TSTP Solution File: SET146+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 03:33:04 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 36 unt; 0 def)
% Number of atoms : 167 ( 54 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 160 ( 78 ~; 58 |; 11 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 123 ( 19 sgn 58 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(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_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(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(prove_th61,conjecture,
! [B] : intersection(B,empty_set) = empty_set ).
fof(subgoal_0,plain,
! [B] : intersection(B,empty_set) = empty_set,
inference(strip,[],[prove_th61]) ).
fof(negate_0_0,plain,
~ ! [B] : intersection(B,empty_set) = empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] : intersection(B,empty_set) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
intersection(skolemFOFtoCNF_B,empty_set) != 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] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_13,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_20,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
intersection(skolemFOFtoCNF_B,empty_set) != 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( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
intersection(skolemFOFtoCNF_B,empty_set) = intersection(empty_set,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_6:[bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
( intersection(empty_set,skolemFOFtoCNF_B) != empty_set
| intersection(skolemFOFtoCNF_B,empty_set) != intersection(empty_set,skolemFOFtoCNF_B)
| intersection(skolemFOFtoCNF_B,empty_set) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,empty_set),intersection(empty_set,skolemFOFtoCNF_B)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_9,plain,
( intersection(empty_set,skolemFOFtoCNF_B) != empty_set
| intersection(skolemFOFtoCNF_B,empty_set) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,empty_set),intersection(empty_set,skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
intersection(empty_set,skolemFOFtoCNF_B) != empty_set,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,empty_set),empty_set) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
( ~ empty(X_9)
| ~ member(skolemFOFtoCNF_D(X_9,X_10),X_9) ),
inference(subst,[],[refute_0_11:[bind(B,$fot(X_9)),bind(C,$fot(skolemFOFtoCNF_D(X_9,X_10)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(X_9,X_10),X_9)
| subset(X_9,X_10) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_15,plain,
( ~ empty(X_9)
| subset(X_9,X_10) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_9,X_10),X_9) )],[refute_0_14,refute_0_12]) ).
cnf(refute_0_16,plain,
( ~ empty(intersection(empty_set,X_34))
| subset(intersection(empty_set,X_34),X_10) ),
inference(subst,[],[refute_0_15:[bind(X_9,$fot(intersection(empty_set,X_34)))]]) ).
cnf(refute_0_17,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
~ member(skolemFOFtoCNF_C(intersection(X_31,empty_set)),empty_set),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_C(intersection(X_31,empty_set))))]]) ).
cnf(refute_0_19,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( empty(intersection(X_26,X_27))
| member(skolemFOFtoCNF_C(intersection(X_26,X_27)),intersection(X_26,X_27)) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(intersection(X_26,X_27)))]]) ).
cnf(refute_0_21,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_22,plain,
( ~ member(skolemFOFtoCNF_C(intersection(X_26,X_27)),intersection(X_26,X_27))
| member(skolemFOFtoCNF_C(intersection(X_26,X_27)),X_27) ),
inference(subst,[],[refute_0_21:[bind(B,$fot(X_26)),bind(C,$fot(X_27)),bind(D,$fot(skolemFOFtoCNF_C(intersection(X_26,X_27))))]]) ).
cnf(refute_0_23,plain,
( empty(intersection(X_26,X_27))
| member(skolemFOFtoCNF_C(intersection(X_26,X_27)),X_27) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_26,X_27)),intersection(X_26,X_27)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( empty(intersection(X_31,empty_set))
| member(skolemFOFtoCNF_C(intersection(X_31,empty_set)),empty_set) ),
inference(subst,[],[refute_0_23:[bind(X_26,$fot(X_31)),bind(X_27,$fot(empty_set))]]) ).
cnf(refute_0_25,plain,
empty(intersection(X_31,empty_set)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(intersection(X_31,empty_set)),empty_set) )],[refute_0_24,refute_0_18]) ).
cnf(refute_0_26,plain,
empty(intersection(X_33,empty_set)),
inference(subst,[],[refute_0_25:[bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_27,plain,
intersection(empty_set,X_33) = intersection(X_33,empty_set),
inference(subst,[],[refute_0_1:[bind(B,$fot(empty_set)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_28,plain,
( intersection(empty_set,X_33) != intersection(X_33,empty_set)
| intersection(X_33,empty_set) = intersection(empty_set,X_33) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(intersection(empty_set,X_33))),bind(Y,$fot(intersection(X_33,empty_set)))]]) ).
cnf(refute_0_29,plain,
intersection(X_33,empty_set) = intersection(empty_set,X_33),
inference(resolve,[$cnf( $equal(intersection(empty_set,X_33),intersection(X_33,empty_set)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( intersection(X_33,empty_set) != intersection(empty_set,X_33)
| ~ empty(intersection(X_33,empty_set))
| empty(intersection(empty_set,X_33)) ),
introduced(tautology,[equality,[$cnf( empty(intersection(X_33,empty_set)) ),[0],$fot(intersection(empty_set,X_33))]]) ).
cnf(refute_0_31,plain,
( ~ empty(intersection(X_33,empty_set))
| empty(intersection(empty_set,X_33)) ),
inference(resolve,[$cnf( $equal(intersection(X_33,empty_set),intersection(empty_set,X_33)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
empty(intersection(empty_set,X_33)),
inference(resolve,[$cnf( empty(intersection(X_33,empty_set)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
empty(intersection(empty_set,X_34)),
inference(subst,[],[refute_0_32:[bind(X_33,$fot(X_34))]]) ).
cnf(refute_0_34,plain,
subset(intersection(empty_set,X_34),X_10),
inference(resolve,[$cnf( empty(intersection(empty_set,X_34)) )],[refute_0_33,refute_0_16]) ).
cnf(refute_0_35,plain,
subset(intersection(empty_set,X_34),empty_set),
inference(subst,[],[refute_0_34:[bind(X_10,$fot(empty_set))]]) ).
cnf(refute_0_36,plain,
~ member(skolemFOFtoCNF_D(empty_set,X_10),empty_set),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,X_10)))]]) ).
cnf(refute_0_37,plain,
( member(skolemFOFtoCNF_D(empty_set,X_10),empty_set)
| subset(empty_set,X_10) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(empty_set)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_38,plain,
subset(empty_set,X_10),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,X_10),empty_set) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
subset(empty_set,X_62),
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_62))]]) ).
cnf(refute_0_40,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_41,plain,
( ~ subset(X_62,empty_set)
| ~ subset(empty_set,X_62)
| empty_set = X_62 ),
inference(subst,[],[refute_0_40:[bind(B,$fot(empty_set)),bind(C,$fot(X_62))]]) ).
cnf(refute_0_42,plain,
( ~ subset(X_62,empty_set)
| empty_set = X_62 ),
inference(resolve,[$cnf( subset(empty_set,X_62) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ subset(intersection(empty_set,X_34),empty_set)
| empty_set = intersection(empty_set,X_34) ),
inference(subst,[],[refute_0_42:[bind(X_62,$fot(intersection(empty_set,X_34)))]]) ).
cnf(refute_0_44,plain,
empty_set = intersection(empty_set,X_34),
inference(resolve,[$cnf( subset(intersection(empty_set,X_34),empty_set) )],[refute_0_35,refute_0_43]) ).
cnf(refute_0_45,plain,
( empty_set != intersection(empty_set,X_34)
| intersection(empty_set,X_34) = empty_set ),
inference(subst,[],[refute_0_4:[bind(X,$fot(empty_set)),bind(Y,$fot(intersection(empty_set,X_34)))]]) ).
cnf(refute_0_46,plain,
intersection(empty_set,X_34) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,intersection(empty_set,X_34)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
intersection(empty_set,skolemFOFtoCNF_B) = empty_set,
inference(subst,[],[refute_0_46:[bind(X_34,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_48,plain,
( empty_set != empty_set
| intersection(empty_set,skolemFOFtoCNF_B) != empty_set
| intersection(empty_set,skolemFOFtoCNF_B) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(intersection(empty_set,skolemFOFtoCNF_B),empty_set) ),[0,0],$fot(empty_set)]]) ).
cnf(refute_0_49,plain,
( empty_set != empty_set
| intersection(empty_set,skolemFOFtoCNF_B) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(empty_set,skolemFOFtoCNF_B),empty_set) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(intersection(empty_set,skolemFOFtoCNF_B),empty_set) )],[refute_0_49,refute_0_10]) ).
cnf(refute_0_51,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_51,refute_0_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 00:59:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------