TSTP Solution File: SET199+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 03:33:31 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 43 |; 14 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 41 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_intersection_of_subsets,conjecture,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ),
inference(strip,[],[prove_intersection_of_subsets]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_1,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [B,C,D] :
( ~ subset(B,intersection(C,D))
& subset(B,C)
& subset(B,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,C) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_4,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| member(X_33,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(X_33))]]) ).
cnf(refute_0_7,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| member(X_33,skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C)))]]) ).
cnf(refute_0_9,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_D_2)
| subset(skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_178),skolemFOFtoCNF_D_2)
| subset(skolemFOFtoCNF_B,X_178) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(X_178))]]) ).
cnf(refute_0_11,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_33,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(X_33))]]) ).
cnf(refute_0_13,plain,
( ~ member(X_33,skolemFOFtoCNF_B)
| member(X_33,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_13:[bind(X_33,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C)))]]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),X_65)
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),intersection(skolemFOFtoCNF_C,X_65)) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(X_65)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C)))]]) ).
cnf(refute_0_18,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),X_65)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),intersection(skolemFOFtoCNF_C,X_65))
| subset(skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_178),skolemFOFtoCNF_D_2)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_178),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,X_178) ),
inference(subst,[],[refute_0_18:[bind(C,$fot(X_178)),bind(X_65,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_20,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_178),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,X_178) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_178),skolemFOFtoCNF_D_2) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_20:[bind(X_178,$fot(intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_22,plain,
subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_22,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 : Sun Jul 10 02:11:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52
% 0.18/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.53
%------------------------------------------------------------------------------