TSTP Solution File: SET673^3 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET673^3 : 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 : n026.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 04:54:59 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 @ eigen__4 )
=> ~ ( eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__1 @ eigen__4 @ X1 )
=> ~ ( ( eigen__2 @ eigen__4 )
=> ~ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP7
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
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 > $o,X2: $i > $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( ( X3 @ X5 )
=> ~ ( X4 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X5: $i,X6: $i] :
~ ( ( X1 @ X6 )
=> ~ ( X2 @ X5 @ X6 ) ) )
= X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( ( X3 @ X5 )
=> ~ ( X4 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X5: $i,X6: $i] :
~ ( ( X1 @ X6 )
=> ~ ( X2 @ X5 @ X6 ) ) )
= X2 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) )
=> ~ ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X4 ) ) )
=> ( ( ^ [X4: $i,X5: $i] :
~ ( ( eigen__0 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ! [X3: $i,X4: $i] :
( ( eigen__1 @ X3 @ X4 )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 ) ) )
=> ( ( ^ [X3: $i,X4: $i] :
~ ( ( eigen__0 @ X4 )
=> ~ ( eigen__1 @ X3 @ X4 ) ) )
= eigen__1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ~ ( ( eigen__2 @ X2 )
=> ~ ( X1 @ X3 ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) )
=> ( ( ^ [X2: $i,X3: $i] :
~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__1 @ X2 @ X3 ) ) )
= eigen__1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP9
=> ~ sP6 )
=> ( ( ^ [X1: $i,X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X1 @ X2 ) ) )
= eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP9
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ^ [X1: $i,X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X1 @ X2 ) ) )
!= eigen__1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X1 @ X2 ) ) )
= ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ eigen__4 @ X1 ) ) )
!= ( eigen__1 @ eigen__4 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ eigen__4 @ X1 ) ) )
= ( eigen__1 @ eigen__4 @ X1 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ~ ( sP1
=> ~ sP7 ) )
!= sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP1
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP7,
introduced(assumption,[]) ).
thf(h15,assumption,
( sP1
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h14,h13,h14,h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[h14,h14]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h14])],[h13,1,h17,h14]) ).
thf(h18,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(3,plain,
( sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h15,h16,h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[3,4,5,6,7,8,h7,h8,h18,h16]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h15,h16,h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[h16,h16]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h16,h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h16])],[h15,9,10,h18,h16]) ).
thf(12,plain,
$false,
inference(tab_be,[status(thm),assumptions([h12,h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_be(discharge,[h13,h14]),tab_be(discharge,[h15,h16])],[h12,2,11,h13,h14,h15,h16]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__5)],[h11,12,h12]) ).
thf(14,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_fe(discharge,[h11])],[h10,13,h11]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h9,14,h10]) ).
thf(16,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_fe(discharge,[h9])],[h6,15,h9]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,16,h7,h8]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,18,h4]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,19,h3]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,20,h2]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( ( X3 @ X5 )
=> ~ ( X4 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X5: $i,X6: $i] :
~ ( ( X1 @ X6 )
=> ~ ( X2 @ X5 @ X6 ) ) )
= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET673^3 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.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 03:29:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 8
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------