%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO266^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 Oct 9 03:25:15 PM UTC 2025
% Result : Theorem 1.10s 1.42s
% Output : Proof 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 41
% Syntax : Number of formulae : 49 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 125 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 182 ( 54 ~; 26 |; 0 &; 53 @)
% ( 18 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 23 con; 0-2 aty)
% Number of variables : 15 ( 3 ^; 12 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( cP @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( ~ ( cQ @ X1 )
=> ( cP @ X1 ) )
=> ~ ( ( cQ @ X1 )
=> ( cQ @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i > $o] :
~ ~ ! [X2: $i] :
~ ( ( ~ ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( cQ @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( cP @ eigen__4 )
=> ( cQ @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( eigen__5 @ eigen__1 )
=> ( cP @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cQ @ eigen__4 )
=> ( cQ @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cQ @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ~ ( ( eigen__5 @ eigen__1 )
=> ( cQ @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cQ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( cP @ X1 )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP4
=> ( cP @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( cP @ eigen__1 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ~ ! [X1: $i > $o] :
~ ! [X2: $i] :
~ ( ( ~ ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( cQ @ X2 ) ) ) )
= sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o] :
~ ! [X2: $i] :
~ ( ( ~ ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
~ ( ( ~ ( cQ @ X1 )
=> ( cP @ X1 ) )
=> ~ ( ( cQ @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
~ ( ( ~ ( eigen__5 @ X1 )
=> ( cP @ X1 ) )
=> ~ ( ( eigen__5 @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__5 @ eigen__1 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP8
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__5 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM44,conjecture,
sP10 ).
thf(h2,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[cTHM44]) ).
thf(1,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP17
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP12
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP15
| ~ sP17
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP5
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP14
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( sP11
| sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(13,plain,
( ~ sP16
| ~ sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP13
| sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(15,plain,
( sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP9
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP7
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(18,plain,
( ~ sP11
| ~ sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP10
| sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP10
| ~ sP11
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h2]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[21,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h2])],[21,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO266^5 : TPTP v9.2.0. Released v4.0.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 01:38:08 EDT 2025
% 0.20/0.35 % CPUTime :
% 1.10/1.42 % SZS status Theorem
% 1.10/1.42 % Mode: mode506
% 1.10/1.42 % Inferences: 98299
% 1.10/1.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------