%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL733^5 : 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 : n026.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 2.04s 2.33s
% Output : Proof 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 23
% Syntax : Number of formulae : 30 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 55 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 119 ( 50 ~; 11 |; 0 &; 33 @)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 32 ( 2 ^; 30 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(ty_eigen__1,type,
eigen__1: b > $o ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: b > $o] :
~ ~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: b] :
~ ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( b > $o ) > b > $o] :
( ! [X2: b > $o] :
~ ! [X3: b] :
~ ( ~ ! [X4: b] :
~ ( X2 @ X4 )
=> ( X2 @ X3 ) )
=> ~ ! [X2: ( b > $o ) > b] :
~ ! [X3: b > $o] :
( ~ ! [X4: b] :
~ ( X3 @ X4 )
=> ( X3 @ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: b] :
~ ( eigen__1 @ X1 )
=> ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: b > $o] :
~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) )
=> ~ ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: b] :
~ ( ~ ! [X2: b] :
~ ( eigen__1 @ X2 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ! [X1: b] :
~ ( eigen__1 @ X1 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
~ ( eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b > $o] :
~ ! [X2: b] :
~ ( ~ ! [X3: b] :
~ ( X1 @ X3 )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cX5310_SUB4,conjecture,
sP8 ).
thf(h2,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[cX5310_SUB4]) ).
thf(1,plain,
( sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP9
| sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(4,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( sP10
| sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( ~ sP4
| ~ sP10
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP8
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP8
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h2])],[11,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.39 % Computer : n026.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 5 21:20:26 UTC 2026
% 0.14/0.40 % CPUTime :
% 2.04/2.33 % SZS status Theorem
% 2.04/2.33 % Mode: mode506
% 2.04/2.33 % Inferences: 99122
% 2.04/2.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------