TSTP Solution File: SET987+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 03:38:48 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 52 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 13 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t141_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ) ).
fof(t40_xboole_1,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(strip,[],[t141_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( set_difference(set_union2(B,singleton(A)),singleton(A)) != B
& ~ in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B
& ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[t40_xboole_1]) ).
fof(normalize_0_4,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( set_difference(A,singleton(B)) != A
<=> in(B,A) ),
inference(canonicalize,[],[t65_zfmisc_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( set_difference(A,singleton(B)) != A
<=> in(B,A) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) != A
| ~ in(B,A) )
& ( set_difference(A,singleton(B)) = A
| in(B,A) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( set_difference(A,singleton(B)) = A
| in(B,A) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) = set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_3,plain,
( set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) != set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2))
| set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B
| set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B) ),[0],$fot(set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_4,plain,
( set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B
| set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)),set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(set_difference(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B) )],[refute_0_4,refute_0_0]) ).
cnf(refute_0_6,plain,
( set_difference(A,singleton(B)) = A
| in(B,A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_8,plain,
( set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B != skolemFOFtoCNF_B
| set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_B
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_B) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_12,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_12,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET987+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 : n012.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 11:55:28 EDT 2022
% 0.12/0.33 % 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
% 0.12/0.34
%------------------------------------------------------------------------------