TSTP Solution File: NUM516+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 : Fri May 3 02:49:41 EDT 2024
% Result : Theorem 17.13s 3.13s
% Output : CNFRefutation 17.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 114 ( 26 unt; 0 def)
% Number of atoms : 447 ( 173 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 580 ( 247 ~; 233 |; 77 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 90 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
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(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(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(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(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& xn != sdtsldt0(xn,xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(f55,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
inference(negated_conjecture,[],[f55]) ).
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(f67,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
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(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(f88,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
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(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(f107,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f107]) ).
fof(f119,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f120,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f126,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
inference(ennf_transformation,[],[f56]) ).
fof(f137,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f138,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f140,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f141,f142]) ).
fof(f146,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f149,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f153,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f164,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f167,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f176,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f177,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f196,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f204,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f214,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f215,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f216,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f231,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f233,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f239,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f240,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f241,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f53]) ).
fof(f243,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
inference(cnf_transformation,[],[f126]) ).
fof(f253,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f196]) ).
fof(f255,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f204]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f146]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_66,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_79,plain,
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f177]) ).
cnf(c_84,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_112,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f255]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f216]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f215]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f214]) ).
cnf(c_133,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f233]) ).
cnf(c_135,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f231]) ).
cnf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f239]) ).
cnf(c_142,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f241]) ).
cnf(c_143,plain,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[],[f240]) ).
cnf(c_145,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_150,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_168,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_191,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).
cnf(c_1192,plain,
sz00 != xr,
inference(resolution_lifted,[status(thm)],[c_191,c_133]) ).
cnf(c_2556,plain,
X0 = X0,
theory(equality) ).
cnf(c_2558,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2560,plain,
( X0 != X1
| X2 != X3
| sdtpldt0(X0,X2) = sdtpldt0(X1,X3) ),
theory(equality) ).
cnf(c_2562,plain,
( X0 != X1
| X2 != X3
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X0,X2) ),
theory(equality) ).
cnf(c_3851,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != X0
| sdtpldt0(sdtpldt0(xn,xm),xp) != X1
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_2562]) ).
cnf(c_3854,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_3869,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = X0 ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_3884,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != X0
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_3851]) ).
cnf(c_3889,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_3969,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_3884]) ).
cnf(c_3976,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(instantiation,[status(thm)],[c_3869]) ).
cnf(c_4127,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_4218,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_4508,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) != sdtpldt0(xn,xm)
| xp != xp
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(instantiation,[status(thm)],[c_2560]) ).
cnf(c_4940,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_2556]) ).
cnf(c_9176,plain,
( X0 != X1
| xr != X1
| X0 = xr ),
inference(instantiation,[status(thm)],[c_2558]) ).
cnf(c_9177,plain,
( sz00 != sz00
| xr != sz00
| sz00 = xr ),
inference(instantiation,[status(thm)],[c_9176]) ).
cnf(c_25443,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
inference(superposition,[status(thm)],[c_84,c_145]) ).
cnf(c_29201,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_25443,c_118,c_117,c_116,c_3889,c_4508,c_4940,c_25443]) ).
cnf(c_29202,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(renaming,[status(thm)],[c_29201]) ).
cnf(c_29205,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_84,c_29202]) ).
cnf(c_29479,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(global_subsumption_just,[status(thm)],[c_29205,c_118,c_117,c_142,c_143,c_4218,c_29205]) ).
cnf(c_29480,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(renaming,[status(thm)],[c_29479]) ).
cnf(c_29481,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sz00 = xr ),
inference(superposition,[status(thm)],[c_100,c_29480]) ).
cnf(c_33613,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c_66,c_145]) ).
cnf(c_34050,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_33613,c_135,c_118,c_117,c_116,c_141,c_1192,c_3854,c_3889,c_3969,c_3976,c_4127,c_29481,c_33613]) ).
cnf(c_34060,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn ),
inference(resolution,[status(thm)],[c_34050,c_66]) ).
cnf(c_35285,plain,
~ aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_34060,c_118,c_117,c_143,c_4218,c_34060]) ).
cnf(c_35291,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| xr = sz00 ),
inference(resolution,[status(thm)],[c_35285,c_100]) ).
cnf(c_35292,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_35291,c_9177,c_1192,c_168,c_150,c_141,c_49,c_118,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n024.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 19:42:35 EDT 2024
% 0.11/0.31 % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.13/3.13 % SZS status Started for theBenchmark.p
% 17.13/3.13 % SZS status Theorem for theBenchmark.p
% 17.13/3.13
% 17.13/3.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.13/3.13
% 17.13/3.13 ------ iProver source info
% 17.13/3.13
% 17.13/3.13 git: date: 2024-05-02 19:28:25 +0000
% 17.13/3.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.13/3.13 git: non_committed_changes: false
% 17.13/3.13
% 17.13/3.13 ------ Parsing...
% 17.13/3.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.13/3.13
% 17.13/3.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 17.13/3.13
% 17.13/3.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.13/3.13
% 17.13/3.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.13/3.13 ------ Proving...
% 17.13/3.13 ------ Problem Properties
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 clauses 89
% 17.13/3.13 conjectures 1
% 17.13/3.13 EPR 33
% 17.13/3.13 Horn 64
% 17.13/3.13 unary 30
% 17.13/3.13 binary 8
% 17.13/3.13 lits 285
% 17.13/3.13 lits eq 79
% 17.13/3.13 fd_pure 0
% 17.13/3.13 fd_pseudo 0
% 17.13/3.13 fd_cond 15
% 17.13/3.13 fd_pseudo_cond 11
% 17.13/3.13 AC symbols 0
% 17.13/3.13
% 17.13/3.13 ------ Input Options Time Limit: Unbounded
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 ------
% 17.13/3.13 Current options:
% 17.13/3.13 ------
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 ------ Proving...
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 % SZS status Theorem for theBenchmark.p
% 17.13/3.13
% 17.13/3.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.13/3.13
% 17.13/3.13
%------------------------------------------------------------------------------