%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:18:54 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 171 ( 69 unt; 0 def)
% Number of atoms : 364 ( 65 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 347 ( 154 ~; 96 |; 60 &)
% ( 16 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 139 ( 2 sgn 117 !; 15 ?)
% 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,Y] :
( rsymProp(X,Y)
=> ( Y = ia
| Y = ib ) ) ).
fof(axiom_3,axiom,
! [X,Y] :
( rsymProp(X,Y)
=> rsymProp(Y,X) ) ).
fof(axiom_5,axiom,
rsymProp(ia,ia) ).
fof(axiom_7,axiom,
rsymProp(ib,ib) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y,Z] :
( ( rsymProp(X,Y)
& rsymProp(Y,Z) )
=> rsymProp(X,Z) )
& ? [X] :
( rsymProp(ia,X)
& cowlThing(X) ) ) ).
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,Z] :
( ( rsymProp(X,Y)
& rsymProp(Y,Z) )
=> rsymProp(X,Z) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_5,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y,Z] :
( ( rsymProp(X,Y)
& rsymProp(Y,Z) )
=> rsymProp(X,Z) ) )
=> ? [X] :
( rsymProp(ia,X)
& cowlThing(X) ) ),
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,Z] :
( ( rsymProp(X,Y)
& rsymProp(Y,Z) )
=> rsymProp(X,Z) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ? [X,Y,Z] :
( ~ rsymProp(X,Z)
& rsymProp(X,Y)
& rsymProp(Y,Z) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_4_2,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_4_2]) ).
fof(normalize_4_4,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_4_1]) ).
fof(normalize_4_5,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_4_7,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_4_6]) ).
fof(normalize_4_8,plain,
? [X,Y,Z] :
( ~ rsymProp(X,Z)
& rsymProp(X,Y)
& rsymProp(Y,Z) ),
inference(simplify,[],[normalize_4_0,normalize_4_3,normalize_4_5,normalize_4_7]) ).
fof(normalize_4_9,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z)
& rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
& rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_11,plain,
rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_12,plain,
! [X,Y] :
( ~ rsymProp(X,Y)
| rsymProp(Y,X) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_13,plain,
! [X,Y] :
( ~ rsymProp(X,Y)
| rsymProp(Y,X) ),
inference(specialize,[],[normalize_4_12]) ).
fof(normalize_4_14,plain,
! [X,Y] :
( ~ rsymProp(X,Y)
| Y = ia
| Y = ib ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_15,plain,
! [X,Y] :
( ~ rsymProp(X,Y)
| Y = ia
| Y = ib ),
inference(specialize,[],[normalize_4_14]) ).
fof(normalize_4_16,plain,
rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_17,plain,
rsymProp(ia,ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_4_18,plain,
rsymProp(ib,ib),
inference(canonicalize,[],[axiom_7]) ).
cnf(refute_4_0,plain,
~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_4_10]) ).
cnf(refute_4_1,plain,
rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_4_11]) ).
cnf(refute_4_2,plain,
( ~ rsymProp(X,Y)
| rsymProp(Y,X) ),
inference(canonicalize,[],[normalize_4_13]) ).
cnf(refute_4_3,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_4_4,plain,
rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_3]) ).
cnf(refute_4_5,plain,
( ~ rsymProp(X,Y)
| Y = ia
| Y = ib ),
inference(canonicalize,[],[normalize_4_15]) ).
cnf(refute_4_6,plain,
( ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 = ia
| skolemFOFtoCNF_X_2 = ib ),
inference(subst,[],[refute_4_5:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_7,plain,
( skolemFOFtoCNF_X_2 = ia
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2) )],[refute_4_4,refute_4_6]) ).
cnf(refute_4_8,plain,
( skolemFOFtoCNF_X_2 != ia
| ~ rsymProp(ia,skolemFOFtoCNF_Z)
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),[0],$fot(ia)]]) ).
cnf(refute_4_9,plain,
( ~ rsymProp(ia,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_X_2 = ib
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_7,refute_4_8]) ).
cnf(refute_4_10,plain,
( ~ rsymProp(ia,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) )],[refute_4_9,refute_4_0]) ).
cnf(refute_4_11,plain,
rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_4_16]) ).
cnf(refute_4_12,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| skolemFOFtoCNF_Y = ia
| skolemFOFtoCNF_Y = ib ),
inference(subst,[],[refute_4_5:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_4_13,plain,
( skolemFOFtoCNF_Y = ia
| skolemFOFtoCNF_Y = ib ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_12]) ).
cnf(refute_4_14,plain,
( skolemFOFtoCNF_Y != ia
| ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| rsymProp(ia,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),[0],$fot(ia)]]) ).
cnf(refute_4_15,plain,
( ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_Y = ib
| rsymProp(ia,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ia) )],[refute_4_13,refute_4_14]) ).
cnf(refute_4_16,plain,
( skolemFOFtoCNF_Y = ib
| rsymProp(ia,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_4_11,refute_4_15]) ).
cnf(refute_4_17,plain,
( skolemFOFtoCNF_X_2 = ib
| skolemFOFtoCNF_Y = ib ),
inference(resolve,[$cnf( rsymProp(ia,skolemFOFtoCNF_Z) )],[refute_4_16,refute_4_10]) ).
cnf(refute_4_18,plain,
( skolemFOFtoCNF_Y != ib
| ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| rsymProp(skolemFOFtoCNF_X_2,ib) ),
introduced(tautology,[equality,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),[1],$fot(ib)]]) ).
cnf(refute_4_19,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| skolemFOFtoCNF_X_2 = ib
| rsymProp(skolemFOFtoCNF_X_2,ib) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ib) )],[refute_4_17,refute_4_18]) ).
cnf(refute_4_20,plain,
( skolemFOFtoCNF_X_2 = ib
| rsymProp(skolemFOFtoCNF_X_2,ib) ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_19]) ).
cnf(refute_4_21,plain,
( ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_Z = ia
| skolemFOFtoCNF_Z = ib ),
inference(subst,[],[refute_4_5:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_4_22,plain,
( skolemFOFtoCNF_Z = ia
| skolemFOFtoCNF_Z = ib ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_4_11,refute_4_21]) ).
cnf(refute_4_23,plain,
( skolemFOFtoCNF_Z != ib
| ~ rsymProp(skolemFOFtoCNF_X_2,ib)
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),[1],$fot(ib)]]) ).
cnf(refute_4_24,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,ib)
| skolemFOFtoCNF_Z = ia
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,ib) )],[refute_4_22,refute_4_23]) ).
cnf(refute_4_25,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,ib)
| skolemFOFtoCNF_Z = ia ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) )],[refute_4_24,refute_4_0]) ).
cnf(refute_4_26,plain,
( skolemFOFtoCNF_X_2 = ib
| skolemFOFtoCNF_Z = ia ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,ib) )],[refute_4_20,refute_4_25]) ).
cnf(refute_4_27,plain,
( skolemFOFtoCNF_Z != ia
| ~ rsymProp(ia,ia)
| rsymProp(ia,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(ia,skolemFOFtoCNF_Z) ),[1],$fot(ia)]]) ).
cnf(refute_4_28,plain,
( ~ rsymProp(ia,ia)
| skolemFOFtoCNF_X_2 = ib
| rsymProp(ia,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,ia) )],[refute_4_26,refute_4_27]) ).
cnf(refute_4_29,plain,
( ~ rsymProp(ia,ia)
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( rsymProp(ia,skolemFOFtoCNF_Z) )],[refute_4_28,refute_4_10]) ).
cnf(refute_4_30,plain,
rsymProp(ia,ia),
inference(canonicalize,[],[normalize_4_17]) ).
cnf(refute_4_31,plain,
skolemFOFtoCNF_X_2 = ib,
inference(resolve,[$cnf( rsymProp(ia,ia) )],[refute_4_30,refute_4_29]) ).
cnf(refute_4_32,plain,
( skolemFOFtoCNF_X_2 != ib
| ~ rsymProp(ib,skolemFOFtoCNF_Z)
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),[0],$fot(ib)]]) ).
cnf(refute_4_33,plain,
( ~ rsymProp(ib,skolemFOFtoCNF_Z)
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_31,refute_4_32]) ).
cnf(refute_4_34,plain,
~ rsymProp(ib,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) )],[refute_4_33,refute_4_0]) ).
cnf(refute_4_35,plain,
( skolemFOFtoCNF_X_2 != ib
| ~ rsymProp(ib,ib)
| rsymProp(skolemFOFtoCNF_X_2,ib) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(skolemFOFtoCNF_X_2,ib) ),[0],$fot(ib)]]) ).
cnf(refute_4_36,plain,
( ~ rsymProp(ib,ib)
| rsymProp(skolemFOFtoCNF_X_2,ib) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_31,refute_4_35]) ).
cnf(refute_4_37,plain,
( ~ rsymProp(ib,ib)
| skolemFOFtoCNF_Z = ia ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,ib) )],[refute_4_36,refute_4_25]) ).
cnf(refute_4_38,plain,
rsymProp(ib,ib),
inference(canonicalize,[],[normalize_4_18]) ).
cnf(refute_4_39,plain,
skolemFOFtoCNF_Z = ia,
inference(resolve,[$cnf( rsymProp(ib,ib) )],[refute_4_38,refute_4_37]) ).
cnf(refute_4_40,plain,
( skolemFOFtoCNF_Z != ia
| ~ rsymProp(ib,ia)
| rsymProp(ib,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(ib,skolemFOFtoCNF_Z) ),[1],$fot(ia)]]) ).
cnf(refute_4_41,plain,
( ~ rsymProp(ib,ia)
| rsymProp(ib,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,ia) )],[refute_4_39,refute_4_40]) ).
cnf(refute_4_42,plain,
~ rsymProp(ib,ia),
inference(resolve,[$cnf( rsymProp(ib,skolemFOFtoCNF_Z) )],[refute_4_41,refute_4_34]) ).
cnf(refute_4_43,plain,
( skolemFOFtoCNF_X_2 != ib
| ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| rsymProp(ib,skolemFOFtoCNF_Y) ),
introduced(tautology,[equality,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),[0],$fot(ib)]]) ).
cnf(refute_4_44,plain,
( ~ rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
| rsymProp(ib,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_31,refute_4_43]) ).
cnf(refute_4_45,plain,
rsymProp(ib,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_44]) ).
cnf(refute_4_46,plain,
( skolemFOFtoCNF_Y != ib
| ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| rsymProp(ib,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),[0],$fot(ib)]]) ).
cnf(refute_4_47,plain,
( ~ rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_Y = ia
| rsymProp(ib,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ib) )],[refute_4_13,refute_4_46]) ).
cnf(refute_4_48,plain,
( skolemFOFtoCNF_Y = ia
| rsymProp(ib,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_4_11,refute_4_47]) ).
cnf(refute_4_49,plain,
( ~ rsymProp(ib,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_X_2 = ia
| rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_7,refute_4_32]) ).
cnf(refute_4_50,plain,
( ~ rsymProp(ib,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_X_2 = ia ),
inference(resolve,[$cnf( rsymProp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) )],[refute_4_49,refute_4_0]) ).
cnf(refute_4_51,plain,
( skolemFOFtoCNF_X_2 = ia
| skolemFOFtoCNF_Y = ia ),
inference(resolve,[$cnf( rsymProp(ib,skolemFOFtoCNF_Z) )],[refute_4_48,refute_4_50]) ).
cnf(refute_4_52,plain,
( skolemFOFtoCNF_X_2 != ia
| skolemFOFtoCNF_X_2 != ib
| ib = ia ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) ),[0],$fot(ib)]]) ).
cnf(refute_4_53,plain,
( skolemFOFtoCNF_X_2 != ia
| ib = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_31,refute_4_52]) ).
cnf(refute_4_54,plain,
( ib = ia
| skolemFOFtoCNF_Y = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_51,refute_4_53]) ).
cnf(refute_4_55,plain,
( skolemFOFtoCNF_Y != ia
| ~ rsymProp(ib,skolemFOFtoCNF_Y)
| rsymProp(ib,ia) ),
introduced(tautology,[equality,[$cnf( rsymProp(ib,skolemFOFtoCNF_Y) ),[1],$fot(ia)]]) ).
cnf(refute_4_56,plain,
( ~ rsymProp(ib,skolemFOFtoCNF_Y)
| ib = ia
| rsymProp(ib,ia) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,ia) )],[refute_4_54,refute_4_55]) ).
cnf(refute_4_57,plain,
( ib = ia
| rsymProp(ib,ia) ),
inference(resolve,[$cnf( rsymProp(ib,skolemFOFtoCNF_Y) )],[refute_4_45,refute_4_56]) ).
cnf(refute_4_58,plain,
ib = ia,
inference(resolve,[$cnf( rsymProp(ib,ia) )],[refute_4_57,refute_4_42]) ).
cnf(refute_4_59,plain,
( ib != ia
| ~ rsymProp(ia,ia)
| rsymProp(ib,ia) ),
introduced(tautology,[equality,[$cnf( ~ rsymProp(ib,ia) ),[0],$fot(ia)]]) ).
cnf(refute_4_60,plain,
( ~ rsymProp(ia,ia)
| rsymProp(ib,ia) ),
inference(resolve,[$cnf( $equal(ib,ia) )],[refute_4_58,refute_4_59]) ).
cnf(refute_4_61,plain,
~ rsymProp(ia,ia),
inference(resolve,[$cnf( rsymProp(ib,ia) )],[refute_4_60,refute_4_42]) ).
cnf(refute_4_62,plain,
$false,
inference(resolve,[$cnf( rsymProp(ia,ia) )],[refute_4_30,refute_4_61]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X,Y,Z] :
( ( rsymProp(X,Y)
& rsymProp(Y,Z) )
=> rsymProp(X,Z) ) )
=> ? [X] :
( rsymProp(ia,X)
& cowlThing(X) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
rsymProp(ia,ia),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_5_1,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ cowlThing(X)
| ~ rsymProp(ia,X) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) )
& ! [X,Y,Z] :
( ~ rsymProp(X,Y)
| ~ rsymProp(Y,Z)
| rsymProp(X,Z) ) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_2,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_5_3,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_5_2]) ).
fof(normalize_5_4,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_5_3]) ).
fof(normalize_5_5,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_5_2]) ).
fof(normalize_5_6,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_5_5]) ).
fof(normalize_5_7,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_5_8,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_5_7]) ).
fof(normalize_5_9,plain,
( ! [X] : ~ rsymProp(ia,X)
& ! [X,Y,Z] :
( ~ rsymProp(X,Y)
| ~ rsymProp(Y,Z)
| rsymProp(X,Z) ) ),
inference(simplify,[],[normalize_5_1,normalize_5_4,normalize_5_6,normalize_5_6,normalize_5_8]) ).
fof(normalize_5_10,plain,
! [X] : ~ rsymProp(ia,X),
inference(conjunct,[],[normalize_5_9]) ).
fof(normalize_5_11,plain,
! [X] : ~ rsymProp(ia,X),
inference(specialize,[],[normalize_5_10]) ).
cnf(refute_5_0,plain,
rsymProp(ia,ia),
inference(canonicalize,[],[normalize_5_0]) ).
cnf(refute_5_1,plain,
~ rsymProp(ia,X),
inference(canonicalize,[],[normalize_5_11]) ).
cnf(refute_5_2,plain,
~ rsymProp(ia,ia),
inference(subst,[],[refute_5_1:[bind(X,$fot(ia))]]) ).
cnf(refute_5_3,plain,
$false,
inference(resolve,[$cnf( rsymProp(ia,ia) )],[refute_5_0,refute_5_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% 0.14/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 7 15:09:51 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.41
%------------------------------------------------------------------------------