TSTP Solution File: NUM503+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 11:30:59 EDT 2023
% Result : Theorem 27.22s 4.63s
% Output : CNFRefutation 27.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 36
% Syntax : Number of formulae : 299 ( 58 unt; 0 def)
% Number of atoms : 1293 ( 459 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1582 ( 588 ~; 735 |; 216 &)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 329 ( 0 sgn; 177 !; 41 ?)
% 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(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(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(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(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
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(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( xk = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f50,axiom,
( sdtlseqdt0(xp,xk)
& ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).
fof(f51,conjecture,
( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X0] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(negated_conjecture,[],[f51]) ).
fof(f56,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(f57,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(f58,plain,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f59,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f49]) ).
fof(f60,plain,
~ ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ? [X1] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(rectify,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
fof(f69,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f75,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f80,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(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f83,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f87,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f86]) ).
fof(f88,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(f89,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f88]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f94,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f96,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f99,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(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f102,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f104,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f106,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f127,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,[],[f56]) ).
fof(f128,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,[],[f127]) ).
fof(f130,plain,
( ~ sdtlseqdt0(xp,xm)
& ! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f132,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f58]) ).
fof(f133,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
( ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ! [X0] :
( sdtasdt0(xp,xk) != sdtpldt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ! [X1] :
( sdtasdt0(xp,xm) != sdtpldt0(sdtasdt0(xn,xm),X1)
| ~ aNaturalNumber0(X1) ) )
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(ennf_transformation,[],[f60]) ).
fof(f138,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,[],[f87]) ).
fof(f139,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,[],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f141,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])],[f139,f140]) ).
fof(f142,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,[],[f89]) ).
fof(f143,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,[],[f142]) ).
fof(f169,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f170,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])],[f128,f169]) ).
fof(f171,plain,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xm,sK11)
& aNaturalNumber0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f172,plain,
( ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xn,sK12)
& aNaturalNumber0(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f173,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])],[f57,f172,f171]) ).
fof(f174,plain,
( ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
=> ( xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f175,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f133,f174]) ).
fof(f176,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f177,plain,
( ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) )
=> ( xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14)
& xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f59,f177,f176]) ).
fof(f179,plain,
( ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) )
=> ( xk = sdtpldt0(xp,sK16)
& aNaturalNumber0(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f180,plain,
( sdtlseqdt0(xp,xk)
& xk = sdtpldt0(xp,sK16)
& aNaturalNumber0(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f50,f179]) ).
fof(f181,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f182,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f183,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f184,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f185,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f188,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f189,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f194,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f195,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f201,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f202,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f205,plain,
! [X0,X1] :
( aNaturalNumber0(sK2(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f206,plain,
! [X0,X1] :
( sdtpldt0(X0,sK2(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f209,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f212,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f213,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f215,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f221,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,[],[f100]) ).
fof(f223,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,[],[f100]) ).
fof(f225,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f226,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f227,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f249,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f250,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f251,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f268,plain,
sz00 != xp,
inference(cnf_transformation,[],[f170]) ).
fof(f278,plain,
! [X0] :
( xm != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f280,plain,
xn != xp,
inference(cnf_transformation,[],[f173]) ).
fof(f283,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f173]) ).
fof(f287,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f173]) ).
fof(f288,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f289,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f293,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f295,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f175]) ).
fof(f306,plain,
aNaturalNumber0(sK14),
inference(cnf_transformation,[],[f178]) ).
fof(f307,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
inference(cnf_transformation,[],[f178]) ).
fof(f309,plain,
aNaturalNumber0(sK16),
inference(cnf_transformation,[],[f180]) ).
fof(f310,plain,
xk = sdtpldt0(xp,sK16),
inference(cnf_transformation,[],[f180]) ).
fof(f311,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f180]) ).
fof(f312,plain,
! [X0,X1] :
( sdtasdt0(xp,xk) != sdtpldt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xm) != sdtpldt0(sdtasdt0(xn,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f134]) ).
fof(f313,plain,
! [X0] :
( sdtasdt0(xp,xk) != sdtpldt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f134]) ).
fof(f314,plain,
! [X1] :
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xm) != sdtpldt0(sdtasdt0(xn,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f134]) ).
fof(f315,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(cnf_transformation,[],[f134]) ).
fof(f316,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f207]) ).
fof(f318,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f209]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f181]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f183]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f182]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_62,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sz00 ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_68,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00 ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f316]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_75,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_77,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f318]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f215]) ).
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,[],[f223]) ).
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,[],[f221]) ).
cnf(c_92,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| sdtlseqdt0(sz10,X0) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f226]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f251]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f250]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f249]) ).
cnf(c_142,plain,
sz00 != xp,
inference(cnf_transformation,[],[f268]) ).
cnf(c_146,plain,
( sdtpldt0(xp,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f278]) ).
cnf(c_147,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f287]) ).
cnf(c_151,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f283]) ).
cnf(c_154,plain,
xp != xn,
inference(cnf_transformation,[],[f280]) ).
cnf(c_156,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f289]) ).
cnf(c_157,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f288]) ).
cnf(c_161,plain,
sz00 != xk,
inference(cnf_transformation,[],[f293]) ).
cnf(c_170,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f295]) ).
cnf(c_172,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
inference(cnf_transformation,[],[f307]) ).
cnf(c_173,plain,
aNaturalNumber0(sK14),
inference(cnf_transformation,[],[f306]) ).
cnf(c_176,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f311]) ).
cnf(c_177,plain,
sdtpldt0(xp,sK16) = xk,
inference(cnf_transformation,[],[f310]) ).
cnf(c_178,plain,
aNaturalNumber0(sK16),
inference(cnf_transformation,[],[f309]) ).
cnf(c_179,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f315]) ).
cnf(c_180,negated_conjecture,
( sdtpldt0(sdtasdt0(xn,xm),X0) != sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f314]) ).
cnf(c_181,negated_conjecture,
( sdtpldt0(sdtasdt0(xp,xm),X0) != sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f313]) ).
cnf(c_182,negated_conjecture,
( sdtpldt0(sdtasdt0(xp,xm),X1) != sdtasdt0(xp,xk)
| sdtpldt0(sdtasdt0(xn,xm),X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f312]) ).
cnf(c_259,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_1114,plain,
sdtasdt0(xp,xk) = sdtasdt0(xr,sK14),
inference(demodulation,[status(thm)],[c_172,c_156]) ).
cnf(c_1705,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(light_normalisation,[status(thm)],[c_179,c_156]) ).
cnf(c_1744,plain,
( sdtpldt0(sdtasdt0(xp,xm),X0) != sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(light_normalisation,[status(thm)],[c_181,c_156]) ).
cnf(c_1753,plain,
( sdtpldt0(sdtasdt0(xp,xk),X0) != sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(light_normalisation,[status(thm)],[c_180,c_156]) ).
cnf(c_1814,plain,
( sdtpldt0(sdtasdt0(xp,xm),X0) != sdtasdt0(xp,xk)
| sdtpldt0(sdtasdt0(xp,xk),X1) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(light_normalisation,[status(thm)],[c_182,c_156]) ).
cnf(c_9200,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xk),X0) != sdtasdt0(xp,xm)
| ~ sP0_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_split])],[c_1814]) ).
cnf(c_9201,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),X0) != sdtasdt0(xp,xk)
| ~ sP1_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_split])],[c_1814]) ).
cnf(c_9203,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sP0_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1753]) ).
cnf(c_9204,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sP1_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1744]) ).
cnf(c_9207,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_11063,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_51,c_56]) ).
cnf(c_11093,plain,
sdtpldt0(xk,sz00) = xk,
inference(superposition,[status(thm)],[c_157,c_57]) ).
cnf(c_11159,plain,
sdtasdt0(sz00,xk) = sz00,
inference(superposition,[status(thm)],[c_157,c_62]) ).
cnf(c_11255,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK14)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_1114,c_53]) ).
cnf(c_11262,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_11255,c_173,c_170]) ).
cnf(c_11315,plain,
( xm != xk
| ~ aNaturalNumber0(sK16) ),
inference(superposition,[status(thm)],[c_177,c_146]) ).
cnf(c_11317,plain,
xm != xk,
inference(forward_subsumption_resolution,[status(thm)],[c_11315,c_178]) ).
cnf(c_11342,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[c_11063,c_259]) ).
cnf(c_11360,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,xk) ),
inference(superposition,[status(thm)],[c_11093,c_259]) ).
cnf(c_11372,plain,
sdtlseqdt0(xk,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_11360,c_157,c_49]) ).
cnf(c_11390,plain,
sdtlseqdt0(sz00,sz10),
inference(forward_subsumption_resolution,[status(thm)],[c_11342,c_51,c_49]) ).
cnf(c_11434,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_82,c_9204]) ).
cnf(c_11437,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_11434,c_11262]) ).
cnf(c_11568,plain,
( sz00 != X0
| xp != X0
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_9207]) ).
cnf(c_11745,plain,
( ~ sdtlseqdt0(sz00,sz10)
| ~ sdtlseqdt0(sz10,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_13485,plain,
( sz00 != sz00
| xp != sz00
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_11568]) ).
cnf(c_13503,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = sz00
| sz00 = sz10
| sdtlseqdt0(sz10,sz00) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_14145,plain,
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_147,c_81]) ).
cnf(c_14147,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_176,c_81]) ).
cnf(c_14148,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_11437,c_81]) ).
cnf(c_14249,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xp,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14147,c_157,c_116]) ).
cnf(c_14257,plain,
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xm,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14145,c_117,c_116]) ).
cnf(c_14294,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_14148,c_11262]) ).
cnf(c_14712,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_82,c_14294]) ).
cnf(c_14713,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X0))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_93,c_14294]) ).
cnf(c_14721,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_14712,c_11262]) ).
cnf(c_14736,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X0))
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_14713,c_11262]) ).
cnf(c_15702,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X1)
| sdtlseqdt0(X0,sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_14721,c_81]) ).
cnf(c_17007,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK14)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_1114,c_53]) ).
cnf(c_17014,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_17007,c_173,c_170]) ).
cnf(c_17944,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_14736,c_77]) ).
cnf(c_19187,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_82,c_9204]) ).
cnf(c_19190,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_19187,c_17014]) ).
cnf(c_20081,plain,
( sdtasdt0(X0,xm) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| X0 = xn
| sz00 = xm ),
inference(superposition,[status(thm)],[c_156,c_68]) ).
cnf(c_20120,plain,
( sdtasdt0(X0,xk) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xk)
| X0 = sz00
| sz00 = xk ),
inference(superposition,[status(thm)],[c_11159,c_68]) ).
cnf(c_20159,plain,
( sdtasdt0(X0,xk) != sz00
| ~ aNaturalNumber0(X0)
| X0 = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_20120,c_161,c_157,c_49]) ).
cnf(c_20354,plain,
( sdtasdt0(X0,xm) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X0)
| X0 = xn
| sz00 = xm ),
inference(forward_subsumption_resolution,[status(thm)],[c_20081,c_118,c_117]) ).
cnf(c_20377,plain,
( sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(xp)
| xp = sz00 ),
inference(instantiation,[status(thm)],[c_20159]) ).
cnf(c_20399,plain,
( sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| xp = xn ),
inference(instantiation,[status(thm)],[c_20354]) ).
cnf(c_21095,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_21663,plain,
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| X0 = xn
| sz00 = xm
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(X0,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21095,c_118,c_117]) ).
cnf(c_21796,plain,
( ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| xp = xn
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_21663]) ).
cnf(c_22234,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| xm = xk
| sP0_iProver_split ),
inference(superposition,[status(thm)],[c_90,c_9203]) ).
cnf(c_22236,plain,
( ~ sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| xm = xk
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_90,c_9204]) ).
cnf(c_22640,plain,
( ~ sdtlseqdt0(xk,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_22236,c_11317,c_142,c_157,c_117,c_116]) ).
cnf(c_22644,plain,
( ~ sdtlseqdt0(xm,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sP0_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_22234,c_11317,c_142,c_157,c_117,c_116]) ).
cnf(c_23496,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(xm,xk)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_82,c_22640]) ).
cnf(c_23497,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(xm,xk)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_23496,c_157,c_117]) ).
cnf(c_23586,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(xm,X0)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_23497,c_81]) ).
cnf(c_23605,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(xm,X0)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_23586,c_157,c_117]) ).
cnf(c_28199,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_30242,plain,
( sdtlseqdt0(xm,X0)
| ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_23605,c_14257,c_14249]) ).
cnf(c_30243,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xm,X0) ),
inference(renaming,[status(thm)],[c_30242]) ).
cnf(c_30256,plain,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xm,xk) ),
inference(superposition,[status(thm)],[c_11372,c_30243]) ).
cnf(c_30262,plain,
sdtlseqdt0(xm,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_30256,c_157]) ).
cnf(c_31347,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = X2
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(X2,X1))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_88,c_15702]) ).
cnf(c_37790,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_17944,c_11262,c_17944,c_28199]) ).
cnf(c_37805,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_53,c_37790]) ).
cnf(c_37806,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_37805,c_117,c_116]) ).
cnf(c_37977,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_19190,c_81]) ).
cnf(c_38115,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_37977,c_17014]) ).
cnf(c_40340,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X0))
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_93,c_38115]) ).
cnf(c_40357,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X0))
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_40340,c_17014]) ).
cnf(c_41422,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X0))
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_40357,c_11262,c_14736,c_28199]) ).
cnf(c_41439,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xp,xk),X0))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_41422,c_77]) ).
cnf(c_55219,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),X0),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),X0)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = sz00
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_41439,c_37806]) ).
cnf(c_55242,plain,
( sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(sdtasdt0(xp,xk),xm),sdtasdt0(xp,xm))) = sdtasdt0(sdtasdt0(xp,xk),xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sz00 = xm
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_117,c_55219]) ).
cnf(c_57543,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_57708,plain,
( sdtpldt0(sdtasdt0(xp,xk),sK2(sdtasdt0(xp,xk),sdtasdt0(xp,xm))) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(sK2(sdtasdt0(xp,xk),sdtasdt0(xp,xm)))
| ~ sP0_iProver_split ),
inference(instantiation,[status(thm)],[c_9200]) ).
cnf(c_57709,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtpldt0(sdtasdt0(xp,xk),sK2(sdtasdt0(xp,xk),sdtasdt0(xp,xm))) = sdtasdt0(xp,xm) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_66150,plain,
( sz00 = xm
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_55242,c_116,c_151,c_154,c_9204,c_20399,c_21796]) ).
cnf(c_71440,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_77991,plain,
( ~ aNaturalNumber0(sdtasdt0(X2,X1))
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = X2
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(X2,X1))
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_31347,c_117,c_116,c_53,c_31347,c_71440]) ).
cnf(c_77992,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X1 = sz00
| X2 = X0
| sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(X0,X1))
| sP1_iProver_split ),
inference(renaming,[status(thm)],[c_77991]) ).
cnf(c_77993,plain,
( ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X1 = sz00
| X2 = X0
| sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(X0,X1))
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_77992,c_53,c_77992]) ).
cnf(c_77994,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(X1,X2))
| sP1_iProver_split ),
inference(renaming,[status(thm)],[c_77993]) ).
cnf(c_78092,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) = X0
| X1 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X1))
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_14721,c_77994]) ).
cnf(c_78758,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) = X0
| X1 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X1))
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_78092,c_11262]) ).
cnf(c_82041,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| aNaturalNumber0(sK2(sdtasdt0(xp,xk),sdtasdt0(xp,xm))) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_83830,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) = X0
| X1 = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),X1))
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),X0)
| sP1_iProver_split ),
inference(global_subsumption_just,[status(thm)],[c_78758,c_117,c_116,c_71440,c_78758]) ).
cnf(c_83987,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) = xp
| sz00 = xk
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),xp)
| sP1_iProver_split ),
inference(superposition,[status(thm)],[c_83830,c_14294]) ).
cnf(c_84379,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) = xp
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(sdtasdt0(xp,xk),xk))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtlseqdt0(sdtasdt0(xp,xm),xp)
| sP1_iProver_split ),
inference(forward_subsumption_resolution,[status(thm)],[c_83987,c_161,c_157,c_116,c_11262]) ).
cnf(c_84938,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_84379,c_117,c_116,c_11262,c_22644,c_30262,c_57543,c_57708,c_57709,c_71440,c_82041]) ).
cnf(c_84944,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1705,c_84938]) ).
cnf(c_84954,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_84938,c_74]) ).
cnf(c_84971,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84954,c_11262]) ).
cnf(c_85186,plain,
( sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(global_subsumption_just,[status(thm)],[c_84971,c_117,c_116,c_71440,c_84971]) ).
cnf(c_85212,plain,
( ~ aNaturalNumber0(sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk)))
| ~ sP1_iProver_split
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_85186,c_9201]) ).
cnf(c_85434,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ sP1_iProver_split
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_75,c_85212]) ).
cnf(c_85435,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sP1_iProver_split
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85434,c_11262]) ).
cnf(c_87593,plain,
( ~ sP1_iProver_split
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(global_subsumption_just,[status(thm)],[c_85435,c_117,c_116,c_71440,c_84938,c_85435]) ).
cnf(c_101634,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_9204,c_84944]) ).
cnf(c_101635,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(renaming,[status(thm)],[c_101634]) ).
cnf(c_101671,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_117,c_56]) ).
cnf(c_101813,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_63]) ).
cnf(c_101878,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK14)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_1114,c_53]) ).
cnf(c_101885,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_101878,c_173,c_170]) ).
cnf(c_101966,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz00,xm) ),
inference(superposition,[status(thm)],[c_101671,c_259]) ).
cnf(c_101992,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_101966,c_117,c_49]) ).
cnf(c_102010,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_82,c_101635]) ).
cnf(c_102013,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102010,c_101885]) ).
cnf(c_102024,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_102013,c_84938]) ).
cnf(c_104066,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| iLess0(sz00,xm) ),
inference(superposition,[status(thm)],[c_101992,c_94]) ).
cnf(c_104116,plain,
( sz00 = xm
| iLess0(sz00,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104066,c_117,c_49]) ).
cnf(c_104579,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_102024,c_74]) ).
cnf(c_104673,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104579,c_101885]) ).
cnf(c_105038,plain,
( sdtpldt0(sdtasdt0(xp,xm),sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk))) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(global_subsumption_just,[status(thm)],[c_104673,c_117,c_116,c_71440,c_84971]) ).
cnf(c_105044,plain,
( sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(sK2(sdtasdt0(xp,xm),sdtasdt0(xp,xk)))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| sdtasdt0(xp,xm) = sz00 ),
inference(superposition,[status(thm)],[c_105038,c_71]) ).
cnf(c_105089,plain,
sdtasdt0(xp,xk) != sz00,
inference(global_subsumption_just,[status(thm)],[c_105044,c_116,c_51,c_49,c_142,c_50,c_11390,c_11745,c_13485,c_13503,c_20377]) ).
cnf(c_105629,plain,
sz00 = xm,
inference(global_subsumption_just,[status(thm)],[c_104116,c_116,c_154,c_20399,c_66150,c_87593]) ).
cnf(c_105645,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,sz00),
inference(demodulation,[status(thm)],[c_156,c_105629]) ).
cnf(c_105656,plain,
sdtasdt0(xp,xk) = sz00,
inference(light_normalisation,[status(thm)],[c_105645,c_101813]) ).
cnf(c_105657,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_105656,c_105089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n031.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 10:48:52 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.17/0.42 Running first-order theorem proving
% 0.17/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.22/4.63 % SZS status Started for theBenchmark.p
% 27.22/4.63 % SZS status Theorem for theBenchmark.p
% 27.22/4.63
% 27.22/4.63 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.22/4.63
% 27.22/4.63 ------ iProver source info
% 27.22/4.63
% 27.22/4.63 git: date: 2023-05-31 18:12:56 +0000
% 27.22/4.63 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.22/4.63 git: non_committed_changes: false
% 27.22/4.63 git: last_make_outside_of_git: false
% 27.22/4.63
% 27.22/4.63 ------ Parsing...
% 27.22/4.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 27.22/4.63
% 27.22/4.63 ------ Preprocessing... sup_sim: 9 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
% 27.22/4.63
% 27.22/4.63 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 27.22/4.63
% 27.22/4.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.22/4.63 ------ Proving...
% 27.22/4.63 ------ Problem Properties
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63 clauses 129
% 27.22/4.63 conjectures 0
% 27.22/4.63 EPR 46
% 27.22/4.63 Horn 86
% 27.22/4.63 unary 44
% 27.22/4.63 binary 13
% 27.22/4.63 lits 412
% 27.22/4.63 lits eq 127
% 27.22/4.63 fd_pure 0
% 27.22/4.63 fd_pseudo 0
% 27.22/4.63 fd_cond 24
% 27.22/4.63 fd_pseudo_cond 11
% 27.22/4.63 AC symbols 0
% 27.22/4.63
% 27.22/4.63 ------ Schedule dynamic 5 is on
% 27.22/4.63
% 27.22/4.63 ------ no conjectures: strip conj schedule
% 27.22/4.63
% 27.22/4.63 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63 ------
% 27.22/4.63 Current options:
% 27.22/4.63 ------
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63 ------ Proving...
% 27.22/4.63
% 27.22/4.63
% 27.22/4.63 % SZS status Theorem for theBenchmark.p
% 27.22/4.63
% 27.22/4.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.22/4.63
% 27.22/4.63
%------------------------------------------------------------------------------