TSTP Solution File: SET581+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:35:36 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 80 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 36 ~; 22 |; 11 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 37 !; 3 ?)
% 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(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ) ).
fof(prove_th24,conjecture,
! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ),
inference(strip,[],[prove_th24]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] :
( ~ not_equal(intersection(C,D),empty_set)
& member(B,C)
& member(B,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ not_equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set)
& member(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
& member(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
member(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
member(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
~ not_equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(canonicalize,[],[not_equal_defn]) ).
fof(normalize_0_10,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( ( B != C
| ~ not_equal(B,C) )
& ( B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( B = C
| not_equal(B,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_14,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
member(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
member(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ member(skolemFOFtoCNF_B,X_253)
| ~ member(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_253)) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(X_253)),bind(D,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_B,X_253)
| member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_253)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1)
| member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) ),
inference(subst,[],[refute_0_4:[bind(X_253,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_6,plain,
member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_B,skolemFOFtoCNF_D_1) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
~ not_equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( B = C
| not_equal(B,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1) = empty_set
| not_equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_10,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1) = empty_set,
inference(resolve,[$cnf( not_equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1) != empty_set
| ~ member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
| member(skolemFOFtoCNF_B,empty_set) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
| member(skolemFOFtoCNF_B,empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1),empty_set) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
member(skolemFOFtoCNF_B,empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
~ member(skolemFOFtoCNF_B,empty_set),
inference(subst,[],[refute_0_14:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_B,empty_set) )],[refute_0_13,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 17:19:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.52
% 0.18/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.52
%------------------------------------------------------------------------------