TSTP Solution File: SET091+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:32:29 EDT 2022
% Result : Theorem 45.24s 45.47s
% Output : CNFRefutation 45.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 89 ( 73 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 34 |; 10 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_universal_self,axiom,
! [X] :
( member(member_of(X),universal_class)
| member_of(X) = X ) ).
fof(singleton_self,axiom,
! [X] :
( singleton(member_of(X)) = X
| member_of(X) = X ) ).
fof(member_when_not_a_singleton,conjecture,
! [X,U] :
( ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& X = U )
=> member_of(X) = U ) ).
fof(subgoal_0,plain,
! [X,U] :
( ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& X = U )
=> member_of(X) = U ),
inference(strip,[],[member_when_not_a_singleton]) ).
fof(negate_0_0,plain,
~ ! [X,U] :
( ( ~ ? [Y] :
( member(Y,universal_class)
& X = singleton(Y) )
& X = U )
=> member_of(X) = U ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,X] :
( member_of(X) != U
& X = U
& ! [Y] :
( X != singleton(Y)
| ~ member(Y,universal_class) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( member_of(skolemFOFtoCNF_X_2) != skolemFOFtoCNF_U_3
& skolemFOFtoCNF_X_2 = skolemFOFtoCNF_U_3
& ! [Y] :
( skolemFOFtoCNF_X_2 != singleton(Y)
| ~ member(Y,universal_class) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] :
( skolemFOFtoCNF_X_2 != singleton(Y)
| ~ member(Y,universal_class) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y] :
( skolemFOFtoCNF_X_2 != singleton(Y)
| ~ member(Y,universal_class) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
skolemFOFtoCNF_X_2 = skolemFOFtoCNF_U_3,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
inference(canonicalize,[],[member_universal_self]) ).
fof(normalize_0_6,plain,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
inference(canonicalize,[],[singleton_self]) ).
fof(normalize_0_8,plain,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
member_of(skolemFOFtoCNF_X_2) != skolemFOFtoCNF_U_3,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_X_2 != singleton(Y)
| ~ member(Y,universal_class) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_X_2 = skolemFOFtoCNF_U_3,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_U_3 != singleton(Y)
| skolemFOFtoCNF_X_2 != skolemFOFtoCNF_U_3
| skolemFOFtoCNF_X_2 = singleton(Y) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_U_3) ),[1],$fot(singleton(Y))]]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_U_3 != singleton(Y)
| skolemFOFtoCNF_X_2 = singleton(Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_U_3) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( skolemFOFtoCNF_U_3 != singleton(Y)
| ~ member(Y,universal_class) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,singleton(Y)) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_U_3 != singleton(member_of(X_86))
| ~ member(member_of(X_86),universal_class) ),
inference(subst,[],[refute_0_4:[bind(Y,$fot(member_of(X_86)))]]) ).
cnf(refute_0_6,plain,
( member_of(X) = X
| member(member_of(X),universal_class) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( member_of(X_86) = X_86
| member(member_of(X_86),universal_class) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_86))]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_U_3 != singleton(member_of(X_86))
| member_of(X_86) = X_86 ),
inference(resolve,[$cnf( member(member_of(X_86),universal_class) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_U_3 != singleton(member_of(X_461))
| member_of(X_461) = X_461 ),
inference(subst,[],[refute_0_8:[bind(X_86,$fot(X_461))]]) ).
cnf(refute_0_10,plain,
( member_of(X) = X
| singleton(member_of(X)) = X ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( member_of(X_461) = X_461
| singleton(member_of(X_461)) = X_461 ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_461))]]) ).
cnf(refute_0_12,plain,
( singleton(member_of(X_461)) != X_461
| skolemFOFtoCNF_U_3 != X_461
| skolemFOFtoCNF_U_3 = singleton(member_of(X_461)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_3,singleton(member_of(X_461))) ),[1],$fot(X_461)]]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_U_3 != X_461
| member_of(X_461) = X_461
| skolemFOFtoCNF_U_3 = singleton(member_of(X_461)) ),
inference(resolve,[$cnf( $equal(singleton(member_of(X_461)),X_461) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_U_3 != X_461
| member_of(X_461) = X_461 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_3,singleton(member_of(X_461))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_U_3 != skolemFOFtoCNF_U_3
| member_of(skolemFOFtoCNF_U_3) = skolemFOFtoCNF_U_3 ),
inference(subst,[],[refute_0_14:[bind(X_461,$fot(skolemFOFtoCNF_U_3))]]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_U_3 = skolemFOFtoCNF_U_3,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_U_3)]]) ).
cnf(refute_0_17,plain,
member_of(skolemFOFtoCNF_U_3) = skolemFOFtoCNF_U_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_3,skolemFOFtoCNF_U_3) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
member_of(skolemFOFtoCNF_X_2) != skolemFOFtoCNF_U_3,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_19,plain,
member_of(skolemFOFtoCNF_X_2) = member_of(skolemFOFtoCNF_X_2),
introduced(tautology,[refl,[$fot(member_of(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_20,plain,
( member_of(skolemFOFtoCNF_X_2) != member_of(skolemFOFtoCNF_X_2)
| skolemFOFtoCNF_X_2 != skolemFOFtoCNF_U_3
| member_of(skolemFOFtoCNF_X_2) = member_of(skolemFOFtoCNF_U_3) ),
introduced(tautology,[equality,[$cnf( $equal(member_of(skolemFOFtoCNF_X_2),member_of(skolemFOFtoCNF_X_2)) ),[1,0],$fot(skolemFOFtoCNF_U_3)]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_U_3
| member_of(skolemFOFtoCNF_X_2) = member_of(skolemFOFtoCNF_U_3) ),
inference(resolve,[$cnf( $equal(member_of(skolemFOFtoCNF_X_2),member_of(skolemFOFtoCNF_X_2)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
member_of(skolemFOFtoCNF_X_2) = member_of(skolemFOFtoCNF_U_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_U_3) )],[refute_0_1,refute_0_21]) ).
cnf(refute_0_23,plain,
( member_of(skolemFOFtoCNF_U_3) != skolemFOFtoCNF_U_3
| member_of(skolemFOFtoCNF_X_2) != member_of(skolemFOFtoCNF_U_3)
| member_of(skolemFOFtoCNF_X_2) = skolemFOFtoCNF_U_3 ),
introduced(tautology,[equality,[$cnf( $equal(member_of(skolemFOFtoCNF_X_2),member_of(skolemFOFtoCNF_U_3)) ),[1],$fot(skolemFOFtoCNF_U_3)]]) ).
cnf(refute_0_24,plain,
( member_of(skolemFOFtoCNF_U_3) != skolemFOFtoCNF_U_3
| member_of(skolemFOFtoCNF_X_2) = skolemFOFtoCNF_U_3 ),
inference(resolve,[$cnf( $equal(member_of(skolemFOFtoCNF_X_2),member_of(skolemFOFtoCNF_U_3)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
member_of(skolemFOFtoCNF_U_3) != skolemFOFtoCNF_U_3,
inference(resolve,[$cnf( $equal(member_of(skolemFOFtoCNF_X_2),skolemFOFtoCNF_U_3) )],[refute_0_24,refute_0_18]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(member_of(skolemFOFtoCNF_U_3),skolemFOFtoCNF_U_3) )],[refute_0_17,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 09:33:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 45.24/45.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.24/45.47
% 45.24/45.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.24/45.47
%------------------------------------------------------------------------------