TSTP Solution File: ITP198^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP198^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 04:02:51 EDT 2023
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_produc1020032539e_real,type,
produc1020032539e_real: $tType ).
thf(ty_set_variable_real,type,
set_variable_real: $tType ).
thf(ty_produc1993135732e_real,type,
produc1993135732e_real: $tType ).
thf(ty_produc104944723e_real,type,
produc104944723e_real: $tType ).
thf(ty_char,type,
char: $tType ).
thf(ty_denotational_interp,type,
denotational_interp: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_denotational_Games,type,
denotational_Games: denotational_interp > char > set_variable_real > set_variable_real ).
thf(ty_produc141013715e_real,type,
produc141013715e_real: ( char > real > real ) > produc104944723e_real > produc1020032539e_real ).
thf(ty_eigen__0,type,
eigen__0: char ).
thf(ty_denotational_Funcs,type,
denotational_Funcs: denotational_interp > char > real > real ).
thf(ty_denotational_Consts,type,
denotational_Consts: denotational_interp > char > real ).
thf(ty_produc2007437005e_real,type,
produc2007437005e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ).
thf(ty_denotational_Preds,type,
denotational_Preds: denotational_interp > char > real > $o ).
thf(ty_d,type,
d: real ).
thf(ty_f,type,
f: char ).
thf(ty_if_real,type,
if_real: $o > real > real > real ).
thf(ty_eigen__1,type,
eigen__1: real ).
thf(ty_produc2125489830e_real,type,
produc2125489830e_real: ( char > real ) > produc1020032539e_real > produc1993135732e_real ).
thf(ty_denota1150374853interp,type,
denota1150374853interp: produc1993135732e_real > denotational_interp ).
thf(ty_i,type,
i: denotational_interp ).
thf(sP1,plain,
( sP1
<=> ( denotational_Preds @ i @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: char > real > $o,X2: char > set_variable_real > set_variable_real] :
( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X3: char] : ( if_real @ ( X3 = f ) @ d @ ( denotational_Consts @ i @ X3 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ X1 @ X2 ) ) ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: char > set_variable_real > set_variable_real] :
( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ X1 ) ) ) ) )
= ( denotational_Preds @ i ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: char > real > real,X2: char > real > $o,X3: char > set_variable_real > set_variable_real] :
( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X4: char] : ( if_real @ ( X4 = f ) @ d @ ( denotational_Consts @ i @ X4 ) )
@ ( produc141013715e_real @ X1 @ ( produc2007437005e_real @ X2 @ X3 ) ) ) ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
= ( denotational_Preds @ i ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
@ eigen__0
@ eigen__1 )
= sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: char] :
( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
@ X1 )
= ( denotational_Preds @ i @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: char > real,X2: char > real > real,X3: char > real > $o,X4: char > set_variable_real > set_variable_real] :
( ( denotational_Preds @ ( denota1150374853interp @ ( produc2125489830e_real @ X1 @ ( produc141013715e_real @ X2 @ ( produc2007437005e_real @ X3 @ X4 ) ) ) ) )
= X3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
@ eigen__0
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: real] :
( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
@ eigen__0
@ X1 )
= ( denotational_Preds @ i @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( denotational_Preds
@ ( denota1150374853interp
@ ( produc2125489830e_real
@ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
@ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
@ eigen__0 )
= ( denotational_Preds @ i @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(conj_0,conjecture,
sP5 ).
thf(h0,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP9
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_0_Preds__mkinterp,axiom,
sP8 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h5,h6,fact_0_Preds__mkinterp]) ).
thf(11,plain,
( ~ sP6
| sP9
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP11
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0])],[11,12,13,14,15,16,17,18,19,h7,h8,fact_0_Preds__mkinterp]) ).
thf(21,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,10,20,h5,h6,h7,h8]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,21,h4]) ).
thf(23,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,22,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,24,h1]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP198^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n003.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 : 300
% 0.13/0.33 % DateTime : Sun Aug 27 12:07:09 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % Mode: cade22sinegrackle2x6978
% 0.19/0.49 % Steps: 848
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------