%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:02:31 PM UTC 2026
% Result : Theorem 16.64s 17.00s
% Output : Proof 16.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 35
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 90 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 49 ~; 18 |; 0 &; 56 @)
% ( 16 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 19 con; 0-2 aty)
% Number of variables : 43 ( 3 ^; 33 !; 0 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(h0,assumption,
! [X1: ( ( a > $o ) > $o ) > $o,X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( a > $o ) > $o] :
~ ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( a > $o ) > a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ( eigen__0 @ X1 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__4
@ @+[X1: a] : ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
~ ( eigen__4 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
~ ( eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( a > $o ) > a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> ( eigen__2
@ @+[X1: a] : ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__2
@ @+[X1: a] : ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cTHM541,conjecture,
sP11 ).
thf(h2,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[cTHM541]) ).
thf(1,plain,
( ~ sP6
| ~ sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP1
| sP3 ),
inference(choice_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP5
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP15
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(7,plain,
( sP16
| sP7 ),
inference(choice_rule,[status(thm)],[]) ).
thf(8,plain,
( sP10
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP10
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP14
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(11,plain,
( ~ sP12
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP8
| ~ sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( sP2
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP2
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP9
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(16,plain,
( sP11
| sP12
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,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,h2]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[17,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h2])],[17,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 21:56:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 16.64/17.00 % SZS status Theorem
% 16.64/17.00 % Mode: mode448
% 16.64/17.00 % Inferences: 254
% 16.64/17.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------