TSTP Solution File: KRS162+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS162+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 03:19:01 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 16
% Syntax : Number of formulae : 191 ( 72 unt; 0 def)
% Number of atoms : 681 ( 307 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 755 ( 265 ~; 319 |; 141 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 226 ( 2 sgn 120 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) ).
fof(axiom_2,axiom,
! [X,Y] :
( rp(X,Y)
=> cA(Y) ) ).
fof(axiom_3,axiom,
! [X,Y] :
( rq(X,Y)
=> cB(Y) ) ).
fof(axiom_4,axiom,
! [X] :
~ ( cB(X)
& cA(X) ) ).
fof(axiom_5,axiom,
! [X,Y] :
( rq(X,Y)
=> rr(X,Y) ) ).
fof(axiom_6,axiom,
! [X,Y] :
( rp(X,Y)
=> rr(X,Y) ) ).
fof(the_axiom,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ( ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 )
& ? [Y0,Y1,Y2] :
( rq(X,Y0)
& rq(X,Y1)
& rq(X,Y2)
& Y0 != Y1
& Y0 != Y2
& Y1 != Y2 ) )
=> ? [Y0,Y1,Y2,Y3,Y4] :
( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3)
& rr(X,Y4)
& Y0 != Y1
& Y0 != Y2
& Y0 != Y3
& Y0 != Y4
& Y1 != Y2
& Y1 != Y3
& Y1 != Y4
& Y2 != Y3
& Y2 != Y4
& Y3 != Y4 ) ) ) ).
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] :
( ( ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 )
& ? [Y0,Y1,Y2] :
( rq(X,Y0)
& rq(X,Y1)
& rq(X,Y2)
& Y0 != Y1
& Y0 != Y2
& Y1 != Y2 ) )
=> ? [Y0,Y1,Y2,Y3,Y4] :
( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3)
& rr(X,Y4)
& Y0 != Y1
& Y0 != Y2
& Y0 != Y3
& Y0 != Y4
& Y1 != Y2
& Y1 != Y3
& Y1 != Y4
& Y2 != Y3
& Y2 != Y4
& Y3 != Y4 ) ) ),
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] :
( ( ? [Y0,Y1] :
( rp(X,Y0)
& rp(X,Y1)
& Y0 != Y1 )
& ? [Y0,Y1,Y2] :
( rq(X,Y0)
& rq(X,Y1)
& rq(X,Y2)
& Y0 != Y1
& Y0 != Y2
& Y1 != Y2 ) )
=> ? [Y0,Y1,Y2,Y3,Y4] :
( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3)
& rr(X,Y4)
& Y0 != Y1
& Y0 != Y2
& Y0 != Y3
& Y0 != Y4
& Y1 != Y2
& Y1 != Y3
& Y1 != Y4
& Y2 != Y3
& Y2 != Y4
& Y3 != Y4 ) ) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
! [X] :
( ~ cA(X)
| ~ cB(X) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_4_1,plain,
! [X] :
( ~ cA(X)
| ~ cB(X) ),
inference(specialize,[],[normalize_4_0]) ).
fof(normalize_4_2,plain,
( ? [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rq(X,Y0)
& rq(X,Y1)
& rq(X,Y2) )
& ! [Y0,Y1,Y2,Y3,Y4] :
( ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3)
| ~ rr(X,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ) )
& ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X)
& ! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_3,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_4_4,plain,
! [X] : ~ cowlNothing(X),
inference(conjunct,[],[normalize_4_3]) ).
fof(normalize_4_5,plain,
! [X] : ~ cowlNothing(X),
inference(specialize,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_4_3]) ).
fof(normalize_4_7,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_4_6]) ).
fof(normalize_4_8,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_4_9,plain,
! [X] :
( ~ xsd_integer(X)
<=> xsd_string(X) ),
inference(specialize,[],[normalize_4_8]) ).
fof(normalize_4_10,plain,
? [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y0)
& rp(X,Y1) )
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rq(X,Y0)
& rq(X,Y1)
& rq(X,Y2) )
& ! [Y0,Y1,Y2,Y3,Y4] :
( ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3)
| ~ rr(X,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ) ),
inference(simplify,[],[normalize_4_2,normalize_4_5,normalize_4_7,normalize_4_9]) ).
fof(normalize_4_11,plain,
( ? [Y0,Y1] :
( Y0 != Y1
& rp(skolemFOFtoCNF_X_2,Y0)
& rp(skolemFOFtoCNF_X_2,Y1) )
& ? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rq(skolemFOFtoCNF_X_2,Y0)
& rq(skolemFOFtoCNF_X_2,Y1)
& rq(skolemFOFtoCNF_X_2,Y2) )
& ! [Y0,Y1,Y2,Y3,Y4] :
( ~ rr(skolemFOFtoCNF_X_2,Y0)
| ~ rr(skolemFOFtoCNF_X_2,Y1)
| ~ rr(skolemFOFtoCNF_X_2,Y2)
| ~ rr(skolemFOFtoCNF_X_2,Y3)
| ~ rr(skolemFOFtoCNF_X_2,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ) ),
inference(skolemize,[],[normalize_4_10]) ).
fof(normalize_4_12,plain,
? [Y0,Y1,Y2] :
( Y0 != Y1
& Y0 != Y2
& Y1 != Y2
& rq(skolemFOFtoCNF_X_2,Y0)
& rq(skolemFOFtoCNF_X_2,Y1)
& rq(skolemFOFtoCNF_X_2,Y2) ),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_13,plain,
( skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1
& skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2
& skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2
& rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
& rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
& rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) ),
inference(skolemize,[],[normalize_4_12]) ).
fof(normalize_4_14,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1),
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_15,plain,
! [X,Y] :
( ~ rq(X,Y)
| cB(Y) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_4_16,plain,
! [X,Y] :
( ~ rq(X,Y)
| cB(Y) ),
inference(specialize,[],[normalize_4_15]) ).
fof(normalize_4_17,plain,
? [Y0,Y1] :
( Y0 != Y1
& rp(skolemFOFtoCNF_X_2,Y0)
& rp(skolemFOFtoCNF_X_2,Y1) ),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_18,plain,
( skolemFOFtoCNF_Y0 != skolemFOFtoCNF_Y1
& rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0)
& rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1) ),
inference(skolemize,[],[normalize_4_17]) ).
fof(normalize_4_19,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1),
inference(conjunct,[],[normalize_4_18]) ).
fof(normalize_4_20,plain,
! [X,Y] :
( ~ rp(X,Y)
| cA(Y) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_4_21,plain,
! [X,Y] :
( ~ rp(X,Y)
| cA(Y) ),
inference(specialize,[],[normalize_4_20]) ).
fof(normalize_4_22,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_23,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2),
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_24,plain,
! [X,Y] :
( ~ rp(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_4_25,plain,
! [X,Y] :
( ~ rp(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_4_24]) ).
fof(normalize_4_26,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0),
inference(conjunct,[],[normalize_4_18]) ).
fof(normalize_4_27,plain,
! [X,Y] :
( ~ rq(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_4_28,plain,
! [X,Y] :
( ~ rq(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_4_27]) ).
fof(normalize_4_29,plain,
! [Y0,Y1,Y2,Y3,Y4] :
( ~ rr(skolemFOFtoCNF_X_2,Y0)
| ~ rr(skolemFOFtoCNF_X_2,Y1)
| ~ rr(skolemFOFtoCNF_X_2,Y2)
| ~ rr(skolemFOFtoCNF_X_2,Y3)
| ~ rr(skolemFOFtoCNF_X_2,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ),
inference(conjunct,[],[normalize_4_11]) ).
fof(normalize_4_30,plain,
! [Y0,Y1,Y2,Y3,Y4] :
( ~ rr(skolemFOFtoCNF_X_2,Y0)
| ~ rr(skolemFOFtoCNF_X_2,Y1)
| ~ rr(skolemFOFtoCNF_X_2,Y2)
| ~ rr(skolemFOFtoCNF_X_2,Y3)
| ~ rr(skolemFOFtoCNF_X_2,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ),
inference(specialize,[],[normalize_4_29]) ).
fof(normalize_4_31,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1,
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_32,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2,
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_33,plain,
skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2,
inference(conjunct,[],[normalize_4_13]) ).
fof(normalize_4_34,plain,
skolemFOFtoCNF_Y0 != skolemFOFtoCNF_Y1,
inference(conjunct,[],[normalize_4_18]) ).
cnf(refute_4_0,plain,
( ~ cA(X)
| ~ cB(X) ),
inference(canonicalize,[],[normalize_4_1]) ).
cnf(refute_4_1,plain,
( ~ cA(skolemFOFtoCNF_Y0_1)
| ~ cB(skolemFOFtoCNF_Y0_1) ),
inference(subst,[],[refute_4_0:[bind(X,$fot(skolemFOFtoCNF_Y0_1))]]) ).
cnf(refute_4_2,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1),
inference(canonicalize,[],[normalize_4_14]) ).
cnf(refute_4_3,plain,
( ~ rq(X,Y)
| cB(Y) ),
inference(canonicalize,[],[normalize_4_16]) ).
cnf(refute_4_4,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
| cB(skolemFOFtoCNF_Y0_1) ),
inference(subst,[],[refute_4_3:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y0_1))]]) ).
cnf(refute_4_5,plain,
cB(skolemFOFtoCNF_Y0_1),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1) )],[refute_4_2,refute_4_4]) ).
cnf(refute_4_6,plain,
~ cA(skolemFOFtoCNF_Y0_1),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_Y0_1) )],[refute_4_5,refute_4_1]) ).
cnf(refute_4_7,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1),
inference(canonicalize,[],[normalize_4_19]) ).
cnf(refute_4_8,plain,
( ~ rp(X,Y)
| cA(Y) ),
inference(canonicalize,[],[normalize_4_21]) ).
cnf(refute_4_9,plain,
( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1)
| cA(skolemFOFtoCNF_Y1) ),
inference(subst,[],[refute_4_8:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_4_10,plain,
cA(skolemFOFtoCNF_Y1),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1) )],[refute_4_7,refute_4_9]) ).
cnf(refute_4_11,plain,
( ~ cA(skolemFOFtoCNF_Y1_1)
| ~ cB(skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_4_0:[bind(X,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_4_12,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_4_22]) ).
cnf(refute_4_13,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
| cB(skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_4_3:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_4_14,plain,
cB(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1) )],[refute_4_12,refute_4_13]) ).
cnf(refute_4_15,plain,
~ cA(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_Y1_1) )],[refute_4_14,refute_4_11]) ).
cnf(refute_4_16,plain,
( ~ cA(skolemFOFtoCNF_Y2)
| ~ cB(skolemFOFtoCNF_Y2) ),
inference(subst,[],[refute_4_0:[bind(X,$fot(skolemFOFtoCNF_Y2))]]) ).
cnf(refute_4_17,plain,
rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2),
inference(canonicalize,[],[normalize_4_23]) ).
cnf(refute_4_18,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2)
| cB(skolemFOFtoCNF_Y2) ),
inference(subst,[],[refute_4_3:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y2))]]) ).
cnf(refute_4_19,plain,
cB(skolemFOFtoCNF_Y2),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) )],[refute_4_17,refute_4_18]) ).
cnf(refute_4_20,plain,
~ cA(skolemFOFtoCNF_Y2),
inference(resolve,[$cnf( cB(skolemFOFtoCNF_Y2) )],[refute_4_19,refute_4_16]) ).
cnf(refute_4_21,plain,
( ~ rp(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_4_25]) ).
cnf(refute_4_22,plain,
( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1)
| rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1) ),
inference(subst,[],[refute_4_21:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_4_23,plain,
rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1) )],[refute_4_7,refute_4_22]) ).
cnf(refute_4_24,plain,
rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0),
inference(canonicalize,[],[normalize_4_26]) ).
cnf(refute_4_25,plain,
( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0)
| rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0) ),
inference(subst,[],[refute_4_21:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y0))]]) ).
cnf(refute_4_26,plain,
rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0) )],[refute_4_24,refute_4_25]) ).
cnf(refute_4_27,plain,
( ~ rq(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_4_28]) ).
cnf(refute_4_28,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2)
| rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) ),
inference(subst,[],[refute_4_27:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y2))]]) ).
cnf(refute_4_29,plain,
rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) )],[refute_4_17,refute_4_28]) ).
cnf(refute_4_30,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
| rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_4_27:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_4_31,plain,
rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1) )],[refute_4_12,refute_4_30]) ).
cnf(refute_4_32,plain,
( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
| rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1) ),
inference(subst,[],[refute_4_27:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y0_1))]]) ).
cnf(refute_4_33,plain,
rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1),
inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1) )],[refute_4_2,refute_4_32]) ).
cnf(refute_4_34,plain,
( ~ rr(skolemFOFtoCNF_X_2,Y0)
| ~ rr(skolemFOFtoCNF_X_2,Y1)
| ~ rr(skolemFOFtoCNF_X_2,Y2)
| ~ rr(skolemFOFtoCNF_X_2,Y3)
| ~ rr(skolemFOFtoCNF_X_2,Y4)
| Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y2 = Y3
| Y2 = Y4
| Y3 = Y4 ),
inference(canonicalize,[],[normalize_4_30]) ).
cnf(refute_4_35,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_22)
| ~ rr(skolemFOFtoCNF_X_2,X_23)
| ~ rr(skolemFOFtoCNF_X_2,X_24)
| ~ rr(skolemFOFtoCNF_X_2,X_25)
| ~ rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1)
| X_22 = X_23
| X_22 = X_24
| X_22 = X_25
| X_23 = X_24
| X_23 = X_25
| X_24 = X_25
| skolemFOFtoCNF_Y0_1 = X_22
| skolemFOFtoCNF_Y0_1 = X_23
| skolemFOFtoCNF_Y0_1 = X_24
| skolemFOFtoCNF_Y0_1 = X_25 ),
inference(subst,[],[refute_4_34:[bind(Y0,$fot(skolemFOFtoCNF_Y0_1)),bind(Y1,$fot(X_22)),bind(Y2,$fot(X_23)),bind(Y3,$fot(X_24)),bind(Y4,$fot(X_25))]]) ).
cnf(refute_4_36,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_22)
| ~ rr(skolemFOFtoCNF_X_2,X_23)
| ~ rr(skolemFOFtoCNF_X_2,X_24)
| ~ rr(skolemFOFtoCNF_X_2,X_25)
| X_22 = X_23
| X_22 = X_24
| X_22 = X_25
| X_23 = X_24
| X_23 = X_25
| X_24 = X_25
| skolemFOFtoCNF_Y0_1 = X_22
| skolemFOFtoCNF_Y0_1 = X_23
| skolemFOFtoCNF_Y0_1 = X_24
| skolemFOFtoCNF_Y0_1 = X_25 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0_1) )],[refute_4_33,refute_4_35]) ).
cnf(refute_4_37,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_27)
| ~ rr(skolemFOFtoCNF_X_2,X_28)
| ~ rr(skolemFOFtoCNF_X_2,X_29)
| ~ rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1)
| X_27 = X_28
| X_27 = X_29
| X_28 = X_29
| skolemFOFtoCNF_Y0_1 = X_27
| skolemFOFtoCNF_Y0_1 = X_28
| skolemFOFtoCNF_Y0_1 = X_29
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y1_1 = X_27
| skolemFOFtoCNF_Y1_1 = X_28
| skolemFOFtoCNF_Y1_1 = X_29 ),
inference(subst,[],[refute_4_36:[bind(X_22,$fot(skolemFOFtoCNF_Y1_1)),bind(X_23,$fot(X_27)),bind(X_24,$fot(X_28)),bind(X_25,$fot(X_29))]]) ).
cnf(refute_4_38,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_27)
| ~ rr(skolemFOFtoCNF_X_2,X_28)
| ~ rr(skolemFOFtoCNF_X_2,X_29)
| X_27 = X_28
| X_27 = X_29
| X_28 = X_29
| skolemFOFtoCNF_Y0_1 = X_27
| skolemFOFtoCNF_Y0_1 = X_28
| skolemFOFtoCNF_Y0_1 = X_29
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y1_1 = X_27
| skolemFOFtoCNF_Y1_1 = X_28
| skolemFOFtoCNF_Y1_1 = X_29 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1_1) )],[refute_4_31,refute_4_37]) ).
cnf(refute_4_39,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1_1,
inference(canonicalize,[],[normalize_4_31]) ).
cnf(refute_4_40,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_27)
| ~ rr(skolemFOFtoCNF_X_2,X_28)
| ~ rr(skolemFOFtoCNF_X_2,X_29)
| X_27 = X_28
| X_27 = X_29
| X_28 = X_29
| skolemFOFtoCNF_Y0_1 = X_27
| skolemFOFtoCNF_Y0_1 = X_28
| skolemFOFtoCNF_Y0_1 = X_29
| skolemFOFtoCNF_Y1_1 = X_27
| skolemFOFtoCNF_Y1_1 = X_28
| skolemFOFtoCNF_Y1_1 = X_29 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y1_1) )],[refute_4_38,refute_4_39]) ).
cnf(refute_4_41,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_31)
| ~ rr(skolemFOFtoCNF_X_2,X_32)
| ~ rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2)
| X_31 = X_32
| skolemFOFtoCNF_Y0_1 = X_31
| skolemFOFtoCNF_Y0_1 = X_32
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y1_1 = X_31
| skolemFOFtoCNF_Y1_1 = X_32
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y2 = X_31
| skolemFOFtoCNF_Y2 = X_32 ),
inference(subst,[],[refute_4_40:[bind(X_27,$fot(skolemFOFtoCNF_Y2)),bind(X_28,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).
cnf(refute_4_42,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_31)
| ~ rr(skolemFOFtoCNF_X_2,X_32)
| X_31 = X_32
| skolemFOFtoCNF_Y0_1 = X_31
| skolemFOFtoCNF_Y0_1 = X_32
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y1_1 = X_31
| skolemFOFtoCNF_Y1_1 = X_32
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y2 = X_31
| skolemFOFtoCNF_Y2 = X_32 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y2) )],[refute_4_29,refute_4_41]) ).
cnf(refute_4_43,plain,
skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y2,
inference(canonicalize,[],[normalize_4_32]) ).
cnf(refute_4_44,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_31)
| ~ rr(skolemFOFtoCNF_X_2,X_32)
| X_31 = X_32
| skolemFOFtoCNF_Y0_1 = X_31
| skolemFOFtoCNF_Y0_1 = X_32
| skolemFOFtoCNF_Y1_1 = X_31
| skolemFOFtoCNF_Y1_1 = X_32
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y2
| skolemFOFtoCNF_Y2 = X_31
| skolemFOFtoCNF_Y2 = X_32 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y2) )],[refute_4_42,refute_4_43]) ).
cnf(refute_4_45,plain,
skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y2,
inference(canonicalize,[],[normalize_4_33]) ).
cnf(refute_4_46,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_31)
| ~ rr(skolemFOFtoCNF_X_2,X_32)
| X_31 = X_32
| skolemFOFtoCNF_Y0_1 = X_31
| skolemFOFtoCNF_Y0_1 = X_32
| skolemFOFtoCNF_Y1_1 = X_31
| skolemFOFtoCNF_Y1_1 = X_32
| skolemFOFtoCNF_Y2 = X_31
| skolemFOFtoCNF_Y2 = X_32 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2) )],[refute_4_44,refute_4_45]) ).
cnf(refute_4_47,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_34)
| ~ rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0)
| skolemFOFtoCNF_Y0 = X_34
| skolemFOFtoCNF_Y0_1 = X_34
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = X_34
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y2 = X_34
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y0 ),
inference(subst,[],[refute_4_46:[bind(X_31,$fot(skolemFOFtoCNF_Y0)),bind(X_32,$fot(X_34))]]) ).
cnf(refute_4_48,plain,
( ~ rr(skolemFOFtoCNF_X_2,X_34)
| skolemFOFtoCNF_Y0 = X_34
| skolemFOFtoCNF_Y0_1 = X_34
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = X_34
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y2 = X_34
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y0 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0) )],[refute_4_26,refute_4_47]) ).
cnf(refute_4_49,plain,
( ~ rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1 ),
inference(subst,[],[refute_4_48:[bind(X_34,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_4_50,plain,
( skolemFOFtoCNF_Y0 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y1) )],[refute_4_23,refute_4_49]) ).
cnf(refute_4_51,plain,
skolemFOFtoCNF_Y0 != skolemFOFtoCNF_Y1,
inference(canonicalize,[],[normalize_4_34]) ).
cnf(refute_4_52,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0,skolemFOFtoCNF_Y1) )],[refute_4_50,refute_4_51]) ).
cnf(refute_4_53,plain,
( skolemFOFtoCNF_Y2 != skolemFOFtoCNF_Y0
| ~ cA(skolemFOFtoCNF_Y0)
| cA(skolemFOFtoCNF_Y2) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_Y2) ),[0],$fot(skolemFOFtoCNF_Y0)]]) ).
cnf(refute_4_54,plain,
( ~ cA(skolemFOFtoCNF_Y0)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1
| cA(skolemFOFtoCNF_Y2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2,skolemFOFtoCNF_Y0) )],[refute_4_52,refute_4_53]) ).
cnf(refute_4_55,plain,
( ~ cA(skolemFOFtoCNF_Y0)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y2) )],[refute_4_54,refute_4_20]) ).
cnf(refute_4_56,plain,
( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0)
| cA(skolemFOFtoCNF_Y0) ),
inference(subst,[],[refute_4_8:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y0))]]) ).
cnf(refute_4_57,plain,
cA(skolemFOFtoCNF_Y0),
inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y0) )],[refute_4_24,refute_4_56]) ).
cnf(refute_4_58,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y2 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y0) )],[refute_4_57,refute_4_55]) ).
cnf(refute_4_59,plain,
( skolemFOFtoCNF_Y2 != skolemFOFtoCNF_Y1
| ~ cA(skolemFOFtoCNF_Y1)
| cA(skolemFOFtoCNF_Y2) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_Y2) ),[0],$fot(skolemFOFtoCNF_Y1)]]) ).
cnf(refute_4_60,plain,
( ~ cA(skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1
| cA(skolemFOFtoCNF_Y2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2,skolemFOFtoCNF_Y1) )],[refute_4_58,refute_4_59]) ).
cnf(refute_4_61,plain,
( ~ cA(skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y2) )],[refute_4_60,refute_4_20]) ).
cnf(refute_4_62,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y1) )],[refute_4_10,refute_4_61]) ).
cnf(refute_4_63,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y1
| ~ cA(skolemFOFtoCNF_Y1)
| cA(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y1)]]) ).
cnf(refute_4_64,plain,
( ~ cA(skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0
| cA(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1) )],[refute_4_62,refute_4_63]) ).
cnf(refute_4_65,plain,
( ~ cA(skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y1_1) )],[refute_4_64,refute_4_15]) ).
cnf(refute_4_66,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y0 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y1) )],[refute_4_10,refute_4_65]) ).
cnf(refute_4_67,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y0
| ~ cA(skolemFOFtoCNF_Y0)
| cA(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y0)]]) ).
cnf(refute_4_68,plain,
( ~ cA(skolemFOFtoCNF_Y0)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1
| cA(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y0) )],[refute_4_66,refute_4_67]) ).
cnf(refute_4_69,plain,
( ~ cA(skolemFOFtoCNF_Y0)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y1_1) )],[refute_4_68,refute_4_15]) ).
cnf(refute_4_70,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y1 ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y0) )],[refute_4_57,refute_4_69]) ).
cnf(refute_4_71,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_4_72,plain,
( X0 != X0
| X0 != Y5
| Y5 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y5)]]) ).
cnf(refute_4_73,plain,
( X0 != Y5
| Y5 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_4_71,refute_4_72]) ).
cnf(refute_4_74,plain,
( skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y1
| skolemFOFtoCNF_Y1 = skolemFOFtoCNF_Y0_1 ),
inference(subst,[],[refute_4_73:[bind(X0,$fot(skolemFOFtoCNF_Y0_1)),bind(Y5,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_4_75,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| skolemFOFtoCNF_Y1 = skolemFOFtoCNF_Y0_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y1) )],[refute_4_70,refute_4_74]) ).
cnf(refute_4_76,plain,
( skolemFOFtoCNF_Y1 != skolemFOFtoCNF_Y0_1
| ~ cA(skolemFOFtoCNF_Y1)
| cA(skolemFOFtoCNF_Y0_1) ),
introduced(tautology,[equality,[$cnf( cA(skolemFOFtoCNF_Y1) ),[0],$fot(skolemFOFtoCNF_Y0_1)]]) ).
cnf(refute_4_77,plain,
( ~ cA(skolemFOFtoCNF_Y1)
| skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| cA(skolemFOFtoCNF_Y0_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1,skolemFOFtoCNF_Y0_1) )],[refute_4_75,refute_4_76]) ).
cnf(refute_4_78,plain,
( skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0
| cA(skolemFOFtoCNF_Y0_1) ),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y1) )],[refute_4_10,refute_4_77]) ).
cnf(refute_4_79,plain,
skolemFOFtoCNF_Y0_1 = skolemFOFtoCNF_Y0,
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y0_1) )],[refute_4_78,refute_4_6]) ).
cnf(refute_4_80,plain,
( skolemFOFtoCNF_Y0_1 != skolemFOFtoCNF_Y0
| ~ cA(skolemFOFtoCNF_Y0)
| cA(skolemFOFtoCNF_Y0_1) ),
introduced(tautology,[equality,[$cnf( ~ cA(skolemFOFtoCNF_Y0_1) ),[0],$fot(skolemFOFtoCNF_Y0)]]) ).
cnf(refute_4_81,plain,
( ~ cA(skolemFOFtoCNF_Y0)
| cA(skolemFOFtoCNF_Y0_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1,skolemFOFtoCNF_Y0) )],[refute_4_79,refute_4_80]) ).
cnf(refute_4_82,plain,
~ cA(skolemFOFtoCNF_Y0),
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y0_1) )],[refute_4_81,refute_4_6]) ).
cnf(refute_4_83,plain,
$false,
inference(resolve,[$cnf( cA(skolemFOFtoCNF_Y0) )],[refute_4_57,refute_4_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 7 20:09:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------