%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS144+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 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 156 ( 67 unt; 0 def)
% Number of atoms : 468 ( 131 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 527 ( 215 ~; 146 |; 121 &)
% ( 16 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 224 ( 0 sgn 158 !; 39 ?)
% 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] :
( cc(X)
=> ( ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 )
& ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) )
=> ( Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ) ) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cc(X)
=> ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) )
=> ( Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) )
& ! [X] :
( cc(X)
=> ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 ) ) ) ).
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] :
( cc(X)
=> ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2)
& Y0 != Y1
& Y0 != Y2 )
=> Y1 = Y2 ) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_5,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cc(X)
=> ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) )
=> ( Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ) )
=> ! [X] :
( cc(X)
=> ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 ) ) ),
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] :
( cc(X)
=> ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2)
& Y0 != Y1
& Y0 != Y2 )
=> Y1 = Y2 ) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ? [X] :
( cc(X)
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) ) )
& ! [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] :
( cc(X)
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) ) ),
inference(simplify,[],[normalize_4_0,normalize_4_3,normalize_4_5,normalize_4_7]) ).
fof(normalize_4_9,plain,
( cc(skolemFOFtoCNF_X_2)
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rp(skolemFOFtoCNF_X_2,Y0)
& rp(skolemFOFtoCNF_X_2,Y1)
& rp(skolemFOFtoCNF_X_2,Y2) ) ),
inference(skolemize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rp(skolemFOFtoCNF_X_2,Y0)
& rp(skolemFOFtoCNF_X_2,Y1)
& rp(skolemFOFtoCNF_X_2,Y2) ),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_11,plain,
( skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1
& skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2
& skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2
& rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
& rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
& rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) ),
inference(skolemize,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_13,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_14,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_15,plain,
! [X] :
( ~ cc(X)
| ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_16,plain,
! [X] :
( ~ cc(X)
| ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(specialize,[],[normalize_4_15]) ).
fof(normalize_4_17,plain,
! [X,Y0,Y1,Y2] :
( ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(X) )
& ( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y1(X)) )
& ( ~ cc(X)
| ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ),
inference(clausify,[],[normalize_4_16]) ).
fof(normalize_4_18,plain,
! [X,Y0,Y1,Y2] :
( ~ cc(X)
| ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ),
inference(conjunct,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
cc(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_20,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1,
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_21,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2,
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_22,plain,
skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2,
inference(conjunct,[],[normalize_4_11]) ).
cnf(refute_4_0,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2),
inference(canonicalize,[],[normalize_4_12]) ).
cnf(refute_4_1,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_4_13]) ).
cnf(refute_4_2,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1),
inference(canonicalize,[],[normalize_4_14]) ).
cnf(refute_4_3,plain,
( ~ cc(X)
| ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ),
inference(canonicalize,[],[normalize_4_18]) ).
cnf(refute_4_4,plain,
( ~ cc(skolemFOFtoCNF_X_2)
| ~ rp(skolemFOFtoCNF_X_2,X_16)
| ~ rp(skolemFOFtoCNF_X_2,X_17)
| ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
| X_16 = X_17
| skolemFOFtoCNF_Y0_1 = X_16
| skolemFOFtoCNF_Y0_1 = X_17 ),
inference(subst,[],[refute_4_3:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(skolemFOFtoCNF_Y0_1)),bind(Y1,$fot(X_16)),bind(Y2,$fot(X_17))]]) ).
cnf(refute_4_5,plain,
( ~ cc(skolemFOFtoCNF_X_2)
| ~ rp(skolemFOFtoCNF_X_2,X_16)
| ~ rp(skolemFOFtoCNF_X_2,X_17)
| X_16 = X_17
| skolemFOFtoCNF_Y0_1 = X_16
| skolemFOFtoCNF_Y0_1 = X_17 ),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1) )],[refute_4_2,refute_4_4]) ).
cnf(refute_4_6,plain,
cc(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_19]) ).
cnf(refute_4_7,plain,
( ~ rp(skolemFOFtoCNF_X_2,X_16)
| ~ rp(skolemFOFtoCNF_X_2,X_17)
| X_16 = X_17
| skolemFOFtoCNF_Y0_1 = X_16
| skolemFOFtoCNF_Y0_1 = X_17 ),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_X_2) )],[refute_4_6,refute_4_5]) ).
cnf(refute_4_8,plain,
( ~ rp(skolemFOFtoCNF_X_2,X_19)
| ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y0_1 = X_19
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y1_1 = X_19 ),
inference(subst,[],[refute_4_7:[bind(X_16,$fot(skolemFOFtoCNF_Y1_1)),bind(X_17,$fot(X_19))]]) ).
cnf(refute_4_9,plain,
( ~ rp(skolemFOFtoCNF_X_2,X_19)
| skolemFOFtoCNF_Y0_1 = X_19
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y1_1 = X_19 ),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1) )],[refute_4_1,refute_4_8]) ).
cnf(refute_4_10,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1,
inference(canonicalize,[],[normalize_4_20]) ).
cnf(refute_4_11,plain,
( ~ rp(skolemFOFtoCNF_X_2,X_19)
| skolemFOFtoCNF_Y0_1 = X_19
| skolemFOFtoCNF_Y1_1 = X_19 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y1_1) )],[refute_4_9,refute_4_10]) ).
cnf(refute_4_12,plain,
( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2 ),
inference(subst,[],[refute_4_11:[bind(X_19,$fot(skolemFOFtoCNF_Y2))]]) ).
cnf(refute_4_13,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2 ),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) )],[refute_4_0,refute_4_12]) ).
cnf(refute_4_14,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2,
inference(canonicalize,[],[normalize_4_21]) ).
cnf(refute_4_15,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y2) )],[refute_4_13,refute_4_14]) ).
cnf(refute_4_16,plain,
skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2,
inference(canonicalize,[],[normalize_4_22]) ).
cnf(refute_4_17,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2) )],[refute_4_15,refute_4_16]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cc(X)
=> ! [Y0,Y1,Y2] :
( ( rp(X,Y0)
& rp(X,Y1)
& rp(X,Y2) )
=> ( Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ) )
=> ! [X] :
( cc(X)
=> ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 ) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
! [X] :
( ~ cc(X)
| ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_5_1,plain,
! [X] :
( ~ cc(X)
| ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(specialize,[],[normalize_5_0]) ).
fof(normalize_5_2,plain,
! [X,Y0,Y1,Y2] :
( ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(X) )
& ( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y1(X)) )
& ( ~ cc(X)
| ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ),
inference(clausify,[],[normalize_5_1]) ).
fof(normalize_5_3,plain,
! [X] :
( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(X) ),
inference(conjunct,[],[normalize_5_2]) ).
fof(normalize_5_4,plain,
( ? [X] :
( cc(X)
& ! [Y0,Y1] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| Y0 = Y1 ) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ cc(X)
| ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) )
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_5,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_5_6,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_5_5]) ).
fof(normalize_5_7,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_5_6]) ).
fof(normalize_5_8,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_5_5]) ).
fof(normalize_5_9,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_5_11,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_5_10]) ).
fof(normalize_5_12,plain,
( ? [X] :
( cc(X)
& ! [Y0,Y1] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| Y0 = Y1 ) )
& ! [X] :
( ~ cc(X)
| ! [Y0,Y1,Y2] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| ~ rp(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(simplify,[],[normalize_5_4,normalize_5_7,normalize_5_9,normalize_5_11]) ).
fof(normalize_5_13,plain,
? [X] :
( cc(X)
& ! [Y0,Y1] :
( ~ rp(X,Y0)
| ~ rp(X,Y1)
| Y0 = Y1 ) ),
inference(conjunct,[],[normalize_5_12]) ).
fof(normalize_5_14,plain,
( cc(skolemFOFtoCNF_X_3)
& ! [Y0,Y1] :
( ~ rp(skolemFOFtoCNF_X_3,Y0)
| ~ rp(skolemFOFtoCNF_X_3,Y1)
| Y0 = Y1 ) ),
inference(skolemize,[],[normalize_5_13]) ).
fof(normalize_5_15,plain,
cc(skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_14]) ).
fof(normalize_5_16,plain,
! [X] :
( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y1(X)) ),
inference(conjunct,[],[normalize_5_2]) ).
fof(normalize_5_17,plain,
! [X] :
( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(conjunct,[],[normalize_5_2]) ).
fof(normalize_5_18,plain,
! [Y0,Y1] :
( ~ rp(skolemFOFtoCNF_X_3,Y0)
| ~ rp(skolemFOFtoCNF_X_3,Y1)
| Y0 = Y1 ),
inference(conjunct,[],[normalize_5_14]) ).
fof(normalize_5_19,plain,
! [Y0,Y1] :
( ~ rp(skolemFOFtoCNF_X_3,Y0)
| ~ rp(skolemFOFtoCNF_X_3,Y1)
| Y0 = Y1 ),
inference(specialize,[],[normalize_5_18]) ).
cnf(refute_5_0,plain,
( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(X) ),
inference(canonicalize,[],[normalize_5_3]) ).
cnf(refute_5_1,plain,
( skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)
| ~ cc(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_0:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_2,plain,
cc(skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_15]) ).
cnf(refute_5_3,plain,
( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y1(X)) ),
inference(canonicalize,[],[normalize_5_16]) ).
cnf(refute_5_4,plain,
( ~ cc(skolemFOFtoCNF_X_3)
| rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_3:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_5,plain,
rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_X_3) )],[refute_5_2,refute_5_4]) ).
cnf(refute_5_6,plain,
( ~ cc(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_5_17]) ).
cnf(refute_5_7,plain,
( ~ cc(skolemFOFtoCNF_X_3)
| rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_6:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_8,plain,
rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_X_3) )],[refute_5_2,refute_5_7]) ).
cnf(refute_5_9,plain,
( ~ rp(skolemFOFtoCNF_X_3,Y0)
| ~ rp(skolemFOFtoCNF_X_3,Y1)
| Y0 = Y1 ),
inference(canonicalize,[],[normalize_5_19]) ).
cnf(refute_5_10,plain,
( ~ rp(skolemFOFtoCNF_X_3,X_29)
| ~ rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3))
| skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = X_29 ),
inference(subst,[],[refute_5_9:[bind(Y0,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3))),bind(Y1,$fot(X_29))]]) ).
cnf(refute_5_11,plain,
( ~ rp(skolemFOFtoCNF_X_3,X_29)
| skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = X_29 ),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)) )],[refute_5_8,refute_5_10]) ).
cnf(refute_5_12,plain,
( ~ rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3))
| skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_11:[bind(X_29,$fot(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_13,plain,
skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)) )],[refute_5_5,refute_5_12]) ).
cnf(refute_5_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_5_15,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_5_16,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_5_14,refute_5_15]) ).
cnf(refute_5_17,plain,
( skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_16:[bind(X0,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3))),bind(Y,$fot(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_18,plain,
skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)) )],[refute_5_13,refute_5_17]) ).
cnf(refute_5_19,plain,
( skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)) ),[1],$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_20,plain,
( skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)) )],[refute_5_18,refute_5_19]) ).
cnf(refute_5_21,plain,
( skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) != skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)
| ~ cc(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y1(skolemFOFtoCNF_X_3)) )],[refute_5_20,refute_5_1]) ).
cnf(refute_5_22,plain,
skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3) = skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_23,plain,
~ cc(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_X_3)) )],[refute_5_22,refute_5_21]) ).
cnf(refute_5_24,plain,
$false,
inference(resolve,[$cnf( cc(skolemFOFtoCNF_X_3) )],[refute_5_2,refute_5_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS144+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.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 10:55:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------