TSTP Solution File: SET008+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:30:59 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 95 ( 30 unt; 0 def)
% Number of atoms : 200 ( 67 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 192 ( 87 ~; 80 |; 10 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 189 ( 23 sgn 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
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_intersection_difference_empty_set,conjecture,
! [B,C] : intersection(difference(B,C),C) = empty_set ).
fof(subgoal_0,plain,
! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(strip,[],[prove_intersection_difference_empty_set]) ).
fof(negate_0_0,plain,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : intersection(difference(B,C),C) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) != empty_set,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_3,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| member(D,B) )
& ( ~ member(D,intersection(B,C))
| member(D,C) )
& ( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_0_13,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_0_13]) ).
fof(normalize_0_15,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_17,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_19,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,difference(B,C)) )
& ( ~ member(D,difference(B,C))
| member(D,B) )
& ( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_23,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) != empty_set,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_0_6,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) = intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_8,plain,
( intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) != intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set
| intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),empty_set) ),[0],$fot(intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_9,plain,
( intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set
| intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set,
inference(resolve,[$cnf( $equal(intersection(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),empty_set) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
( ~ empty(X_155)
| ~ member(skolemFOFtoCNF_D_1(X_155,intersection(X_155,X_154)),X_155) ),
inference(subst,[],[refute_0_11:[bind(B,$fot(X_155)),bind(C,$fot(skolemFOFtoCNF_D_1(X_155,intersection(X_155,X_154))))]]) ).
cnf(refute_0_13,plain,
( ~ member(D,intersection(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
( ~ member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),intersection(B,C))
| member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),B) ),
inference(subst,[],[refute_0_13:[bind(D,$fot(skolemFOFtoCNF_D_1(X_144,intersection(B,C))))]]) ).
cnf(refute_0_15,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_16,plain,
( X_144 = intersection(B,C)
| member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),X_144)
| member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),intersection(B,C)) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_144)),bind(C,$fot(intersection(B,C)))]]) ).
cnf(refute_0_17,plain,
( X_144 = intersection(B,C)
| member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),B)
| member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),X_144) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_144,intersection(B,C)),intersection(B,C)) )],[refute_0_16,refute_0_14]) ).
cnf(refute_0_18,plain,
( X_155 = intersection(X_155,X_154)
| member(skolemFOFtoCNF_D_1(X_155,intersection(X_155,X_154)),X_155) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(X_155)),bind(C,$fot(X_154)),bind(X_144,$fot(X_155))]]) ).
cnf(refute_0_19,plain,
( ~ empty(X_155)
| X_155 = intersection(X_155,X_154) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_155,intersection(X_155,X_154)),X_155) )],[refute_0_18,refute_0_12]) ).
cnf(refute_0_20,plain,
( ~ empty(intersection(X_208,difference(X_207,X_208)))
| intersection(X_208,difference(X_207,X_208)) = intersection(intersection(X_208,difference(X_207,X_208)),X_154) ),
inference(subst,[],[refute_0_19:[bind(X_155,$fot(intersection(X_208,difference(X_207,X_208))))]]) ).
cnf(refute_0_21,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
( empty(intersection(X_17,X_18))
| member(skolemFOFtoCNF_C(intersection(X_17,X_18)),intersection(X_17,X_18)) ),
inference(subst,[],[refute_0_21:[bind(B,$fot(intersection(X_17,X_18)))]]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_17,X_18)),intersection(X_17,X_18))
| member(skolemFOFtoCNF_C(intersection(X_17,X_18)),X_17) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_17)),bind(C,$fot(X_18)),bind(D,$fot(skolemFOFtoCNF_C(intersection(X_17,X_18))))]]) ).
cnf(refute_0_24,plain,
( empty(intersection(X_17,X_18))
| member(skolemFOFtoCNF_C(intersection(X_17,X_18)),X_17) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_17,X_18)),intersection(X_17,X_18)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( empty(intersection(X_206,difference(X_205,X_206)))
| member(skolemFOFtoCNF_C(intersection(X_206,difference(X_205,X_206))),X_206) ),
inference(subst,[],[refute_0_24:[bind(X_17,$fot(X_206)),bind(X_18,$fot(difference(X_205,X_206)))]]) ).
cnf(refute_0_26,plain,
( empty(intersection(X_20,X_21))
| member(skolemFOFtoCNF_C(intersection(X_20,X_21)),intersection(X_20,X_21)) ),
inference(subst,[],[refute_0_21:[bind(B,$fot(intersection(X_20,X_21)))]]) ).
cnf(refute_0_27,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_28,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_20,X_21)),intersection(X_20,X_21))
| member(skolemFOFtoCNF_C(intersection(X_20,X_21)),X_21) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_20)),bind(C,$fot(X_21)),bind(D,$fot(skolemFOFtoCNF_C(intersection(X_20,X_21))))]]) ).
cnf(refute_0_29,plain,
( empty(intersection(X_20,X_21))
| member(skolemFOFtoCNF_C(intersection(X_20,X_21)),X_21) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_20,X_21)),intersection(X_20,X_21)) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( empty(intersection(X_20,difference(X_37,X_38)))
| member(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38))),difference(X_37,X_38)) ),
inference(subst,[],[refute_0_29:[bind(X_21,$fot(difference(X_37,X_38)))]]) ).
cnf(refute_0_31,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_32,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38))),X_38)
| ~ member(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38))),difference(X_37,X_38)) ),
inference(subst,[],[refute_0_31:[bind(B,$fot(X_37)),bind(C,$fot(X_38)),bind(D,$fot(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38)))))]]) ).
cnf(refute_0_33,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38))),X_38)
| empty(intersection(X_20,difference(X_37,X_38))) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_20,difference(X_37,X_38))),difference(X_37,X_38)) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_206,difference(X_205,X_206))),X_206)
| empty(intersection(X_206,difference(X_205,X_206))) ),
inference(subst,[],[refute_0_33:[bind(X_20,$fot(X_206)),bind(X_37,$fot(X_205)),bind(X_38,$fot(X_206))]]) ).
cnf(refute_0_35,plain,
empty(intersection(X_206,difference(X_205,X_206))),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_206,difference(X_205,X_206))),X_206) )],[refute_0_25,refute_0_34]) ).
cnf(refute_0_36,plain,
empty(intersection(X_208,difference(X_207,X_208))),
inference(subst,[],[refute_0_35:[bind(X_205,$fot(X_207)),bind(X_206,$fot(X_208))]]) ).
cnf(refute_0_37,plain,
intersection(X_208,difference(X_207,X_208)) = intersection(intersection(X_208,difference(X_207,X_208)),X_154),
inference(resolve,[$cnf( empty(intersection(X_208,difference(X_207,X_208))) )],[refute_0_36,refute_0_20]) ).
cnf(refute_0_38,plain,
( ~ empty(X_152)
| ~ member(skolemFOFtoCNF_D_1(empty_set,intersection(X_152,X_153)),X_152) ),
inference(subst,[],[refute_0_11:[bind(B,$fot(X_152)),bind(C,$fot(skolemFOFtoCNF_D_1(empty_set,intersection(X_152,X_153))))]]) ).
cnf(refute_0_39,plain,
( ~ member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C))
| member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),B) ),
inference(subst,[],[refute_0_13:[bind(D,$fot(skolemFOFtoCNF_D_1(empty_set,intersection(B,C))))]]) ).
cnf(refute_0_40,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_41,plain,
~ member(skolemFOFtoCNF_D_1(empty_set,X_145),empty_set),
inference(subst,[],[refute_0_40:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,X_145)))]]) ).
cnf(refute_0_42,plain,
( empty_set = X_145
| member(skolemFOFtoCNF_D_1(empty_set,X_145),X_145)
| member(skolemFOFtoCNF_D_1(empty_set,X_145),empty_set) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(empty_set)),bind(C,$fot(X_145))]]) ).
cnf(refute_0_43,plain,
( empty_set = X_145
| member(skolemFOFtoCNF_D_1(empty_set,X_145),X_145) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,X_145),empty_set) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
( empty_set = intersection(B,C)
| member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C)) ),
inference(subst,[],[refute_0_43:[bind(X_145,$fot(intersection(B,C)))]]) ).
cnf(refute_0_45,plain,
( empty_set = intersection(B,C)
| member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C)) )],[refute_0_44,refute_0_39]) ).
cnf(refute_0_46,plain,
( empty_set = intersection(X_152,X_153)
| member(skolemFOFtoCNF_D_1(empty_set,intersection(X_152,X_153)),X_152) ),
inference(subst,[],[refute_0_45:[bind(B,$fot(X_152)),bind(C,$fot(X_153))]]) ).
cnf(refute_0_47,plain,
( ~ empty(X_152)
| empty_set = intersection(X_152,X_153) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,intersection(X_152,X_153)),X_152) )],[refute_0_46,refute_0_38]) ).
cnf(refute_0_48,plain,
( ~ empty(intersection(X_208,difference(X_207,X_208)))
| empty_set = intersection(intersection(X_208,difference(X_207,X_208)),X_153) ),
inference(subst,[],[refute_0_47:[bind(X_152,$fot(intersection(X_208,difference(X_207,X_208))))]]) ).
cnf(refute_0_49,plain,
empty_set = intersection(intersection(X_208,difference(X_207,X_208)),X_153),
inference(resolve,[$cnf( empty(intersection(X_208,difference(X_207,X_208))) )],[refute_0_36,refute_0_48]) ).
cnf(refute_0_50,plain,
( empty_set != intersection(intersection(X_208,difference(X_207,X_208)),X_153)
| intersection(intersection(X_208,difference(X_207,X_208)),X_153) = empty_set ),
inference(subst,[],[refute_0_4:[bind(X,$fot(empty_set)),bind(Y,$fot(intersection(intersection(X_208,difference(X_207,X_208)),X_153)))]]) ).
cnf(refute_0_51,plain,
intersection(intersection(X_208,difference(X_207,X_208)),X_153) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,intersection(intersection(X_208,difference(X_207,X_208)),X_153)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
intersection(intersection(X_208,difference(X_207,X_208)),X_154) = empty_set,
inference(subst,[],[refute_0_51:[bind(X_153,$fot(X_154))]]) ).
cnf(refute_0_53,plain,
( intersection(X_208,difference(X_207,X_208)) != intersection(intersection(X_208,difference(X_207,X_208)),X_154)
| intersection(intersection(X_208,difference(X_207,X_208)),X_154) != empty_set
| intersection(X_208,difference(X_207,X_208)) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(X_208,difference(X_207,X_208)),empty_set) ),[0],$fot(intersection(intersection(X_208,difference(X_207,X_208)),X_154))]]) ).
cnf(refute_0_54,plain,
( intersection(X_208,difference(X_207,X_208)) != intersection(intersection(X_208,difference(X_207,X_208)),X_154)
| intersection(X_208,difference(X_207,X_208)) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(intersection(X_208,difference(X_207,X_208)),X_154),empty_set) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
intersection(X_208,difference(X_207,X_208)) = empty_set,
inference(resolve,[$cnf( $equal(intersection(X_208,difference(X_207,X_208)),intersection(intersection(X_208,difference(X_207,X_208)),X_154)) )],[refute_0_37,refute_0_54]) ).
cnf(refute_0_56,plain,
intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set,
inference(subst,[],[refute_0_55:[bind(X_207,$fot(skolemFOFtoCNF_B)),bind(X_208,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_57,plain,
( empty_set != empty_set
| intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) != empty_set
| intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_58,plain,
( empty_set != empty_set
| intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),empty_set) )],[refute_0_58,refute_0_10]) ).
cnf(refute_0_60,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_60,refute_0_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 02:07:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40
%------------------------------------------------------------------------------