TSTP Solution File: SET648^3 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET648^3 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %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 04:54:48 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( eigen__0 @ X1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP2
=> ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ~ ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_cartesian_product,definition,
( cartesian_product
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) ) ) ).
thf(def_pair_rel,definition,
( pair_rel
= ( ^ [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 != X1 )
=> ( X4 = X2 ) ) ) ) ).
thf(def_id_rel,definition,
( id_rel
= ( ^ [X1: $i > $o,X2: $i,X3: $i] :
~ ( ( X1 @ X2 )
=> ( X2 != X3 ) ) ) ) ).
thf(def_sub_rel,definition,
( sub_rel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_is_rel_on,definition,
( is_rel_on
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ).
thf(def_restrict_rel_domain,definition,
( restrict_rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_diagonal,definition,
rel_diagonal = (=) ).
thf(def_rel_composition,definition,
( rel_composition
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i,X4: $i] :
~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X2 @ X5 @ X4 ) ) ) ) ).
thf(def_reflexive,definition,
( reflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irreflexive,definition,
( irreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_symmetric,definition,
( symmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_transitive,definition,
( transitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_equiv_rel,definition,
( equiv_rel
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( reflexive @ X1 )
=> ~ ( symmetric @ X1 ) )
=> ~ ( transitive @ X1 ) ) ) ) ).
thf(def_rel_codomain,definition,
( rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X3 @ X2 ) ) ) ).
thf(def_rel_domain,definition,
( rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_rel_inverse,definition,
( rel_inverse
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_equiv_classes,definition,
( equiv_classes
= ( ^ [X1: $i > $i > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
= ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(def_restrict_rel_codomain,definition,
( restrict_rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_field,definition,
( rel_field
= ( ^ [X1: $i > $i > $o,X2: $i] :
( ~ ( rel_domain @ X1 @ X2 )
=> ( rel_codomain @ X1 @ X2 ) ) ) ) ).
thf(def_well_founded,definition,
( well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ).
thf(def_upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X4 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ~ ! [X4: $i] :
~ ( X1 @ X4 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( ~ ! [X5: $i] :
~ ( X1 @ X3 @ X5 )
=> ~ ( X2 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ~ ! [X4: $i] :
~ ( X1 @ X4 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( ~ ! [X5: $i] :
~ ( X1 @ X3 @ X5 )
=> ~ ( X2 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ~ ! [X3: $i] :
~ ( eigen__0 @ X3 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ( ~ ! [X4: $i] :
~ ( eigen__0 @ X2 @ X4 )
=> ~ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP4
=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
~ ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
~ ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ~ ( ~ sP5
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ ( ~ sP5
=> ~ sP6 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP5
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h4,h2,h1,h0])],[1,h7,h9]) ).
thf(3,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h7,h8,h6,h5,h3,h4,h2,h1,h0])],[3,4,5,h3,h7,h10]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,2,6,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,7,h7,h8]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,8,h6]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,9,h5]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,10,h3,h4]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ~ ! [X4: $i] :
~ ( X1 @ X4 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( ~ ! [X5: $i] :
~ ( X1 @ X3 @ X5 )
=> ~ ( X2 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET648^3 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 17:20:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 5
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------