TSTP Solution File: SET867+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 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 03:37:59 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 82 ( 33 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 88 ( 38 ~; 32 |; 9 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 3 sgn 23 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ) ).
fof(t2_zfmisc_1,conjecture,
union(empty_set) = empty_set ).
fof(subgoal_0,plain,
union(empty_set) = empty_set,
inference(strip,[],[t2_zfmisc_1]) ).
fof(negate_0_0,plain,
union(empty_set) != empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_1,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_tarski]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) )
& ( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) )
& ( B = union(A)
| in(skolemFOFtoCNF_C(A,B),B)
| in(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_D(A,B)) )
& ( B = union(A)
| in(skolemFOFtoCNF_C(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) )
& ( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) )
& ( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ in(skolemFOFtoCNF_C(A,B),D)
| B = union(A) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
union(empty_set) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_2,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_3,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
~ in(skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(union(empty_set))),empty_set),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(union(empty_set)))))]]) ).
cnf(refute_0_5,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_6,plain,
( union(X_9) = empty_set
| in(skolemFOFtoCNF_B(union(X_9)),union(X_9)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(union(X_9)))]]) ).
cnf(refute_0_7,plain,
( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( union(A) != union(A)
| ~ in(C,union(A))
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(union(A)))]]) ).
cnf(refute_0_9,plain,
union(A) = union(A),
introduced(tautology,[refl,[$fot(union(A))]]) ).
cnf(refute_0_10,plain,
( ~ in(C,union(A))
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(resolve,[$cnf( $equal(union(A),union(A)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_B(union(X_9)),union(X_9))
| in(skolemFOFtoCNF_D_1(X_9,skolemFOFtoCNF_B(union(X_9))),X_9) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_9)),bind(C,$fot(skolemFOFtoCNF_B(union(X_9))))]]) ).
cnf(refute_0_12,plain,
( union(X_9) = empty_set
| in(skolemFOFtoCNF_D_1(X_9,skolemFOFtoCNF_B(union(X_9))),X_9) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(union(X_9)),union(X_9)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( union(empty_set) = empty_set
| in(skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(union(empty_set))),empty_set) ),
inference(subst,[],[refute_0_12:[bind(X_9,$fot(empty_set))]]) ).
cnf(refute_0_14,plain,
union(empty_set) = empty_set,
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(union(empty_set))),empty_set) )],[refute_0_13,refute_0_4]) ).
cnf(refute_0_15,plain,
union(empty_set) != empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( $equal(union(empty_set),empty_set) )],[refute_0_14,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % 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 : Mon Jul 11 02:21:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------