%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET933+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:38:28 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 67 ( 11 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 65 ( 31 ~; 21 |; 4 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t80_zfmisc_1,conjecture,
! [A] : subset(singleton(A),powerset(A)) ).
fof(subgoal_0,plain,
! [A] : subset(singleton(A),powerset(A)),
inference(strip,[],[t80_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A] : subset(singleton(A),powerset(A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ subset(singleton(A),powerset(A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(singleton(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_A_2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_3,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ( B != powerset(A)
| ~ in(C,B)
| subset(C,A) )
& ( B != powerset(A)
| ~ subset(C,A)
| in(C,B) )
& ( ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ subset(skolemFOFtoCNF_C(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C(A,B),B)
| subset(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
~ subset(singleton(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
subset(X_6,X_6),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_5,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_6,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ subset(X_6,X_6)
| in(X_6,powerset(X_6)) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_6)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_8,plain,
in(X_6,powerset(X_6)),
inference(resolve,[$cnf( subset(X_6,X_6) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
in(X_9,powerset(X_9)),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_10,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ in(X_9,powerset(X_9))
| subset(singleton(X_9),powerset(X_9)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_9)),bind(B,$fot(powerset(X_9)))]]) ).
cnf(refute_0_12,plain,
subset(singleton(X_9),powerset(X_9)),
inference(resolve,[$cnf( in(X_9,powerset(X_9)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
subset(singleton(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_12:[bind(X_9,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET933+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 : n020.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 : Sat Jul 9 17:00:28 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
%------------------------------------------------------------------------------