TSTP Solution File: SET635+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:36:13 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 41 unt; 0 def)
% Number of atoms : 82 ( 68 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 20 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 4 sgn 52 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ) ).
fof(union_empty_set,axiom,
! [B] : union(B,empty_set) = B ).
fof(difference_and_intersection_and_union,axiom,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)) ).
fof(difference_and_intersection,axiom,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(prove_th117,conjecture,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)) ).
fof(subgoal_0,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(strip,[],[prove_th117]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] : intersection(B,difference(C,D)) != difference(intersection(B,C),intersection(B,D)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(canonicalize,[],[difference_and_intersection]) ).
fof(normalize_0_3,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(canonicalize,[],[difference_and_intersection_and_union]) ).
fof(normalize_0_5,plain,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] : subset(intersection(B,C),B),
inference(canonicalize,[],[intersection_is_subset]) ).
fof(normalize_0_7,plain,
! [B,C] : subset(intersection(B,C),B),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( difference(B,C) != empty_set
<=> ~ subset(B,C) ),
inference(canonicalize,[],[difference_empty_set]) ).
fof(normalize_0_9,plain,
! [B,C] :
( difference(B,C) != empty_set
<=> ~ subset(B,C) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ( difference(B,C) != empty_set
| subset(B,C) )
& ( ~ subset(B,C)
| difference(B,C) = empty_set ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( ~ subset(B,C)
| difference(B,C) = empty_set ),
inference(conjunct,[],[normalize_0_10]) ).
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]) ).
cnf(refute_0_0,plain,
intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_3,plain,
( difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)
| intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)) ),[1],$fot(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_4,plain,
( difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))
| intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))) )],[refute_0_4,refute_0_0]) ).
cnf(refute_0_6,plain,
difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_7,plain,
difference(intersection(X_45,C),intersection(X_45,X_46)) = union(difference(intersection(X_45,C),X_45),difference(intersection(X_45,C),X_46)),
inference(subst,[],[refute_0_6:[bind(B,$fot(intersection(X_45,C))),bind(C,$fot(X_45)),bind(D,$fot(X_46))]]) ).
cnf(refute_0_8,plain,
subset(intersection(B,C),B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
subset(intersection(X_27,C),X_27),
inference(subst,[],[refute_0_8:[bind(B,$fot(X_27))]]) ).
cnf(refute_0_10,plain,
( ~ subset(B,C)
| difference(B,C) = empty_set ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ subset(intersection(X_27,C),X_27)
| difference(intersection(X_27,C),X_27) = empty_set ),
inference(subst,[],[refute_0_10:[bind(B,$fot(intersection(X_27,C))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_12,plain,
difference(intersection(X_27,C),X_27) = empty_set,
inference(resolve,[$cnf( subset(intersection(X_27,C),X_27) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
difference(intersection(X_45,C),X_45) = empty_set,
inference(subst,[],[refute_0_12:[bind(X_27,$fot(X_45))]]) ).
cnf(refute_0_14,plain,
( difference(intersection(X_45,C),X_45) != empty_set
| difference(intersection(X_45,C),intersection(X_45,X_46)) != union(difference(intersection(X_45,C),X_45),difference(intersection(X_45,C),X_46))
| difference(intersection(X_45,C),intersection(X_45,X_46)) = union(empty_set,difference(intersection(X_45,C),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(intersection(X_45,C),intersection(X_45,X_46)),union(difference(intersection(X_45,C),X_45),difference(intersection(X_45,C),X_46))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_15,plain,
( difference(intersection(X_45,C),intersection(X_45,X_46)) != union(difference(intersection(X_45,C),X_45),difference(intersection(X_45,C),X_46))
| difference(intersection(X_45,C),intersection(X_45,X_46)) = union(empty_set,difference(intersection(X_45,C),X_46)) ),
inference(resolve,[$cnf( $equal(difference(intersection(X_45,C),X_45),empty_set) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
difference(intersection(X_45,C),intersection(X_45,X_46)) = union(empty_set,difference(intersection(X_45,C),X_46)),
inference(resolve,[$cnf( $equal(difference(intersection(X_45,C),intersection(X_45,X_46)),union(difference(intersection(X_45,C),X_45),difference(intersection(X_45,C),X_46))) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
union(B,empty_set) = B,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_19,plain,
union(B,empty_set) = union(empty_set,B),
inference(subst,[],[refute_0_18:[bind(C,$fot(empty_set))]]) ).
cnf(refute_0_20,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_21,plain,
( union(B,empty_set) != B
| union(empty_set,B) = B ),
inference(resolve,[$cnf( $equal(union(B,empty_set),union(empty_set,B)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
union(empty_set,B) = B,
inference(resolve,[$cnf( $equal(union(B,empty_set),B) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
union(empty_set,difference(intersection(X_45,C),X_46)) = difference(intersection(X_45,C),X_46),
inference(subst,[],[refute_0_22:[bind(B,$fot(difference(intersection(X_45,C),X_46)))]]) ).
cnf(refute_0_24,plain,
( difference(intersection(X_45,C),intersection(X_45,X_46)) != union(empty_set,difference(intersection(X_45,C),X_46))
| union(empty_set,difference(intersection(X_45,C),X_46)) != difference(intersection(X_45,C),X_46)
| difference(intersection(X_45,C),intersection(X_45,X_46)) = difference(intersection(X_45,C),X_46) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(intersection(X_45,C),intersection(X_45,X_46)),difference(intersection(X_45,C),X_46)) ),[0],$fot(union(empty_set,difference(intersection(X_45,C),X_46)))]]) ).
cnf(refute_0_25,plain,
( difference(intersection(X_45,C),intersection(X_45,X_46)) != union(empty_set,difference(intersection(X_45,C),X_46))
| difference(intersection(X_45,C),intersection(X_45,X_46)) = difference(intersection(X_45,C),X_46) ),
inference(resolve,[$cnf( $equal(union(empty_set,difference(intersection(X_45,C),X_46)),difference(intersection(X_45,C),X_46)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
difference(intersection(X_45,C),intersection(X_45,X_46)) = difference(intersection(X_45,C),X_46),
inference(resolve,[$cnf( $equal(difference(intersection(X_45,C),intersection(X_45,X_46)),union(empty_set,difference(intersection(X_45,C),X_46))) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),
inference(subst,[],[refute_0_26:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(X_45,$fot(skolemFOFtoCNF_B)),bind(X_46,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_28,plain,
( difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)
| difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)
| difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))) ),[1],$fot(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_29,plain,
( difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)
| difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)) ),
inference(resolve,[$cnf( $equal(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) != difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( $equal(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2))) )],[refute_0_29,refute_0_5]) ).
cnf(refute_0_31,plain,
difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2) = difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),
introduced(tautology,[refl,[$fot(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2),difference(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_D_2)) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 13:36:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------