%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS132+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 0.14s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 260 ( 64 unt; 0 def)
% Number of atoms : 641 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 699 ( 318 ~; 210 |; 96 &)
% ( 52 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 292 ( 9 sgn 202 !; 31 ?)
% 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] :
( cAorB(X)
<=> ? [Y] :
( rs(X,Y)
& cowlThing(Y) ) ) ).
fof(axiom_4,axiom,
! [X] :
( cB(X)
<=> ? [Y] :
( rr(X,Y)
& cowlThing(Y) ) ) ).
fof(axiom_5,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ) ).
fof(axiom_6,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ) ).
fof(axiom_7,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ) ).
fof(axiom_8,axiom,
! [X] :
( cnotAorB(X)
<=> ! [Y] :
( rs(X,Y)
=> cNothing(Y) ) ) ).
fof(axiom_9,axiom,
! [X] :
( cnotAorB(X)
<=> ( cnotB(X)
& cnotA(X) ) ) ).
fof(axiom_10,axiom,
! [X] :
( cnotB(X)
<=> ! [Y] :
( rr(X,Y)
=> cNothing(Y) ) ) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cAorB(X)
<=> ( cB(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] :
( ( cAorB(X)
& ~ cB(X) )
=> cA(X) ) ),
inference(strip,[],[the_axiom]) ).
fof(subgoal_5,plain,
( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X] :
( ( cB(X)
| cA(X) )
=> cAorB(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] :
( ( cAorB(X)
& ~ cB(X) )
=> cA(X) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(canonicalize,[],[axiom_6]) ).
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_5]) ).
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)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_7,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(specialize,[],[normalize_4_6]) ).
fof(normalize_4_8,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_7]) ).
fof(normalize_4_9,plain,
! [X,Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ),
inference(conjunct,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_4_11,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_4_11]) ).
fof(normalize_4_13,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_4_14,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(specialize,[],[normalize_4_13]) ).
fof(normalize_4_15,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_3(X))
| cnotA(X) )
& ( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_3(X)) )
& ( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_4_14]) ).
fof(normalize_4_16,plain,
! [X] :
( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_3(X)) ),
inference(conjunct,[],[normalize_4_15]) ).
fof(normalize_4_17,plain,
! [X] :
( ~ cnotB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rr(X,Y) ) ),
inference(canonicalize,[],[axiom_10]) ).
fof(normalize_4_18,plain,
! [X] :
( ~ cnotB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rr(X,Y) ) ),
inference(specialize,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_5(X))
| cnotB(X) )
& ( cnotB(X)
| rr(X,skolemFOFtoCNF_Y_5(X)) )
& ( ~ cnotB(X)
| ~ rr(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_4_18]) ).
fof(normalize_4_20,plain,
! [X] :
( cnotB(X)
| rr(X,skolemFOFtoCNF_Y_5(X)) ),
inference(conjunct,[],[normalize_4_19]) ).
fof(normalize_4_21,plain,
! [X] :
( ~ cB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) ) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_4_22,plain,
! [X] :
( ~ cB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) ) ),
inference(specialize,[],[normalize_4_21]) ).
fof(normalize_4_23,plain,
! [X,Y] :
( ( ~ cB(X)
| cowlThing(skolemFOFtoCNF_Y_2(X)) )
& ( ~ cB(X)
| rr(X,skolemFOFtoCNF_Y_2(X)) )
& ( ~ cowlThing(Y)
| ~ rr(X,Y)
| cB(X) ) ),
inference(clausify,[],[normalize_4_22]) ).
fof(normalize_4_24,plain,
! [X,Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y)
| cB(X) ),
inference(conjunct,[],[normalize_4_23]) ).
fof(normalize_4_25,plain,
! [X] :
( ~ cnotAorB(X)
<=> ( ~ cnotA(X)
| ~ cnotB(X) ) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_4_26,plain,
! [X] :
( ~ cnotAorB(X)
<=> ( ~ cnotA(X)
| ~ cnotB(X) ) ),
inference(specialize,[],[normalize_4_25]) ).
fof(normalize_4_27,plain,
! [X] :
( ( ~ cnotAorB(X)
| cnotA(X) )
& ( ~ cnotAorB(X)
| cnotB(X) )
& ( ~ cnotA(X)
| ~ cnotB(X)
| cnotAorB(X) ) ),
inference(clausify,[],[normalize_4_26]) ).
fof(normalize_4_28,plain,
! [X] :
( ~ cnotA(X)
| ~ cnotB(X)
| cnotAorB(X) ),
inference(conjunct,[],[normalize_4_27]) ).
fof(normalize_4_29,plain,
( ? [X] :
( ~ cA(X)
& ~ cB(X)
& cAorB(X) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_30,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_4_10]) ).
fof(normalize_4_31,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_4_30]) ).
fof(normalize_4_32,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_4_33,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_4_32]) ).
fof(normalize_4_34,plain,
? [X] :
( ~ cA(X)
& ~ cB(X)
& cAorB(X) ),
inference(simplify,[],[normalize_4_29,normalize_4_31,normalize_4_12,normalize_4_33]) ).
fof(normalize_4_35,plain,
( ~ cA(skolemFOFtoCNF_X_2)
& ~ cB(skolemFOFtoCNF_X_2)
& cAorB(skolemFOFtoCNF_X_2) ),
inference(skolemize,[],[normalize_4_34]) ).
fof(normalize_4_36,plain,
cAorB(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_35]) ).
fof(normalize_4_37,plain,
! [X] :
( ~ cAorB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_38,plain,
! [X] :
( ~ cAorB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) ) ),
inference(specialize,[],[normalize_4_37]) ).
fof(normalize_4_39,plain,
! [X,Y] :
( ( ~ cAorB(X)
| cowlThing(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cAorB(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cowlThing(Y)
| ~ rs(X,Y)
| cAorB(X) ) ),
inference(clausify,[],[normalize_4_38]) ).
fof(normalize_4_40,plain,
! [X] :
( ~ cAorB(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_4_39]) ).
fof(normalize_4_41,plain,
! [X] :
( ~ cnotAorB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rs(X,Y) ) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_4_42,plain,
! [X] :
( ~ cnotAorB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rs(X,Y) ) ),
inference(specialize,[],[normalize_4_41]) ).
fof(normalize_4_43,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_4(X))
| cnotAorB(X) )
& ( cnotAorB(X)
| rs(X,skolemFOFtoCNF_Y_4(X)) )
& ( ~ cnotAorB(X)
| ~ rs(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_4_42]) ).
fof(normalize_4_44,plain,
! [X,Y] :
( ~ cnotAorB(X)
| ~ rs(X,Y)
| cNothing(Y) ),
inference(conjunct,[],[normalize_4_43]) ).
fof(normalize_4_45,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_35]) ).
fof(normalize_4_46,plain,
~ cB(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_35]) ).
cnf(refute_4_0,plain,
( ~ cNothing(X)
| ~ rp(X,Y) ),
inference(canonicalize,[],[normalize_4_2]) ).
cnf(refute_4_1,plain,
( ~ cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))
| ~ rp(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))) ),
inference(subst,[],[refute_4_0:[bind(X,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(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_1(skolemFOFtoCNF_X_2))
| rp(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))) ),
inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_4_4,plain,
( ~ cowlThing(Y)
| ~ rq(X,Y)
| cA(X) ),
inference(canonicalize,[],[normalize_4_9]) ).
cnf(refute_4_5,plain,
cowlThing(X),
inference(canonicalize,[],[normalize_4_12]) ).
cnf(refute_4_6,plain,
cowlThing(Y),
inference(subst,[],[refute_4_5:[bind(X,$fot(Y))]]) ).
cnf(refute_4_7,plain,
( ~ rq(X,Y)
| cA(X) ),
inference(resolve,[$cnf( cowlThing(Y) )],[refute_4_6,refute_4_4]) ).
cnf(refute_4_8,plain,
( ~ rq(X_24,skolemFOFtoCNF_Y_3(X_24))
| cA(X_24) ),
inference(subst,[],[refute_4_7:[bind(X,$fot(X_24)),bind(Y,$fot(skolemFOFtoCNF_Y_3(X_24)))]]) ).
cnf(refute_4_9,plain,
( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_3(X)) ),
inference(canonicalize,[],[normalize_4_16]) ).
cnf(refute_4_10,plain,
( cnotA(X_24)
| rq(X_24,skolemFOFtoCNF_Y_3(X_24)) ),
inference(subst,[],[refute_4_9:[bind(X,$fot(X_24))]]) ).
cnf(refute_4_11,plain,
( cA(X_24)
| cnotA(X_24) ),
inference(resolve,[$cnf( rq(X_24,skolemFOFtoCNF_Y_3(X_24)) )],[refute_4_10,refute_4_8]) ).
cnf(refute_4_12,plain,
( cA(X_38)
| cnotA(X_38) ),
inference(subst,[],[refute_4_11:[bind(X_24,$fot(X_38))]]) ).
cnf(refute_4_13,plain,
( cnotB(X)
| rr(X,skolemFOFtoCNF_Y_5(X)) ),
inference(canonicalize,[],[normalize_4_20]) ).
cnf(refute_4_14,plain,
( cnotB(X_32)
| rr(X_32,skolemFOFtoCNF_Y_5(X_32)) ),
inference(subst,[],[refute_4_13:[bind(X,$fot(X_32))]]) ).
cnf(refute_4_15,plain,
( ~ cowlThing(Y)
| ~ rr(X,Y)
| cB(X) ),
inference(canonicalize,[],[normalize_4_24]) ).
cnf(refute_4_16,plain,
( ~ rr(X,Y)
| cB(X) ),
inference(resolve,[$cnf( cowlThing(Y) )],[refute_4_6,refute_4_15]) ).
cnf(refute_4_17,plain,
( ~ rr(X_32,skolemFOFtoCNF_Y_5(X_32))
| cB(X_32) ),
inference(subst,[],[refute_4_16:[bind(X,$fot(X_32)),bind(Y,$fot(skolemFOFtoCNF_Y_5(X_32)))]]) ).
cnf(refute_4_18,plain,
( cB(X_32)
| cnotB(X_32) ),
inference(resolve,[$cnf( rr(X_32,skolemFOFtoCNF_Y_5(X_32)) )],[refute_4_14,refute_4_17]) ).
cnf(refute_4_19,plain,
( cB(X_37)
| cnotB(X_37) ),
inference(subst,[],[refute_4_18:[bind(X_32,$fot(X_37))]]) ).
cnf(refute_4_20,plain,
( ~ cnotA(X)
| ~ cnotB(X)
| cnotAorB(X) ),
inference(canonicalize,[],[normalize_4_28]) ).
cnf(refute_4_21,plain,
( ~ cnotA(X_37)
| ~ cnotB(X_37)
| cnotAorB(X_37) ),
inference(subst,[],[refute_4_20:[bind(X,$fot(X_37))]]) ).
cnf(refute_4_22,plain,
( ~ cnotA(X_37)
| cB(X_37)
| cnotAorB(X_37) ),
inference(resolve,[$cnf( cnotB(X_37) )],[refute_4_19,refute_4_21]) ).
cnf(refute_4_23,plain,
( ~ cnotA(X_38)
| cB(X_38)
| cnotAorB(X_38) ),
inference(subst,[],[refute_4_22:[bind(X_37,$fot(X_38))]]) ).
cnf(refute_4_24,plain,
( cA(X_38)
| cB(X_38)
| cnotAorB(X_38) ),
inference(resolve,[$cnf( cnotA(X_38) )],[refute_4_12,refute_4_23]) ).
cnf(refute_4_25,plain,
( cA(skolemFOFtoCNF_X_2)
| cB(skolemFOFtoCNF_X_2)
| cnotAorB(skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_4_24:[bind(X_38,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_26,plain,
cAorB(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_36]) ).
cnf(refute_4_27,plain,
( ~ cAorB(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_4_40]) ).
cnf(refute_4_28,plain,
( ~ cAorB(skolemFOFtoCNF_X_2)
| rs(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) ),
inference(subst,[],[refute_4_27:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_29,plain,
rs(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( cAorB(skolemFOFtoCNF_X_2) )],[refute_4_26,refute_4_28]) ).
cnf(refute_4_30,plain,
( ~ cnotAorB(X)
| ~ rs(X,Y)
| cNothing(Y) ),
inference(canonicalize,[],[normalize_4_44]) ).
cnf(refute_4_31,plain,
( ~ cnotAorB(skolemFOFtoCNF_X_2)
| ~ rs(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))
| cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) ),
inference(subst,[],[refute_4_30:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_4_32,plain,
( ~ cnotAorB(skolemFOFtoCNF_X_2)
| cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) ),
inference(resolve,[$cnf( rs(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) )],[refute_4_29,refute_4_31]) ).
cnf(refute_4_33,plain,
( cA(skolemFOFtoCNF_X_2)
| cB(skolemFOFtoCNF_X_2)
| cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) ),
inference(resolve,[$cnf( cnotAorB(skolemFOFtoCNF_X_2) )],[refute_4_25,refute_4_32]) ).
cnf(refute_4_34,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_45]) ).
cnf(refute_4_35,plain,
( cB(skolemFOFtoCNF_X_2)
| cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_33,refute_4_34]) ).
cnf(refute_4_36,plain,
~ cB(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_46]) ).
cnf(refute_4_37,plain,
cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_X_2) )],[refute_4_35,refute_4_36]) ).
cnf(refute_4_38,plain,
rp(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))),
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) )],[refute_4_37,refute_4_3]) ).
cnf(refute_4_39,plain,
~ cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2))) )],[refute_4_38,refute_4_1]) ).
cnf(refute_4_40,plain,
$false,
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X_2)) )],[refute_4_37,refute_4_39]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X] :
( ( cB(X)
| cA(X) )
=> cAorB(X) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_5_1,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(specialize,[],[normalize_5_0]) ).
fof(normalize_5_2,plain,
! [X,Y] :
( ~ cNothing(X)
| ~ rp(X,Y) ),
inference(clausify,[],[normalize_5_1]) ).
fof(normalize_5_3,plain,
! [X] :
( ~ cNothing(X)
| ? [Y0] : rp(X,Y0) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_5_4,plain,
! [X] :
( ~ cNothing(X)
| ? [Y0] : rp(X,Y0) ),
inference(specialize,[],[normalize_5_3]) ).
fof(normalize_5_5,plain,
! [X] :
( ~ cNothing(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(clausify,[],[normalize_5_4]) ).
fof(normalize_5_6,plain,
! [X] :
( ~ cnotAorB(X)
<=> ( ~ cnotA(X)
| ~ cnotB(X) ) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_5_7,plain,
! [X] :
( ~ cnotAorB(X)
<=> ( ~ cnotA(X)
| ~ cnotB(X) ) ),
inference(specialize,[],[normalize_5_6]) ).
fof(normalize_5_8,plain,
! [X] :
( ( ~ cnotAorB(X)
| cnotA(X) )
& ( ~ cnotAorB(X)
| cnotB(X) )
& ( ~ cnotA(X)
| ~ cnotB(X)
| cnotAorB(X) ) ),
inference(clausify,[],[normalize_5_7]) ).
fof(normalize_5_9,plain,
! [X] :
( ~ cnotAorB(X)
| cnotA(X) ),
inference(conjunct,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
! [X] :
( ~ cnotAorB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rs(X,Y) ) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_5_11,plain,
! [X] :
( ~ cnotAorB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rs(X,Y) ) ),
inference(specialize,[],[normalize_5_10]) ).
fof(normalize_5_12,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_4(X))
| cnotAorB(X) )
& ( cnotAorB(X)
| rs(X,skolemFOFtoCNF_Y_4(X)) )
& ( ~ cnotAorB(X)
| ~ rs(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_5_11]) ).
fof(normalize_5_13,plain,
! [X] :
( cnotAorB(X)
| rs(X,skolemFOFtoCNF_Y_4(X)) ),
inference(conjunct,[],[normalize_5_12]) ).
fof(normalize_5_14,plain,
! [X] :
( ~ cAorB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_5_15,plain,
! [X] :
( ~ cAorB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) ) ),
inference(specialize,[],[normalize_5_14]) ).
fof(normalize_5_16,plain,
! [X,Y] :
( ( ~ cAorB(X)
| cowlThing(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cAorB(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cowlThing(Y)
| ~ rs(X,Y)
| cAorB(X) ) ),
inference(clausify,[],[normalize_5_15]) ).
fof(normalize_5_17,plain,
! [X,Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y)
| cAorB(X) ),
inference(conjunct,[],[normalize_5_16]) ).
fof(normalize_5_18,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_5_19,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_5_18]) ).
fof(normalize_5_20,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_5_19]) ).
fof(normalize_5_21,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_5_22,plain,
! [X] :
( ~ cnotA(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) ) ),
inference(specialize,[],[normalize_5_21]) ).
fof(normalize_5_23,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_3(X))
| cnotA(X) )
& ( cnotA(X)
| rq(X,skolemFOFtoCNF_Y_3(X)) )
& ( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_5_22]) ).
fof(normalize_5_24,plain,
! [X,Y] :
( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ),
inference(conjunct,[],[normalize_5_23]) ).
fof(normalize_5_25,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_5_26,plain,
! [X] :
( ~ cA(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) ) ),
inference(specialize,[],[normalize_5_25]) ).
fof(normalize_5_27,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_26]) ).
fof(normalize_5_28,plain,
! [X] :
( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_5_27]) ).
fof(normalize_5_29,plain,
! [X] :
( ~ cnotAorB(X)
| cnotB(X) ),
inference(conjunct,[],[normalize_5_8]) ).
fof(normalize_5_30,plain,
( ? [X] :
( ~ cAorB(X)
& ( cA(X)
| cB(X) ) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_31,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_5_18]) ).
fof(normalize_5_32,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_5_31]) ).
fof(normalize_5_33,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_5_34,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_5_33]) ).
fof(normalize_5_35,plain,
? [X] :
( ~ cAorB(X)
& ( cA(X)
| cB(X) ) ),
inference(simplify,[],[normalize_5_30,normalize_5_32,normalize_5_20,normalize_5_34]) ).
fof(normalize_5_36,plain,
( ~ cAorB(skolemFOFtoCNF_X_3)
& ( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ) ),
inference(skolemize,[],[normalize_5_35]) ).
fof(normalize_5_37,plain,
( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ),
inference(conjunct,[],[normalize_5_36]) ).
fof(normalize_5_38,plain,
! [X] :
( ~ cB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) ) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_5_39,plain,
! [X] :
( ~ cB(X)
<=> ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) ) ),
inference(specialize,[],[normalize_5_38]) ).
fof(normalize_5_40,plain,
! [X,Y] :
( ( ~ cB(X)
| cowlThing(skolemFOFtoCNF_Y_2(X)) )
& ( ~ cB(X)
| rr(X,skolemFOFtoCNF_Y_2(X)) )
& ( ~ cowlThing(Y)
| ~ rr(X,Y)
| cB(X) ) ),
inference(clausify,[],[normalize_5_39]) ).
fof(normalize_5_41,plain,
! [X] :
( ~ cB(X)
| rr(X,skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_5_40]) ).
fof(normalize_5_42,plain,
! [X] :
( ~ cnotB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rr(X,Y) ) ),
inference(canonicalize,[],[axiom_10]) ).
fof(normalize_5_43,plain,
! [X] :
( ~ cnotB(X)
<=> ? [Y] :
( ~ cNothing(Y)
& rr(X,Y) ) ),
inference(specialize,[],[normalize_5_42]) ).
fof(normalize_5_44,plain,
! [X,Y] :
( ( ~ cNothing(skolemFOFtoCNF_Y_5(X))
| cnotB(X) )
& ( cnotB(X)
| rr(X,skolemFOFtoCNF_Y_5(X)) )
& ( ~ cnotB(X)
| ~ rr(X,Y)
| cNothing(Y) ) ),
inference(clausify,[],[normalize_5_43]) ).
fof(normalize_5_45,plain,
! [X,Y] :
( ~ cnotB(X)
| ~ rr(X,Y)
| cNothing(Y) ),
inference(conjunct,[],[normalize_5_44]) ).
fof(normalize_5_46,plain,
~ cAorB(skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_36]) ).
cnf(refute_5_0,plain,
( ~ cNothing(X)
| ~ rp(X,Y) ),
inference(canonicalize,[],[normalize_5_2]) ).
cnf(refute_5_1,plain,
( ~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))
| ~ rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))) ),
inference(subst,[],[refute_5_0:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))))]]) ).
cnf(refute_5_2,plain,
( ~ cNothing(X)
| rp(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_5_5]) ).
cnf(refute_5_3,plain,
( ~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))
| rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))) ),
inference(subst,[],[refute_5_2:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_4,plain,
( ~ cnotAorB(X)
| cnotA(X) ),
inference(canonicalize,[],[normalize_5_9]) ).
cnf(refute_5_5,plain,
( ~ cnotAorB(X_65)
| cnotA(X_65) ),
inference(subst,[],[refute_5_4:[bind(X,$fot(X_65))]]) ).
cnf(refute_5_6,plain,
( cnotAorB(X)
| rs(X,skolemFOFtoCNF_Y_4(X)) ),
inference(canonicalize,[],[normalize_5_13]) ).
cnf(refute_5_7,plain,
( cnotAorB(X_63)
| rs(X_63,skolemFOFtoCNF_Y_4(X_63)) ),
inference(subst,[],[refute_5_6:[bind(X,$fot(X_63))]]) ).
cnf(refute_5_8,plain,
( ~ cowlThing(Y)
| ~ rs(X,Y)
| cAorB(X) ),
inference(canonicalize,[],[normalize_5_17]) ).
cnf(refute_5_9,plain,
cowlThing(X),
inference(canonicalize,[],[normalize_5_20]) ).
cnf(refute_5_10,plain,
cowlThing(Y),
inference(subst,[],[refute_5_9:[bind(X,$fot(Y))]]) ).
cnf(refute_5_11,plain,
( ~ rs(X,Y)
| cAorB(X) ),
inference(resolve,[$cnf( cowlThing(Y) )],[refute_5_10,refute_5_8]) ).
cnf(refute_5_12,plain,
( ~ rs(X_63,skolemFOFtoCNF_Y_4(X_63))
| cAorB(X_63) ),
inference(subst,[],[refute_5_11:[bind(X,$fot(X_63)),bind(Y,$fot(skolemFOFtoCNF_Y_4(X_63)))]]) ).
cnf(refute_5_13,plain,
( cAorB(X_63)
| cnotAorB(X_63) ),
inference(resolve,[$cnf( rs(X_63,skolemFOFtoCNF_Y_4(X_63)) )],[refute_5_7,refute_5_12]) ).
cnf(refute_5_14,plain,
( cAorB(X_65)
| cnotAorB(X_65) ),
inference(subst,[],[refute_5_13:[bind(X_63,$fot(X_65))]]) ).
cnf(refute_5_15,plain,
( cAorB(X_65)
| cnotA(X_65) ),
inference(resolve,[$cnf( cnotAorB(X_65) )],[refute_5_14,refute_5_5]) ).
cnf(refute_5_16,plain,
( cAorB(skolemFOFtoCNF_X_3)
| cnotA(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_15:[bind(X_65,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_17,plain,
( ~ cnotA(X)
| ~ rq(X,Y)
| cNothing(Y) ),
inference(canonicalize,[],[normalize_5_24]) ).
cnf(refute_5_18,plain,
( ~ cnotA(skolemFOFtoCNF_X_3)
| ~ rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))
| cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_17:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_19,plain,
( ~ cA(X)
| rq(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_5_28]) ).
cnf(refute_5_20,plain,
( ~ cA(skolemFOFtoCNF_X_3)
| rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_19:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_21,plain,
( ~ cnotAorB(X)
| cnotB(X) ),
inference(canonicalize,[],[normalize_5_29]) ).
cnf(refute_5_22,plain,
( ~ cnotAorB(X_65)
| cnotB(X_65) ),
inference(subst,[],[refute_5_21:[bind(X,$fot(X_65))]]) ).
cnf(refute_5_23,plain,
( cAorB(X_65)
| cnotB(X_65) ),
inference(resolve,[$cnf( cnotAorB(X_65) )],[refute_5_14,refute_5_22]) ).
cnf(refute_5_24,plain,
( cAorB(skolemFOFtoCNF_X_3)
| cnotB(skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_5_23:[bind(X_65,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_25,plain,
( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ),
inference(canonicalize,[],[normalize_5_37]) ).
cnf(refute_5_26,plain,
( ~ cB(X)
| rr(X,skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_5_41]) ).
cnf(refute_5_27,plain,
( ~ cB(skolemFOFtoCNF_X_3)
| rr(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_26:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_28,plain,
( cA(skolemFOFtoCNF_X_3)
| rr(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_X_3) )],[refute_5_25,refute_5_27]) ).
cnf(refute_5_29,plain,
( ~ cnotB(X)
| ~ rr(X,Y)
| cNothing(Y) ),
inference(canonicalize,[],[normalize_5_45]) ).
cnf(refute_5_30,plain,
( ~ cnotB(skolemFOFtoCNF_X_3)
| ~ rr(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))
| cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(subst,[],[refute_5_29:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_31,plain,
( ~ cnotB(skolemFOFtoCNF_X_3)
| cA(skolemFOFtoCNF_X_3)
| cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) )],[refute_5_28,refute_5_30]) ).
cnf(refute_5_32,plain,
( cA(skolemFOFtoCNF_X_3)
| cAorB(skolemFOFtoCNF_X_3)
| cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( cnotB(skolemFOFtoCNF_X_3) )],[refute_5_24,refute_5_31]) ).
cnf(refute_5_33,plain,
~ cAorB(skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_46]) ).
cnf(refute_5_34,plain,
( cA(skolemFOFtoCNF_X_3)
| cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( cAorB(skolemFOFtoCNF_X_3) )],[refute_5_32,refute_5_33]) ).
cnf(refute_5_35,plain,
( ~ cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))
| ~ rp(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))) ),
inference(subst,[],[refute_5_0:[bind(X,$fot(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))))]]) ).
cnf(refute_5_36,plain,
( ~ cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))
| rp(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))) ),
inference(subst,[],[refute_5_2:[bind(X,$fot(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_5_37,plain,
( cA(skolemFOFtoCNF_X_3)
| rp(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))) ),
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) )],[refute_5_34,refute_5_36]) ).
cnf(refute_5_38,plain,
( ~ cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))
| cA(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3))) )],[refute_5_37,refute_5_35]) ).
cnf(refute_5_39,plain,
cA(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_X_3)) )],[refute_5_34,refute_5_38]) ).
cnf(refute_5_40,plain,
rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_3) )],[refute_5_39,refute_5_20]) ).
cnf(refute_5_41,plain,
( ~ cnotA(skolemFOFtoCNF_X_3)
| cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) )],[refute_5_40,refute_5_18]) ).
cnf(refute_5_42,plain,
( cAorB(skolemFOFtoCNF_X_3)
| cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) ),
inference(resolve,[$cnf( cnotA(skolemFOFtoCNF_X_3) )],[refute_5_16,refute_5_41]) ).
cnf(refute_5_43,plain,
cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)),
inference(resolve,[$cnf( cAorB(skolemFOFtoCNF_X_3) )],[refute_5_42,refute_5_33]) ).
cnf(refute_5_44,plain,
rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))),
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) )],[refute_5_43,refute_5_3]) ).
cnf(refute_5_45,plain,
~ cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3))) )],[refute_5_44,refute_5_1]) ).
cnf(refute_5_46,plain,
$false,
inference(resolve,[$cnf( cNothing(skolemFOFtoCNF_Y(skolemFOFtoCNF_X_3)) )],[refute_5_43,refute_5_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS132+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n017.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jun 7 13:05:47 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------