TSTP Solution File: SEU820^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU820^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 17:36:04 EDT 2023
% Result : Theorem 25.10s 25.38s
% Output : Proof 25.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = emptyset ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset @ eigen__0 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( subset @ X1 @ emptyset )
=> ( X1 = emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__0 @ ( powerset @ emptyset ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__7 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__6 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__0 @ ( powerset @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( subset @ X1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ eigen__10 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__4 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_nonempty,definition,
( nonempty
= ( ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).
thf(def_vacuousDall,definition,
( vacuousDall
= ( ! [X1: $i > $o,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ emptyset )
@ ( X1 @ X2 ) ) ) ) ).
thf(def_subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( subset @ X1 @ emptyset )
@ ( X1 = emptyset ) ) ) ) ).
thf(def_powersetE1,definition,
( powersetE1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ( subset @ X2 @ X1 ) ) ) ) ).
thf(def_transitiveset,definition,
( transitiveset
= ( ^ [X1: $i] :
! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( subset @ X2 @ X1 ) ) ) ) ).
thf(def_stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [X1: $i] :
( ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( in @ X2 @ X3 )
& ( in @ X3 @ X4 ) )
@ ( in @ X2 @ X4 ) ) ) ) )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ( X2 = X3 )
| ( in @ X2 @ X3 )
| ( in @ X3 @ X2 ) ) ) )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( (~) @ ( in @ X2 @ X2 ) ) ) ) ) ) ).
thf(def_wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [X1: $i] :
( ( stricttotalorderedByIn @ X1 )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( powerset @ X1 ) )
@ ( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( nonempty @ X2 )
@ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X2 )
@ ( ( X3 = X4 )
| ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).
thf(def_ordinal,definition,
( ordinal
= ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) ) ) ).
thf(emptysetOrdinal,conjecture,
( sP7
=> ( sP3
=> ( sP13
=> ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ( sP3
=> ( sP13
=> ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[emptysetOrdinal]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ( sP13
=> ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP13
=> ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP11
=> ( subset @ eigen__10 @ emptyset ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP11,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( subset @ eigen__10 @ emptyset ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,h1,h10]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,3,h10,h11]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__10)],[h7,4,h9]) ).
thf(h12,assumption,
( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP6
=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( in @ eigen__7 @ X1 )
=> ~ ( in @ X1 @ X2 ) )
=> ( in @ eigen__7 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP6,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( in @ eigen__7 @ X1 )
=> ~ ( in @ X1 @ X2 ) )
=> ( in @ eigen__7 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ( in @ eigen__8 @ emptyset )
=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( ~ ( ( in @ eigen__7 @ eigen__8 )
=> ~ ( in @ eigen__8 @ X1 ) )
=> ( in @ eigen__7 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
in @ eigen__8 @ emptyset,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( ~ ( ( in @ eigen__7 @ eigen__8 )
=> ~ ( in @ eigen__8 @ X1 ) )
=> ( in @ eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ( in @ eigen__9 @ emptyset )
=> ( ~ ( ( in @ eigen__7 @ eigen__8 )
=> ~ ( in @ eigen__8 @ eigen__9 ) )
=> ( in @ eigen__7 @ eigen__9 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
in @ eigen__9 @ emptyset,
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ~ ( ( in @ eigen__7 @ eigen__8 )
=> ~ ( in @ eigen__8 @ eigen__9 ) )
=> ( in @ eigen__7 @ eigen__9 ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ( in @ eigen__7 @ eigen__8 )
=> ~ ( in @ eigen__8 @ eigen__9 ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( in @ eigen__7 @ eigen__9 ),
introduced(assumption,[]) ).
thf(h29,assumption,
in @ eigen__7 @ eigen__8,
introduced(assumption,[]) ).
thf(h30,assumption,
in @ eigen__8 @ eigen__9,
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP4
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[6,7,h1,h19]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h27,8,h29,h30]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,9,h27,h28]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h24,10,h25,h26]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__9)],[h23,11,h24]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[h21,12,h22,h23]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__8)],[h20,13,h21]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,14,h19,h20]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__7)],[h16,15,h18]) ).
thf(h31,assumption,
~ ( ( in @ eigen__5 @ emptyset )
=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( ~ ( ( eigen__5 != X1 )
=> ( in @ eigen__5 @ X1 ) )
=> ( in @ X1 @ eigen__5 ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
in @ eigen__5 @ emptyset,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( ~ ( ( eigen__5 != X1 )
=> ( in @ eigen__5 @ X1 ) )
=> ( in @ X1 @ eigen__5 ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( sP8
=> ( ~ ( ( eigen__5 != eigen__6 )
=> ( in @ eigen__5 @ eigen__6 ) )
=> ( in @ eigen__6 @ eigen__5 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
sP8,
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ~ ( ( eigen__5 != eigen__6 )
=> ( in @ eigen__5 @ eigen__6 ) )
=> ( in @ eigen__6 @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ( eigen__5 != eigen__6 )
=> ( in @ eigen__5 @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
~ ( in @ eigen__6 @ eigen__5 ),
introduced(assumption,[]) ).
thf(h39,assumption,
eigen__5 != eigen__6,
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( in @ eigen__5 @ eigen__6 ),
introduced(assumption,[]) ).
thf(17,plain,
( ~ sP4
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[17,18,h1,h35]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h37,19,h39,h40]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h36,20,h37,h38]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h34,21,h35,h36]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__6)],[h33,22,h34]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h32,h33])],[h31,23,h32,h33]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__5)],[h17,24,h31]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,16,25,h16,h17]) ).
thf(h41,assumption,
~ ( sP14
=> ~ ( in @ eigen__4 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
sP14,
introduced(assumption,[]) ).
thf(h43,assumption,
in @ eigen__4 @ eigen__4,
introduced(assumption,[]) ).
thf(27,plain,
( ~ sP4
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h42,h43,h41,h15,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[27,28,h1,h42]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h15,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h42,h43])],[h41,29,h42,h43]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h41]),tab_negall(eigenvar,eigen__4)],[h15,30,h41]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h12,26,31,h14,h15]) ).
thf(h44,assumption,
~ ( sP9
=> ( ~ sP1
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
sP9,
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( ~ sP1
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h48,assumption,
! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(33,plain,
( ~ sP5
| ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP12
| ~ sP2
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h47,h48,h45,h46,h44,h13,h8,h5,h6,h3,h4,h1,h2,h0])],[33,34,35,36,37,h3,h5,h45,h47]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h44,h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h47,h48])],[h46,38,h47,h48]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h44,h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h45,h46])],[h44,39,h45,h46]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__0)],[h13,40,h44]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h8,32,41,h12,h13]) ).
thf(43,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,5,42,h7,h8]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,43,h5,h6]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,44,h3,h4]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,45,h1,h2]) ).
thf(0,theorem,
( sP7
=> ( sP3
=> ( sP13
=> ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ( subset @ X1 @ emptyset ) )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ ( in @ X1 @ X1 ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( ( X1 != emptyset )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU820^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n008.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
% 0.13/0.35 % DateTime : Wed Aug 23 18:58:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 25.10/25.38 % SZS status Theorem
% 25.10/25.38 % Mode: cade22grackle2x798d
% 25.10/25.38 % Steps: 331
% 25.10/25.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------