%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:35:45 EDT 2022
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 53 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 17 ~; 12 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ) ).
fof(intersection_of_subset,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ) ).
fof(prove_th55,conjecture,
! [B,C,D] :
( ( subset(B,C)
& intersection(C,D) = empty_set )
=> intersection(B,D) = empty_set ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(B,C)
& intersection(C,D) = empty_set )
=> intersection(B,D) = empty_set ),
inference(strip,[],[prove_th55]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(B,C)
& intersection(C,D) = empty_set )
=> intersection(B,D) = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] :
( ~ subset(B,empty_set)
| B = empty_set ),
inference(canonicalize,[],[subset_of_empty_set_is_empty_set]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ subset(B,empty_set)
| B = empty_set ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B,C,D] :
( intersection(B,D) != empty_set
& intersection(C,D) = empty_set
& subset(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) != empty_set
& intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ subset(B,C)
| ! [D] : subset(intersection(B,D),intersection(C,D)) ),
inference(canonicalize,[],[intersection_of_subset]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ subset(B,C)
| ! [D] : subset(intersection(B,D),intersection(C,D)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ subset(B,C)
| subset(intersection(B,D),intersection(C,D)) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) != empty_set,
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ subset(B,empty_set)
| B = empty_set ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set)
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) = empty_set ),
inference(subst,[],[refute_0_0:[bind(B,$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ subset(B,C)
| subset(intersection(B,D),intersection(C,D)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| subset(intersection(skolemFOFtoCNF_B,X_44),intersection(skolemFOFtoCNF_C_1,X_44)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_44))]]) ).
cnf(refute_0_5,plain,
subset(intersection(skolemFOFtoCNF_B,X_44),intersection(skolemFOFtoCNF_C_1,X_44)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(subst,[],[refute_0_5:[bind(X_44,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_7,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) != empty_set
| ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set) ),
introduced(tautology,[equality,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_9,plain,
( ~ subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set),
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) = empty_set,
inference(resolve,[$cnf( subset(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) != empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_11,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.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 : Sun Jul 10 19:25:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.36
%------------------------------------------------------------------------------