TSTP Solution File: SET600+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Tue Jul 19 03:35:48 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 29
% Syntax : Number of formulae : 238 ( 82 unt; 0 def)
% Number of atoms : 502 ( 187 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 489 ( 225 ~; 183 |; 45 &)
% ( 29 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 297 ( 36 sgn 137 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
fof(prove_th59,conjecture,
! [B,C] :
( union(B,C) = empty_set
<=> ( B = empty_set
& C = empty_set ) ) ).
fof(subgoal_0,plain,
! [B,C] :
( union(B,C) = empty_set
=> B = empty_set ),
inference(strip,[],[prove_th59]) ).
fof(subgoal_1,plain,
! [B,C] :
( ( union(B,C) = empty_set
& B = empty_set )
=> C = empty_set ),
inference(strip,[],[prove_th59]) ).
fof(subgoal_2,plain,
! [B,C] :
( ( B = empty_set
& C = empty_set )
=> union(B,C) = empty_set ),
inference(strip,[],[prove_th59]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( union(B,C) = empty_set
=> B = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
? [B] :
( B != empty_set
& ? [C] : union(B,C) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_14,plain,
( skolemFOFtoCNF_B != empty_set
& ? [C] : union(skolemFOFtoCNF_B,C) = empty_set ),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
? [C] : union(skolemFOFtoCNF_B,C) = empty_set,
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_18,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_20,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_22,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
skolemFOFtoCNF_B != empty_set,
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ empty(X_9)
| ~ member(skolemFOFtoCNF_D(X_9,X_10),X_9) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(X_9)),bind(C,$fot(skolemFOFtoCNF_D(X_9,X_10)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(X_9,X_10),X_9)
| subset(X_9,X_10) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_4,plain,
( ~ empty(X_9)
| subset(X_9,X_10) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_9,X_10),X_9) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
( ~ empty(skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,X_10) ),
inference(subst,[],[refute_0_4:[bind(X_9,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( empty(X_14)
| member(skolemFOFtoCNF_C(X_14),X_14) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_C(X_14),X_14)
| member(skolemFOFtoCNF_C(X_14),union(X_14,X_15)) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(X_14)),bind(C,$fot(X_15)),bind(D,$fot(skolemFOFtoCNF_C(X_14)))]]) ).
cnf(refute_0_10,plain,
( empty(X_14)
| member(skolemFOFtoCNF_C(X_14),union(X_14,X_15)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_14),X_14) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( empty(skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_10:[bind(X_14,$fot(skolemFOFtoCNF_B)),bind(X_15,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_12,plain,
union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),empty_set) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_14,plain,
( ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),empty_set) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( empty(skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),empty_set) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),empty_set),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_18,plain,
empty(skolemFOFtoCNF_B),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),empty_set) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
subset(skolemFOFtoCNF_B,X_10),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B) )],[refute_0_18,refute_0_5]) ).
cnf(refute_0_20,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_19:[bind(X_10,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_21,plain,
( ~ empty(skolemFOFtoCNF_C_1)
| subset(skolemFOFtoCNF_C_1,X_10) ),
inference(subst,[],[refute_0_4:[bind(X_9,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_22,plain,
( ~ empty(union(X_17,X_18))
| ~ member(skolemFOFtoCNF_C(X_17),union(X_17,X_18)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(union(X_17,X_18))),bind(C,$fot(skolemFOFtoCNF_C(X_17)))]]) ).
cnf(refute_0_23,plain,
( empty(X_17)
| member(skolemFOFtoCNF_C(X_17),union(X_17,X_18)) ),
inference(subst,[],[refute_0_10:[bind(X_14,$fot(X_17)),bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_24,plain,
( ~ empty(union(X_17,X_18))
| empty(X_17) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_17),union(X_17,X_18)) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( ~ empty(union(X_20,X_21))
| empty(X_20) ),
inference(subst,[],[refute_0_24:[bind(X_17,$fot(X_20)),bind(X_18,$fot(X_21))]]) ).
cnf(refute_0_26,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_27,plain,
union(X_21,X_20) = union(X_20,X_21),
inference(subst,[],[refute_0_26:[bind(B,$fot(X_21)),bind(C,$fot(X_20))]]) ).
cnf(refute_0_28,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_29,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_30,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( union(X_21,X_20) != union(X_20,X_21)
| union(X_20,X_21) = union(X_21,X_20) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(union(X_21,X_20))),bind(Y,$fot(union(X_20,X_21)))]]) ).
cnf(refute_0_32,plain,
union(X_20,X_21) = union(X_21,X_20),
inference(resolve,[$cnf( $equal(union(X_21,X_20),union(X_20,X_21)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( union(X_20,X_21) != union(X_21,X_20)
| ~ empty(union(X_21,X_20))
| empty(union(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( ~ empty(union(X_20,X_21)) ),[0],$fot(union(X_21,X_20))]]) ).
cnf(refute_0_34,plain,
( ~ empty(union(X_21,X_20))
| empty(union(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(union(X_20,X_21),union(X_21,X_20)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ empty(union(X_21,X_20))
| empty(X_20) ),
inference(resolve,[$cnf( empty(union(X_20,X_21)) )],[refute_0_34,refute_0_25]) ).
cnf(refute_0_36,plain,
( ~ empty(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| empty(skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_35:[bind(X_20,$fot(skolemFOFtoCNF_C_1)),bind(X_21,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_37,plain,
( union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| ~ empty(empty_set)
| empty(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
introduced(tautology,[equality,[$cnf( ~ empty(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_38,plain,
( ~ empty(empty_set)
| empty(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_12,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ empty(empty_set)
| empty(skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( empty(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_38,refute_0_36]) ).
cnf(refute_0_40,plain,
~ member(skolemFOFtoCNF_C(empty_set),empty_set),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_C(empty_set)))]]) ).
cnf(refute_0_41,plain,
( empty(empty_set)
| member(skolemFOFtoCNF_C(empty_set),empty_set) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_42,plain,
empty(empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(empty_set),empty_set) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
empty(skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_42,refute_0_39]) ).
cnf(refute_0_44,plain,
subset(skolemFOFtoCNF_C_1,X_10),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_C_1) )],[refute_0_43,refute_0_21]) ).
cnf(refute_0_45,plain,
subset(skolemFOFtoCNF_C_1,X_31),
inference(subst,[],[refute_0_44:[bind(X_10,$fot(X_31))]]) ).
cnf(refute_0_46,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_47,plain,
( ~ subset(X_31,skolemFOFtoCNF_C_1)
| ~ subset(skolemFOFtoCNF_C_1,X_31)
| skolemFOFtoCNF_C_1 = X_31 ),
inference(subst,[],[refute_0_46:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_48,plain,
( ~ subset(X_31,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_C_1 = X_31 ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1,X_31) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_48:[bind(X_31,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_50,plain,
skolemFOFtoCNF_C_1 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_20,refute_0_49]) ).
cnf(refute_0_51,plain,
~ member(skolemFOFtoCNF_D(empty_set,X_10),empty_set),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,X_10)))]]) ).
cnf(refute_0_52,plain,
( member(skolemFOFtoCNF_D(empty_set,X_10),empty_set)
| subset(empty_set,X_10) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(empty_set)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_53,plain,
subset(empty_set,X_10),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,X_10),empty_set) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
subset(empty_set,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_53:[bind(X_10,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_55,plain,
( ~ subset(empty_set,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_C_1 = empty_set ),
inference(subst,[],[refute_0_48:[bind(X_31,$fot(empty_set))]]) ).
cnf(refute_0_56,plain,
skolemFOFtoCNF_C_1 = empty_set,
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_C_1) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( skolemFOFtoCNF_C_1 != empty_set
| skolemFOFtoCNF_C_1 != skolemFOFtoCNF_B
| empty_set = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_C_1 != skolemFOFtoCNF_B
| empty_set = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,empty_set) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
empty_set = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) )],[refute_0_50,refute_0_58]) ).
cnf(refute_0_60,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_61,plain,
( empty_set != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_30:[bind(X,$fot(empty_set)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_62,plain,
empty_set != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B) )],[refute_0_59,refute_0_62]) ).
fof(negate_1_0,plain,
~ ! [B,C] :
( ( union(B,C) = empty_set
& B = empty_set )
=> C = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_1_1,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_1_3,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_1_7,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_11,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_1_12,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_1_16,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
? [B,C] :
( C != empty_set
& B = empty_set
& union(B,C) = empty_set ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_18,plain,
( skolemFOFtoCNF_C_2 != empty_set
& skolemFOFtoCNF_B_1 = empty_set
& union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set ),
inference(skolemize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set,
inference(conjunct,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
skolemFOFtoCNF_B_1 = empty_set,
inference(conjunct,[],[normalize_1_18]) ).
fof(normalize_1_21,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_1_22,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
skolemFOFtoCNF_C_2 != empty_set,
inference(conjunct,[],[normalize_1_18]) ).
cnf(refute_1_0,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ member(skolemFOFtoCNF_D(empty_set,X_43),empty_set),
inference(subst,[],[refute_1_0:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,X_43)))]]) ).
cnf(refute_1_2,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_3,plain,
( member(skolemFOFtoCNF_D(empty_set,X_43),empty_set)
| subset(empty_set,X_43) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(empty_set)),bind(C,$fot(X_43))]]) ).
cnf(refute_1_4,plain,
subset(empty_set,X_43),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,X_43),empty_set) )],[refute_1_3,refute_1_1]) ).
cnf(refute_1_5,plain,
subset(empty_set,skolemFOFtoCNF_C_2),
inference(subst,[],[refute_1_4:[bind(X_43,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_6,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_7,plain,
( ~ empty(X_42)
| ~ member(skolemFOFtoCNF_D(X_42,X_43),X_42) ),
inference(subst,[],[refute_1_6:[bind(B,$fot(X_42)),bind(C,$fot(skolemFOFtoCNF_D(X_42,X_43)))]]) ).
cnf(refute_1_8,plain,
( member(skolemFOFtoCNF_D(X_42,X_43),X_42)
| subset(X_42,X_43) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(X_42)),bind(C,$fot(X_43))]]) ).
cnf(refute_1_9,plain,
( ~ empty(X_42)
| subset(X_42,X_43) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_42,X_43),X_42) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
( ~ empty(skolemFOFtoCNF_C_2)
| subset(skolemFOFtoCNF_C_2,X_43) ),
inference(subst,[],[refute_1_9:[bind(X_42,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_11,plain,
( ~ empty(union(X_50,X_51))
| ~ member(skolemFOFtoCNF_C(X_50),union(X_50,X_51)) ),
inference(subst,[],[refute_1_6:[bind(B,$fot(union(X_50,X_51))),bind(C,$fot(skolemFOFtoCNF_C(X_50)))]]) ).
cnf(refute_1_12,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_13,plain,
( empty(X_47)
| member(skolemFOFtoCNF_C(X_47),X_47) ),
inference(subst,[],[refute_1_12:[bind(B,$fot(X_47))]]) ).
cnf(refute_1_14,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_15,plain,
( ~ member(skolemFOFtoCNF_C(X_47),X_47)
| member(skolemFOFtoCNF_C(X_47),union(X_47,X_48)) ),
inference(subst,[],[refute_1_14:[bind(B,$fot(X_47)),bind(C,$fot(X_48)),bind(D,$fot(skolemFOFtoCNF_C(X_47)))]]) ).
cnf(refute_1_16,plain,
( empty(X_47)
| member(skolemFOFtoCNF_C(X_47),union(X_47,X_48)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_47),X_47) )],[refute_1_13,refute_1_15]) ).
cnf(refute_1_17,plain,
( empty(X_50)
| member(skolemFOFtoCNF_C(X_50),union(X_50,X_51)) ),
inference(subst,[],[refute_1_16:[bind(X_47,$fot(X_50)),bind(X_48,$fot(X_51))]]) ).
cnf(refute_1_18,plain,
( ~ empty(union(X_50,X_51))
| empty(X_50) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_50),union(X_50,X_51)) )],[refute_1_17,refute_1_11]) ).
cnf(refute_1_19,plain,
( ~ empty(union(X_52,X_53))
| empty(X_52) ),
inference(subst,[],[refute_1_18:[bind(X_50,$fot(X_52)),bind(X_51,$fot(X_53))]]) ).
cnf(refute_1_20,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_21,plain,
union(X_53,X_52) = union(X_52,X_53),
inference(subst,[],[refute_1_20:[bind(B,$fot(X_53)),bind(C,$fot(X_52))]]) ).
cnf(refute_1_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
( union(X_53,X_52) != union(X_52,X_53)
| union(X_52,X_53) = union(X_53,X_52) ),
inference(subst,[],[refute_1_24:[bind(X,$fot(union(X_53,X_52))),bind(Y,$fot(union(X_52,X_53)))]]) ).
cnf(refute_1_26,plain,
union(X_52,X_53) = union(X_53,X_52),
inference(resolve,[$cnf( $equal(union(X_53,X_52),union(X_52,X_53)) )],[refute_1_21,refute_1_25]) ).
cnf(refute_1_27,plain,
( union(X_52,X_53) != union(X_53,X_52)
| ~ empty(union(X_53,X_52))
| empty(union(X_52,X_53)) ),
introduced(tautology,[equality,[$cnf( ~ empty(union(X_52,X_53)) ),[0],$fot(union(X_53,X_52))]]) ).
cnf(refute_1_28,plain,
( ~ empty(union(X_53,X_52))
| empty(union(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(union(X_52,X_53),union(X_53,X_52)) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ empty(union(X_53,X_52))
| empty(X_52) ),
inference(resolve,[$cnf( empty(union(X_52,X_53)) )],[refute_1_28,refute_1_19]) ).
cnf(refute_1_30,plain,
( ~ empty(union(empty_set,skolemFOFtoCNF_C_2))
| empty(skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_29:[bind(X_52,$fot(skolemFOFtoCNF_C_2)),bind(X_53,$fot(empty_set))]]) ).
cnf(refute_1_31,plain,
union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set,
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_32,plain,
skolemFOFtoCNF_B_1 = empty_set,
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_33,plain,
union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
introduced(tautology,[refl,[$fot(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_34,plain,
( skolemFOFtoCNF_B_1 != empty_set
| union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = union(empty_set,skolemFOFtoCNF_C_2) ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_1_35,plain,
( skolemFOFtoCNF_B_1 != empty_set
| union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = union(empty_set,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = union(empty_set,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,empty_set) )],[refute_1_32,refute_1_35]) ).
cnf(refute_1_37,plain,
( union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
| union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != union(empty_set,skolemFOFtoCNF_C_2)
| union(empty_set,skolemFOFtoCNF_C_2) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),[0],$fot(union(empty_set,skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_38,plain,
( union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
| union(empty_set,skolemFOFtoCNF_C_2) = empty_set ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),union(empty_set,skolemFOFtoCNF_C_2)) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
union(empty_set,skolemFOFtoCNF_C_2) = empty_set,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_31,refute_1_38]) ).
cnf(refute_1_40,plain,
( union(empty_set,skolemFOFtoCNF_C_2) != empty_set
| ~ empty(empty_set)
| empty(union(empty_set,skolemFOFtoCNF_C_2)) ),
introduced(tautology,[equality,[$cnf( ~ empty(union(empty_set,skolemFOFtoCNF_C_2)) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_41,plain,
( ~ empty(empty_set)
| empty(union(empty_set,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_39,refute_1_40]) ).
cnf(refute_1_42,plain,
( ~ empty(empty_set)
| empty(skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( empty(union(empty_set,skolemFOFtoCNF_C_2)) )],[refute_1_41,refute_1_30]) ).
cnf(refute_1_43,plain,
~ member(skolemFOFtoCNF_C(empty_set),empty_set),
inference(subst,[],[refute_1_0:[bind(B,$fot(skolemFOFtoCNF_C(empty_set)))]]) ).
cnf(refute_1_44,plain,
( empty(empty_set)
| member(skolemFOFtoCNF_C(empty_set),empty_set) ),
inference(subst,[],[refute_1_12:[bind(B,$fot(empty_set))]]) ).
cnf(refute_1_45,plain,
empty(empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(empty_set),empty_set) )],[refute_1_44,refute_1_43]) ).
cnf(refute_1_46,plain,
empty(skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( empty(empty_set) )],[refute_1_45,refute_1_42]) ).
cnf(refute_1_47,plain,
subset(skolemFOFtoCNF_C_2,X_43),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_C_2) )],[refute_1_46,refute_1_10]) ).
cnf(refute_1_48,plain,
subset(skolemFOFtoCNF_C_2,X_63),
inference(subst,[],[refute_1_47:[bind(X_43,$fot(X_63))]]) ).
cnf(refute_1_49,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_50,plain,
( ~ subset(X_63,skolemFOFtoCNF_C_2)
| ~ subset(skolemFOFtoCNF_C_2,X_63)
| skolemFOFtoCNF_C_2 = X_63 ),
inference(subst,[],[refute_1_49:[bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(X_63))]]) ).
cnf(refute_1_51,plain,
( ~ subset(X_63,skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C_2 = X_63 ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_2,X_63) )],[refute_1_48,refute_1_50]) ).
cnf(refute_1_52,plain,
( ~ subset(empty_set,skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C_2 = empty_set ),
inference(subst,[],[refute_1_51:[bind(X_63,$fot(empty_set))]]) ).
cnf(refute_1_53,plain,
skolemFOFtoCNF_C_2 = empty_set,
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_C_2) )],[refute_1_5,refute_1_52]) ).
cnf(refute_1_54,plain,
skolemFOFtoCNF_C_2 != empty_set,
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_55,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_2,empty_set) )],[refute_1_53,refute_1_54]) ).
fof(negate_2_0,plain,
~ ! [B,C] :
( ( B = empty_set
& C = empty_set )
=> union(B,C) = empty_set ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_2_1,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_2_3,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [B,C,D] :
( ( B != C
| ~ member(D,B)
| member(D,C) )
& ( B != C
| ~ member(D,C)
| member(D,B) )
& ( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C )
& ( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ) ),
inference(clausify,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_2_7,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
? [B,C] :
( union(B,C) != empty_set
& B = empty_set
& C = empty_set ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_11,plain,
( union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != empty_set
& skolemFOFtoCNF_B_2 = empty_set
& skolemFOFtoCNF_C_3 = empty_set ),
inference(skolemize,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != empty_set,
inference(conjunct,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
skolemFOFtoCNF_C_3 = empty_set,
inference(conjunct,[],[normalize_2_11]) ).
fof(normalize_2_14,plain,
skolemFOFtoCNF_B_2 = empty_set,
inference(conjunct,[],[normalize_2_11]) ).
cnf(refute_2_0,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_2_1]) ).
cnf(refute_2_1,plain,
~ member(skolemFOFtoCNF_D_1(empty_set,union(empty_set,empty_set)),empty_set),
inference(subst,[],[refute_2_0:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,union(empty_set,empty_set))))]]) ).
cnf(refute_2_2,plain,
~ member(skolemFOFtoCNF_D_1(empty_set,X_141),empty_set),
inference(subst,[],[refute_2_0:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,X_141)))]]) ).
cnf(refute_2_3,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_4,plain,
( empty_set = X_141
| member(skolemFOFtoCNF_D_1(empty_set,X_141),X_141)
| member(skolemFOFtoCNF_D_1(empty_set,X_141),empty_set) ),
inference(subst,[],[refute_2_3:[bind(B,$fot(empty_set)),bind(C,$fot(X_141))]]) ).
cnf(refute_2_5,plain,
( empty_set = X_141
| member(skolemFOFtoCNF_D_1(empty_set,X_141),X_141) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,X_141),empty_set) )],[refute_2_4,refute_2_2]) ).
cnf(refute_2_6,plain,
( empty_set = union(X_170,X_171)
| member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),union(X_170,X_171)) ),
inference(subst,[],[refute_2_5:[bind(X_141,$fot(union(X_170,X_171)))]]) ).
cnf(refute_2_7,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_8,plain,
( ~ member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),union(X_170,X_171))
| member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),X_170)
| member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),X_171) ),
inference(subst,[],[refute_2_7:[bind(B,$fot(X_170)),bind(C,$fot(X_171)),bind(D,$fot(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171))))]]) ).
cnf(refute_2_9,plain,
( empty_set = union(X_170,X_171)
| member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),X_170)
| member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),X_171) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,union(X_170,X_171)),union(X_170,X_171)) )],[refute_2_6,refute_2_8]) ).
cnf(refute_2_10,plain,
( empty_set = union(empty_set,empty_set)
| member(skolemFOFtoCNF_D_1(empty_set,union(empty_set,empty_set)),empty_set) ),
inference(subst,[],[refute_2_9:[bind(X_170,$fot(empty_set)),bind(X_171,$fot(empty_set))]]) ).
cnf(refute_2_11,plain,
empty_set = union(empty_set,empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,union(empty_set,empty_set)),empty_set) )],[refute_2_10,refute_2_1]) ).
cnf(refute_2_12,plain,
union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != empty_set,
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_13,plain,
skolemFOFtoCNF_C_3 = empty_set,
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_14,plain,
union(empty_set,skolemFOFtoCNF_C_3) = union(empty_set,skolemFOFtoCNF_C_3),
introduced(tautology,[refl,[$fot(union(empty_set,skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_15,plain,
( skolemFOFtoCNF_C_3 != empty_set
| union(empty_set,skolemFOFtoCNF_C_3) != union(empty_set,skolemFOFtoCNF_C_3)
| union(empty_set,skolemFOFtoCNF_C_3) = union(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_C_3),union(empty_set,skolemFOFtoCNF_C_3)) ),[1,1],$fot(empty_set)]]) ).
cnf(refute_2_16,plain,
( skolemFOFtoCNF_C_3 != empty_set
| union(empty_set,skolemFOFtoCNF_C_3) = union(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_C_3),union(empty_set,skolemFOFtoCNF_C_3)) )],[refute_2_14,refute_2_15]) ).
cnf(refute_2_17,plain,
union(empty_set,skolemFOFtoCNF_C_3) = union(empty_set,empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_3,empty_set) )],[refute_2_13,refute_2_16]) ).
cnf(refute_2_18,plain,
skolemFOFtoCNF_B_2 = empty_set,
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_19,plain,
union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),
introduced(tautology,[refl,[$fot(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_20,plain,
( skolemFOFtoCNF_B_2 != empty_set
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_2_21,plain,
( skolemFOFtoCNF_B_2 != empty_set
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)) )],[refute_2_19,refute_2_20]) ).
cnf(refute_2_22,plain,
union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,empty_set) )],[refute_2_18,refute_2_21]) ).
cnf(refute_2_23,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_24,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_25,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_23,refute_2_24]) ).
cnf(refute_2_26,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_27,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_25,refute_2_26]) ).
cnf(refute_2_28,plain,
( union(empty_set,skolemFOFtoCNF_C_3) != union(empty_set,empty_set)
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != union(empty_set,skolemFOFtoCNF_C_3)
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,empty_set) ),
inference(subst,[],[refute_2_27:[bind(X,$fot(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3))),bind(Y,$fot(union(empty_set,skolemFOFtoCNF_C_3))),bind(Z,$fot(union(empty_set,empty_set)))]]) ).
cnf(refute_2_29,plain,
( union(empty_set,skolemFOFtoCNF_C_3) != union(empty_set,empty_set)
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),union(empty_set,skolemFOFtoCNF_C_3)) )],[refute_2_22,refute_2_28]) ).
cnf(refute_2_30,plain,
union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = union(empty_set,empty_set),
inference(resolve,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_C_3),union(empty_set,empty_set)) )],[refute_2_17,refute_2_29]) ).
cnf(refute_2_31,plain,
( union(empty_set,empty_set) != empty_set
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) != union(empty_set,empty_set)
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),union(empty_set,empty_set)) ),[1],$fot(empty_set)]]) ).
cnf(refute_2_32,plain,
( union(empty_set,empty_set) != empty_set
| union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) = empty_set ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),union(empty_set,empty_set)) )],[refute_2_30,refute_2_31]) ).
cnf(refute_2_33,plain,
union(empty_set,empty_set) != empty_set,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),empty_set) )],[refute_2_32,refute_2_12]) ).
cnf(refute_2_34,plain,
( empty_set != union(empty_set,empty_set)
| union(empty_set,empty_set) = empty_set ),
inference(subst,[],[refute_2_25:[bind(X,$fot(empty_set)),bind(Y,$fot(union(empty_set,empty_set)))]]) ).
cnf(refute_2_35,plain,
empty_set != union(empty_set,empty_set),
inference(resolve,[$cnf( $equal(union(empty_set,empty_set),empty_set) )],[refute_2_34,refute_2_33]) ).
cnf(refute_2_36,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,union(empty_set,empty_set)) )],[refute_2_11,refute_2_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 23:26:11 EDT 2022
% 0.21/0.36 % CPUTime :
% 0.21/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43
% 0.21/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.45
%------------------------------------------------------------------------------