TSTP Solution File: NUM502+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM502+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:30:58 EDT 2023
% Result : Theorem 242.40s 32.85s
% Output : CNFRefutation 242.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 33
% Syntax : Number of formulae : 266 ( 47 unt; 0 def)
% Number of atoms : 1111 ( 427 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1427 ( 582 ~; 649 |; 153 &)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 336 ( 0 sgn; 201 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,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)
=> ( sz00 != X0
=> ! [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) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
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] :
( sdtmndt0(X1,X0) = X2
<=> ( 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)
& X0 != X1 )
| 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(X1,X2) != sdtpldt0(X0,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
& 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) ) ) ),
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) )
=> ( ( sz00 != X1
& 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] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
~ ( sdtlseqdt0(xp,xm)
| ? [X0] :
( xm = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& 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,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f50,conjecture,
( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( xp = sdtpldt0(xk,X0)
& aNaturalNumber0(X0) ) )
& xp != xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( xp = sdtpldt0(xk,X0)
& aNaturalNumber0(X0) ) )
& xp != xk ),
inference(negated_conjecture,[],[f50]) ).
fof(f55,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f56,plain,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f73,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f76,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f77,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f79,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f81,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f83,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f85,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f92,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f94,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f113,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f114,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f116,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f125,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f55]) ).
fof(f126,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
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] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f85]) ).
fof(f137,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f137,f138]) ).
fof(f140,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f87]) ).
fof(f141,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f140]) ).
fof(f167,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f168,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f126,f167]) ).
fof(f169,plain,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xm,sK11)
& aNaturalNumber0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f170,plain,
( ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xn,sK12)
& aNaturalNumber0(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f171,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK11)
& aNaturalNumber0(sK11)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK12)
& aNaturalNumber0(sK12)
& xn != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f56,f170,f169]) ).
fof(f177,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f179,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f180,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f181,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f184,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f190,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f194,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f196,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f198,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f200,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0,X1] :
( aNaturalNumber0(sK2(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f202,plain,
! [X0,X1] :
( sdtpldt0(X0,sK2(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f203,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f204,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f205,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f208,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f209,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f211,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f213,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f217,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f232,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f233,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f245,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f246,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f264,plain,
sz00 != xp,
inference(cnf_transformation,[],[f168]) ).
fof(f266,plain,
! [X2,X1] :
( xp = X1
| sz10 = X1
| sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f168]) ).
fof(f274,plain,
! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f275,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f128]) ).
fof(f276,plain,
xn != xp,
inference(cnf_transformation,[],[f171]) ).
fof(f279,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f171]) ).
fof(f280,plain,
xm != xp,
inference(cnf_transformation,[],[f171]) ).
fof(f283,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f171]) ).
fof(f284,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f285,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f289,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f306,plain,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f132]) ).
fof(f307,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f203]) ).
fof(f309,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f205]) ).
fof(f310,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f204]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f177]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f179]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_67,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_69,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_72,plain,
( sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f307]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_75,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_77,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f309]) ).
cnf(c_78,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f310]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_86,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_88,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_90,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1)) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_103,plain,
( ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_104,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f247]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f246]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f245]) ).
cnf(c_140,plain,
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz10
| X0 = xp ),
inference(cnf_transformation,[],[f266]) ).
cnf(c_142,plain,
sz00 != xp,
inference(cnf_transformation,[],[f264]) ).
cnf(c_145,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f275]) ).
cnf(c_146,plain,
( sdtpldt0(xp,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f274]) ).
cnf(c_147,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f283]) ).
cnf(c_150,plain,
xp != xm,
inference(cnf_transformation,[],[f280]) ).
cnf(c_151,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f279]) ).
cnf(c_154,plain,
xp != xn,
inference(cnf_transformation,[],[f276]) ).
cnf(c_156,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f285]) ).
cnf(c_157,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f284]) ).
cnf(c_161,plain,
sz00 != xk,
inference(cnf_transformation,[],[f289]) ).
cnf(c_176,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f306]) ).
cnf(c_182,plain,
( ~ aNaturalNumber0(sz00)
| sdtasdt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_185,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_214,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_224,plain,
( sdtasdt0(sz00,sz00) != xp
| ~ aNaturalNumber0(sz00)
| sz00 = sz10
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_251,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_9073,plain,
X0 = X0,
theory(equality) ).
cnf(c_9075,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_9079,plain,
( X0 != X1
| X2 != X3
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X0,X2) ),
theory(equality) ).
cnf(c_10869,plain,
sdtpldt0(xk,sz00) = xk,
inference(superposition,[status(thm)],[c_157,c_57]) ).
cnf(c_11136,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,xk) ),
inference(superposition,[status(thm)],[c_10869,c_251]) ).
cnf(c_11182,plain,
sdtlseqdt0(xk,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_11136,c_157,c_49]) ).
cnf(c_11205,plain,
( sdtasdt0(X0,X1) != X2
| xp != X2
| sdtasdt0(X0,X1) = xp ),
inference(instantiation,[status(thm)],[c_9075]) ).
cnf(c_11206,plain,
( sdtasdt0(sz00,sz00) != sz00
| xp != sz00
| sdtasdt0(sz00,sz00) = xp ),
inference(instantiation,[status(thm)],[c_11205]) ).
cnf(c_11215,plain,
( xp != X0
| xm != X0
| xp = xm ),
inference(instantiation,[status(thm)],[c_9075]) ).
cnf(c_11221,plain,
( sz00 != X0
| xk != X0
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_9075]) ).
cnf(c_11222,plain,
( sz00 != sz00
| xk != sz00
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_11221]) ).
cnf(c_11244,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_82,c_176]) ).
cnf(c_11247,plain,
( xp = xk
| sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11244,c_157,c_116]) ).
cnf(c_11836,plain,
( xp != X0
| xm != X1
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_9079]) ).
cnf(c_12679,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_11247,c_74]) ).
cnf(c_12724,plain,
( sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_12679,c_157,c_116]) ).
cnf(c_12849,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_11247,c_77]) ).
cnf(c_12894,plain,
( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_12849,c_157,c_116]) ).
cnf(c_12949,plain,
( sdtasdt0(xp,X0) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| X0 = sz00
| xp = sz00 ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_12972,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_9073]) ).
cnf(c_14504,plain,
( xp != xk
| xm != xk
| xp = xm ),
inference(instantiation,[status(thm)],[c_11215]) ).
cnf(c_16223,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(superposition,[status(thm)],[c_12894,c_67]) ).
cnf(c_16375,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_16223,c_116]) ).
cnf(c_16566,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(superposition,[status(thm)],[c_12724,c_16375]) ).
cnf(c_16580,plain,
( ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(superposition,[status(thm)],[c_75,c_16566]) ).
cnf(c_16581,plain,
( ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ sdtlseqdt0(xp,xk)
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_16580,c_157,c_116]) ).
cnf(c_16599,plain,
( ~ aNaturalNumber0(sdtmndt0(xk,xp))
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(global_subsumption_just,[status(thm)],[c_16581,c_11247,c_16581]) ).
cnf(c_16607,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(superposition,[status(thm)],[c_78,c_16599]) ).
cnf(c_16608,plain,
( ~ sdtlseqdt0(xp,xk)
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_16607,c_157,c_116]) ).
cnf(c_17097,plain,
( xp != xp
| xm != X0
| ~ sdtlseqdt0(xp,X0)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_11836]) ).
cnf(c_17370,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| xp = xk
| doDivides0(X0,sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_12724,c_103]) ).
cnf(c_17451,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| xp = xk
| doDivides0(X0,sK2(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17370,c_116]) ).
cnf(c_17704,plain,
( X0 != X1
| xp != X2
| ~ sdtlseqdt0(X2,X1)
| sdtlseqdt0(xp,X0) ),
inference(instantiation,[status(thm)],[c_9079]) ).
cnf(c_17985,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ doDivides0(X0,xp)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| sK2(xp,xk) = sz00
| xp = xk
| sdtlseqdt0(X0,sK2(xp,xk)) ),
inference(superposition,[status(thm)],[c_17451,c_104]) ).
cnf(c_18201,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_82,c_176]) ).
cnf(c_18204,plain,
( xp = xk
| sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18201,c_157,c_116]) ).
cnf(c_19490,plain,
( ~ sdtlseqdt0(sdtmndt0(xk,xp),X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sdtmndt0(xk,xp) = X0
| xp = xk
| sdtlseqdt0(xk,sdtpldt0(xp,X0)) ),
inference(superposition,[status(thm)],[c_12894,c_86]) ).
cnf(c_19869,plain,
( ~ sdtlseqdt0(sdtmndt0(xk,xp),X0)
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk
| sdtlseqdt0(xk,sdtpldt0(xp,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19490,c_116]) ).
cnf(c_23017,plain,
xk = xk,
inference(instantiation,[status(thm)],[c_9073]) ).
cnf(c_23219,plain,
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| X0 = sz00
| X1 = X2 ),
inference(superposition,[status(thm)],[c_90,c_80]) ).
cnf(c_24402,plain,
( sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = sz00
| xk = sz00 ),
inference(instantiation,[status(thm)],[c_12949]) ).
cnf(c_24793,plain,
( ~ doDivides0(sdtmndt0(xk,xp),xp)
| ~ doDivides0(sdtmndt0(xk,xp),xk)
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| sK2(xp,xk) = sdtmndt0(xk,xp)
| sK2(xp,xk) = sz00
| xp = xk
| sdtlseqdt0(xk,sdtpldt0(xp,sK2(xp,xk))) ),
inference(superposition,[status(thm)],[c_17985,c_19869]) ).
cnf(c_26659,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_18204,c_74]) ).
cnf(c_26704,plain,
( sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_26659,c_157,c_116]) ).
cnf(c_28817,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_18204,c_77]) ).
cnf(c_28862,plain,
( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_28817,c_157,c_116]) ).
cnf(c_31607,plain,
( xp != xp
| xm != xk
| ~ sdtlseqdt0(xp,xk)
| sdtlseqdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_17097]) ).
cnf(c_31748,plain,
( xm != xk
| ~ aNaturalNumber0(sK2(xp,xk))
| xp = xk ),
inference(superposition,[status(thm)],[c_26704,c_146]) ).
cnf(c_31841,plain,
xm != xk,
inference(global_subsumption_just,[status(thm)],[c_31748,c_145,c_150,c_11247,c_12972,c_14504,c_31607]) ).
cnf(c_38381,plain,
( xp = xk
| sK2(xp,xk) = sdtmndt0(xk,xp) ),
inference(global_subsumption_just,[status(thm)],[c_24793,c_11247,c_16608]) ).
cnf(c_38382,plain,
( sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(renaming,[status(thm)],[c_38381]) ).
cnf(c_38387,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk
| aNaturalNumber0(sdtmndt0(xk,xp)) ),
inference(superposition,[status(thm)],[c_38382,c_75]) ).
cnf(c_38414,plain,
( ~ sdtlseqdt0(xp,xk)
| xp = xk
| aNaturalNumber0(sdtmndt0(xk,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38387,c_157,c_116]) ).
cnf(c_47605,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(superposition,[status(thm)],[c_28862,c_67]) ).
cnf(c_47757,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_47605,c_116]) ).
cnf(c_49563,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(global_subsumption_just,[status(thm)],[c_47757,c_11247,c_16375,c_38414]) ).
cnf(c_71342,plain,
( X0 != X1
| xp != xk
| ~ sdtlseqdt0(xk,X1)
| sdtlseqdt0(xp,X0) ),
inference(instantiation,[status(thm)],[c_17704]) ).
cnf(c_82402,plain,
sdtpldt0(xp,sz00) = xp,
inference(superposition,[status(thm)],[c_116,c_57]) ).
cnf(c_82881,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xp,xp) ),
inference(superposition,[status(thm)],[c_82402,c_251]) ).
cnf(c_82921,plain,
sdtlseqdt0(xp,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_82881,c_116,c_49]) ).
cnf(c_82936,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_82,c_176]) ).
cnf(c_82939,plain,
( xp = xk
| sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82936,c_157,c_116]) ).
cnf(c_85798,plain,
( ~ aNaturalNumber0(xp)
| sdtpldt0(xp,sK2(xp,xp)) = xp ),
inference(superposition,[status(thm)],[c_82921,c_74]) ).
cnf(c_85822,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_82939,c_74]) ).
cnf(c_85841,plain,
sdtpldt0(xp,sK2(xp,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_85798,c_116]) ).
cnf(c_85878,plain,
( sdtpldt0(xp,sK2(xp,xk)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_85822,c_157,c_116]) ).
cnf(c_85940,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(superposition,[status(thm)],[c_82939,c_77]) ).
cnf(c_85996,plain,
( sdtpldt0(xp,sdtmndt0(xk,xp)) = xk
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_85940,c_157,c_116]) ).
cnf(c_88346,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(superposition,[status(thm)],[c_85996,c_67]) ).
cnf(c_88547,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(sdtmndt0(xk,xp))
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_88346,c_116]) ).
cnf(c_88728,plain,
( sdtpldt0(xp,X0) != xk
| ~ aNaturalNumber0(X0)
| sdtmndt0(xk,xp) = X0
| xp = xk ),
inference(global_subsumption_just,[status(thm)],[c_88547,c_49563]) ).
cnf(c_88739,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(superposition,[status(thm)],[c_85878,c_88728]) ).
cnf(c_88744,plain,
( sK2(xp,xk) = sdtmndt0(xk,xp)
| xp = xk ),
inference(global_subsumption_just,[status(thm)],[c_88739,c_38382]) ).
cnf(c_90973,plain,
( X0 != xk
| xp != xk
| ~ sdtlseqdt0(xk,xk)
| sdtlseqdt0(xp,X0) ),
inference(instantiation,[status(thm)],[c_71342]) ).
cnf(c_93001,plain,
( ~ sdtlseqdt0(X0,sK2(xp,xk))
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sK2(xp,xk) = X0
| xp = xk
| sdtlseqdt0(sdtpldt0(xp,X0),xk) ),
inference(superposition,[status(thm)],[c_85878,c_86]) ).
cnf(c_93498,plain,
( ~ sdtlseqdt0(X0,sK2(xp,xk))
| ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(X0)
| sK2(xp,xk) = X0
| xp = xk
| sdtlseqdt0(sdtpldt0(xp,X0),xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93001,c_116]) ).
cnf(c_107786,plain,
( xp != xk
| xk != xk
| ~ sdtlseqdt0(xk,xk)
| sdtlseqdt0(xp,xk) ),
inference(instantiation,[status(thm)],[c_90973]) ).
cnf(c_109144,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(X0)
| sK2(xp,xk) = X0
| xp = xk
| sdtlseqdt0(sdtpldt0(xp,X0),xk)
| sdtlseqdt0(sK2(xp,xk),X0) ),
inference(superposition,[status(thm)],[c_82,c_93498]) ).
cnf(c_133944,plain,
( ~ aNaturalNumber0(sK2(xp,xk))
| ~ aNaturalNumber0(X0)
| sK2(xp,xk) = X0
| xp = xk
| sdtlseqdt0(sdtpldt0(xp,X0),xk)
| sdtlseqdt0(sdtmndt0(xk,xp),X0) ),
inference(superposition,[status(thm)],[c_88744,c_109144]) ).
cnf(c_134417,plain,
( ~ aNaturalNumber0(sK2(xp,xp))
| ~ aNaturalNumber0(sK2(xp,xk))
| sK2(xp,xp) = sK2(xp,xk)
| xp = xk
| sdtlseqdt0(sdtmndt0(xk,xp),sK2(xp,xp))
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_85841,c_133944]) ).
cnf(c_149357,plain,
sdtlseqdt0(xp,xk),
inference(global_subsumption_just,[status(thm)],[c_134417,c_11182,c_11247,c_23017,c_107786]) ).
cnf(c_727258,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_63]) ).
cnf(c_727886,plain,
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_147,c_81]) ).
cnf(c_727892,plain,
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xm,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_727886,c_117,c_116]) ).
cnf(c_728147,plain,
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| X0 = sz00
| X1 = X2 ),
inference(superposition,[status(thm)],[c_90,c_80]) ).
cnf(c_731229,plain,
( sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xm
| sz00 = xn ),
inference(superposition,[status(thm)],[c_156,c_72]) ).
cnf(c_731234,plain,
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| X0 = xn
| sz00 = xm
| sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_156,c_88]) ).
cnf(c_731236,plain,
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| X0 = xn
| sz00 = xm
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm)) ),
inference(superposition,[status(thm)],[c_156,c_88]) ).
cnf(c_731247,plain,
( sdtasdt0(xp,xk) != sz00
| sz00 = xm
| sz00 = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_731229,c_118,c_117]) ).
cnf(c_731272,plain,
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| X0 = xn
| sz00 = xm
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_731236,c_118,c_117]) ).
cnf(c_731284,plain,
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| X0 = xn
| sz00 = xm
| sdtlseqdt0(sdtasdt0(X0,xm),sdtasdt0(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_731234,c_118,c_117]) ).
cnf(c_731534,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_82,c_176]) ).
cnf(c_731536,plain,
( xp = xk
| sdtlseqdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_731534,c_157,c_116]) ).
cnf(c_783997,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| X0 = sz00
| X1 = X2 ),
inference(global_subsumption_just,[status(thm)],[c_728147,c_53,c_69,c_23219]) ).
cnf(c_783998,plain,
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(renaming,[status(thm)],[c_783997]) ).
cnf(c_784007,plain,
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_783998,c_53]) ).
cnf(c_787006,plain,
sdtlseqdt0(xp,xk),
inference(global_subsumption_just,[status(thm)],[c_731536,c_149357]) ).
cnf(c_787047,plain,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xm,xk) ),
inference(superposition,[status(thm)],[c_787006,c_727892]) ).
cnf(c_787050,plain,
sdtlseqdt0(xm,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_787047,c_157]) ).
cnf(c_885822,plain,
sdtasdt0(xp,xk) != sz00,
inference(global_subsumption_just,[status(thm)],[c_731247,c_157,c_116,c_49,c_161,c_142,c_50,c_182,c_185,c_214,c_224,c_11206,c_11222,c_24402]) ).
cnf(c_886818,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xp
| sz00 = xm
| xp = xn
| xm = xk ),
inference(superposition,[status(thm)],[c_731272,c_784007]) ).
cnf(c_886832,plain,
( sz00 = xm
| xm = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_886818,c_154,c_142,c_157,c_117,c_116,c_151,c_787050]) ).
cnf(c_888132,plain,
sz00 = xm,
inference(global_subsumption_just,[status(thm)],[c_731284,c_31841,c_886832]) ).
cnf(c_888246,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,sz00),
inference(demodulation,[status(thm)],[c_156,c_888132]) ).
cnf(c_888269,plain,
sdtasdt0(xp,xk) = sz00,
inference(light_normalisation,[status(thm)],[c_888246,c_727258]) ).
cnf(c_888270,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_888269,c_885822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM502+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 12:23:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 242.40/32.85 % SZS status Started for theBenchmark.p
% 242.40/32.85 % SZS status Theorem for theBenchmark.p
% 242.40/32.85
% 242.40/32.85 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 242.40/32.85
% 242.40/32.85 ------ iProver source info
% 242.40/32.85
% 242.40/32.85 git: date: 2023-05-31 18:12:56 +0000
% 242.40/32.85 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 242.40/32.85 git: non_committed_changes: false
% 242.40/32.85 git: last_make_outside_of_git: false
% 242.40/32.85
% 242.40/32.85 ------ Parsing...
% 242.40/32.85 ------ Clausification by vclausify_rel & Parsing by iProver...
% 242.40/32.85
% 242.40/32.85 ------ 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
% 242.40/32.85
% 242.40/32.85 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 242.40/32.85
% 242.40/32.85 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 242.40/32.85 ------ Proving...
% 242.40/32.85 ------ Problem Properties
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 clauses 122
% 242.40/32.85 conjectures 2
% 242.40/32.85 EPR 45
% 242.40/32.85 Horn 82
% 242.40/32.85 unary 41
% 242.40/32.85 binary 14
% 242.40/32.85 lits 396
% 242.40/32.85 lits eq 123
% 242.40/32.85 fd_pure 0
% 242.40/32.85 fd_pseudo 0
% 242.40/32.85 fd_cond 24
% 242.40/32.85 fd_pseudo_cond 11
% 242.40/32.85 AC symbols 0
% 242.40/32.85
% 242.40/32.85 ------ Schedule dynamic 5 is on
% 242.40/32.85
% 242.40/32.85 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------
% 242.40/32.85 Current options:
% 242.40/32.85 ------
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------ Proving...
% 242.40/32.85 Proof_search_loop: time out after: 9607 full_loop iterations
% 242.40/32.85
% 242.40/32.85 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------
% 242.40/32.85 Current options:
% 242.40/32.85 ------
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------ Proving...
% 242.40/32.85 Proof_search_loop: time out after: 11062 full_loop iterations
% 242.40/32.85
% 242.40/32.85 ------ Option_1: Negative Selections Time Limit: 35.
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------
% 242.40/32.85 Current options:
% 242.40/32.85 ------
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 ------ Proving...
% 242.40/32.85
% 242.40/32.85
% 242.40/32.85 % SZS status Theorem for theBenchmark.p
% 242.40/32.85
% 242.40/32.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 242.40/32.86
% 242.40/32.87
%------------------------------------------------------------------------------