TSTP Solution File: SET027+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 03:31:29 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 11 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_transitivity_of_subset,conjecture,
! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ),
inference(strip,[],[prove_transitivity_of_subset]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,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,D] :
( ~ subset(B,D)
& subset(B,C)
& subset(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1)
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),
inference(conjunct,[],[normalize_0_5]) ).
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,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ member(X_7,skolemFOFtoCNF_C)
| ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)
| member(X_7,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(X_7))]]) ).
cnf(refute_0_5,plain,
( ~ member(X_7,skolemFOFtoCNF_C)
| member(X_7,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10),skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_5:[bind(X_7,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10)))]]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,C) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_9,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ member(X_7,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_7,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(X_7))]]) ).
cnf(refute_0_11,plain,
( ~ member(X_7,skolemFOFtoCNF_B)
| member(X_7,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_11:[bind(X_7,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,C),skolemFOFtoCNF_B) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,X_10) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(X_10))]]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10),skolemFOFtoCNF_D_1)
| subset(skolemFOFtoCNF_B,X_10) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,X_10),skolemFOFtoCNF_C) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_17,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 04:40:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------