%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:38:04 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 76 ( 53 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 79 ( 36 ~; 25 |; 6 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ) ).
fof(t21_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ) ).
fof(subgoal_0,plain,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(strip,[],[t21_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( set_difference(singleton(A),B) != empty_set
<=> ~ in(A,B) ),
inference(canonicalize,[],[l36_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( set_difference(singleton(A),B) != empty_set
<=> ~ in(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( set_difference(singleton(A),B) != empty_set
| in(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B] :
( A != B
& set_difference(singleton(A),singleton(B)) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
& set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = empty_set ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = empty_set,
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
( set_difference(singleton(A),B) != empty_set
| in(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != empty_set
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_7,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = empty_set,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( empty_set != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_9,plain,
( empty_set != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),empty_set) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( empty_set != empty_set
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),empty_set) )],[refute_0_9,refute_0_6]) ).
cnf(refute_0_11,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_12,plain,
in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_13,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 04:05:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------