%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM476+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : 600s
% DateTime : Mon Jul 18 12:27:00 EDT 2022
% Result : Theorem 0.40s 0.59s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 114 ( 39 unt; 0 def)
% Number of atoms : 328 ( 230 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 301 ( 87 ~; 95 |; 111 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 14 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ) ).
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1324_04,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W0) )
& doDivides0(xl,sdtpldt0(xm,xn)) ) ).
fof(m__,conjecture,
( ( xl != sz00
=> ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0)
& W0 = sdtsldt0(xm,xl)
& ? [W1] :
( aNaturalNumber0(W1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& xn = sdtasdt0(xl,W2) ) ) ) )
=> ( ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xl,W0) )
| doDivides0(xl,xn) ) ) ).
fof(subgoal_0,plain,
( ( ( xl != sz00
=> ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0)
& W0 = sdtsldt0(xm,xl)
& ? [W1] :
( aNaturalNumber0(W1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& xn = sdtasdt0(xl,W2) ) ) ) )
& ~ ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xl,W0) ) )
=> doDivides0(xl,xn) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ( xl != sz00
=> ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0)
& W0 = sdtsldt0(xm,xl)
& ? [W1] :
( aNaturalNumber0(W1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& xn = sdtasdt0(xl,W2) ) ) ) )
& ~ ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xl,W0) ) )
=> doDivides0(xl,xn) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm)
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[m__1324_04]) ).
fof(normalize_0_1,plain,
? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0)
& aNaturalNumber0(skolemFOFtoCNF_W0) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
aNaturalNumber0(skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(canonicalize,[],[m_MulZero]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ( ~ aNaturalNumber0(W0)
| sdtasdt0(W0,sz00) = sz00 )
& ( ~ aNaturalNumber0(W0)
| sz00 = sdtasdt0(sz00,W0) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| sz00 = sdtasdt0(sz00,W0) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ~ doDivides0(xl,xn)
& ( xl = sz00
| ? [W0] :
( W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0)
& ? [W1] :
( W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1)
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& ? [W2] :
( W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& xn = sdtasdt0(xl,W2)
& aNaturalNumber0(W2) ) ) ) )
& ! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( xl = sz00
| ? [W0] :
( W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0)
& ? [W1] :
( W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1)
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& ? [W2] :
( W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& xn = sdtasdt0(xl,W2)
& aNaturalNumber0(W2) ) ) ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( ( sdtpldt0(sdtasdt0(xl,skolemFOFtoCNF_W0_2),sdtasdt0(xl,skolemFOFtoCNF_W2_2)) = sdtpldt0(sdtasdt0(xl,skolemFOFtoCNF_W0_2),xn)
| xl = sz00 )
& ( sdtpldt0(skolemFOFtoCNF_W0_2,skolemFOFtoCNF_W2_2) = skolemFOFtoCNF_W1
| xl = sz00 )
& ( sdtpldt0(skolemFOFtoCNF_W0_2,skolemFOFtoCNF_W2_3) = skolemFOFtoCNF_W1
| xl = sz00 )
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W1)
| xl = sz00 )
& ( skolemFOFtoCNF_W0_2 = sdtsldt0(xm,xl)
| xl = sz00 )
& ( skolemFOFtoCNF_W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
| xl = sz00 )
& ( skolemFOFtoCNF_W2_2 = sdtmndt0(skolemFOFtoCNF_W1,skolemFOFtoCNF_W0_2)
| xl = sz00 )
& ( xl = sz00
| xm = sdtasdt0(xl,skolemFOFtoCNF_W0_2) )
& ( xl = sz00
| xn = sdtasdt0(xl,skolemFOFtoCNF_W2_2) )
& ( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W0_2) )
& ( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W1) )
& ( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W2_2) )
& ( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W2_3) )
& ( xl = sz00
| sdtlseqdt0(skolemFOFtoCNF_W0_2,skolemFOFtoCNF_W1) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W2_2) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
( xl = sz00
| xn = sdtasdt0(xl,skolemFOFtoCNF_W2_2) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_16,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(canonicalize,[],[m__1324]) ).
fof(normalize_0_17,plain,
aNaturalNumber0(xn),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
inference(canonicalize,[],[m_AddZero]) ).
fof(normalize_0_19,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [W0] :
( ( ~ aNaturalNumber0(W0)
| W0 = sdtpldt0(sz00,W0) )
& ( ~ aNaturalNumber0(W0)
| sdtpldt0(W0,sz00) = W0 ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| W0 = sdtpldt0(sz00,W0) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_23,plain,
( xm = sdtasdt0(xl,skolemFOFtoCNF_W0_1)
& aNaturalNumber0(skolemFOFtoCNF_W0_1) ),
inference(skolemize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
xm = sdtasdt0(xl,skolemFOFtoCNF_W0_1),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
aNaturalNumber0(skolemFOFtoCNF_W0_1),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_26,plain,
aNaturalNumber0(xl),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_27,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| sdtasdt0(W0,sz00) = sz00 ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_28,plain,
aNaturalNumber0(sz00),
inference(canonicalize,[],[mSortsC]) ).
cnf(refute_0_0,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
aNaturalNumber0(skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ aNaturalNumber0(W0)
| sz00 = sdtasdt0(sz00,W0) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ aNaturalNumber0(skolemFOFtoCNF_W0)
| sz00 = sdtasdt0(sz00,skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_4,plain,
sz00 = sdtasdt0(sz00,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aNaturalNumber0(skolemFOFtoCNF_W0) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( sz00 != sdtasdt0(sz00,skolemFOFtoCNF_W0)
| sdtasdt0(sz00,skolemFOFtoCNF_W0) = sz00 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(sz00)),bind(Y,$fot(sdtasdt0(sz00,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_9,plain,
sdtasdt0(sz00,skolemFOFtoCNF_W0) = sz00,
inference(resolve,[$cnf( $equal(sz00,sdtasdt0(sz00,skolemFOFtoCNF_W0)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( xl = sz00
| aNaturalNumber0(skolemFOFtoCNF_W2_2) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( xn != sdtasdt0(xl,skolemFOFtoCNF_W2_2)
| ~ aNaturalNumber0(skolemFOFtoCNF_W2_2) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(skolemFOFtoCNF_W2_2))]]) ).
cnf(refute_0_13,plain,
( xl = sz00
| xn = sdtasdt0(xl,skolemFOFtoCNF_W2_2) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( xn != sdtasdt0(xl,skolemFOFtoCNF_W2_2)
| sdtasdt0(xl,skolemFOFtoCNF_W2_2) = xn ),
inference(subst,[],[refute_0_7:[bind(X,$fot(xn)),bind(Y,$fot(sdtasdt0(xl,skolemFOFtoCNF_W2_2)))]]) ).
cnf(refute_0_15,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W2_2) = xn
| xl = sz00 ),
inference(resolve,[$cnf( $equal(xn,sdtasdt0(xl,skolemFOFtoCNF_W2_2)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W2_2) != xn
| xn != xn
| xn = sdtasdt0(xl,skolemFOFtoCNF_W2_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xn,sdtasdt0(xl,skolemFOFtoCNF_W2_2)) ),[1],$fot(xn)]]) ).
cnf(refute_0_17,plain,
( xn != xn
| xl = sz00
| xn = sdtasdt0(xl,skolemFOFtoCNF_W2_2) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W2_2),xn) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( xn != xn
| ~ aNaturalNumber0(skolemFOFtoCNF_W2_2)
| xl = sz00 ),
inference(resolve,[$cnf( $equal(xn,sdtasdt0(xl,skolemFOFtoCNF_W2_2)) )],[refute_0_17,refute_0_12]) ).
cnf(refute_0_19,plain,
xn = xn,
introduced(tautology,[refl,[$fot(xn)]]) ).
cnf(refute_0_20,plain,
( ~ aNaturalNumber0(skolemFOFtoCNF_W2_2)
| xl = sz00 ),
inference(resolve,[$cnf( $equal(xn,xn) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
xl = sz00,
inference(resolve,[$cnf( aNaturalNumber0(skolemFOFtoCNF_W2_2) )],[refute_0_10,refute_0_20]) ).
cnf(refute_0_22,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0) = sdtasdt0(xl,skolemFOFtoCNF_W0),
introduced(tautology,[refl,[$fot(sdtasdt0(xl,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_23,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| xl != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0) = sdtasdt0(sz00,skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0),sdtasdt0(xl,skolemFOFtoCNF_W0)) ),[1,0],$fot(sz00)]]) ).
cnf(refute_0_24,plain,
( xl != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0) = sdtasdt0(sz00,skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0) = sdtasdt0(sz00,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(xl,sz00) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_26]) ).
cnf(refute_0_28,plain,
( sdtasdt0(sz00,skolemFOFtoCNF_W0) != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0) != sdtasdt0(sz00,skolemFOFtoCNF_W0)
| sdtasdt0(xl,skolemFOFtoCNF_W0) = sz00 ),
inference(subst,[],[refute_0_27:[bind(X,$fot(sdtasdt0(xl,skolemFOFtoCNF_W0))),bind(Y,$fot(sdtasdt0(sz00,skolemFOFtoCNF_W0))),bind(Z,$fot(sz00))]]) ).
cnf(refute_0_29,plain,
( sdtasdt0(sz00,skolemFOFtoCNF_W0) != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0) = sz00 ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0),sdtasdt0(sz00,skolemFOFtoCNF_W0)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0) = sz00,
inference(resolve,[$cnf( $equal(sdtasdt0(sz00,skolemFOFtoCNF_W0),sz00) )],[refute_0_9,refute_0_29]) ).
cnf(refute_0_31,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0) != sz00
| sdtpldt0(xm,xn) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) = sz00 ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) ),[1],$fot(sz00)]]) ).
cnf(refute_0_32,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,skolemFOFtoCNF_W0)
| sdtpldt0(xm,xn) = sz00 ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0),sz00) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
sdtpldt0(xm,xn) = sz00,
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtasdt0(xl,skolemFOFtoCNF_W0)) )],[refute_0_0,refute_0_32]) ).
cnf(refute_0_34,plain,
aNaturalNumber0(xn),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_35,plain,
( ~ aNaturalNumber0(W0)
| W0 = sdtpldt0(sz00,W0) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_36,plain,
( ~ aNaturalNumber0(xn)
| xn = sdtpldt0(sz00,xn) ),
inference(subst,[],[refute_0_35:[bind(W0,$fot(xn))]]) ).
cnf(refute_0_37,plain,
xn = sdtpldt0(sz00,xn),
inference(resolve,[$cnf( aNaturalNumber0(xn) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( xn != sdtpldt0(sz00,xn)
| sdtpldt0(sz00,xn) = xn ),
inference(subst,[],[refute_0_7:[bind(X,$fot(xn)),bind(Y,$fot(sdtpldt0(sz00,xn)))]]) ).
cnf(refute_0_39,plain,
sdtpldt0(sz00,xn) = xn,
inference(resolve,[$cnf( $equal(xn,sdtpldt0(sz00,xn)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
xm = sdtasdt0(xl,skolemFOFtoCNF_W0_1),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_41,plain,
aNaturalNumber0(skolemFOFtoCNF_W0_1),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_42,plain,
( ~ aNaturalNumber0(skolemFOFtoCNF_W0_1)
| sz00 = sdtasdt0(sz00,skolemFOFtoCNF_W0_1) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_0_43,plain,
sz00 = sdtasdt0(sz00,skolemFOFtoCNF_W0_1),
inference(resolve,[$cnf( aNaturalNumber0(skolemFOFtoCNF_W0_1) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( sz00 != sdtasdt0(sz00,skolemFOFtoCNF_W0_1)
| sdtasdt0(sz00,skolemFOFtoCNF_W0_1) = sz00 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(sz00)),bind(Y,$fot(sdtasdt0(sz00,skolemFOFtoCNF_W0_1)))]]) ).
cnf(refute_0_45,plain,
sdtasdt0(sz00,skolemFOFtoCNF_W0_1) = sz00,
inference(resolve,[$cnf( $equal(sz00,sdtasdt0(sz00,skolemFOFtoCNF_W0_1)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sdtasdt0(xl,skolemFOFtoCNF_W0_1),
introduced(tautology,[refl,[$fot(sdtasdt0(xl,skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_0_47,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0_1) != sdtasdt0(xl,skolemFOFtoCNF_W0_1)
| xl != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sdtasdt0(sz00,skolemFOFtoCNF_W0_1) ),
introduced(tautology,[equality,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0_1),sdtasdt0(xl,skolemFOFtoCNF_W0_1)) ),[1,0],$fot(sz00)]]) ).
cnf(refute_0_48,plain,
( xl != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sdtasdt0(sz00,skolemFOFtoCNF_W0_1) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0_1),sdtasdt0(xl,skolemFOFtoCNF_W0_1)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sdtasdt0(sz00,skolemFOFtoCNF_W0_1),
inference(resolve,[$cnf( $equal(xl,sz00) )],[refute_0_21,refute_0_48]) ).
cnf(refute_0_50,plain,
( sdtasdt0(sz00,skolemFOFtoCNF_W0_1) != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0_1) != sdtasdt0(sz00,skolemFOFtoCNF_W0_1)
| sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sz00 ),
inference(subst,[],[refute_0_27:[bind(X,$fot(sdtasdt0(xl,skolemFOFtoCNF_W0_1))),bind(Y,$fot(sdtasdt0(sz00,skolemFOFtoCNF_W0_1))),bind(Z,$fot(sz00))]]) ).
cnf(refute_0_51,plain,
( sdtasdt0(sz00,skolemFOFtoCNF_W0_1) != sz00
| sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sz00 ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0_1),sdtasdt0(sz00,skolemFOFtoCNF_W0_1)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
sdtasdt0(xl,skolemFOFtoCNF_W0_1) = sz00,
inference(resolve,[$cnf( $equal(sdtasdt0(sz00,skolemFOFtoCNF_W0_1),sz00) )],[refute_0_45,refute_0_51]) ).
cnf(refute_0_53,plain,
( sdtasdt0(xl,skolemFOFtoCNF_W0_1) != sz00
| xm != sdtasdt0(xl,skolemFOFtoCNF_W0_1)
| xm = sz00 ),
introduced(tautology,[equality,[$cnf( $equal(xm,sdtasdt0(xl,skolemFOFtoCNF_W0_1)) ),[1],$fot(sz00)]]) ).
cnf(refute_0_54,plain,
( xm != sdtasdt0(xl,skolemFOFtoCNF_W0_1)
| xm = sz00 ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,skolemFOFtoCNF_W0_1),sz00) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
xm = sz00,
inference(resolve,[$cnf( $equal(xm,sdtasdt0(xl,skolemFOFtoCNF_W0_1)) )],[refute_0_40,refute_0_54]) ).
cnf(refute_0_56,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,xn),
introduced(tautology,[refl,[$fot(sdtpldt0(xm,xn))]]) ).
cnf(refute_0_57,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| xm != sz00
| sdtpldt0(xm,xn) = sdtpldt0(sz00,xn) ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(xm,xn),sdtpldt0(xm,xn)) ),[1,0],$fot(sz00)]]) ).
cnf(refute_0_58,plain,
( xm != sz00
| sdtpldt0(xm,xn) = sdtpldt0(sz00,xn) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtpldt0(xm,xn)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
sdtpldt0(xm,xn) = sdtpldt0(sz00,xn),
inference(resolve,[$cnf( $equal(xm,sz00) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( sdtpldt0(sz00,xn) != xn
| sdtpldt0(xm,xn) != sdtpldt0(sz00,xn)
| sdtpldt0(xm,xn) = xn ),
inference(subst,[],[refute_0_27:[bind(X,$fot(sdtpldt0(xm,xn))),bind(Y,$fot(sdtpldt0(sz00,xn))),bind(Z,$fot(xn))]]) ).
cnf(refute_0_61,plain,
( sdtpldt0(sz00,xn) != xn
| sdtpldt0(xm,xn) = xn ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sdtpldt0(sz00,xn)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
sdtpldt0(xm,xn) = xn,
inference(resolve,[$cnf( $equal(sdtpldt0(sz00,xn),xn) )],[refute_0_39,refute_0_61]) ).
cnf(refute_0_63,plain,
( sdtpldt0(xm,xn) != sz00
| sdtpldt0(xm,xn) != xn
| xn = sz00 ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(xm,xn),sz00) ),[0],$fot(xn)]]) ).
cnf(refute_0_64,plain,
( sdtpldt0(xm,xn) != sz00
| xn = sz00 ),
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),xn) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
xn = sz00,
inference(resolve,[$cnf( $equal(sdtpldt0(xm,xn),sz00) )],[refute_0_33,refute_0_64]) ).
cnf(refute_0_66,plain,
( xn != sdtasdt0(xl,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(sz00))]]) ).
cnf(refute_0_67,plain,
aNaturalNumber0(xl),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_68,plain,
( ~ aNaturalNumber0(W0)
| sdtasdt0(W0,sz00) = sz00 ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_69,plain,
( ~ aNaturalNumber0(xl)
| sdtasdt0(xl,sz00) = sz00 ),
inference(subst,[],[refute_0_68:[bind(W0,$fot(xl))]]) ).
cnf(refute_0_70,plain,
sdtasdt0(xl,sz00) = sz00,
inference(resolve,[$cnf( aNaturalNumber0(xl) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
( sdtasdt0(xl,sz00) != sz00
| xn != sz00
| xn = sdtasdt0(xl,sz00) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xn,sdtasdt0(xl,sz00)) ),[1],$fot(sz00)]]) ).
cnf(refute_0_72,plain,
( xn != sz00
| xn = sdtasdt0(xl,sz00) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xl,sz00),sz00) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( xn != sz00
| ~ aNaturalNumber0(sz00) ),
inference(resolve,[$cnf( $equal(xn,sdtasdt0(xl,sz00)) )],[refute_0_72,refute_0_66]) ).
cnf(refute_0_74,plain,
aNaturalNumber0(sz00),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_75,plain,
xn != sz00,
inference(resolve,[$cnf( aNaturalNumber0(sz00) )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
$false,
inference(resolve,[$cnf( $equal(xn,sz00) )],[refute_0_65,refute_0_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM476+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 09:13:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.59
% 0.40/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.61
%------------------------------------------------------------------------------