TSTP Solution File: SET063+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 03:32:02 EDT 2022
% Result : Theorem 0.18s 0.34s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 48 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 46 ( 22 ~; 13 |; 5 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 1 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [B] : subset(empty_set,B) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(prove_subset_of_empty_set_is_empty_set,conjecture,
! [B] :
( subset(B,empty_set)
=> B = empty_set ) ).
fof(subgoal_0,plain,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(strip,[],[prove_subset_of_empty_set_is_empty_set]) ).
fof(negate_0_0,plain,
~ ! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( B != empty_set
& subset(B,empty_set) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_B != empty_set
& subset(skolemFOFtoCNF_B,empty_set) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(skolemFOFtoCNF_B,empty_set),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_4,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B] : subset(empty_set,B),
inference(canonicalize,[],[empty_set_subset]) ).
fof(normalize_0_8,plain,
! [B] : subset(empty_set,B),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_B != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_B,empty_set),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ subset(empty_set,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,empty_set)
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_3,plain,
( ~ subset(empty_set,skolemFOFtoCNF_B)
| skolemFOFtoCNF_B = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,empty_set) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
subset(empty_set,B),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
subset(empty_set,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_B = empty_set,
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_B) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_6,refute_0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.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 21:45:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.34
% 0.18/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34
%------------------------------------------------------------------------------