TSTP Solution File: NUM471+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM471+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 11:30:43 EDT 2023
% Result : Theorem 193.50s 26.37s
% Output : CNFRefutation 193.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 128 ( 43 unt; 0 def)
% Number of atoms : 446 ( 135 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 520 ( 202 ~; 209 |; 84 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn; 113 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [X0] :
( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
sz00 != xl,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(f39,conjecture,
( sdtlseqdt0(xp,xq)
| ? [X0] :
( xq = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( sdtlseqdt0(xp,xq)
| ? [X0] :
( xq = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f43,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [X0] :
( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f35]) ).
fof(f45,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f47]) ).
fof(f53,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f70,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f79,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f80,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f79]) ).
fof(f83,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(f84,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,[],[f83]) ).
fof(f89,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,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(f92,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,[],[f91]) ).
fof(f97,plain,
( ~ sdtlseqdt0(xp,xq)
& ! [X0] :
( xq != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f98,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,[],[f71]) ).
fof(f99,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,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f99,f100]) ).
fof(f104,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f90]) ).
fof(f105,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f105,f106]) ).
fof(f108,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,[],[f92]) ).
fof(f109,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,[],[f108]) ).
fof(f110,plain,
( ? [X0] :
( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
=> ( xm = sdtasdt0(xl,sK3)
& aNaturalNumber0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK3)
& aNaturalNumber0(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f43,f111,f110]) ).
fof(f113,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f116,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f117,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f120,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f139,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f144,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f147,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f153,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,[],[f84]) ).
fof(f161,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f167,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f169,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f173,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f112]) ).
fof(f174,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f112]) ).
fof(f176,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f177,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f37]) ).
fof(f178,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[],[f37]) ).
fof(f179,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f180,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f38]) ).
fof(f181,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f38]) ).
fof(f182,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f183,plain,
! [X0] :
( xq != sdtpldt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f184,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f97]) ).
fof(f185,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f139]) ).
fof(f191,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f192,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f164]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f113]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f147]) ).
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,[],[f153]) ).
cnf(c_94,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f191]) ).
cnf(c_97,plain,
( ~ doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtsldt0(sdtasdt0(X0,X1),X0) = X1
| X0 = sz00 ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_102,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f169]) ).
cnf(c_103,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f168]) ).
cnf(c_104,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f167]) ).
cnf(c_106,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f174]) ).
cnf(c_107,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f173]) ).
cnf(c_111,plain,
sz00 != xl,
inference(cnf_transformation,[],[f176]) ).
cnf(c_112,plain,
sdtsldt0(xm,xl) = xp,
inference(cnf_transformation,[],[f179]) ).
cnf(c_113,plain,
sdtasdt0(xl,xp) = xm,
inference(cnf_transformation,[],[f178]) ).
cnf(c_114,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f177]) ).
cnf(c_115,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnf_transformation,[],[f182]) ).
cnf(c_116,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f181]) ).
cnf(c_117,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f180]) ).
cnf(c_118,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f184]) ).
cnf(c_119,negated_conjecture,
( sdtpldt0(xp,X0) != xq
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_154,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_53,c_94]) ).
cnf(c_157,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_167,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtsldt0(sdtasdt0(X0,X1),X0) = X1
| X0 = sz00 ),
inference(global_subsumption_just,[status(thm)],[c_97,c_53,c_97,c_154]) ).
cnf(c_589,plain,
sdtsldt0(sdtasdt0(xl,xq),xl) = xq,
inference(light_normalisation,[status(thm)],[c_115,c_116]) ).
cnf(c_590,plain,
sdtasdt0(xl,sK2) = sdtasdt0(xl,xq),
inference(light_normalisation,[status(thm)],[c_106,c_116]) ).
cnf(c_155066,plain,
sdtpldt0(xp,sz00) = xp,
inference(superposition,[status(thm)],[c_114,c_57]) ).
cnf(c_155104,plain,
( xp != xq
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_155066,c_119]) ).
cnf(c_155105,plain,
xp != xq,
inference(forward_subsumption_resolution,[status(thm)],[c_155104,c_49]) ).
cnf(c_155138,plain,
( ~ aNaturalNumber0(X0)
| sdtsldt0(sdtasdt0(X0,sK2),X0) = sK2
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_107,c_167]) ).
cnf(c_155265,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c_116,c_52]) ).
cnf(c_155297,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(forward_subsumption_resolution,[status(thm)],[c_155265,c_103,c_102]) ).
cnf(c_155506,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c_116,c_157]) ).
cnf(c_155540,plain,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(forward_subsumption_resolution,[status(thm)],[c_155506,c_103,c_102]) ).
cnf(c_155590,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| sdtlseqdt0(xq,xp) ),
inference(superposition,[status(thm)],[c_82,c_118]) ).
cnf(c_155594,plain,
sdtlseqdt0(xq,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_155590,c_117,c_114]) ).
cnf(c_156574,plain,
( ~ sdtlseqdt0(sK2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK2)
| X0 = sK2
| sz00 = xl
| sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,X0)) ),
inference(superposition,[status(thm)],[c_590,c_90]) ).
cnf(c_156713,plain,
( ~ sdtlseqdt0(sK2,X0)
| ~ aNaturalNumber0(X0)
| X0 = sK2
| sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_156574,c_111,c_107,c_104]) ).
cnf(c_187088,plain,
( sdtsldt0(sdtasdt0(xl,sK2),xl) = sK2
| sz00 = xl ),
inference(superposition,[status(thm)],[c_104,c_155138]) ).
cnf(c_187111,plain,
( sz00 = xl
| sK2 = xq ),
inference(demodulation,[status(thm)],[c_187088,c_589,c_590]) ).
cnf(c_187112,plain,
sK2 = xq,
inference(forward_subsumption_resolution,[status(thm)],[c_187111,c_111]) ).
cnf(c_222712,plain,
( ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(X0)
| X0 = xq
| sdtlseqdt0(sdtasdt0(xl,xq),sdtasdt0(xl,X0)) ),
inference(light_normalisation,[status(thm)],[c_156713,c_187112]) ).
cnf(c_222713,plain,
( ~ sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xp)
| xp = xq
| sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
inference(superposition,[status(thm)],[c_113,c_222712]) ).
cnf(c_222738,plain,
sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(forward_subsumption_resolution,[status(thm)],[c_222713,c_155105,c_114,c_155594]) ).
cnf(c_222992,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xm)
| sdtasdt0(xl,xq) = xm ),
inference(superposition,[status(thm)],[c_222738,c_80]) ).
cnf(c_223002,plain,
sdtasdt0(xl,xq) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_222992,c_103,c_155297,c_155540]) ).
cnf(c_223074,plain,
sdtsldt0(xm,xl) = xq,
inference(demodulation,[status(thm)],[c_589,c_223002]) ).
cnf(c_223079,plain,
xp = xq,
inference(demodulation,[status(thm)],[c_223074,c_112]) ).
cnf(c_223080,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_223079,c_155105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM471+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.17/0.35 % Computer : n027.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Fri Aug 25 08:44:18 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 193.50/26.37 % SZS status Started for theBenchmark.p
% 193.50/26.37 % SZS status Theorem for theBenchmark.p
% 193.50/26.37
% 193.50/26.37 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 193.50/26.37
% 193.50/26.37 ------ iProver source info
% 193.50/26.37
% 193.50/26.37 git: date: 2023-05-31 18:12:56 +0000
% 193.50/26.37 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 193.50/26.37 git: non_committed_changes: false
% 193.50/26.37 git: last_make_outside_of_git: false
% 193.50/26.37
% 193.50/26.37 ------ Parsing...
% 193.50/26.37 ------ Clausification by vclausify_rel & Parsing by iProver...
% 193.50/26.37
% 193.50/26.37 ------ Preprocessing... sup_sim: 3 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
% 193.50/26.37
% 193.50/26.37 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 193.50/26.37
% 193.50/26.37 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 193.50/26.37 ------ Proving...
% 193.50/26.37 ------ Problem Properties
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37 clauses 66
% 193.50/26.37 conjectures 2
% 193.50/26.37 EPR 19
% 193.50/26.37 Horn 53
% 193.50/26.37 unary 20
% 193.50/26.37 binary 8
% 193.50/26.37 lits 207
% 193.50/26.37 lits eq 57
% 193.50/26.37 fd_pure 0
% 193.50/26.37 fd_pseudo 0
% 193.50/26.37 fd_cond 6
% 193.50/26.37 fd_pseudo_cond 9
% 193.50/26.37 AC symbols 0
% 193.50/26.37
% 193.50/26.37 ------ Input Options Time Limit: Unbounded
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37 ------
% 193.50/26.37 Current options:
% 193.50/26.37 ------
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37 ------ Proving...
% 193.50/26.37
% 193.50/26.37
% 193.50/26.37 % SZS status Theorem for theBenchmark.p
% 193.50/26.37
% 193.50/26.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 193.50/26.37
% 193.50/26.37
%------------------------------------------------------------------------------