TSTP Solution File: SET592+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 03:35:42 EDT 2022
% Result : Theorem 0.44s 0.62s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 66 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 17 |; 13 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 30 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ) ).
fof(intersection_of_subsets,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D) )
=> subset(B,intersection(C,D)) ) ).
fof(prove_th51,conjecture,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
=> B = empty_set ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
=> B = empty_set ),
inference(strip,[],[prove_th51]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
=> B = 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] :
( B != empty_set
& intersection(C,D) = empty_set
& subset(B,C)
& subset(B,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( skolemFOFtoCNF_B != empty_set
& intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[intersection_of_subsets]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(specialize,[],[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,
skolemFOFtoCNF_B != 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(skolemFOFtoCNF_B,empty_set)
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ subset(B,C)
| ~ subset(B,D)
| subset(B,intersection(C,D)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ subset(skolemFOFtoCNF_B,X_182)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_182)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_182))]]) ).
cnf(refute_0_6,plain,
( ~ subset(skolemFOFtoCNF_B,X_182)
| subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_182)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
| subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),
inference(subst,[],[refute_0_6:[bind(X_182,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_8,plain,
subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) != empty_set
| ~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,empty_set) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
( ~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| subset(skolemFOFtoCNF_B,empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
subset(skolemFOFtoCNF_B,empty_set),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_B = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,empty_set) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_13,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.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 09:51:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.44/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.62
% 0.44/0.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.44/0.62
%------------------------------------------------------------------------------