%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : 600s
% DateTime : Sun Jul 17 03:18:53 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 34
% Syntax : Number of formulae : 316 ( 123 unt; 0 def)
% Number of atoms : 778 ( 229 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 788 ( 326 ~; 209 |; 156 &)
% ( 49 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 304 ( 2 sgn 252 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) ).
fof(axiom_2,axiom,
! [X] :
( cA(X)
<=> ( X = ib
| X = ia ) ) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( requalityOnA(Y,X)
& requalityOnA(Z,X) )
=> Y = Z ) ).
fof(axiom_4,axiom,
! [X,Y] :
( requalityOnA(X,Y)
=> cA(Y) ) ).
fof(axiom_5,axiom,
cowlThing(ia) ).
fof(axiom_6,axiom,
requalityOnA(ia,ia) ).
fof(axiom_7,axiom,
cowlThing(ib) ).
fof(axiom_8,axiom,
requalityOnA(ib,ib) ).
fof(axiom_9,axiom,
cowlThing(ic) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia)
& requalityOnA(ia,ia)
& cowlThing(ib)
& cowlThing(ic) ) ).
fof(subgoal_0,plain,
! [X] : cowlThing(X),
inference(strip,[],[the_axiom]) ).
fof(subgoal_1,plain,
! [X] :
( cowlThing(X)
=> ~ cowlNothing(X) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_2,plain,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
=> ! [X] :
( xsd_string(X)
=> ~ xsd_integer(X) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_3,plain,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
=> ! [X] :
( ~ xsd_integer(X)
=> xsd_string(X) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_4,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X,Y] :
( ( requalityOnA(X,Y)
& X != ia
& X != ib )
=> X = ic ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_5,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) ) )
=> ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_6,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) ) )
=> cowlThing(ia) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_7,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia) )
=> requalityOnA(ia,ia) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_8,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia)
& requalityOnA(ia,ia) )
=> cowlThing(ib) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_9,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia)
& requalityOnA(ia,ia)
& cowlThing(ib) )
=> cowlThing(ic) ),
inference(strip,[],[the_axiom]) ).
fof(negate_0_0,plain,
~ ! [X] : cowlThing(X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] : ~ cowlThing(X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_0_2,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_3]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_4]) ).
fof(negate_1_0,plain,
~ ! [X] :
( cowlThing(X)
=> ~ cowlNothing(X) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X] :
( cowlNothing(X)
& cowlThing(X) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_1_2,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_5,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
$false,
inference(simplify,[],[normalize_1_0,normalize_1_3,normalize_1_5]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_6]) ).
fof(negate_2_0,plain,
~ ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
=> ! [X] :
( xsd_string(X)
=> ~ xsd_integer(X) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [X] :
( xsd_integer(X)
& xsd_string(X) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_2_2,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_5,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
? [X] :
( xsd_integer(X)
& xsd_string(X) ),
inference(simplify,[],[normalize_2_0,normalize_2_3,normalize_2_5]) ).
fof(normalize_2_7,plain,
( xsd_integer(skolemFOFtoCNF_X)
& xsd_string(skolemFOFtoCNF_X) ),
inference(skolemize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
xsd_string(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_2_10,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [X] :
( ( ~ xsd_integer(X)
| ~ xsd_string(X) )
& ( xsd_integer(X)
| xsd_string(X) ) ),
inference(clausify,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ),
inference(conjunct,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
xsd_integer(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_2_7]) ).
cnf(refute_2_0,plain,
xsd_string(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_1,plain,
( ~ xsd_integer(X)
| ~ xsd_string(X) ),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_2,plain,
( ~ xsd_integer(skolemFOFtoCNF_X)
| ~ xsd_string(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_2_1:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_3,plain,
~ xsd_integer(skolemFOFtoCNF_X),
inference(resolve,[$cnf( xsd_string(skolemFOFtoCNF_X) )],[refute_2_0,refute_2_2]) ).
cnf(refute_2_4,plain,
xsd_integer(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_5,plain,
$false,
inference(resolve,[$cnf( xsd_integer(skolemFOFtoCNF_X) )],[refute_2_4,refute_2_3]) ).
fof(negate_3_0,plain,
~ ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
=> ! [X] :
( ~ xsd_integer(X)
=> xsd_string(X) ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ? [X] :
( ~ xsd_integer(X)
& ~ xsd_string(X) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_3_2,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_3_2]) ).
fof(normalize_3_4,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_3_1]) ).
fof(normalize_3_5,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
? [X] :
( ~ xsd_integer(X)
& ~ xsd_string(X) ),
inference(simplify,[],[normalize_3_0,normalize_3_3,normalize_3_5]) ).
fof(normalize_3_7,plain,
( ~ xsd_integer(skolemFOFtoCNF_X_1)
& ~ xsd_string(skolemFOFtoCNF_X_1) ),
inference(skolemize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
~ xsd_string(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_3_7]) ).
fof(normalize_3_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_3_10,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
! [X] :
( ( ~ xsd_integer(X)
| ~ xsd_string(X) )
& ( xsd_integer(X)
| xsd_string(X) ) ),
inference(clausify,[],[normalize_3_10]) ).
fof(normalize_3_12,plain,
! [X] :
( xsd_integer(X)
| xsd_string(X) ),
inference(conjunct,[],[normalize_3_11]) ).
fof(normalize_3_13,plain,
~ xsd_integer(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_3_7]) ).
cnf(refute_3_0,plain,
~ xsd_string(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_3_8]) ).
cnf(refute_3_1,plain,
( xsd_integer(X)
| xsd_string(X) ),
inference(canonicalize,[],[normalize_3_12]) ).
cnf(refute_3_2,plain,
( xsd_integer(skolemFOFtoCNF_X_1)
| xsd_string(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_3_1:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_3_3,plain,
xsd_integer(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( xsd_string(skolemFOFtoCNF_X_1) )],[refute_3_2,refute_3_0]) ).
cnf(refute_3_4,plain,
~ xsd_integer(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_3_13]) ).
cnf(refute_3_5,plain,
$false,
inference(resolve,[$cnf( xsd_integer(skolemFOFtoCNF_X_1) )],[refute_3_3,refute_3_4]) ).
fof(negate_4_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X,Y] :
( ( requalityOnA(X,Y)
& X != ia
& X != ib )
=> X = ic ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ? [X] :
( X != ia
& X != ib
& X != ic
& ? [Y] : requalityOnA(X,Y) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_2,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_4_4,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_4_3]) ).
fof(normalize_4_5,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_4_3]) ).
fof(normalize_4_7,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_4_6]) ).
fof(normalize_4_8,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_4_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
? [X] :
( X != ic
& ~ cA(X)
& ? [Y] : requalityOnA(X,Y) ),
inference(simplify,[],[normalize_4_0,normalize_4_2,normalize_4_5,normalize_4_7,normalize_4_9]) ).
fof(normalize_4_11,plain,
( skolemFOFtoCNF_X_2 != ic
& ~ cA(skolemFOFtoCNF_X_2)
& ? [Y] : requalityOnA(skolemFOFtoCNF_X_2,Y) ),
inference(skolemize,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_13,plain,
? [Y] : requalityOnA(skolemFOFtoCNF_X_2,Y),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_14,plain,
requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
inference(skolemize,[],[normalize_4_13]) ).
fof(normalize_4_15,plain,
! [X,Y] :
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_4_16,plain,
! [X,Y] :
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(specialize,[],[normalize_4_15]) ).
fof(normalize_4_17,plain,
! [X] :
( ( X != ia
| cA(X) )
& ( X != ib
| cA(X) )
& ( ~ cA(X)
| X = ia
| X = ib ) ),
inference(clausify,[],[normalize_4_2]) ).
fof(normalize_4_18,plain,
! [X] :
( ~ cA(X)
| X = ia
| X = ib ),
inference(conjunct,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
requalityOnA(ib,ib),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_4_20,plain,
! [X,Y,Z] :
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_21,plain,
! [X,Y,Z] :
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(specialize,[],[normalize_4_20]) ).
fof(normalize_4_22,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_4_23,plain,
! [X] :
( X != ia
| cA(X) ),
inference(conjunct,[],[normalize_4_17]) ).
fof(normalize_4_24,plain,
! [X] :
( X != ib
| cA(X) ),
inference(conjunct,[],[normalize_4_17]) ).
cnf(refute_4_0,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_12]) ).
cnf(refute_4_1,plain,
requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_4_14]) ).
cnf(refute_4_2,plain,
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(canonicalize,[],[normalize_4_16]) ).
cnf(refute_4_3,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| cA(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_4_4,plain,
cA(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_3]) ).
cnf(refute_4_5,plain,
( ~ cA(X)
| X = ia
| X = ib ),
inference(canonicalize,[],[normalize_4_18]) ).
cnf(refute_4_6,plain,
( ~ cA(skolemFOFtoCNF_Y)
| skolemFOFtoCNF_Y = ia
| skolemFOFtoCNF_Y = ib ),
inference(subst,[],[refute_4_5:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_4_7,plain,
( skolemFOFtoCNF_Y = ia
| skolemFOFtoCNF_Y = ib ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y) )],[refute_4_4,refute_4_6]) ).
cnf(refute_4_8,plain,
( skolemFOFtoCNF_Y != ib
| ~ requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| requalityOnA(skolemFOFtoCNF_X_2,ib) ),
introduced(tautology,[equality,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),[1],$fot(ib)]]) ).
cnf(refute_4_9,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| skolemFOFtoCNF_Y = ia
| requalityOnA(skolemFOFtoCNF_X_2,ib) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ib) )],[refute_4_7,refute_4_8]) ).
cnf(refute_4_10,plain,
( skolemFOFtoCNF_Y = ia
| requalityOnA(skolemFOFtoCNF_X_2,ib) ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_9]) ).
cnf(refute_4_11,plain,
requalityOnA(ib,ib),
inference(canonicalize,[],[normalize_4_19]) ).
cnf(refute_4_12,plain,
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(canonicalize,[],[normalize_4_21]) ).
cnf(refute_4_13,plain,
( ~ requalityOnA(X_18,ib)
| ~ requalityOnA(ib,ib)
| ib = X_18 ),
inference(subst,[],[refute_4_12:[bind(X,$fot(ib)),bind(Y,$fot(ib)),bind(Z,$fot(X_18))]]) ).
cnf(refute_4_14,plain,
( ~ requalityOnA(X_18,ib)
| ib = X_18 ),
inference(resolve,[$cnf( requalityOnA(ib,ib) )],[refute_4_11,refute_4_13]) ).
cnf(refute_4_15,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_2,ib)
| ib = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_4_14:[bind(X_18,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_16,plain,
( ib = skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Y = ia ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,ib) )],[refute_4_10,refute_4_15]) ).
cnf(refute_4_17,plain,
( skolemFOFtoCNF_Y != ia
| ~ requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| requalityOnA(skolemFOFtoCNF_X_2,ia) ),
introduced(tautology,[equality,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),[1],$fot(ia)]]) ).
cnf(refute_4_18,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| ib = skolemFOFtoCNF_X_2
| requalityOnA(skolemFOFtoCNF_X_2,ia) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ia) )],[refute_4_16,refute_4_17]) ).
cnf(refute_4_19,plain,
( ib = skolemFOFtoCNF_X_2
| requalityOnA(skolemFOFtoCNF_X_2,ia) ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_18]) ).
cnf(refute_4_20,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[normalize_4_22]) ).
cnf(refute_4_21,plain,
( ~ requalityOnA(X_18,ia)
| ~ requalityOnA(ia,ia)
| ia = X_18 ),
inference(subst,[],[refute_4_12:[bind(X,$fot(ia)),bind(Y,$fot(ia)),bind(Z,$fot(X_18))]]) ).
cnf(refute_4_22,plain,
( ~ requalityOnA(X_18,ia)
| ia = X_18 ),
inference(resolve,[$cnf( requalityOnA(ia,ia) )],[refute_4_20,refute_4_21]) ).
cnf(refute_4_23,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_2,ia)
| ia = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_4_22:[bind(X_18,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_24,plain,
( ia = skolemFOFtoCNF_X_2
| ib = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_2,ia) )],[refute_4_19,refute_4_23]) ).
cnf(refute_4_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_4_26,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_4_27,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_4_25,refute_4_26]) ).
cnf(refute_4_28,plain,
( ia != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = ia ),
inference(subst,[],[refute_4_27:[bind(X0,$fot(ia)),bind(Y0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_29,plain,
( ib = skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = ia ),
inference(resolve,[$cnf( $equal(ia,skolemFOFtoCNF_X_2) )],[refute_4_24,refute_4_28]) ).
cnf(refute_4_30,plain,
( skolemFOFtoCNF_X_2 != ia
| ~ cA(ia)
| cA(skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_X_2) ),[0],$fot(ia)]]) ).
cnf(refute_4_31,plain,
( ~ cA(ia)
| ib = skolemFOFtoCNF_X_2
| cA(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_29,refute_4_30]) ).
cnf(refute_4_32,plain,
( ~ cA(ia)
| ib = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_31,refute_4_0]) ).
cnf(refute_4_33,plain,
( X != ia
| cA(X) ),
inference(canonicalize,[],[normalize_4_23]) ).
cnf(refute_4_34,plain,
( ia != ia
| cA(ia) ),
inference(subst,[],[refute_4_33:[bind(X,$fot(ia))]]) ).
cnf(refute_4_35,plain,
ia = ia,
introduced(tautology,[refl,[$fot(ia)]]) ).
cnf(refute_4_36,plain,
cA(ia),
inference(resolve,[$cnf( $equal(ia,ia) )],[refute_4_35,refute_4_34]) ).
cnf(refute_4_37,plain,
ib = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( cA(ia) )],[refute_4_36,refute_4_32]) ).
cnf(refute_4_38,plain,
( ib != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = ib ),
inference(subst,[],[refute_4_27:[bind(X0,$fot(ib)),bind(Y0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_39,plain,
( ia = skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( $equal(ib,skolemFOFtoCNF_X_2) )],[refute_4_24,refute_4_38]) ).
cnf(refute_4_40,plain,
( skolemFOFtoCNF_X_2 != ib
| ~ cA(ib)
| cA(skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_X_2) ),[0],$fot(ib)]]) ).
cnf(refute_4_41,plain,
( ~ cA(ib)
| ia = skolemFOFtoCNF_X_2
| cA(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_39,refute_4_40]) ).
cnf(refute_4_42,plain,
( ~ cA(ib)
| ia = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_41,refute_4_0]) ).
cnf(refute_4_43,plain,
skolemFOFtoCNF_X_2 = ib,
inference(resolve,[$cnf( $equal(ib,skolemFOFtoCNF_X_2) )],[refute_4_37,refute_4_38]) ).
cnf(refute_4_44,plain,
( ia != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 != ib
| ia = ib ),
introduced(tautology,[equality,[$cnf( ~ $equal(ia,ib) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_4_45,plain,
( ia != skolemFOFtoCNF_X_2
| ia = ib ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_43,refute_4_44]) ).
cnf(refute_4_46,plain,
( ~ cA(ib)
| ia = ib ),
inference(resolve,[$cnf( $equal(ia,skolemFOFtoCNF_X_2) )],[refute_4_42,refute_4_45]) ).
cnf(refute_4_47,plain,
( X != ib
| cA(X) ),
inference(canonicalize,[],[normalize_4_24]) ).
cnf(refute_4_48,plain,
( ib != ib
| cA(ib) ),
inference(subst,[],[refute_4_47:[bind(X,$fot(ib))]]) ).
cnf(refute_4_49,plain,
ib = ib,
introduced(tautology,[refl,[$fot(ib)]]) ).
cnf(refute_4_50,plain,
cA(ib),
inference(resolve,[$cnf( $equal(ib,ib) )],[refute_4_49,refute_4_48]) ).
cnf(refute_4_51,plain,
ia = ib,
inference(resolve,[$cnf( cA(ib) )],[refute_4_50,refute_4_46]) ).
cnf(refute_4_52,plain,
( ia != ib
| ib = ia ),
inference(subst,[],[refute_4_27:[bind(X0,$fot(ia)),bind(Y0,$fot(ib))]]) ).
cnf(refute_4_53,plain,
ib = ia,
inference(resolve,[$cnf( $equal(ia,ib) )],[refute_4_51,refute_4_52]) ).
cnf(refute_4_54,plain,
( ib != ia
| ib != skolemFOFtoCNF_X_2
| ia = skolemFOFtoCNF_X_2 ),
introduced(tautology,[equality,[$cnf( $equal(ib,skolemFOFtoCNF_X_2) ),[0],$fot(ia)]]) ).
cnf(refute_4_55,plain,
( ib != skolemFOFtoCNF_X_2
| ia = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(ib,ia) )],[refute_4_53,refute_4_54]) ).
cnf(refute_4_56,plain,
ia = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(ib,skolemFOFtoCNF_X_2) )],[refute_4_37,refute_4_55]) ).
cnf(refute_4_57,plain,
skolemFOFtoCNF_X_2 = ia,
inference(resolve,[$cnf( $equal(ia,skolemFOFtoCNF_X_2) )],[refute_4_56,refute_4_28]) ).
cnf(refute_4_58,plain,
( ~ cA(ia)
| cA(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_57,refute_4_30]) ).
cnf(refute_4_59,plain,
~ cA(ia),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_58,refute_4_0]) ).
cnf(refute_4_60,plain,
$false,
inference(resolve,[$cnf( cA(ia) )],[refute_4_36,refute_4_59]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) ) )
=> ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
( ? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( X = ia
| X = ib
| X = ic
| ! [Y] : ~ requalityOnA(X,Y) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_5_2,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_5_1]) ).
fof(normalize_5_3,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_5_2]) ).
fof(normalize_5_4,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_5_1]) ).
fof(normalize_5_5,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_5_4]) ).
fof(normalize_5_6,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_5_7,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_5_6]) ).
fof(normalize_5_8,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_5_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
( ? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) )
& ! [X] :
( X = ic
| cA(X)
| ! [Y] : ~ requalityOnA(X,Y) ) ),
inference(simplify,[],[normalize_5_0,normalize_5_3,normalize_5_5,normalize_5_7,normalize_5_9]) ).
fof(normalize_5_11,plain,
? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) ),
inference(conjunct,[],[normalize_5_10]) ).
fof(normalize_5_12,plain,
( ~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3)
& requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_5_11]) ).
fof(normalize_5_13,plain,
~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_12]) ).
fof(normalize_5_14,plain,
requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_5_12]) ).
fof(normalize_5_15,plain,
! [X,Y] :
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_5_16,plain,
! [X,Y] :
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(specialize,[],[normalize_5_15]) ).
fof(normalize_5_17,plain,
! [X] :
( ( X != ia
| cA(X) )
& ( X != ib
| cA(X) )
& ( ~ cA(X)
| X = ia
| X = ib ) ),
inference(clausify,[],[normalize_5_7]) ).
fof(normalize_5_18,plain,
! [X] :
( ~ cA(X)
| X = ia
| X = ib ),
inference(conjunct,[],[normalize_5_17]) ).
fof(normalize_5_19,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_5_20,plain,
! [X,Y,Z] :
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_5_21,plain,
! [X,Y,Z] :
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(specialize,[],[normalize_5_20]) ).
fof(normalize_5_22,plain,
requalityOnA(ib,ib),
inference(canonicalize,[],[axiom_8]) ).
cnf(refute_5_0,plain,
~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_13]) ).
cnf(refute_5_1,plain,
requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_5_14]) ).
cnf(refute_5_2,plain,
( ~ requalityOnA(X,Y)
| cA(Y) ),
inference(canonicalize,[],[normalize_5_16]) ).
cnf(refute_5_3,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| cA(skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_5_2:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_5_4,plain,
cA(skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_3]) ).
cnf(refute_5_5,plain,
( ~ cA(X)
| X = ia
| X = ib ),
inference(canonicalize,[],[normalize_5_18]) ).
cnf(refute_5_6,plain,
( ~ cA(skolemFOFtoCNF_Y_1)
| skolemFOFtoCNF_Y_1 = ia
| skolemFOFtoCNF_Y_1 = ib ),
inference(subst,[],[refute_5_5:[bind(X,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_5_7,plain,
( skolemFOFtoCNF_Y_1 = ia
| skolemFOFtoCNF_Y_1 = ib ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y_1) )],[refute_5_4,refute_5_6]) ).
cnf(refute_5_8,plain,
( skolemFOFtoCNF_Y_1 != ia
| ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| requalityOnA(skolemFOFtoCNF_X_3,ia) ),
introduced(tautology,[equality,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),[1],$fot(ia)]]) ).
cnf(refute_5_9,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| skolemFOFtoCNF_Y_1 = ib
| requalityOnA(skolemFOFtoCNF_X_3,ia) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ia) )],[refute_5_7,refute_5_8]) ).
cnf(refute_5_10,plain,
( skolemFOFtoCNF_Y_1 = ib
| requalityOnA(skolemFOFtoCNF_X_3,ia) ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_9]) ).
cnf(refute_5_11,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[normalize_5_19]) ).
cnf(refute_5_12,plain,
( ~ requalityOnA(Y,X)
| ~ requalityOnA(Z,X)
| Y = Z ),
inference(canonicalize,[],[normalize_5_21]) ).
cnf(refute_5_13,plain,
( ~ requalityOnA(X_33,ia)
| ~ requalityOnA(ia,ia)
| ia = X_33 ),
inference(subst,[],[refute_5_12:[bind(X,$fot(ia)),bind(Y,$fot(ia)),bind(Z,$fot(X_33))]]) ).
cnf(refute_5_14,plain,
( ~ requalityOnA(X_33,ia)
| ia = X_33 ),
inference(resolve,[$cnf( requalityOnA(ia,ia) )],[refute_5_11,refute_5_13]) ).
cnf(refute_5_15,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,ia)
| ia = skolemFOFtoCNF_X_3 ),
inference(subst,[],[refute_5_14:[bind(X_33,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_16,plain,
( ia = skolemFOFtoCNF_X_3
| skolemFOFtoCNF_Y_1 = ib ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,ia) )],[refute_5_10,refute_5_15]) ).
cnf(refute_5_17,plain,
( skolemFOFtoCNF_Y_1 != ib
| ~ requalityOnA(ib,skolemFOFtoCNF_X_3)
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),[0],$fot(ib)]]) ).
cnf(refute_5_18,plain,
( ~ requalityOnA(ib,skolemFOFtoCNF_X_3)
| ia = skolemFOFtoCNF_X_3
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ib) )],[refute_5_16,refute_5_17]) ).
cnf(refute_5_19,plain,
( ~ requalityOnA(ib,skolemFOFtoCNF_X_3)
| ia = skolemFOFtoCNF_X_3 ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) )],[refute_5_18,refute_5_0]) ).
cnf(refute_5_20,plain,
( skolemFOFtoCNF_Y_1 != ib
| ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| requalityOnA(skolemFOFtoCNF_X_3,ib) ),
introduced(tautology,[equality,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),[1],$fot(ib)]]) ).
cnf(refute_5_21,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| ia = skolemFOFtoCNF_X_3
| requalityOnA(skolemFOFtoCNF_X_3,ib) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ib) )],[refute_5_16,refute_5_20]) ).
cnf(refute_5_22,plain,
( ia = skolemFOFtoCNF_X_3
| requalityOnA(skolemFOFtoCNF_X_3,ib) ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_21]) ).
cnf(refute_5_23,plain,
requalityOnA(ib,ib),
inference(canonicalize,[],[normalize_5_22]) ).
cnf(refute_5_24,plain,
( ~ requalityOnA(X_33,ib)
| ~ requalityOnA(ib,ib)
| ib = X_33 ),
inference(subst,[],[refute_5_12:[bind(X,$fot(ib)),bind(Y,$fot(ib)),bind(Z,$fot(X_33))]]) ).
cnf(refute_5_25,plain,
( ~ requalityOnA(X_33,ib)
| ib = X_33 ),
inference(resolve,[$cnf( requalityOnA(ib,ib) )],[refute_5_23,refute_5_24]) ).
cnf(refute_5_26,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,ib)
| ib = skolemFOFtoCNF_X_3 ),
inference(subst,[],[refute_5_25:[bind(X_33,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_27,plain,
( ia = skolemFOFtoCNF_X_3
| ib = skolemFOFtoCNF_X_3 ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,ib) )],[refute_5_22,refute_5_26]) ).
cnf(refute_5_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_5_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_5_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_5_28,refute_5_29]) ).
cnf(refute_5_31,plain,
( ib != skolemFOFtoCNF_X_3
| skolemFOFtoCNF_X_3 = ib ),
inference(subst,[],[refute_5_30:[bind(X0,$fot(ib)),bind(Y0,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_32,plain,
( ia = skolemFOFtoCNF_X_3
| skolemFOFtoCNF_X_3 = ib ),
inference(resolve,[$cnf( $equal(ib,skolemFOFtoCNF_X_3) )],[refute_5_27,refute_5_31]) ).
cnf(refute_5_33,plain,
( skolemFOFtoCNF_X_3 != ib
| ~ requalityOnA(ib,ib)
| requalityOnA(ib,skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(ib,skolemFOFtoCNF_X_3) ),[1],$fot(ib)]]) ).
cnf(refute_5_34,plain,
( ~ requalityOnA(ib,ib)
| ia = skolemFOFtoCNF_X_3
| requalityOnA(ib,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ib) )],[refute_5_32,refute_5_33]) ).
cnf(refute_5_35,plain,
( ~ requalityOnA(ib,ib)
| ia = skolemFOFtoCNF_X_3 ),
inference(resolve,[$cnf( requalityOnA(ib,skolemFOFtoCNF_X_3) )],[refute_5_34,refute_5_19]) ).
cnf(refute_5_36,plain,
ia = skolemFOFtoCNF_X_3,
inference(resolve,[$cnf( requalityOnA(ib,ib) )],[refute_5_23,refute_5_35]) ).
cnf(refute_5_37,plain,
( ia != skolemFOFtoCNF_X_3
| skolemFOFtoCNF_X_3 = ia ),
inference(subst,[],[refute_5_30:[bind(X0,$fot(ia)),bind(Y0,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_38,plain,
skolemFOFtoCNF_X_3 = ia,
inference(resolve,[$cnf( $equal(ia,skolemFOFtoCNF_X_3) )],[refute_5_36,refute_5_37]) ).
cnf(refute_5_39,plain,
( skolemFOFtoCNF_X_3 != ia
| ~ requalityOnA(skolemFOFtoCNF_Y_1,ia)
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),[1],$fot(ia)]]) ).
cnf(refute_5_40,plain,
( ~ requalityOnA(skolemFOFtoCNF_Y_1,ia)
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_38,refute_5_39]) ).
cnf(refute_5_41,plain,
~ requalityOnA(skolemFOFtoCNF_Y_1,ia),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) )],[refute_5_40,refute_5_0]) ).
cnf(refute_5_42,plain,
( skolemFOFtoCNF_Y_1 != ia
| ~ requalityOnA(ia,skolemFOFtoCNF_X_3)
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),[0],$fot(ia)]]) ).
cnf(refute_5_43,plain,
( ~ requalityOnA(ia,skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y_1 = ib
| requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ia) )],[refute_5_7,refute_5_42]) ).
cnf(refute_5_44,plain,
( ~ requalityOnA(ia,skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y_1 = ib ),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) )],[refute_5_43,refute_5_0]) ).
cnf(refute_5_45,plain,
( skolemFOFtoCNF_X_3 != ia
| ~ requalityOnA(ia,ia)
| requalityOnA(ia,skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(ia,skolemFOFtoCNF_X_3) ),[1],$fot(ia)]]) ).
cnf(refute_5_46,plain,
( ~ requalityOnA(ia,ia)
| requalityOnA(ia,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_38,refute_5_45]) ).
cnf(refute_5_47,plain,
( ~ requalityOnA(ia,ia)
| skolemFOFtoCNF_Y_1 = ib ),
inference(resolve,[$cnf( requalityOnA(ia,skolemFOFtoCNF_X_3) )],[refute_5_46,refute_5_44]) ).
cnf(refute_5_48,plain,
skolemFOFtoCNF_Y_1 = ib,
inference(resolve,[$cnf( requalityOnA(ia,ia) )],[refute_5_11,refute_5_47]) ).
cnf(refute_5_49,plain,
( skolemFOFtoCNF_Y_1 != ib
| ~ requalityOnA(ib,ia)
| requalityOnA(skolemFOFtoCNF_Y_1,ia) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(skolemFOFtoCNF_Y_1,ia) ),[0],$fot(ib)]]) ).
cnf(refute_5_50,plain,
( ~ requalityOnA(ib,ia)
| requalityOnA(skolemFOFtoCNF_Y_1,ia) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ib) )],[refute_5_48,refute_5_49]) ).
cnf(refute_5_51,plain,
~ requalityOnA(ib,ia),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_Y_1,ia) )],[refute_5_50,refute_5_41]) ).
cnf(refute_5_52,plain,
( ~ requalityOnA(ia,ib)
| ib = ia ),
inference(subst,[],[refute_5_25:[bind(X_33,$fot(ia))]]) ).
cnf(refute_5_53,plain,
( skolemFOFtoCNF_X_3 != ia
| ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| requalityOnA(ia,skolemFOFtoCNF_Y_1) ),
introduced(tautology,[equality,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),[0],$fot(ia)]]) ).
cnf(refute_5_54,plain,
( ~ requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| requalityOnA(ia,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_38,refute_5_53]) ).
cnf(refute_5_55,plain,
requalityOnA(ia,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( requalityOnA(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_54]) ).
cnf(refute_5_56,plain,
( skolemFOFtoCNF_Y_1 != ib
| ~ requalityOnA(ia,skolemFOFtoCNF_Y_1)
| requalityOnA(ia,ib) ),
introduced(tautology,[equality,[$cnf( requalityOnA(ia,skolemFOFtoCNF_Y_1) ),[1],$fot(ib)]]) ).
cnf(refute_5_57,plain,
( ~ requalityOnA(ia,skolemFOFtoCNF_Y_1)
| requalityOnA(ia,ib) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,ib) )],[refute_5_48,refute_5_56]) ).
cnf(refute_5_58,plain,
requalityOnA(ia,ib),
inference(resolve,[$cnf( requalityOnA(ia,skolemFOFtoCNF_Y_1) )],[refute_5_55,refute_5_57]) ).
cnf(refute_5_59,plain,
ib = ia,
inference(resolve,[$cnf( requalityOnA(ia,ib) )],[refute_5_58,refute_5_52]) ).
cnf(refute_5_60,plain,
( ib != ia
| ~ requalityOnA(ia,ia)
| requalityOnA(ib,ia) ),
introduced(tautology,[equality,[$cnf( ~ requalityOnA(ib,ia) ),[0],$fot(ia)]]) ).
cnf(refute_5_61,plain,
( ~ requalityOnA(ia,ia)
| requalityOnA(ib,ia) ),
inference(resolve,[$cnf( $equal(ib,ia) )],[refute_5_59,refute_5_60]) ).
cnf(refute_5_62,plain,
~ requalityOnA(ia,ia),
inference(resolve,[$cnf( requalityOnA(ib,ia) )],[refute_5_61,refute_5_51]) ).
cnf(refute_5_63,plain,
$false,
inference(resolve,[$cnf( requalityOnA(ia,ia) )],[refute_5_11,refute_5_62]) ).
fof(negate_6_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) ) )
=> cowlThing(ia) ),
inference(negate,[],[subgoal_6]) ).
fof(normalize_6_0,plain,
( ~ cowlThing(ia)
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( X = ia
| X = ib
| X = ic
| ! [Y] : ~ requalityOnA(X,Y) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) )
& ! [X,Y] :
( ~ requalityOnA(X,Y)
| requalityOnA(Y,X) ) ),
inference(canonicalize,[],[negate_6_0]) ).
fof(normalize_6_1,plain,
cowlThing(ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_6_2,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_6_3,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_6_2]) ).
fof(normalize_6_4,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_6_3]) ).
fof(normalize_6_5,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_6_2]) ).
fof(normalize_6_6,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_6_5]) ).
fof(normalize_6_7,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_6_8,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_6_7]) ).
fof(normalize_6_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_6_10,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_6_9]) ).
fof(normalize_6_11,plain,
$false,
inference(simplify,[],[normalize_6_0,normalize_6_1,normalize_6_4,normalize_6_6,normalize_6_8,normalize_6_10]) ).
cnf(refute_6_0,plain,
$false,
inference(canonicalize,[],[normalize_6_11]) ).
fof(negate_7_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia) )
=> requalityOnA(ia,ia) ),
inference(negate,[],[subgoal_7]) ).
fof(normalize_7_0,plain,
( ~ requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( X = ia
| X = ib
| X = ic
| ! [Y] : ~ requalityOnA(X,Y) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) )
& ! [X,Y] :
( ~ requalityOnA(X,Y)
| requalityOnA(Y,X) ) ),
inference(canonicalize,[],[negate_7_0]) ).
fof(normalize_7_1,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_7_2,plain,
cowlThing(ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_7_3,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_7_4,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_7_3]) ).
fof(normalize_7_5,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_7_4]) ).
fof(normalize_7_6,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_7_3]) ).
fof(normalize_7_7,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_7_6]) ).
fof(normalize_7_8,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_7_9,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_7_8]) ).
fof(normalize_7_10,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_7_11,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_7_10]) ).
fof(normalize_7_12,plain,
$false,
inference(simplify,[],[normalize_7_0,normalize_7_1,normalize_7_2,normalize_7_5,normalize_7_7,normalize_7_9,normalize_7_11]) ).
cnf(refute_7_0,plain,
$false,
inference(canonicalize,[],[normalize_7_12]) ).
fof(negate_8_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia)
& requalityOnA(ia,ia) )
=> cowlThing(ib) ),
inference(negate,[],[subgoal_8]) ).
fof(normalize_8_0,plain,
( ~ cowlThing(ib)
& cowlThing(ia)
& requalityOnA(ia,ia)
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( X = ia
| X = ib
| X = ic
| ! [Y] : ~ requalityOnA(X,Y) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) )
& ! [X,Y] :
( ~ requalityOnA(X,Y)
| requalityOnA(Y,X) ) ),
inference(canonicalize,[],[negate_8_0]) ).
fof(normalize_8_1,plain,
cowlThing(ib),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_8_2,plain,
cowlThing(ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_8_3,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_8_4,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_8_5,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_8_4]) ).
fof(normalize_8_6,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_8_5]) ).
fof(normalize_8_7,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_8_4]) ).
fof(normalize_8_8,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_8_7]) ).
fof(normalize_8_9,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_8_10,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_8_9]) ).
fof(normalize_8_11,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_8_12,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_8_11]) ).
fof(normalize_8_13,plain,
$false,
inference(simplify,[],[normalize_8_0,normalize_8_1,normalize_8_2,normalize_8_3,normalize_8_6,normalize_8_8,normalize_8_10,normalize_8_12]) ).
cnf(refute_8_0,plain,
$false,
inference(canonicalize,[],[normalize_8_13]) ).
fof(negate_9_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ia
| X = ib
| X = ic ) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& cowlThing(ia)
& requalityOnA(ia,ia)
& cowlThing(ib) )
=> cowlThing(ic) ),
inference(negate,[],[subgoal_9]) ).
fof(normalize_9_0,plain,
( ~ cowlThing(ic)
& cowlThing(ia)
& cowlThing(ib)
& requalityOnA(ia,ia)
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( X = ia
| X = ib
| X = ic
| ! [Y] : ~ requalityOnA(X,Y) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) )
& ! [X,Y] :
( ~ requalityOnA(X,Y)
| requalityOnA(Y,X) ) ),
inference(canonicalize,[],[negate_9_0]) ).
fof(normalize_9_1,plain,
cowlThing(ic),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_9_2,plain,
cowlThing(ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_9_3,plain,
cowlThing(ib),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_9_4,plain,
requalityOnA(ia,ia),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_9_5,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_9_6,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_9_5]) ).
fof(normalize_9_7,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_9_6]) ).
fof(normalize_9_8,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_9_5]) ).
fof(normalize_9_9,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_9_8]) ).
fof(normalize_9_10,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_9_11,plain,
! [X] :
( ~ cA(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_9_10]) ).
fof(normalize_9_12,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_9_13,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_9_12]) ).
fof(normalize_9_14,plain,
$false,
inference(simplify,[],[normalize_9_0,normalize_9_1,normalize_9_2,normalize_9_3,normalize_9_4,normalize_9_7,normalize_9_9,normalize_9_11,normalize_9_13]) ).
cnf(refute_9_0,plain,
$false,
inference(canonicalize,[],[normalize_9_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 10:50:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------