TSTP Solution File: SET638+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 03:36:15 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 43 unt; 0 def)
% Number of atoms : 116 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 38 ~; 33 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 2 sgn 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B) ).
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ) ).
fof(union_empty_set,axiom,
! [B] : union(B,empty_set) = B ).
fof(intersection_distributes_over_union,axiom,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_th120,conjecture,
! [B,C,D] :
( ( subset(B,union(C,D))
& intersection(B,D) = empty_set )
=> subset(B,C) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(B,union(C,D))
& intersection(B,D) = empty_set )
=> subset(B,C) ),
inference(strip,[],[prove_th120]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(B,union(C,D))
& intersection(B,D) = empty_set )
=> subset(B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_0_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[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,C,D] :
( ~ subset(B,C)
& intersection(B,D) = empty_set
& subset(B,union(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
& intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) = empty_set
& subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[subset_intersection]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(canonicalize,[],[intersection_distributes_over_union]) ).
fof(normalize_0_10,plain,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) = empty_set,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
! [B] : union(B,empty_set) = B,
inference(canonicalize,[],[union_empty_set]) ).
fof(normalize_0_13,plain,
! [B] : union(B,empty_set) = B,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_15,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
subset(intersection(B,C),B),
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,
( intersection(B,C) != intersection(C,B)
| ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
introduced(tautology,[equality,[$cnf( subset(intersection(B,C),B) ),[0],$fot(intersection(C,B))]]) ).
cnf(refute_0_3,plain,
( ~ subset(intersection(B,C),B)
| subset(intersection(C,B),B) ),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
subset(intersection(C,B),B),
inference(resolve,[$cnf( subset(intersection(B,C),B) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( ~ subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_7:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_9,plain,
intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = union(intersection(skolemFOFtoCNF_B,X_32),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_10:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_32)),bind(D,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_12,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) = empty_set,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) != empty_set
| intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) != union(intersection(skolemFOFtoCNF_B,X_32),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = union(intersection(skolemFOFtoCNF_B,X_32),empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)),union(intersection(skolemFOFtoCNF_B,X_32),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))) ),[1,1],$fot(empty_set)]]) ).
cnf(refute_0_14,plain,
( intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) != union(intersection(skolemFOFtoCNF_B,X_32),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = union(intersection(skolemFOFtoCNF_B,X_32),empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = union(intersection(skolemFOFtoCNF_B,X_32),empty_set),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)),union(intersection(skolemFOFtoCNF_B,X_32),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
union(B,empty_set) = B,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
union(B,empty_set) = union(empty_set,B),
inference(subst,[],[refute_0_17:[bind(C,$fot(empty_set))]]) ).
cnf(refute_0_19,plain,
( union(B,empty_set) != B
| union(B,empty_set) != union(empty_set,B)
| union(empty_set,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(union(B,empty_set),B) ),[0],$fot(union(empty_set,B))]]) ).
cnf(refute_0_20,plain,
( union(B,empty_set) != B
| union(empty_set,B) = B ),
inference(resolve,[$cnf( $equal(union(B,empty_set),union(empty_set,B)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
union(empty_set,B) = B,
inference(resolve,[$cnf( $equal(union(B,empty_set),B) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
union(empty_set,intersection(skolemFOFtoCNF_B,X_32)) = intersection(skolemFOFtoCNF_B,X_32),
inference(subst,[],[refute_0_21:[bind(B,$fot(intersection(skolemFOFtoCNF_B,X_32)))]]) ).
cnf(refute_0_23,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( union(B,C) != union(C,B)
| union(C,B) = union(B,C) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(union(B,C))),bind(Y,$fot(union(C,B)))]]) ).
cnf(refute_0_27,plain,
union(C,B) = union(B,C),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_0_17,refute_0_26]) ).
cnf(refute_0_28,plain,
union(intersection(skolemFOFtoCNF_B,X_32),empty_set) = union(empty_set,intersection(skolemFOFtoCNF_B,X_32)),
inference(subst,[],[refute_0_27:[bind(B,$fot(empty_set)),bind(C,$fot(intersection(skolemFOFtoCNF_B,X_32)))]]) ).
cnf(refute_0_29,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( union(empty_set,intersection(skolemFOFtoCNF_B,X_32)) != intersection(skolemFOFtoCNF_B,X_32)
| union(intersection(skolemFOFtoCNF_B,X_32),empty_set) != union(empty_set,intersection(skolemFOFtoCNF_B,X_32))
| union(intersection(skolemFOFtoCNF_B,X_32),empty_set) = intersection(skolemFOFtoCNF_B,X_32) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(union(intersection(skolemFOFtoCNF_B,X_32),empty_set))),bind(Y,$fot(union(empty_set,intersection(skolemFOFtoCNF_B,X_32)))),bind(Z,$fot(intersection(skolemFOFtoCNF_B,X_32)))]]) ).
cnf(refute_0_32,plain,
( union(empty_set,intersection(skolemFOFtoCNF_B,X_32)) != intersection(skolemFOFtoCNF_B,X_32)
| union(intersection(skolemFOFtoCNF_B,X_32),empty_set) = intersection(skolemFOFtoCNF_B,X_32) ),
inference(resolve,[$cnf( $equal(union(intersection(skolemFOFtoCNF_B,X_32),empty_set),union(empty_set,intersection(skolemFOFtoCNF_B,X_32))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
union(intersection(skolemFOFtoCNF_B,X_32),empty_set) = intersection(skolemFOFtoCNF_B,X_32),
inference(resolve,[$cnf( $equal(union(empty_set,intersection(skolemFOFtoCNF_B,X_32)),intersection(skolemFOFtoCNF_B,X_32)) )],[refute_0_22,refute_0_32]) ).
cnf(refute_0_34,plain,
( intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) != union(intersection(skolemFOFtoCNF_B,X_32),empty_set)
| union(intersection(skolemFOFtoCNF_B,X_32),empty_set) != intersection(skolemFOFtoCNF_B,X_32)
| intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = intersection(skolemFOFtoCNF_B,X_32) ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,X_32)) ),[0],$fot(union(intersection(skolemFOFtoCNF_B,X_32),empty_set))]]) ).
cnf(refute_0_35,plain,
( intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) != union(intersection(skolemFOFtoCNF_B,X_32),empty_set)
| intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = intersection(skolemFOFtoCNF_B,X_32) ),
inference(resolve,[$cnf( $equal(union(intersection(skolemFOFtoCNF_B,X_32),empty_set),intersection(skolemFOFtoCNF_B,X_32)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)) = intersection(skolemFOFtoCNF_B,X_32),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(X_32,skolemFOFtoCNF_D_2)),union(intersection(skolemFOFtoCNF_B,X_32),empty_set)) )],[refute_0_15,refute_0_35]) ).
cnf(refute_0_37,plain,
intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_36:[bind(X_32,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_38,plain,
( intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) ),[0],$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_39,plain,
( intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != skolemFOFtoCNF_B
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) )],[refute_0_9,refute_0_39]) ).
cnf(refute_0_41,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B
| ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_42,plain,
( ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_43,refute_0_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n012.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 : Sun Jul 10 23:49:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.41
%------------------------------------------------------------------------------