%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 03:18:50 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 148 ( 58 unt; 0 def)
% Number of atoms : 317 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 331 ( 162 ~; 61 |; 60 &)
% ( 27 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 162 ( 4 sgn 125 !; 19 ?)
% 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)
<=> ? [Y] :
( rq(X,Y)
& cowlThing(Y) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ) ).
fof(axiom_4,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ) ).
fof(axiom_5,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cnotA(X)
<=> ~ cA(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] :
( cnotA(X)
=> ~ cA(X) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_5,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X] :
( ~ cA(X)
=> cnotA(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] :
( cnotA(X)
=> ~ cA(X) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_1,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(specialize,[],[normalize_4_0]) ).
fof(normalize_4_2,plain,
! [X,Y] :
( ~ cNothing(X)
| ~ rp(X,Y) ),
inference(clausify,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
! [X] :
( ~ cNothing(X)
| ? [Y0] : rp(X,Y0) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_4_4,plain,
! [X] :
( ~ cNothing(X)
| ? [Y0] : rp(X,Y0) ),
inference(specialize,[],[normalize_4_3]) ).
fof(normalize_4_5,plain,
! [X] :
( ~ cNothing(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(clausify,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
( ? [X] :
( cA(X)
& cnotA(X) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_7,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_4_8,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_4_7]) ).
fof(normalize_4_9,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_4_7]) ).
fof(normalize_4_11,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_4_13,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_4_12]) ).
fof(normalize_4_14,plain,
? [X] :
( cA(X)
& cnotA(X) ),
inference(simplify,[],[normalize_4_6,normalize_4_9,normalize_4_11,normalize_4_13]) ).
fof(normalize_4_15,plain,
( cA(skolemFOFtoCNF_X_2)
& cnotA(skolemFOFtoCNF_X_2) ),
inference(skolemize,[],[normalize_4_14]) ).
fof(normalize_4_16,plain,
cA(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_15]) ).
fof(normalize_4_17,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_18,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(specialize,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
! [X,Y] :
( ( ~ cA(X)
| cowlThing(skolemFOFtoCNF_Y(X)) )
& ( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ) ),
inference(clausify,[],[normalize_4_18]) ).
fof(normalize_4_20,plain,
! [X] :
( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_4_19]) ).
fof(normalize_4_21,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_4_22,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(specialize,[],[normalize_4_21]) ).
fof(normalize_4_23,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_1(X))
| cnotA(X) )
& ( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_4_22]) ).
fof(normalize_4_24,plain,
! [X,Y] :
( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ),
inference(conjunct,[],[normalize_4_23]) ).
fof(normalize_4_25,plain,
cnotA(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_15]) ).
cnf(refute_4_0,plain,
( ~ cNothing(X)
| ~ rp(X,Y) ),
inference(canonicalize,[],[normalize_4_2]) ).
cnf(refute_4_1,plain,
( ~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))
| ~ rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))) ),
inference(subst,[],[refute_4_0:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))))]]) ).
cnf(refute_4_2,plain,
( ~ cNothing(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_4_5]) ).
cnf(refute_4_3,plain,
( ~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))
| rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))) ),
inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_4_4,plain,
cA(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_16]) ).
cnf(refute_4_5,plain,
( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_4_20]) ).
cnf(refute_4_6,plain,
( ~ cA(skolemFOFtoCNF_X_2)
| rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) ),
inference(subst,[],[refute_4_5:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_7,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_4,refute_4_6]) ).
cnf(refute_4_8,plain,
( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ),
inference(canonicalize,[],[normalize_4_24]) ).
cnf(refute_4_9,plain,
( ~ cnotA(skolemFOFtoCNF_X_2)
| ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))
| cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) ),
inference(subst,[],[refute_4_8:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_4_10,plain,
( ~ cnotA(skolemFOFtoCNF_X_2)
| cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) ),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) )],[refute_4_7,refute_4_9]) ).
cnf(refute_4_11,plain,
cnotA(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_25]) ).
cnf(refute_4_12,plain,
cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( cnotA(skolemFOFtoCNF_X_2) )],[refute_4_11,refute_4_10]) ).
cnf(refute_4_13,plain,
rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))),
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) )],[refute_4_12,refute_4_3]) ).
cnf(refute_4_14,plain,
~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2))) )],[refute_4_13,refute_4_1]) ).
cnf(refute_4_15,plain,
$false,
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_2)) )],[refute_4_12,refute_4_14]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X] :
( ~ cA(X)
=> cnotA(X) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
( ? [X] :
( ~ cA(X)
& ~ cnotA(X) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [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] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_5_7,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_5_6]) ).
fof(normalize_5_8,plain,
? [X] :
( ~ cA(X)
& ~ cnotA(X) ),
inference(simplify,[],[normalize_5_0,normalize_5_3,normalize_5_5,normalize_5_7]) ).
fof(normalize_5_9,plain,
( ~ cA(skolemFOFtoCNF_X_3)
& ~ cnotA(skolemFOFtoCNF_X_3) ),
inference(skolemize,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
~ cnotA(skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_9]) ).
fof(normalize_5_11,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_5_12,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(specialize,[],[normalize_5_11]) ).
fof(normalize_5_13,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_1(X))
| cnotA(X) )
& ( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_5_12]) ).
fof(normalize_5_14,plain,
! [X] :
( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_5_13]) ).
fof(normalize_5_15,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_5_16,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(specialize,[],[normalize_5_15]) ).
fof(normalize_5_17,plain,
! [X,Y] :
( ( ~ cA(X)
| cowlThing(skolemFOFtoCNF_Y(X)) )
& ( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ) ),
inference(clausify,[],[normalize_5_16]) ).
fof(normalize_5_18,plain,
! [X,Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ),
inference(conjunct,[],[normalize_5_17]) ).
fof(normalize_5_19,plain,
~ cA(skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_9]) ).
cnf(refute_5_0,plain,
~ cnotA(skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_10]) ).
cnf(refute_5_1,plain,
( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_5_14]) ).
cnf(refute_5_2,plain,
( cnotA(X_30)
| rq(X_30,skolemFOFtoCNF_Y_1(X_30)) ),
inference(subst,[],[refute_5_1:[bind(X,$fot(X_30))]]) ).
cnf(refute_5_3,plain,
( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ),
inference(canonicalize,[],[normalize_5_18]) ).
cnf(refute_5_4,plain,
cowlThing(X),
inference(canonicalize,[],[normalize_5_5]) ).
cnf(refute_5_5,plain,
cowlThing(Y),
inference(subst,[],[refute_5_4:[bind(X,$fot(Y))]]) ).
cnf(refute_5_6,plain,
( ~ rq(X,Y)
| cA(X) ),
inference(resolve,[$cnf( cowlThing(Y) )],[refute_5_5,refute_5_3]) ).
cnf(refute_5_7,plain,
( ~ rq(X_30,skolemFOFtoCNF_Y_1(X_30))
| cA(X_30) ),
inference(subst,[],[refute_5_6:[bind(X,$fot(X_30)),bind(Y,$fot(skolemFOFtoCNF_Y_1(X_30)))]]) ).
cnf(refute_5_8,plain,
( cA(X_30)
| cnotA(X_30) ),
inference(resolve,[$cnf( rq(X_30,skolemFOFtoCNF_Y_1(X_30)) )],[refute_5_2,refute_5_7]) ).
cnf(refute_5_9,plain,
( cA(skolemFOFtoCNF_X_3)
| cnotA(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_8:[bind(X_30,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_10,plain,
cA(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( cnotA(skolemFOFtoCNF_X_3) )],[refute_5_9,refute_5_0]) ).
cnf(refute_5_11,plain,
~ cA(skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_19]) ).
cnf(refute_5_12,plain,
$false,
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_3) )],[refute_5_10,refute_5_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 7 11:57:32 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------