X0) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4812,c_94,c_2855]) ).
tcf(c_4916,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4811,c_94,c_2855]) ).
tcf(c_4920,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4809,c_94,c_2832]) ).
tcf(c_4924,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4808,c_94,c_2832]) ).
tcf(c_4928,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xl,xn),X0) != sdtpldt0(xl,sdtpldt0(xl,xn)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4810,c_49,c_2855]) ).
tcf(c_4932,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xl,sdtpldt0(xl,xm)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4807,c_49,c_2832]) ).
tcf(c_4941,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0) != sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4813,c_49,c_2880]) ).
tcf(c_5074,plain,
! [X0: $i] :
( ( sdtasdt0(xl,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ( sdtpldt0(X0,sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(superposition,[status(thm)],[c_59,c_71]) ).
tcf(c_5075,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != sz00 ) ),
inference(superposition,[status(thm)],[c_2540,c_71]) ).
tcf(c_5076,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ( sdtpldt0(X0,sK0(sz00,sz00)) != sz00 ) ),
inference(superposition,[status(thm)],[c_3299,c_71]) ).
tcf(c_5077,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xl ) ),
inference(superposition,[status(thm)],[c_2537,c_71]) ).
tcf(c_5078,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xm ) ),
inference(superposition,[status(thm)],[c_2538,c_71]) ).
tcf(c_5079,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xn ) ),
inference(superposition,[status(thm)],[c_2539,c_71]) ).
tcf(c_5080,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != xl ) ),
inference(superposition,[status(thm)],[c_2545,c_71]) ).
tcf(c_5081,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xm) != xm ) ),
inference(superposition,[status(thm)],[c_2546,c_71]) ).
tcf(c_5082,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xn) != xn ) ),
inference(superposition,[status(thm)],[c_2547,c_71]) ).
tcf(c_5083,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2800,c_71]) ).
tcf(c_5084,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2801,c_71]) ).
tcf(c_5085,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(xl,sdtpldt0(xl,xm)) != sdtpldt0(X0,xl) ) ),
inference(superposition,[status(thm)],[c_2836,c_71]) ).
tcf(c_5086,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(X0,sdtpldt0(xl,xm)) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2840,c_71]) ).
tcf(c_5087,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ( sdtpldt0(X0,sz00) != sdtpldt0(xl,xm) ) ),
inference(superposition,[status(thm)],[c_2841,c_71]) ).
tcf(c_5088,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(xl,sdtpldt0(xl,xn)) != sdtpldt0(X0,xl) ) ),
inference(superposition,[status(thm)],[c_2859,c_71]) ).
tcf(c_5089,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(X0,sdtpldt0(xl,xn)) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2863,c_71]) ).
tcf(c_5090,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ( sdtpldt0(X0,sz00) != sdtpldt0(xl,xn) ) ),
inference(superposition,[status(thm)],[c_2864,c_71]) ).
tcf(c_5091,plain,
! [X0: $i] :
( ( sdtpldt0(xl,sdtpldt0(xl,xm)) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ( sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) != sdtpldt0(X0,xl) ) ),
inference(superposition,[status(thm)],[c_3117,c_71]) ).
tcf(c_5092,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ( sdtpldt0(X0,sK0(xl,xl)) != xl ) ),
inference(superposition,[status(thm)],[c_3298,c_71]) ).
tcf(c_5093,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ( sdtpldt0(X0,sK0(xm,xm)) != xm ) ),
inference(superposition,[status(thm)],[c_3297,c_71]) ).
tcf(c_5094,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ( sdtpldt0(X0,sK0(xn,xn)) != xn ) ),
inference(superposition,[status(thm)],[c_3296,c_71]) ).
tcf(c_5095,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ( sdtpldt0(X0,sK0(sz00,xl)) != xl ) ),
inference(superposition,[status(thm)],[c_3304,c_71]) ).
tcf(c_5096,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( sdtpldt0(X0,sK0(sz00,xm)) != xm ) ),
inference(superposition,[status(thm)],[c_3303,c_71]) ).
tcf(c_5097,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( sdtpldt0(X0,sK0(sz00,xn)) != xn ) ),
inference(superposition,[status(thm)],[c_3302,c_71]) ).
tcf(c_5098,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xp) != xp ) ),
inference(superposition,[status(thm)],[c_3842,c_71]) ).
tcf(c_5099,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xp ) ),
inference(superposition,[status(thm)],[c_3843,c_71]) ).
tcf(c_5100,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xq) != xq ) ),
inference(superposition,[status(thm)],[c_4378,c_71]) ).
tcf(c_5101,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xq ) ),
inference(superposition,[status(thm)],[c_4379,c_71]) ).
tcf(c_5103,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5075,c_94]) ).
tcf(c_5107,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xq ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5101,c_4368,c_94]) ).
tcf(c_5111,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xq) != xq ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5100,c_4368,c_94]) ).
tcf(c_5115,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5099,c_3490,c_94]) ).
tcf(c_5119,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xp) != xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5098,c_3490,c_94]) ).
tcf(c_5123,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xn) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5082,c_94,c_51]) ).
tcf(c_5127,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xm) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5081,c_94,c_50]) ).
tcf(c_5131,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5080,c_94,c_49]) ).
tcf(c_5135,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5079,c_94,c_51]) ).
tcf(c_5139,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5078,c_94,c_50]) ).
tcf(c_5143,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5077,c_94,c_49]) ).
tcf(c_5147,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5084,c_51,c_49]) ).
tcf(c_5151,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5083,c_50,c_49]) ).
tcf(c_5155,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ( sdtpldt0(X0,sK0(sz00,xn)) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5097,c_94]) ).
tcf(c_5160,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ( sdtpldt0(X0,sK0(sz00,xm)) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5096,c_94]) ).
tcf(c_5165,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ( sdtpldt0(X0,sK0(sz00,xl)) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5095,c_94]) ).
tcf(c_5170,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ( sdtpldt0(X0,sK0(xn,xn)) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5094,c_51]) ).
tcf(c_5175,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ( sdtpldt0(X0,sK0(xm,xm)) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5093,c_50]) ).
tcf(c_5180,plain,
! [X0: $i] :
( ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ( sdtpldt0(X0,sK0(xl,xl)) != xl ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5092,c_49]) ).
tcf(c_5185,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ( sdtpldt0(X0,sK0(sz00,sz00)) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5076,c_94]) ).
tcf(c_5190,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5090,c_94,c_2855]) ).
tcf(c_5194,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sdtpldt0(xl,xn)) != sdtpldt0(xl,xn) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5089,c_94,c_2855]) ).
tcf(c_5198,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5087,c_94,c_2832]) ).
tcf(c_5202,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sdtpldt0(xl,xm)) != sdtpldt0(xl,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5086,c_94,c_2832]) ).
tcf(c_5206,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,sdtpldt0(xl,xn)) != sdtpldt0(X0,xl) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5088,c_49,c_2855]) ).
tcf(c_5210,plain,
! [X0: $i] :
( ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,sdtpldt0(xl,xm)) != sdtpldt0(X0,xl) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5085,c_49,c_2832]) ).
tcf(c_5219,plain,
! [X0: $i] :
( ( sdtpldt0(xl,sdtpldt0(xl,xm)) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))) != sdtpldt0(X0,xl) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5091,c_49,c_2880]) ).
tcf(c_5292,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(sdtasdt0(xl,xp),xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ doDivides0(X0,sdtasdt0(xl,xr))
| ~ doDivides0(X0,sdtasdt0(xl,xp)) ),
inference(superposition,[status(thm)],[c_59,c_79]) ).
tcf(c_5301,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xl) ),
inference(superposition,[status(thm)],[c_2800,c_79]) ).
tcf(c_5302,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xn)
| ~ doDivides0(X0,xl) ),
inference(superposition,[status(thm)],[c_2801,c_79]) ).
tcf(c_5303,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ doDivides0(X0,sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2836,c_79]) ).
tcf(c_5306,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xn)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ doDivides0(X0,sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2859,c_79]) ).
tcf(c_5309,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_3117,c_79]) ).
tcf(c_5313,plain,
! [X0: $i] :
( doDivides0(X0,xl)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ doDivides0(X0,sK0(sz00,xl)) ),
inference(superposition,[status(thm)],[c_3304,c_79]) ).
tcf(c_5314,plain,
! [X0: $i] :
( doDivides0(X0,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ doDivides0(X0,sK0(sz00,xm)) ),
inference(superposition,[status(thm)],[c_3303,c_79]) ).
tcf(c_5315,plain,
! [X0: $i] :
( doDivides0(X0,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ doDivides0(X0,sK0(sz00,xn)) ),
inference(superposition,[status(thm)],[c_3302,c_79]) ).
tcf(c_5320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X3,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X3,X2)
| ~ doDivides0(X2,X1)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_5321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X2,sK1(X2,sdtpldt0(X0,X1))) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,X1)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_79,c_83]) ).
tcf(c_5322,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,xn))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xn)
| ~ doDivides0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5302,c_51,c_49]) ).
tcf(c_5327,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xm)
| ~ doDivides0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5301,c_50,c_49]) ).
tcf(c_5332,plain,
! [X0: $i] :
( doDivides0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ doDivides0(X0,sK0(sz00,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5315,c_94]) ).
tcf(c_5338,plain,
! [X0: $i] :
( doDivides0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ doDivides0(X0,sK0(sz00,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5314,c_94]) ).
tcf(c_5344,plain,
! [X0: $i] :
( doDivides0(X0,xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ doDivides0(X0,sK0(sz00,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5313,c_94]) ).
tcf(c_5350,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xn)))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ doDivides0(X0,sdtpldt0(xl,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5306,c_49,c_2855]) ).
tcf(c_5355,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ doDivides0(X0,sdtpldt0(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5303,c_49,c_2832]) ).
tcf(c_5382,plain,
! [X0: $i] :
( doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xl)
| ~ doDivides0(X0,sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5309,c_49,c_2880]) ).
tcf(c_5449,plain,
( doDivides0(xr,sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4437,c_141]) ).
tcf(c_5451,plain,
doDivides0(xr,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_5449,c_4369,c_94]) ).
tcf(c_5452,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xr) ),
inference(superposition,[status(thm)],[c_5451,c_80]) ).
tcf(c_5453,plain,
( ( sdtasdt0(xr,sK1(xr,sz00)) = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5451,c_83]) ).
tcf(c_5454,plain,
sdtasdt0(xr,sK1(xr,sz00)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_5453,c_4369,c_94]) ).
tcf(c_5455,plain,
! [X0: $i] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5452,c_4369,c_94]) ).
tcf(c_5463,plain,
( sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4438,c_144]) ).
tcf(c_5465,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xr ) ),
inference(superposition,[status(thm)],[c_4438,c_70]) ).
tcf(c_5467,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xr) != xr ) ),
inference(superposition,[status(thm)],[c_4438,c_71]) ).
tcf(c_5468,plain,
sdtlseqdt0(sz00,xr),
inference(forward_subsumption_resolution,[status(thm)],[c_5463,c_4369,c_94]) ).
tcf(c_5469,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xr) != xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5467,c_4369,c_94]) ).
tcf(c_5473,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5465,c_4369,c_94]) ).
tcf(c_5478,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_5468,c_100]) ).
tcf(c_5479,plain,
( ( sdtpldt0(sz00,sdtmndt0(xr,sz00)) = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5468,c_105]) ).
tcf(c_5480,plain,
( ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xr,sz00) ),
inference(superposition,[status(thm)],[c_5468,c_101]) ).
tcf(c_5481,plain,
( ( sdtpldt0(sz00,sK0(sz00,xr)) = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5468,c_67]) ).
tcf(c_5482,plain,
sdtpldt0(sz00,sK0(sz00,xr)) = xr,
inference(forward_subsumption_resolution,[status(thm)],[c_5481,c_4369,c_94]) ).
tcf(c_5483,plain,
( ( sz00 = xr )
| ~ sdtlseqdt0(xr,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5480,c_4369,c_94]) ).
tcf(c_5486,plain,
sdtpldt0(sz00,sdtmndt0(xr,sz00)) = xr,
inference(forward_subsumption_resolution,[status(thm)],[c_5479,c_4369,c_94]) ).
tcf(c_5487,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5478,c_4369,c_94]) ).
tcf(c_5495,plain,
( sdtlseqdt0(xr,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4439,c_144]) ).
tcf(c_5497,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xr,X0) != xr ) ),
inference(superposition,[status(thm)],[c_4439,c_70]) ).
tcf(c_5499,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xr ) ),
inference(superposition,[status(thm)],[c_4439,c_71]) ).
tcf(c_5500,plain,
sdtlseqdt0(xr,xr),
inference(forward_subsumption_resolution,[status(thm)],[c_5495,c_4369,c_94]) ).
tcf(c_5501,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,sz00) != xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5499,c_4369,c_94]) ).
tcf(c_5505,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xr,X0) != xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5497,c_4369,c_94]) ).
tcf(c_5514,plain,
( ( sdtpldt0(xr,sdtmndt0(xr,xr)) = xr )
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm)],[c_5500,c_105]) ).
tcf(c_5516,plain,
( ( sdtpldt0(xr,sK0(xr,xr)) = xr )
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm)],[c_5500,c_67]) ).
tcf(c_5517,plain,
sdtpldt0(xr,sK0(xr,xr)) = xr,
inference(forward_subsumption_resolution,[status(thm)],[c_5516,c_4369]) ).
tcf(c_5518,plain,
sdtpldt0(xr,sdtmndt0(xr,xr)) = xr,
inference(forward_subsumption_resolution,[status(thm)],[c_5514,c_4369]) ).
tcf(c_5520,plain,
( ( sdtpldt0(sdtpldt0(xl,xn),sdtmndt0(sdtpldt0(xl,xn),sdtpldt0(xl,xn))) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3968,c_105]) ).
tcf(c_5522,plain,
( ( sdtpldt0(sdtpldt0(xl,xn),sK0(sdtpldt0(xl,xn),sdtpldt0(xl,xn))) = sdtpldt0(xl,xn) )
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3968,c_67]) ).
tcf(c_5523,plain,
sdtpldt0(sdtpldt0(xl,xn),sK0(sdtpldt0(xl,xn),sdtpldt0(xl,xn))) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_5522,c_2855]) ).
tcf(c_5524,plain,
sdtpldt0(sdtpldt0(xl,xn),sdtmndt0(sdtpldt0(xl,xn),sdtpldt0(xl,xn))) = sdtpldt0(xl,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_5520,c_2855]) ).
tcf(c_5533,plain,
( sdtlseqdt0(xm,sz00)
| ( sK1(xm,sz00) = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK1(xm,sz00)) ),
inference(superposition,[status(thm)],[c_3350,c_84]) ).
tcf(c_5534,plain,
( ( xm = sz00 )
| ( sK1(xm,sz00) = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK1(xm,sz00)) ),
inference(superposition,[status(thm)],[c_3350,c_89]) ).
tcf(c_5537,plain,
( sdtlseqdt0(xm,sz00)
| ( sK1(xm,sz00) = sz00 )
| ~ aNaturalNumber0(sK1(xm,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5533,c_50]) ).
tcf(c_5541,plain,
( ( xm = sz00 )
| ( sK1(xm,sz00) = sz00 )
| ~ aNaturalNumber0(sK1(xm,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5534,c_50]) ).
tcf(c_5545,plain,
( sdtlseqdt0(xl,sz00)
| ( sK1(xl,sz00) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK1(xl,sz00)) ),
inference(superposition,[status(thm)],[c_3351,c_84]) ).
tcf(c_5546,plain,
( ( xl = sz00 )
| ( sK1(xl,sz00) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK1(xl,sz00)) ),
inference(superposition,[status(thm)],[c_3351,c_89]) ).
tcf(c_5549,plain,
( ( sK1(xl,sz00) = sz00 )
| ~ aNaturalNumber0(sK1(xl,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5545,c_3584,c_49]) ).
tcf(c_5553,plain,
( sdtlseqdt0(xl,xm)
| ( sK1(xl,xm) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK1(xl,xm)) ),
inference(superposition,[status(thm)],[c_3352,c_84]) ).
tcf(c_5554,plain,
( ( xl = sz00 )
| ( sK1(xl,xm) = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK1(xl,xm))
| ( xm != sz00 ) ),
inference(superposition,[status(thm)],[c_3352,c_89]) ).
tcf(c_5557,plain,
( sdtlseqdt0(xl,xm)
| ( sK1(xl,xm) = sz00 )
| ~ aNaturalNumber0(sK1(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5553,c_49]) ).
tcf(c_5561,plain,
( ( sK1(xl,xm) = sz00 )
| ~ aNaturalNumber0(sK1(xl,xm))
| ( xm != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5554,c_54,c_49]) ).
tcf(c_5591,plain,
( ( xl = sz00 )
| ( sdtasdt0(xl,sdtsldt0(xm,xl)) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_52,c_97]) ).
tcf(c_5592,plain,
( ( xl = sz00 )
| ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_53,c_97]) ).
tcf(c_5593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sz00 )
| ( sdtasdt0(X2,sdtsldt0(sdtpldt0(X0,X1),X2)) = sdtpldt0(X0,X1) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,X1)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_79,c_97]) ).
tcf(c_5594,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(sdtasdt0(X0,X1),X0)) = sdtasdt0(X0,X1) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_141,c_97]) ).
tcf(c_5596,plain,
( ( xl = sz00 )
| ( sdtasdt0(xl,sdtsldt0(sz00,xl)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2638,c_97]) ).
tcf(c_5597,plain,
( ( xm = sz00 )
| ( sdtasdt0(xm,sdtsldt0(sz00,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2637,c_97]) ).
tcf(c_5598,plain,
( ( xn = sz00 )
| ( sdtasdt0(xn,sdtsldt0(sz00,xn)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2636,c_97]) ).
tcf(c_5599,plain,
( ( sdtpldt0(xl,xm) = sz00 )
| ( sdtasdt0(sdtpldt0(xl,xm),sdtsldt0(sz00,sdtpldt0(xl,xm))) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_3135,c_97]) ).
tcf(c_5600,plain,
( ( sdtpldt0(xl,xn) = sz00 )
| ( sdtasdt0(sdtpldt0(xl,xn),sdtsldt0(sz00,sdtpldt0(xl,xn))) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_3146,c_97]) ).
tcf(c_5601,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_3919,c_97]) ).
tcf(c_5602,plain,
( ( sz00 = xq )
| ( sdtasdt0(xq,sdtsldt0(sz00,xq)) = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4465,c_97]) ).
tcf(c_5603,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(sz00,xr)) = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5451,c_97]) ).
tcf(c_5604,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(sz00,xr)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5603,c_4369,c_94]) ).
tcf(c_5607,plain,
( ( sz00 = xq )
| ( sdtasdt0(xq,sdtsldt0(sz00,xq)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5602,c_4368,c_94]) ).
tcf(c_5610,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5601,c_3490,c_94]) ).
tcf(c_5613,plain,
( ( xn = sz00 )
| ( sdtasdt0(xn,sdtsldt0(sz00,xn)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5598,c_94,c_51]) ).
tcf(c_5616,plain,
( ( xm = sz00 )
| ( sdtasdt0(xm,sdtsldt0(sz00,xm)) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5597,c_94,c_50]) ).
tcf(c_5619,plain,
sdtasdt0(xl,sdtsldt0(sz00,xl)) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_5596,c_54,c_94,c_49]) ).
tcf(c_5620,plain,
( ( xl = sz00 )
| ( sdtasdt0(xl,xp) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(light_normalisation,[status(thm)],[c_5591,c_55]) ).
tcf(c_5621,plain,
sdtasdt0(xl,xp) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_5620,c_54,c_50,c_49]) ).
tcf(c_5622,plain,
( ( xl = sz00 )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(light_normalisation,[status(thm)],[c_5592,c_56]) ).
tcf(c_5623,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5622,c_54,c_49]) ).
tcf(c_5626,plain,
sdtasdt0(sdtpldt0(xl,xn),sdtsldt0(sz00,sdtpldt0(xl,xn))) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_5600,c_3262,c_94,c_2855]) ).
tcf(c_5627,plain,
sdtasdt0(sdtpldt0(xl,xm),sdtsldt0(sz00,sdtpldt0(xl,xm))) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_5599,c_3263,c_94,c_2832]) ).
tcf(c_5641,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[c_59,c_5621]) ).
tcf(c_5654,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xl)) = sdtasdt0(X0,sdtpldt0(X1,xl)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_72]) ).
tcf(c_5655,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xm)) = sdtasdt0(X0,sdtpldt0(X1,xm)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_72]) ).
tcf(c_5656,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xn)) = sdtasdt0(X0,sdtpldt0(X1,xn)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_72]) ).
tcf(c_5657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtpldt0(X0,X1))) = sdtasdt0(X2,sdtpldt0(X3,sdtpldt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_72]) ).
tcf(c_5658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sK0(X0,X1))) = sdtasdt0(X2,sdtpldt0(X3,sK0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_72]) ).
tcf(c_5659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtasdt0(X0,X1))) = sdtasdt0(X2,sdtpldt0(X3,sdtasdt0(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_72]) ).
tcf(c_5660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sK1(X0,X1))) = sdtasdt0(X2,sdtpldt0(X3,sK1(X0,X1))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_72]) ).
tcf(c_5661,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz00)) = sdtasdt0(X0,sdtpldt0(X1,sz00)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_72]) ).
tcf(c_5662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtsldt0(X1,X0))) = sdtasdt0(X2,sdtpldt0(X3,sdtsldt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_72]) ).
tcf(c_5663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,sdtmndt0(X1,X0))) = sdtasdt0(X2,sdtpldt0(X3,sdtmndt0(X1,X0))) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_72]) ).
tcf(c_5664,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(xl,xm))) = sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(xl,xm))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_72]) ).
tcf(c_5665,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(xl,xn))) = sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(xl,xn))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_72]) ).
tcf(c_5666,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xm)))) = sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xm)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_72]) ).
tcf(c_5667,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xr)) = sdtasdt0(X0,sdtpldt0(X1,xr)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_72]) ).
tcf(c_5668,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xp)) = sdtasdt0(X0,sdtpldt0(X1,xp)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_72]) ).
tcf(c_5669,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,xq)) = sdtasdt0(X0,sdtpldt0(X1,xq)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_72]) ).
tcf(c_5670,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sdtpldt0(xl,sdtpldt0(xl,xn)))) = sdtasdt0(X0,sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xn)))) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_72]) ).
tcf(c_5820,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xl,X0)) = sdtasdt0(sdtpldt0(X1,xl),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_73]) ).
tcf(c_5821,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xm,X0)) = sdtasdt0(sdtpldt0(X1,xm),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_73]) ).
tcf(c_5822,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xn,X0)) = sdtasdt0(sdtpldt0(X1,xn),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_51,c_73]) ).
tcf(c_5823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sdtpldt0(X0,X1),X2)) = sdtasdt0(sdtpldt0(X3,sdtpldt0(X0,X1)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_78,c_73]) ).
tcf(c_5824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sK0(X0,X1),X2)) = sdtasdt0(sdtpldt0(X3,sK0(X0,X1)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_66,c_73]) ).
tcf(c_5825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sdtasdt0(X0,X1),X2)) = sdtasdt0(sdtpldt0(X3,sdtasdt0(X0,X1)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_73]) ).
tcf(c_5826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sK1(X0,X1),X2)) = sdtasdt0(sdtpldt0(X3,sK1(X0,X1)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_73]) ).
tcf(c_5827,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sz00,X0)) = sdtasdt0(sdtpldt0(X1,sz00),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_94,c_73]) ).
tcf(c_5828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sdtsldt0(X1,X0),X2)) = sdtasdt0(sdtpldt0(X3,sdtsldt0(X1,X0)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_73]) ).
tcf(c_5829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(sdtmndt0(X1,X0),X2)) = sdtasdt0(sdtpldt0(X3,sdtmndt0(X1,X0)),X2) )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_104,c_73]) ).
tcf(c_5830,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sdtpldt0(xl,xm),X0)) = sdtasdt0(sdtpldt0(X1,sdtpldt0(xl,xm)),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2832,c_73]) ).
tcf(c_5831,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sdtpldt0(xl,xn),X0)) = sdtasdt0(sdtpldt0(X1,sdtpldt0(xl,xn)),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2855,c_73]) ).
tcf(c_5832,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0)) = sdtasdt0(sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xm))),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2880,c_73]) ).
tcf(c_5833,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xr,X0)) = sdtasdt0(sdtpldt0(X1,xr),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4369,c_73]) ).
tcf(c_5834,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xp,X0)) = sdtasdt0(sdtpldt0(X1,xp),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3490,c_73]) ).
tcf(c_5835,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xq,X0)) = sdtasdt0(sdtpldt0(X1,xq),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4368,c_73]) ).
tcf(c_5836,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),X0)) = sdtasdt0(sdtpldt0(X1,sdtpldt0(xl,sdtpldt0(xl,xn))),X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_3168,c_73]) ).
tcf(c_5967,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtpldt0(sz00,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2540,c_62]) ).
tcf(c_5968,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtpldt0(sz00,X0))
| ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ~ sdtlseqdt0(sK0(sz00,sz00),X0) ),
inference(superposition,[status(thm)],[c_3299,c_62]) ).
tcf(c_5969,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(xl,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2537,c_62]) ).
tcf(c_5970,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2538,c_62]) ).
tcf(c_5971,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2539,c_62]) ).
tcf(c_5972,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(sz00,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(superposition,[status(thm)],[c_2545,c_62]) ).
tcf(c_5973,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(sz00,X0))
| ( X0 = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_2546,c_62]) ).
tcf(c_5974,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(sz00,X0))
| ( X0 = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_2547,c_62]) ).
tcf(c_5975,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xm,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(superposition,[status(thm)],[c_2800,c_62]) ).
tcf(c_5976,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xn,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(superposition,[status(thm)],[c_2801,c_62]) ).
tcf(c_5977,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(sdtpldt0(xl,xm),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2836,c_62]) ).
tcf(c_5978,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(sz00,X0))
| ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ sdtlseqdt0(sdtpldt0(xl,xm),X0) ),
inference(superposition,[status(thm)],[c_2840,c_62]) ).
tcf(c_5979,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(sdtpldt0(xl,xm),X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2841,c_62]) ).
tcf(c_5980,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),sdtpldt0(sdtpldt0(xl,xn),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2859,c_62]) ).
tcf(c_5981,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(sz00,X0))
| ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ sdtlseqdt0(sdtpldt0(xl,xn),X0) ),
inference(superposition,[status(thm)],[c_2863,c_62]) ).
tcf(c_5982,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(sdtpldt0(xl,xn),X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2864,c_62]) ).
tcf(c_5983,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))),sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_3117,c_62]) ).
tcf(c_5984,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(xl,X0))
| ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ~ sdtlseqdt0(sK0(xl,xl),X0) ),
inference(superposition,[status(thm)],[c_3298,c_62]) ).
tcf(c_5985,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ~ sdtlseqdt0(sK0(xm,xm),X0) ),
inference(superposition,[status(thm)],[c_3297,c_62]) ).
tcf(c_5986,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ~ sdtlseqdt0(sK0(xn,xn),X0) ),
inference(superposition,[status(thm)],[c_3296,c_62]) ).
tcf(c_5987,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(sz00,X0))
| ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ sdtlseqdt0(sK0(sz00,xl),X0) ),
inference(superposition,[status(thm)],[c_3304,c_62]) ).
tcf(c_5988,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(sz00,X0))
| ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ sdtlseqdt0(sK0(sz00,xm),X0) ),
inference(superposition,[status(thm)],[c_3303,c_62]) ).
tcf(c_5989,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(sz00,X0))
| ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ sdtlseqdt0(sK0(sz00,xn),X0) ),
inference(superposition,[status(thm)],[c_3302,c_62]) ).
tcf(c_5990,plain,
! [X0: $i] :
( sdtlseqdt0(xp,sdtpldt0(sz00,X0))
| ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_3842,c_62]) ).
tcf(c_5991,plain,
! [X0: $i] :
( sdtlseqdt0(xp,sdtpldt0(xp,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_3843,c_62]) ).
tcf(c_5992,plain,
! [X0: $i] :
( sdtlseqdt0(xq,sdtpldt0(sz00,X0))
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(superposition,[status(thm)],[c_4378,c_62]) ).
tcf(c_5993,plain,
! [X0: $i] :
( sdtlseqdt0(xq,sdtpldt0(xq,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_4379,c_62]) ).
tcf(c_5994,plain,
! [X0: $i] :
( sdtlseqdt0(xr,sdtpldt0(sz00,X0))
| ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0) ),
inference(superposition,[status(thm)],[c_4438,c_62]) ).
tcf(c_5995,plain,
! [X0: $i] :
( sdtlseqdt0(xr,sdtpldt0(xr,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_4439,c_62]) ).
tcf(c_5996,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sz00)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2540,c_62]) ).
tcf(c_5997,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sz00)
| ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ~ sdtlseqdt0(X0,sK0(sz00,sz00)) ),
inference(superposition,[status(thm)],[c_3299,c_62]) ).
tcf(c_5998,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,X0),xl)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2537,c_62]) ).
tcf(c_5999,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2538,c_62]) ).
tcf(c_6000,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2539,c_62]) ).
tcf(c_6001,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xl)
| ( X0 = xl )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(superposition,[status(thm)],[c_2545,c_62]) ).
tcf(c_6002,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xm)
| ( X0 = xm )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(superposition,[status(thm)],[c_2546,c_62]) ).
tcf(c_6003,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xn)
| ( X0 = xn )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(superposition,[status(thm)],[c_2547,c_62]) ).
tcf(c_6004,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),sdtpldt0(xl,xm))
| ( X0 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(superposition,[status(thm)],[c_2800,c_62]) ).
tcf(c_6005,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),sdtpldt0(xl,xn))
| ( X0 = xl )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(superposition,[status(thm)],[c_2801,c_62]) ).
tcf(c_6006,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,sdtpldt0(xl,xm)))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2836,c_62]) ).
tcf(c_6007,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(xl,xm))
| ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm))
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2840,c_62]) ).
tcf(c_6008,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,xm))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) ),
inference(superposition,[status(thm)],[c_2841,c_62]) ).
tcf(c_6009,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,sdtpldt0(xl,xn)))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2859,c_62]) ).
tcf(c_6010,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(xl,xn))
| ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xn))
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2863,c_62]) ).
tcf(c_6011,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,xn))
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtpldt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_2864,c_62]) ).
tcf(c_6012,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0),sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ( X0 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl)
| ~ aNaturalNumber0(sdtpldt0(xl,sdtpldt0(xl,xm))) ),
inference(superposition,[status(thm)],[c_3117,c_62]) ).
tcf(c_6013,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,X0),xl)
| ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ~ sdtlseqdt0(X0,sK0(xl,xl)) ),
inference(superposition,[status(thm)],[c_3298,c_62]) ).
tcf(c_6014,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ~ sdtlseqdt0(X0,sK0(xm,xm)) ),
inference(superposition,[status(thm)],[c_3297,c_62]) ).
tcf(c_6015,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ~ sdtlseqdt0(X0,sK0(xn,xn)) ),
inference(superposition,[status(thm)],[c_3296,c_62]) ).
tcf(c_6016,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xl)
| ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ sdtlseqdt0(X0,sK0(sz00,xl)) ),
inference(superposition,[status(thm)],[c_3304,c_62]) ).
tcf(c_6017,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xm)
| ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ sdtlseqdt0(X0,sK0(sz00,xm)) ),
inference(superposition,[status(thm)],[c_3303,c_62]) ).
tcf(c_6018,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xn)
| ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ sdtlseqdt0(X0,sK0(sz00,xn)) ),
inference(superposition,[status(thm)],[c_3302,c_62]) ).
tcf(c_6019,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xp)
| ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(superposition,[status(thm)],[c_3842,c_62]) ).
tcf(c_6020,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xp,X0),xp)
| ( X0 = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_3843,c_62]) ).
tcf(c_6021,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xq)
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xq) ),
inference(superposition,[status(thm)],[c_4378,c_62]) ).
tcf(c_6022,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xq,X0),xq)
| ( X0 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_4379,c_62]) ).
tcf(c_6023,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xr)
| ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xr) ),
inference(superposition,[status(thm)],[c_4438,c_62]) ).
tcf(c_6024,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xr,X0),xr)
| ( X0 = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_4439,c_62]) ).
tcf(c_6025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,sdtpldt0(X1,X3))
| ( X2 = X3 )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(sdtpldt0(X1,X3))
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ sdtlseqdt0(X0,sdtpldt0(X1,X2)) ),
inference(superposition,[status(thm)],[c_62,c_100]) ).
tcf(c_6026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sdtpldt0(sdtpldt0(X0,X1),sdtmndt0(sdtpldt0(X0,X2),sdtpldt0(X0,X1))) = sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_105]) ).
tcf(c_6027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(X0,X2)) ),
inference(superposition,[status(thm)],[c_62,c_101]) ).
tcf(c_6028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sdtpldt0(sdtpldt0(X0,X1),sK0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))) = sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_67]) ).
tcf(c_6029,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sz00)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5996,c_94]) ).
tcf(c_6034,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtpldt0(sz00,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5967,c_94]) ).
tcf(c_6039,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xr,X0),xr)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6024,c_4369,c_94]) ).
tcf(c_6044,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xr)
| ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6023,c_4369,c_94]) ).
tcf(c_6049,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xq,X0),xq)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6022,c_4368,c_94]) ).
tcf(c_6054,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xq)
| ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xq) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6021,c_4368,c_94]) ).
tcf(c_6059,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xp,X0),xp)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6020,c_3490,c_94]) ).
tcf(c_6064,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xp)
| ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6019,c_3490,c_94]) ).
tcf(c_6069,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xn)
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6003,c_94,c_51]) ).
tcf(c_6074,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xm)
| ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6002,c_94,c_50]) ).
tcf(c_6079,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xl)
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6001,c_94,c_49]) ).
tcf(c_6084,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6000,c_94,c_51]) ).
tcf(c_6089,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5999,c_94,c_50]) ).
tcf(c_6094,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,X0),xl)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5998,c_94,c_49]) ).
tcf(c_6099,plain,
! [X0: $i] :
( sdtlseqdt0(xr,sdtpldt0(xr,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5995,c_4369,c_94]) ).
tcf(c_6104,plain,
! [X0: $i] :
( sdtlseqdt0(xr,sdtpldt0(sz00,X0))
| ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5994,c_4369,c_94]) ).
tcf(c_6109,plain,
! [X0: $i] :
( sdtlseqdt0(xq,sdtpldt0(xq,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5993,c_4368,c_94]) ).
tcf(c_6114,plain,
! [X0: $i] :
( sdtlseqdt0(xq,sdtpldt0(sz00,X0))
| ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5992,c_4368,c_94]) ).
tcf(c_6119,plain,
! [X0: $i] :
( sdtlseqdt0(xp,sdtpldt0(xp,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5991,c_3490,c_94]) ).
tcf(c_6124,plain,
! [X0: $i] :
( sdtlseqdt0(xp,sdtpldt0(sz00,X0))
| ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5990,c_3490,c_94]) ).
tcf(c_6129,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(sz00,X0))
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5974,c_94,c_51]) ).
tcf(c_6134,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(sz00,X0))
| ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xm,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5973,c_94,c_50]) ).
tcf(c_6139,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(sz00,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5972,c_94,c_49]) ).
tcf(c_6144,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5971,c_94,c_51]) ).
tcf(c_6149,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5970,c_94,c_50]) ).
tcf(c_6154,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(xl,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5969,c_94,c_49]) ).
tcf(c_6159,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),sdtpldt0(xl,xn))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6005,c_51,c_49]) ).
tcf(c_6164,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),sdtpldt0(xl,xm))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6004,c_50,c_49]) ).
tcf(c_6169,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(xn,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5976,c_51,c_49]) ).
tcf(c_6174,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xm,X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5975,c_50,c_49]) ).
tcf(c_6179,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xn)
| ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ sdtlseqdt0(X0,sK0(sz00,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6018,c_94]) ).
tcf(c_6185,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xm)
| ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ sdtlseqdt0(X0,sK0(sz00,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6017,c_94]) ).
tcf(c_6191,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),xl)
| ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ sdtlseqdt0(X0,sK0(sz00,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6016,c_94]) ).
tcf(c_6197,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ~ sdtlseqdt0(X0,sK0(xn,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6015,c_51]) ).
tcf(c_6203,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,X0),xm)
| ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ~ sdtlseqdt0(X0,sK0(xm,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6014,c_50]) ).
tcf(c_6209,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,X0),xl)
| ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ~ sdtlseqdt0(X0,sK0(xl,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6013,c_49]) ).
tcf(c_6215,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,xn))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6011,c_94,c_2855]) ).
tcf(c_6220,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,xm))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6008,c_94,c_2832]) ).
tcf(c_6225,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sz00)
| ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ~ sdtlseqdt0(X0,sK0(sz00,sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5997,c_94]) ).
tcf(c_6231,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(sz00,X0))
| ( sK0(sz00,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xn))
| ~ sdtlseqdt0(sK0(sz00,xn),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5989,c_94]) ).
tcf(c_6237,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(sz00,X0))
| ( sK0(sz00,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xm))
| ~ sdtlseqdt0(sK0(sz00,xm),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5988,c_94]) ).
tcf(c_6243,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(sz00,X0))
| ( sK0(sz00,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,xl))
| ~ sdtlseqdt0(sK0(sz00,xl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5987,c_94]) ).
tcf(c_6249,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ( sK0(xn,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xn))
| ~ sdtlseqdt0(sK0(xn,xn),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5986,c_51]) ).
tcf(c_6255,plain,
! [X0: $i] :
( sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ( sK0(xm,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xm))
| ~ sdtlseqdt0(sK0(xm,xm),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5985,c_50]) ).
tcf(c_6261,plain,
! [X0: $i] :
( sdtlseqdt0(xl,sdtpldt0(xl,X0))
| ( sK0(xl,xl) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xl,xl))
| ~ sdtlseqdt0(sK0(xl,xl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5984,c_49]) ).
tcf(c_6267,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(sdtpldt0(xl,xn),X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5982,c_94,c_2855]) ).
tcf(c_6272,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(sdtpldt0(xl,xm),X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5979,c_94,c_2832]) ).
tcf(c_6277,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtpldt0(sz00,X0))
| ( sK0(sz00,sz00) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(sz00,sz00))
| ~ sdtlseqdt0(sK0(sz00,sz00),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5968,c_94]) ).
tcf(c_6283,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(xl,xn))
| ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6010,c_94,c_2855]) ).
tcf(c_6288,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xn),X0),sdtpldt0(xl,sdtpldt0(xl,xn)))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6009,c_49,c_2855]) ).
tcf(c_6293,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sz00,X0),sdtpldt0(xl,xm))
| ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(xl,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6007,c_94,c_2832]) ).
tcf(c_6298,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,xm),X0),sdtpldt0(xl,sdtpldt0(xl,xm)))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6006,c_49,c_2832]) ).
tcf(c_6303,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xn),sdtpldt0(sz00,X0))
| ( sdtpldt0(xl,xn) = X0 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtpldt0(xl,xn),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5981,c_94,c_2855]) ).
tcf(c_6308,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xn)),sdtpldt0(sdtpldt0(xl,xn),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5980,c_49,c_2855]) ).
tcf(c_6313,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(sz00,X0))
| ( sdtpldt0(xl,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtpldt0(xl,xm),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5978,c_94,c_2832]) ).
tcf(c_6318,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,xm)),sdtpldt0(sdtpldt0(xl,xm),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5977,c_49,c_2832]) ).
tcf(c_6323,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0),sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6012,c_49,c_2880]) ).
tcf(c_6328,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xl,sdtpldt0(xl,sdtpldt0(xl,xm))),sdtpldt0(sdtpldt0(xl,sdtpldt0(xl,xm)),X0))
| ( X0 = xl )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5983,c_49,c_2880]) ).
tcf(c_6601,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_6328,c_6323,c_6318,c_6313,c_6308,c_6303,c_6298,c_6293,c_6288,c_6283,c_6277,c_6272,c_6267,c_6261,c_6255,c_6249,c_6243,c_6237,c_6231,c_6225,c_6220,c_6215,c_6209,c_6203,c_6197,c_6191,c_6185,c_6179,c_6174,c_6169,c_6164,c_6159,c_6154,c_6149,c_6144,c_6139,c_6134,c_6129,c_6124,c_6119,c_6114,c_6109,c_6104,c_6099,c_6094,c_6089,c_6084,c_6079,c_6074,c_6069,c_6064,c_6059,c_6054,c_6049,c_6044,c_6039,c_6034,c_6029,c_6028,c_6027,c_6026,c_6025,c_6024,c_6023,c_6022,c_6021,c_6020,c_6019,c_6018,c_6017,c_6016,c_6015,c_6014,c_6013,c_6012,c_6011,c_6010,c_6009,c_6008,c_6007,c_6006,c_6005,c_6004,c_6003,c_6002,c_6001,c_6000,c_5999,c_5998,c_5997,c_5996,c_5995,c_5994,c_5993,c_5992,c_5991,c_5990,c_5989,c_5988,c_5987,c_5986,c_5985,c_5984,c_5983,c_5982,c_5981,c_5980,c_5979,c_5978,c_5977,c_5976,c_5975,c_5974,c_5973,c_5972,c_5971,c_5970,c_5969,c_5968,c_5967,c_5836,c_5835,c_5834,c_5833,c_5832,c_5831,c_5830,c_5829,c_5828,c_5827,c_5826,c_5825,c_5824,c_5823,c_5822,c_5821,c_5820,c_5670,c_5669,c_5668,c_5667,c_5666,c_5665,c_5664,c_5663,c_5662,c_5661,c_5660,c_5659,c_5658,c_5657,c_5656,c_5655,c_5654,c_5641,c_5627,c_5626,c_5623,c_5622,c_5621,c_5620,c_5619,c_5616,c_5613,c_5610,c_5607,c_5604,c_5603,c_5602,c_5601,c_5600,c_5599,c_5598,c_5597,c_5596,c_5594,c_5593,c_5592,c_5591,c_5561,c_5557,c_5554,c_5553,c_5549,c_5546,c_5545,c_5541,c_5537,c_5534,c_5533,c_5524,c_5523,c_5522,c_5520,c_5518,c_5517,c_5516,c_5514,c_5505,c_5501,c_5500,c_5495,c_5497,c_5499,c_5487,c_5486,c_5483,c_5482,c_5481,c_5480,c_5479,c_5478,c_5473,c_5469,c_5468,c_5463,c_5465,c_5467,c_5455,c_5454,c_5453,c_5452,c_5451,c_5449,c_5382,c_5355,c_5350,c_5344,c_5338,c_5332,c_5327,c_5322,c_5321,c_5320,c_5315,c_5314,c_5313,c_5309,c_5306,c_5303,c_5302,c_5301,c_5292,c_5219,c_5210,c_5206,c_5202,c_5198,c_5194,c_5190,c_5185,c_5180,c_5175,c_5170,c_5165,c_5160,c_5155,c_5151,c_5147,c_5143,c_5139,c_5135,c_5131,c_5127,c_5123,c_5119,c_5115,c_5111,c_5107,c_5103,c_5101,c_5100,c_5099,c_5098,c_5097,c_5096,c_5095,c_5094,c_5093,c_5092,c_5091,c_5090,c_5089,c_5088,c_5087,c_5086,c_5085,c_5084,c_5083,c_5082,c_5081,c_5080,c_5079,c_5078,c_5077,c_5076,c_5075,c_5074,c_4941,c_4932,c_4928,c_4924,c_4920,c_4916,c_4912,c_4907,c_4902,c_4897,c_4892,c_4887,c_4882,c_4877,c_4873,c_4869,c_4865,c_4861,c_4857,c_4853,c_4849,c_4845,c_4841,c_4837,c_4833,c_4829,c_4825,c_4823,c_4822,c_4821,c_4820,c_4819,c_4818,c_4817,c_4816,c_4815,c_4814,c_4813,c_4812,c_4811,c_4810,c_4809,c_4808,c_4807,c_4806,c_4805,c_4804,c_4803,c_4802,c_4801,c_4800,c_4799,c_4798,c_4797,c_4796,c_4609,c_4608,c_4607,c_4606,c_4605,c_4604,c_4603,c_4602,c_4601,c_4600,c_4599,c_4598,c_4597,c_4596,c_4595,c_4594,c_4593,c_4568,c_4567,c_4566,c_4565,c_4564,c_4562,c_4519,c_4518,c_4517,c_4515,c_4513,c_4511,c_4495,c_4494,c_4491,c_4490,c_4489,c_4488,c_4487,c_4486,c_4477,c_4475,c_4469,c_4468,c_4467,c_4466,c_4465,c_4463,c_4439,c_4438,c_4437,c_4436,c_4435,c_4434,c_4433,c_4432,c_4431,c_4430,c_4379,c_4378,c_4377,c_4376,c_4375,c_4374,c_4373,c_4372,c_4371,c_4370,c_4369,c_4368,c_4367,c_4357,c_4354,c_4214,c_4213,c_4212,c_4211,c_4210,c_4209,c_4208,c_4207,c_4206,c_4205,c_4204,c_4203,c_4202,c_4201,c_4200,c_4160,c_4143,c_4139,c_4135,c_4131,c_4120,c_4116,c_4112,c_4108,c_4104,c_4102,c_4101,c_4099,c_4098,c_4097,c_4096,c_4095,c_4094,c_4093,c_4086,c_4085,c_4088,c_4083,c_4019,c_4015,c_4011,c_4007,c_4003,c_3999,c_3995,c_3991,c_3990,c_3989,c_3988,c_3987,c_3986,c_3985,c_3983,c_3982,c_3981,c_3968,c_3966,c_3963,c_3962,c_3961,c_3959,c_3958,c_3956,c_3937,c_3934,c_3933,c_3932,c_3931,c_3930,c_3926,c_3924,c_3921,c_3920,c_3919,c_3917,c_3906,c_3905,c_3904,c_3903,c_3902,c_3901,c_3843,c_3842,c_3841,c_3840,c_3839,c_3838,c_3837,c_3836,c_3835,c_3760,c_3757,c_3754,c_3747,c_3746,c_3745,c_3744,c_3743,c_3742,c_3740,c_3739,c_3738,c_3737,c_3736,c_3735,c_3734,c_3689,c_3679,c_3678,c_3677,c_3676,c_3664,c_3663,c_3662,c_3661,c_3658,c_3657,c_3656,c_3655,c_3654,c_3653,c_3652,c_3651,c_3650,c_3649,c_3648,c_3647,c_3646,c_3645,c_3644,c_3643,c_3642,c_3641,c_3640,c_3639,c_3638,c_3637,c_3607,c_3593,c_3590,c_3589,c_3584,c_3581,c_3578,c_3576,c_3575,c_3574,c_3573,c_3572,c_3571,c_3570,c_3563,c_3562,c_3560,c_3537,c_3491,c_3490,c_3489,c_3488,c_3487,c_3486,c_3485,c_3484,c_3483,c_3482,c_3481,c_3480,c_3469,c_3467,c_3461,c_3458,c_3447,c_3443,c_3439,c_3435,c_3432,c_3428,c_3420,c_3416,c_3412,c_3408,c_3398,c_3397,c_3396,c_3395,c_3394,c_3393,c_3392,c_3391,c_3355,c_3354,c_3353,c_3352,c_3351,c_3350,c_3349,c_3348,c_3347,c_3346,c_3345,c_3344,c_3343,c_3342,c_3341,c_3340,c_3339,c_3329,c_3319,c_3318,c_3317,c_3316,c_3304,c_3303,c_3302,c_3299,c_3298,c_3297,c_3296,c_3295,c_3294,c_3293,c_3292,c_3291,c_3290,c_3289,c_3288,c_3287,c_3286,c_3285,c_3284,c_3283,c_3282,c_3281,c_3280,c_3279,c_3278,c_3265,c_3264,c_3263,c_3262,c_3261,c_3258,c_3257,c_3256,c_3248,c_3201,c_3198,c_3195,c_3192,c_3191,c_3188,c_3187,c_3186,c_3178,c_3169,c_3168,c_3167,c_3166,c_3165,c_3163,c_3162,c_3160,c_3146,c_3144,c_3135,c_3133,c_3122,c_3121,c_3120,c_3119,c_3118,c_3117,c_3116,c_3115,c_3053,c_3052,c_3051,c_3050,c_3049,c_3048,c_3047,c_3046,c_3045,c_3044,c_3043,c_2956,c_2955,c_2954,c_2953,c_2952,c_2951,c_2950,c_2949,c_2948,c_2947,c_2946,c_2897,c_2896,c_2895,c_2894,c_2893,c_2892,c_2891,c_2890,c_2881,c_2880,c_2879,c_2878,c_2864,c_2863,c_2862,c_2861,c_2860,c_2859,c_2856,c_2855,c_2854,c_2853,c_2841,c_2840,c_2839,c_2838,c_2837,c_2836,c_2833,c_2832,c_2831,c_2830,c_2806,c_2805,c_2804,c_2803,c_2802,c_2801,c_2800,c_2769,c_2768,c_2767,c_2766,c_2765,c_2730,c_2729,c_2728,c_2727,c_2726,c_2725,c_2724,c_2697,c_2696,c_2695,c_2694,c_2669,c_2668,c_2667,c_2666,c_2665,c_2664,c_2663,c_2662,c_2661,c_2660,c_2659,c_2658,c_2657,c_2656,c_2655,c_2641,c_2639,c_2638,c_2637,c_2636,c_2635,c_2634,c_2633,c_2610,c_2609,c_2608,c_2607,c_2581,c_2580,c_2579,c_2578,c_2563,c_2562,c_2561,c_2556,c_2555,c_2554,c_2553,c_2547,c_2546,c_2545,c_2540,c_2539,c_2538,c_2537,c_154,c_147,c_144,c_141,c_2654,c_108,c_107,c_106,c_105,c_104,c_101,c_100,c_99,c_102,c_97,c_96,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_86,c_84,c_83,c_82,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_64,c_62,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.44 % Computer : n011.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Thu Sep 24 04:10:18 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.21/5.50 Running first-order theorem proving
% 0.21/5.50 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/5.51
% 0.21/5.51 % ======== iProver multi-core TPTP/SMT =========
% 0.21/5.51
% 0.21/5.52 % Detected problem language: tptp
% 0.21/5.53 % Proving...
% 3.69/6.42 % SZS status Started for theBenchmark.p
% 3.69/6.42 % SZS status Theorem for theBenchmark.p
% 3.69/6.42
% 3.69/6.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/6.42
% 3.69/6.42 % ------ iProver source info
% 3.69/6.42
% 3.69/6.42 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/6.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/6.42 % git: non_committed_changes: false
% 3.69/6.42
% 3.69/6.42 % ------ Parsing...
% 3.69/6.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.69/6.42
% 3.69/6.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.69/6.42
% 3.69/6.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.69/6.42
% 3.69/6.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/6.42 % ------ Proving...
% 3.69/6.42 % ------ Problem Properties
% 3.69/6.42
% 3.69/6.42 %
% 3.69/6.42 % clauses 55
% 3.69/6.42 % conjectures 1
% 3.69/6.42 % EPR 12
% 3.69/6.42 % Horn 43
% 3.69/6.42 % unary 13
% 3.69/6.42 % binary 5
% 3.69/6.42 % lits 190
% 3.69/6.42 % lits eq 50
% 3.69/6.42 % fd_pure 0
% 3.69/6.42 % fd_pseudo 0
% 3.69/6.42 % fd_cond 5
% 3.69/6.42 % fd_pseudo_cond 9
% 3.69/6.42 % AC symbols 0
% 3.69/6.42
% 3.69/6.42 % ------ Schedule dynamic 5 is on
% 3.69/6.42
% 3.69/6.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/6.42
% 3.69/6.42
% 3.69/6.42 % ------
% 3.69/6.42 % Current options:
% 3.69/6.42 % ------
% 3.69/6.42
% 3.69/6.42
% 3.69/6.42 %
% 3.69/6.42
% 3.69/6.42 % ------ Proving...
% 3.69/6.42 %
% 3.69/6.42
% 3.69/6.42 % SZS status Theorem for theBenchmark.p
% 3.69/6.42
% 3.69/6.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.86/6.45
% 4.86/6.45
%------------------------------------------------------------------------------