TSTP Solution File: KRS174+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS174+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 03:19:04 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 186 ( 67 unt; 0 def)
% Number of atoms : 398 ( 109 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 406 ( 194 ~; 98 |; 64 &)
% ( 32 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 132 ( 0 sgn 113 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) ).
fof(axiom_2,axiom,
! [X] :
( cA(X)
<=> X = ia ) ).
fof(axiom_3,axiom,
! [X] :
( cA_and_B(X)
<=> ( X = ib
| X = ia ) ) ).
fof(axiom_4,axiom,
! [X] :
( cB(X)
<=> X = ib ) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cA_and_B(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] :
( ( cA_and_B(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) )
=> cA_and_B(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] :
( ( cA_and_B(X)
& ~ cB(X) )
=> cA(X) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ? [X] :
( ~ cA(X)
& ~ cB(X)
& cA_and_B(X) )
& ! [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] :
( ~ cA(X)
& ~ cB(X)
& cA_and_B(X) ),
inference(simplify,[],[normalize_4_0,normalize_4_3,normalize_4_5,normalize_4_7]) ).
fof(normalize_4_9,plain,
( ~ cA(skolemFOFtoCNF_X_2)
& ~ cB(skolemFOFtoCNF_X_2)
& cA_and_B(skolemFOFtoCNF_X_2) ),
inference(skolemize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_11,plain,
cA_and_B(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_12,plain,
! [X] :
( ~ cA_and_B(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_13,plain,
! [X] :
( ~ cA_and_B(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_4_12]) ).
fof(normalize_4_14,plain,
! [X] :
( ( X != ia
| cA_and_B(X) )
& ( X != ib
| cA_and_B(X) )
& ( ~ cA_and_B(X)
| X = ia
| X = ib ) ),
inference(clausify,[],[normalize_4_13]) ).
fof(normalize_4_15,plain,
! [X] :
( ~ cA_and_B(X)
| X = ia
| X = ib ),
inference(conjunct,[],[normalize_4_14]) ).
fof(normalize_4_16,plain,
! [X] :
( X != ia
<=> ~ cA(X) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_17,plain,
! [X] :
( X != ia
<=> ~ cA(X) ),
inference(specialize,[],[normalize_4_16]) ).
fof(normalize_4_18,plain,
! [X] :
( ( X != ia
| cA(X) )
& ( ~ cA(X)
| X = ia ) ),
inference(clausify,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
! [X] :
( X != ia
| cA(X) ),
inference(conjunct,[],[normalize_4_18]) ).
fof(normalize_4_20,plain,
~ cB(skolemFOFtoCNF_X_2),
inference(conjunct,[],[normalize_4_9]) ).
fof(normalize_4_21,plain,
! [X] :
( X != ib
<=> ~ cB(X) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_4_22,plain,
! [X] :
( X != ib
<=> ~ cB(X) ),
inference(specialize,[],[normalize_4_21]) ).
fof(normalize_4_23,plain,
! [X] :
( ( X != ib
| cB(X) )
& ( ~ cB(X)
| X = ib ) ),
inference(clausify,[],[normalize_4_22]) ).
fof(normalize_4_24,plain,
! [X] :
( X != ib
| cB(X) ),
inference(conjunct,[],[normalize_4_23]) ).
cnf(refute_4_0,plain,
~ cA(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_10]) ).
cnf(refute_4_1,plain,
cA_and_B(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_11]) ).
cnf(refute_4_2,plain,
( ~ cA_and_B(X)
| X = ia
| X = ib ),
inference(canonicalize,[],[normalize_4_15]) ).
cnf(refute_4_3,plain,
( ~ cA_and_B(skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 = ia
| skolemFOFtoCNF_X_2 = ib ),
inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_4_4,plain,
( skolemFOFtoCNF_X_2 = ia
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( cA_and_B(skolemFOFtoCNF_X_2) )],[refute_4_1,refute_4_3]) ).
cnf(refute_4_5,plain,
( skolemFOFtoCNF_X_2 != ia
| ~ cA(ia)
| cA(skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_X_2) ),[0],$fot(ia)]]) ).
cnf(refute_4_6,plain,
( ~ cA(ia)
| skolemFOFtoCNF_X_2 = ib
| cA(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_4,refute_4_5]) ).
cnf(refute_4_7,plain,
( ~ cA(ia)
| skolemFOFtoCNF_X_2 = ib ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_6,refute_4_0]) ).
cnf(refute_4_8,plain,
( X != ia
| cA(X) ),
inference(canonicalize,[],[normalize_4_19]) ).
cnf(refute_4_9,plain,
( ia != ia
| cA(ia) ),
inference(subst,[],[refute_4_8:[bind(X,$fot(ia))]]) ).
cnf(refute_4_10,plain,
ia = ia,
introduced(tautology,[refl,[$fot(ia)]]) ).
cnf(refute_4_11,plain,
cA(ia),
inference(resolve,[$cnf( $equal(ia,ia) )],[refute_4_10,refute_4_9]) ).
cnf(refute_4_12,plain,
skolemFOFtoCNF_X_2 = ib,
inference(resolve,[$cnf( cA(ia) )],[refute_4_11,refute_4_7]) ).
cnf(refute_4_13,plain,
~ cB(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_4_20]) ).
cnf(refute_4_14,plain,
( skolemFOFtoCNF_X_2 != ib
| ~ cB(ib)
| cB(skolemFOFtoCNF_X_2) ),
introduced(tautology,[equality,[$cnf( ~ cB(skolemFOFtoCNF_X_2) ),[0],$fot(ib)]]) ).
cnf(refute_4_15,plain,
( ~ cB(ib)
| skolemFOFtoCNF_X_2 = ia
| cB(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_4,refute_4_14]) ).
cnf(refute_4_16,plain,
( ~ cB(ib)
| skolemFOFtoCNF_X_2 = ia ),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_X_2) )],[refute_4_15,refute_4_13]) ).
cnf(refute_4_17,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_18,plain,
( skolemFOFtoCNF_X_2 != ia
| ib = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_12,refute_4_17]) ).
cnf(refute_4_19,plain,
( ~ cB(ib)
| ib = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_16,refute_4_18]) ).
cnf(refute_4_20,plain,
( X != ib
| cB(X) ),
inference(canonicalize,[],[normalize_4_24]) ).
cnf(refute_4_21,plain,
( ib != ib
| cB(ib) ),
inference(subst,[],[refute_4_20:[bind(X,$fot(ib))]]) ).
cnf(refute_4_22,plain,
ib = ib,
introduced(tautology,[refl,[$fot(ib)]]) ).
cnf(refute_4_23,plain,
cB(ib),
inference(resolve,[$cnf( $equal(ib,ib) )],[refute_4_22,refute_4_21]) ).
cnf(refute_4_24,plain,
ib = ia,
inference(resolve,[$cnf( cB(ib) )],[refute_4_23,refute_4_19]) ).
cnf(refute_4_25,plain,
( ib != ia
| skolemFOFtoCNF_X_2 != ib
| skolemFOFtoCNF_X_2 = ia ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) ),[1],$fot(ia)]]) ).
cnf(refute_4_26,plain,
( skolemFOFtoCNF_X_2 != ib
| skolemFOFtoCNF_X_2 = ia ),
inference(resolve,[$cnf( $equal(ib,ia) )],[refute_4_24,refute_4_25]) ).
cnf(refute_4_27,plain,
skolemFOFtoCNF_X_2 = ia,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ib) )],[refute_4_12,refute_4_26]) ).
cnf(refute_4_28,plain,
( ~ cA(ia)
| cA(skolemFOFtoCNF_X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,ia) )],[refute_4_27,refute_4_5]) ).
cnf(refute_4_29,plain,
~ cA(ia),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_2) )],[refute_4_28,refute_4_0]) ).
cnf(refute_4_30,plain,
$false,
inference(resolve,[$cnf( cA(ia) )],[refute_4_11,refute_4_29]) ).
fof(negate_5_0,plain,
~ ( ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) )
=> ! [X] :
( ( cB(X)
| cA(X) )
=> cA_and_B(X) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
( ? [X] :
( ~ cA_and_B(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_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_and_B(X)
& ( cA(X)
| cB(X) ) ),
inference(simplify,[],[normalize_5_0,normalize_5_3,normalize_5_5,normalize_5_7]) ).
fof(normalize_5_9,plain,
( ~ cA_and_B(skolemFOFtoCNF_X_3)
& ( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ) ),
inference(skolemize,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
~ cA_and_B(skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_5_9]) ).
fof(normalize_5_11,plain,
! [X] :
( X != ia
<=> ~ cA(X) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_5_12,plain,
! [X] :
( X != ia
<=> ~ cA(X) ),
inference(specialize,[],[normalize_5_11]) ).
fof(normalize_5_13,plain,
! [X] :
( ( X != ia
| cA(X) )
& ( ~ cA(X)
| X = ia ) ),
inference(clausify,[],[normalize_5_12]) ).
fof(normalize_5_14,plain,
! [X] :
( ~ cA(X)
| X = ia ),
inference(conjunct,[],[normalize_5_13]) ).
fof(normalize_5_15,plain,
( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ),
inference(conjunct,[],[normalize_5_9]) ).
fof(normalize_5_16,plain,
! [X] :
( X != ib
<=> ~ cB(X) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_5_17,plain,
! [X] :
( X != ib
<=> ~ cB(X) ),
inference(specialize,[],[normalize_5_16]) ).
fof(normalize_5_18,plain,
! [X] :
( ( X != ib
| cB(X) )
& ( ~ cB(X)
| X = ib ) ),
inference(clausify,[],[normalize_5_17]) ).
fof(normalize_5_19,plain,
! [X] :
( ~ cB(X)
| X = ib ),
inference(conjunct,[],[normalize_5_18]) ).
fof(normalize_5_20,plain,
! [X] :
( ~ cA_and_B(X)
<=> ( X != ia
& X != ib ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_5_21,plain,
! [X] :
( ~ cA_and_B(X)
<=> ( X != ia
& X != ib ) ),
inference(specialize,[],[normalize_5_20]) ).
fof(normalize_5_22,plain,
! [X] :
( ( X != ia
| cA_and_B(X) )
& ( X != ib
| cA_and_B(X) )
& ( ~ cA_and_B(X)
| X = ia
| X = ib ) ),
inference(clausify,[],[normalize_5_21]) ).
fof(normalize_5_23,plain,
! [X] :
( X != ia
| cA_and_B(X) ),
inference(conjunct,[],[normalize_5_22]) ).
fof(normalize_5_24,plain,
! [X] :
( X != ib
| cA_and_B(X) ),
inference(conjunct,[],[normalize_5_22]) ).
cnf(refute_5_0,plain,
~ cA_and_B(skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_5_10]) ).
cnf(refute_5_1,plain,
( ~ cA(X)
| X = ia ),
inference(canonicalize,[],[normalize_5_14]) ).
cnf(refute_5_2,plain,
( ~ cA(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_X_3 = ia ),
inference(subst,[],[refute_5_1:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_3,plain,
( cA(skolemFOFtoCNF_X_3)
| cB(skolemFOFtoCNF_X_3) ),
inference(canonicalize,[],[normalize_5_15]) ).
cnf(refute_5_4,plain,
( ~ cB(X)
| X = ib ),
inference(canonicalize,[],[normalize_5_19]) ).
cnf(refute_5_5,plain,
( ~ cB(skolemFOFtoCNF_X_3)
| skolemFOFtoCNF_X_3 = ib ),
inference(subst,[],[refute_5_4:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_5_6,plain,
( skolemFOFtoCNF_X_3 = ib
| cA(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_X_3) )],[refute_5_3,refute_5_5]) ).
cnf(refute_5_7,plain,
( skolemFOFtoCNF_X_3 = ia
| skolemFOFtoCNF_X_3 = ib ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_X_3) )],[refute_5_6,refute_5_2]) ).
cnf(refute_5_8,plain,
( skolemFOFtoCNF_X_3 != ia
| ~ cA_and_B(ia)
| cA_and_B(skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ cA_and_B(skolemFOFtoCNF_X_3) ),[0],$fot(ia)]]) ).
cnf(refute_5_9,plain,
( ~ cA_and_B(ia)
| skolemFOFtoCNF_X_3 = ib
| cA_and_B(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_7,refute_5_8]) ).
cnf(refute_5_10,plain,
( ~ cA_and_B(ia)
| skolemFOFtoCNF_X_3 = ib ),
inference(resolve,[$cnf( cA_and_B(skolemFOFtoCNF_X_3) )],[refute_5_9,refute_5_0]) ).
cnf(refute_5_11,plain,
( X != ia
| cA_and_B(X) ),
inference(canonicalize,[],[normalize_5_23]) ).
cnf(refute_5_12,plain,
( ia != ia
| cA_and_B(ia) ),
inference(subst,[],[refute_5_11:[bind(X,$fot(ia))]]) ).
cnf(refute_5_13,plain,
ia = ia,
introduced(tautology,[refl,[$fot(ia)]]) ).
cnf(refute_5_14,plain,
cA_and_B(ia),
inference(resolve,[$cnf( $equal(ia,ia) )],[refute_5_13,refute_5_12]) ).
cnf(refute_5_15,plain,
skolemFOFtoCNF_X_3 = ib,
inference(resolve,[$cnf( cA_and_B(ia) )],[refute_5_14,refute_5_10]) ).
cnf(refute_5_16,plain,
( skolemFOFtoCNF_X_3 != ib
| ~ cA_and_B(ib)
| cA_and_B(skolemFOFtoCNF_X_3) ),
introduced(tautology,[equality,[$cnf( ~ cA_and_B(skolemFOFtoCNF_X_3) ),[0],$fot(ib)]]) ).
cnf(refute_5_17,plain,
( ~ cA_and_B(ib)
| skolemFOFtoCNF_X_3 = ia
| cA_and_B(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ib) )],[refute_5_7,refute_5_16]) ).
cnf(refute_5_18,plain,
( ~ cA_and_B(ib)
| skolemFOFtoCNF_X_3 = ia ),
inference(resolve,[$cnf( cA_and_B(skolemFOFtoCNF_X_3) )],[refute_5_17,refute_5_0]) ).
cnf(refute_5_19,plain,
( skolemFOFtoCNF_X_3 != ia
| skolemFOFtoCNF_X_3 != ib
| ib = ia ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) ),[0],$fot(ib)]]) ).
cnf(refute_5_20,plain,
( skolemFOFtoCNF_X_3 != ia
| ib = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ib) )],[refute_5_15,refute_5_19]) ).
cnf(refute_5_21,plain,
( ~ cA_and_B(ib)
| ib = ia ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_18,refute_5_20]) ).
cnf(refute_5_22,plain,
( X != ib
| cA_and_B(X) ),
inference(canonicalize,[],[normalize_5_24]) ).
cnf(refute_5_23,plain,
( ib != ib
| cA_and_B(ib) ),
inference(subst,[],[refute_5_22:[bind(X,$fot(ib))]]) ).
cnf(refute_5_24,plain,
ib = ib,
introduced(tautology,[refl,[$fot(ib)]]) ).
cnf(refute_5_25,plain,
cA_and_B(ib),
inference(resolve,[$cnf( $equal(ib,ib) )],[refute_5_24,refute_5_23]) ).
cnf(refute_5_26,plain,
ib = ia,
inference(resolve,[$cnf( cA_and_B(ib) )],[refute_5_25,refute_5_21]) ).
cnf(refute_5_27,plain,
( ib != ia
| skolemFOFtoCNF_X_3 != ib
| skolemFOFtoCNF_X_3 = ia ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_3,ib) ),[1],$fot(ia)]]) ).
cnf(refute_5_28,plain,
( skolemFOFtoCNF_X_3 != ib
| skolemFOFtoCNF_X_3 = ia ),
inference(resolve,[$cnf( $equal(ib,ia) )],[refute_5_26,refute_5_27]) ).
cnf(refute_5_29,plain,
skolemFOFtoCNF_X_3 = ia,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ib) )],[refute_5_15,refute_5_28]) ).
cnf(refute_5_30,plain,
( ~ cA_and_B(ia)
| cA_and_B(skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,ia) )],[refute_5_29,refute_5_8]) ).
cnf(refute_5_31,plain,
~ cA_and_B(ia),
inference(resolve,[$cnf( cA_and_B(skolemFOFtoCNF_X_3) )],[refute_5_30,refute_5_0]) ).
cnf(refute_5_32,plain,
$false,
inference(resolve,[$cnf( cA_and_B(ia) )],[refute_5_14,refute_5_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS174+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n023.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 12:58:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------