%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM502+3 : 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 : n026.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 02:25:21 PM UTC 2026
% Result : Theorem 229.81s 41.10s
% Output : CNFRefutation 229.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 28
% Syntax : Number of formulae : 260 ( 45 unt; 0 def)
% Number of atoms : 1086 ( 413 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1402 ( 576 ~; 643 |; 144 &)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 326 ( 0 sgn 308 !; 18 ?; 110 :)
% 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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(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(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( X1 != sz00
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
~ ( sdtlseqdt0(xp,xm)
| ? [X0] :
( sdtpldt0(xp,X0) = xm
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( sdtpldt0(xm,X0) = xp
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f50,conjecture,
( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( sdtpldt0(xk,X0) = xp
& aNaturalNumber0(X0) ) )
& xk != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( sdtpldt0(xk,X0) = xp
& aNaturalNumber0(X0) ) )
& xk != xp ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f55,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(rectify,[],[f41]) ).
fof(f56,plain,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( xp = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f73,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f76,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(f77,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,[],[f76]) ).
fof(f78,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(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f84]) ).
fof(f86,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(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f93]) ).
fof(f95,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(f96,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,[],[f95]) ).
fof(f97,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(f98,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,[],[f97]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f115]) ).
fof(f125,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(ennf_transformation,[],[f55]) ).
fof(f126,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(flattening,[],[f125]) ).
fof(f128,plain,
( ~ sdtlseqdt0(xp,xm)
& ! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f132,plain,
( ( ~ sdtlseqdt0(xk,xp)
& ! [X0] :
( xp != sdtpldt0(xk,X0)
| ~ aNaturalNumber0(X0) ) )
| xp = xk ),
inference(ennf_transformation,[],[f51]) ).
fof(f136,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,[],[f85]) ).
fof(f137,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,[],[f136]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f137]) ).
fof(f139,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,[],[f87]) ).
fof(f140,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,[],[f139]) ).
fof(f159,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10)
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f126]) ).
fof(f160,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK12)
& aNaturalNumber0(sK12)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK11)
& aNaturalNumber0(sK11)
& xn != xp ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f56]) ).
fof(f163,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f166,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f167,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f170,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f171,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f177,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f73]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f186,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f83]) ).
fof(f187,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f140]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f140]) ).
fof(f194,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f90]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f196,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f200,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,[],[f96]) ).
fof(f202,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,[],[f98]) ).
fof(f204,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,[],[f98]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f219,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f231,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f232,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f233,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f257,plain,
sz00 != xp,
inference(cnf_transformation,[],[f159]) ).
fof(f260,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f128]) ).
fof(f261,plain,
! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f262,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f160]) ).
fof(f265,plain,
xm != xp,
inference(cnf_transformation,[],[f160]) ).
fof(f266,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f160]) ).
fof(f269,plain,
xn != xp,
inference(cnf_transformation,[],[f160]) ).
fof(f271,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f272,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f276,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f291,plain,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f132]) ).
fof(f293,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f189]) ).
fof(f295,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f191]) ).
fof(f296,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f190]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f163]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_68,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,[],[f183]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK2(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK2(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_81,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,[],[f195]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_85,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,[],[f200]) ).
tcf(c_89,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,[],[f204]) ).
tcf(c_91,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,[],[f202]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f233]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f232]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f231]) ).
tcf(c_135,plain,
sz00 != xp,
inference(cnf_transformation,[],[f257]) ).
tcf(c_145,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xp,X0) != xm ) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_146,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f260]) ).
tcf(c_147,plain,
xn != xp,
inference(cnf_transformation,[],[f269]) ).
tcf(c_150,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f266]) ).
tcf(c_151,plain,
xm != xp,
inference(cnf_transformation,[],[f265]) ).
tcf(c_154,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f262]) ).
tcf(c_155,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f272]) ).
tcf(c_156,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f271]) ).
tcf(c_160,plain,
sz00 != xk,
inference(cnf_transformation,[],[f276]) ).
tcf(c_177,negated_conjecture,
( ( xp = xk )
| ~ sdtlseqdt0(xk,xp) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_185,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_214,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_9069,negated_conjecture,
( ( xp = xk )
| ~ sdtlseqdt0(xk,xp) ),
inference(demodulation,[status(thm)],[c_177]) ).
tcf(c_9071,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_9073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_10846,plain,
sdtpldt0(xk,sz00) = xk,
inference(superposition,[status(thm)],[c_155,c_56]) ).
tcf(c_11134,plain,
( sdtlseqdt0(xk,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_10846,c_251]) ).
tcf(c_11180,plain,
sdtlseqdt0(xk,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_11134,c_155,c_49]) ).
tcf(c_11198,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( xp != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_9073]) ).
tcf(c_11199,plain,
( ( sz00 = xp )
| ( xp != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_11198]) ).
tcf(c_11210,plain,
! [X0: $i] :
( ( xm = xp )
| ( xp != X0 )
| ( xm != X0 ) ),
inference(instantiation,[status(thm)],[c_9073]) ).
tcf(c_11212,plain,
! [X0: $i] :
( ( sz00 = xk )
| ( xk != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_9073]) ).
tcf(c_11213,plain,
( ( sz00 = xk )
| ( xk != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_11212]) ).
tcf(c_11237,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_9069]) ).
tcf(c_11240,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11237,c_155,c_118]) ).
tcf(c_11833,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xp,xm)
| ~ sdtlseqdt0(X1,X0)
| ( xp != X1 )
| ( xm != X0 ) ),
inference(instantiation,[status(thm)],[c_9077]) ).
tcf(c_12673,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_11240,c_75]) ).
tcf(c_12718,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12673,c_155,c_118]) ).
tcf(c_12773,plain,
! [X0: $i] :
( ( xp = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != sz00 ) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_12849,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_11240,c_78]) ).
tcf(c_12894,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12849,c_155,c_118]) ).
tcf(c_12977,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_9071]) ).
tcf(c_15782,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(superposition,[status(thm)],[c_12894,c_66]) ).
tcf(c_15904,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15782,c_118]) ).
tcf(c_16370,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_12718,c_15904]) ).
tcf(c_16384,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(sdtmndt0(xk,xp)) ),
inference(superposition,[status(thm)],[c_74,c_16370]) ).
tcf(c_16385,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(sdtmndt0(xk,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16384,c_155,c_118]) ).
tcf(c_16425,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(sdtmndt0(xk,xp)) ),
inference(global_subsumption_just,[status(thm)],[c_16385,c_11240,c_16385]) ).
tcf(c_16433,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_77,c_16425]) ).
tcf(c_16434,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16433,c_155,c_118]) ).
tcf(c_17173,plain,
! [X0: $i] :
( doDivides0(X0,sK2(xp,xk))
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_12718,c_103]) ).
tcf(c_17254,plain,
! [X0: $i] :
( doDivides0(X0,sK2(xp,xk))
| ( xp = xk )
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17173,c_118]) ).
tcf(c_17706,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sK2(xp,xk))
| ( xp = xk )
| ( sK2(xp,xk) = sz00 )
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_17254,c_104]) ).
tcf(c_17864,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_9069]) ).
tcf(c_17867,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17864,c_155,c_118]) ).
tcf(c_18437,plain,
! [X0: $i] :
( sdtlseqdt0(xk,sdtpldt0(xp,X0))
| ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ sdtlseqdt0(sdtmndt0(xk,xp),X0) ),
inference(superposition,[status(thm)],[c_12894,c_85]) ).
tcf(c_18816,plain,
! [X0: $i] :
( sdtlseqdt0(xk,sdtpldt0(xp,X0))
| ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ sdtlseqdt0(sdtmndt0(xk,xp),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18437,c_118]) ).
tcf(c_18948,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xp != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_9077]) ).
tcf(c_19097,plain,
! [X0: $i] :
( sdtlseqdt0(xp,xm)
| ~ sdtlseqdt0(xp,X0)
| ( xp != xp )
| ( xm != X0 ) ),
inference(instantiation,[status(thm)],[c_11833]) ).
tcf(c_22171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(superposition,[status(thm)],[c_89,c_80]) ).
tcf(c_22858,plain,
xk = xk,
inference(instantiation,[status(thm)],[c_9071]) ).
tcf(c_24047,plain,
( ( xk = sz00 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xp,xk) != sz00 ) ),
inference(instantiation,[status(thm)],[c_12773]) ).
tcf(c_24836,plain,
( sdtlseqdt0(xk,sdtpldt0(xp,sK2(xp,xk)))
| ( xp = xk )
| ( sK2(xp,xk) = sz00 )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ doDivides0(sdtmndt0(xk,xp),xk)
| ~ doDivides0(sdtmndt0(xk,xp),xp) ),
inference(superposition,[status(thm)],[c_17706,c_18816]) ).
tcf(c_26688,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_17867,c_75]) ).
tcf(c_26733,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26688,c_155,c_118]) ).
tcf(c_28934,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_17867,c_78]) ).
tcf(c_28979,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28934,c_155,c_118]) ).
tcf(c_31508,plain,
( sdtlseqdt0(xp,xm)
| ~ sdtlseqdt0(xp,xk)
| ( xp != xp )
| ( xm != xk ) ),
inference(instantiation,[status(thm)],[c_19097]) ).
tcf(c_31795,plain,
( ( xp = xk )
| ~ aNaturalNumber0(sK2(xp,xk))
| ( xm != xk ) ),
inference(superposition,[status(thm)],[c_26733,c_145]) ).
tcf(c_31819,plain,
( ( xp = xk )
| ( xm != xk ) ),
inference(global_subsumption_just,[status(thm)],[c_31795,c_146,c_11240,c_12977,c_31508]) ).
tcf(c_35213,plain,
( ( xm = xp )
| ( xp != xk )
| ( xm != xk ) ),
inference(instantiation,[status(thm)],[c_11210]) ).
tcf(c_38814,plain,
( ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ( xp = xk ) ),
inference(global_subsumption_just,[status(thm)],[c_24836,c_11240,c_16434]) ).
tcf(c_38815,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) ) ),
inference(renaming,[status(thm)],[c_38814]) ).
tcf(c_38820,plain,
( aNaturalNumber0(sdtmndt0(xk,xp))
| ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_38815,c_74]) ).
tcf(c_38847,plain,
( aNaturalNumber0(sdtmndt0(xk,xp))
| ( xp = xk )
| ~ sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38820,c_155,c_118]) ).
tcf(c_46445,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(xk,X1)
| ( xp != xk )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_18948]) ).
tcf(c_47588,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(superposition,[status(thm)],[c_28979,c_66]) ).
tcf(c_47710,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47588,c_118]) ).
tcf(c_51339,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xp,X0) != xk ) ),
inference(global_subsumption_just,[status(thm)],[c_47710,c_11240,c_15904,c_38847]) ).
tcf(c_66197,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(xk,xk)
| ( xp != xk )
| ( X0 != xk ) ),
inference(instantiation,[status(thm)],[c_46445]) ).
tcf(c_82386,plain,
sdtpldt0(xp,sz00) = xp,
inference(superposition,[status(thm)],[c_118,c_56]) ).
tcf(c_82893,plain,
( sdtlseqdt0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_82386,c_251]) ).
tcf(c_82933,plain,
sdtlseqdt0(xp,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_82893,c_118,c_49]) ).
tcf(c_82948,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_9069]) ).
tcf(c_82951,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82948,c_155,c_118]) ).
tcf(c_86013,plain,
( ( sdtpldt0(xp,sK2(xp,xp)) = xp )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_82933,c_75]) ).
tcf(c_86037,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_82951,c_75]) ).
tcf(c_86052,plain,
sdtpldt0(xp,sK2(xp,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_86013,c_118]) ).
tcf(c_86079,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sK2(xp,xk)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86037,c_155,c_118]) ).
tcf(c_86141,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_82951,c_78]) ).
tcf(c_86183,plain,
( ( xp = xk )
| ( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86141,c_155,c_118]) ).
tcf(c_86227,plain,
( ( xp = xk )
| ~ aNaturalNumber0(sK2(xp,xk))
| ( xm != xk ) ),
inference(superposition,[status(thm)],[c_86079,c_145]) ).
tcf(c_86251,plain,
xm != xk,
inference(global_subsumption_just,[status(thm)],[c_86227,c_151,c_31819,c_35213]) ).
tcf(c_88112,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(superposition,[status(thm)],[c_86183,c_66]) ).
tcf(c_88284,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ( sdtpldt0(xp,X0) != xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88112,c_118]) ).
tcf(c_88709,plain,
! [X0: $i] :
( ( xp = xk )
| ( sdtmndt0(xk,xp) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xp,X0) != xk ) ),
inference(global_subsumption_just,[status(thm)],[c_88284,c_51339]) ).
tcf(c_88720,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) )
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_86079,c_88709]) ).
tcf(c_88725,plain,
( ( xp = xk )
| ( sK2(xp,xk) = sdtmndt0(xk,xp) ) ),
inference(global_subsumption_just,[status(thm)],[c_88720,c_38815]) ).
tcf(c_90261,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xp,X0),xk)
| ( xp = xk )
| ( sK2(xp,xk) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ sdtlseqdt0(X0,sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_86079,c_85]) ).
tcf(c_90768,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xp,X0),xk)
| ( xp = xk )
| ( sK2(xp,xk) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ sdtlseqdt0(X0,sK2(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90261,c_118]) ).
tcf(c_92008,plain,
( sdtlseqdt0(xp,xk)
| ~ sdtlseqdt0(xk,xk)
| ( xk != xk )
| ( xp != xk ) ),
inference(instantiation,[status(thm)],[c_66197]) ).
tcf(c_110894,plain,
! [X0: $i] :
( sdtlseqdt0(sK2(xp,xk),X0)
| sdtlseqdt0(sdtpldt0(xp,X0),xk)
| ( xp = xk )
| ( sK2(xp,xk) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_83,c_90768]) ).
tcf(c_138373,plain,
! [X0: $i] :
( sdtlseqdt0(sdtmndt0(xk,xp),X0)
| sdtlseqdt0(sdtpldt0(xp,X0),xk)
| ( xp = xk )
| ( sK2(xp,xk) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_88725,c_110894]) ).
tcf(c_138776,plain,
( sdtlseqdt0(xp,xk)
| sdtlseqdt0(sdtmndt0(xk,xp),sK2(xp,xp))
| ( xp = xk )
| ( sK2(xp,xp) = sK2(xp,xk) )
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(sK2(xp,xp)) ),
inference(superposition,[status(thm)],[c_86052,c_138373]) ).
tcf(c_149199,plain,
sdtlseqdt0(xp,xk),
inference(global_subsumption_just,[status(thm)],[c_138776,c_11180,c_11240,c_22858,c_92008]) ).
tcf(c_515923,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_116,c_62]) ).
tcf(c_516535,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_154,c_81]) ).
tcf(c_516536,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_516535,c_118,c_117]) ).
tcf(c_516736,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(superposition,[status(thm)],[c_89,c_80]) ).
tcf(c_519559,plain,
( ( sz00 = xm )
| ( sz00 = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xp,xk) != sz00 ) ),
inference(superposition,[status(thm)],[c_156,c_72]) ).
tcf(c_519564,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(superposition,[status(thm)],[c_156,c_91]) ).
tcf(c_519565,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_156,c_91]) ).
tcf(c_519577,plain,
( ( sz00 = xm )
| ( sz00 = xn )
| ( sdtasdt0(xp,xk) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_519559,c_117,c_116]) ).
tcf(c_519606,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm))
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_519565,c_117,c_116]) ).
tcf(c_519612,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk))
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_519564,c_117,c_116]) ).
tcf(c_520787,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_9069]) ).
tcf(c_520789,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xk ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_520787,c_155,c_118]) ).
tcf(c_565367,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(global_subsumption_just,[status(thm)],[c_516736,c_53,c_68,c_22171]) ).
tcf(c_565368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(renaming,[status(thm)],[c_565367]) ).
tcf(c_565377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_565368,c_53]) ).
tcf(c_577717,plain,
sdtlseqdt0(xp,xk),
inference(global_subsumption_just,[status(thm)],[c_520789,c_149199]) ).
tcf(c_577759,plain,
( sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_577717,c_516536]) ).
tcf(c_577760,plain,
sdtlseqdt0(xm,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_577759,c_155]) ).
tcf(c_682693,plain,
sdtasdt0(xp,xk) != sz00,
inference(global_subsumption_just,[status(thm)],[c_519577,c_155,c_118,c_49,c_160,c_135,c_185,c_214,c_11199,c_11213,c_24047]) ).
tcf(c_687010,plain,
( ( xm = xk )
| ( xn = xp )
| ( sz00 = xp )
| ( sz00 = xm )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,xk)
| ~ sdtlseqdt0(xn,xp) ),
inference(superposition,[status(thm)],[c_519606,c_565377]) ).
tcf(c_687020,plain,
( ( xm = xk )
| ( sz00 = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_687010,c_147,c_135,c_155,c_118,c_117,c_577760,c_150]) ).
tcf(c_687724,plain,
sz00 = xm,
inference(global_subsumption_just,[status(thm)],[c_519612,c_86251,c_687020]) ).
tcf(c_687810,plain,
sdtasdt0(xn,sz00) = sdtasdt0(xp,xk),
inference(demodulation,[status(thm)],[c_156,c_687724]) ).
tcf(c_687828,plain,
sdtasdt0(xp,xk) = sz00,
inference(light_normalisation,[status(thm)],[c_687810,c_515923]) ).
tcf(c_687829,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_687828,c_682693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM502+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 04:21:59 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 229.81/41.10 % SZS status Started for theBenchmark.p
% 229.81/41.10 % SZS status Theorem for theBenchmark.p
% 229.81/41.10
% 229.81/41.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 229.81/41.10
% 229.81/41.10 % ------ iProver source info
% 229.81/41.10
% 229.81/41.10 % git: date: 2026-07-19 20:42:38 +0200
% 229.81/41.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 229.81/41.10 % git: non_committed_changes: false
% 229.81/41.10
% 229.81/41.10 % ------ Parsing...
% 229.81/41.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 229.81/41.10
% 229.81/41.10 % ------ Preprocessing... sup_sim: 5 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 %
% 229.81/41.10
% 229.81/41.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 229.81/41.10
% 229.81/41.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 229.81/41.10 % ------ Proving...
% 229.81/41.10 % ------ Problem Properties
% 229.81/41.10
% 229.81/41.10 %
% 229.81/41.10 % clauses 122
% 229.81/41.10 % conjectures 2
% 229.81/41.10 % EPR 45
% 229.81/41.10 % Horn 82
% 229.81/41.10 % unary 41
% 229.81/41.10 % binary 14
% 229.81/41.10 % lits 396
% 229.81/41.10 % lits eq 123
% 229.81/41.10 % fd_pure 0
% 229.81/41.10 % fd_pseudo 0
% 229.81/41.10 % fd_cond 24
% 229.81/41.10 % fd_pseudo_cond 11
% 229.81/41.10 % AC symbols 0
% 229.81/41.10
% 229.81/41.10 % ------ Schedule dynamic 5 is on
% 229.81/41.10
% 229.81/41.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 % ------
% 229.81/41.10 % Current options:
% 229.81/41.10 % ------
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 %
% 229.81/41.10
% 229.81/41.10 % ------ Proving...
% 229.81/41.10 % Proof_search_loop: time out after: 7513 full_loop iterations
% 229.81/41.10
% 229.81/41.10 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 % ------
% 229.81/41.10 % Current options:
% 229.81/41.10 % ------
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 %
% 229.81/41.10
% 229.81/41.10 % ------ Proving...
% 229.81/41.10 % Proof_search_loop: time out after: 6078 full_loop iterations
% 229.81/41.10
% 229.81/41.10 % ------ Option_1: Negative Selections Time Limit: 35.
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 % ------
% 229.81/41.10 % Current options:
% 229.81/41.10 % ------
% 229.81/41.10
% 229.81/41.10
% 229.81/41.10 %
% 229.81/41.10
% 229.81/41.10 % ------ Proving...
% 229.81/41.10 %
% 229.81/41.10
% 229.81/41.10 % SZS status Theorem for theBenchmark.p
% 229.81/41.10
% 229.81/41.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 229.81/41.10
% 229.81/41.10
%------------------------------------------------------------------------------