TSTP Solution File: SET680^3 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 : 300s
% DateTime : Thu Aug 31 15:18:14 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( ( eigen__1 @ eigen__3 )
=> ~ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__3 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> ~ ( ( eigen__1 @ eigen__3 )
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__1 @ eigen__3 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( 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] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( 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
= ( ^ [X1: $i,X2: $i] : ( X1 = X2 ) ) ) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_transitive,definition,
( transitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X5 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(def_upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X4 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ( ( ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) )
= ( ~ ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ( ( ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) )
= ( ~ ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( ( ~ ! [X4: $i] :
~ ( eigen__0 @ X3 @ X4 ) )
= ( ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( eigen__0 @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X3 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( ( ~ ! [X3: $i] :
~ ( eigen__0 @ X2 @ X3 ) )
= ( ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP10
=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) )
= ( ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) )
= ( ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( eigen__1 @ eigen__3 )
=> ( ~ sP4 = ~ sP8 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
eigen__1 @ eigen__3,
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP4 != ~ sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
sP4,
introduced(assumption,[]) ).
thf(h12,assumption,
sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| ~ sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,h4,h13,h10]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h9,7,h13]) ).
thf(h14,assumption,
~ ( ( eigen__2 @ eigen__5 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
eigen__2 @ eigen__5,
introduced(assumption,[]) ).
thf(h16,assumption,
sP1,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP4
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h11,h12,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[9,h11,h16]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h11,h12,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,10,h15,h16]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h12,11,h14]) ).
thf(13,plain,
$false,
inference(tab_be,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,8,12,h9,h10,h11,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,15,h4,h5]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,16,h3]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,17,h2]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,18,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ( ( ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) )
= ( ~ ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:23:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: cade22grackle2xfee4
% 0.19/0.41 % Steps: 57
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------