%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL738^5 : 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 01:02:32 PM UTC 2026
% Result : Theorem 17.76s 18.21s
% Output : Proof 17.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 34 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 26 ~; 6 |; 0 &; 33 @)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 23 ( 1 ^; 18 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ! [X1: b] :
~ ( eigen__4 @ X1 )
=> ( eigen__4
@ @+[X1: b] : ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
~ ( ! [X3: b > $o] :
~ ! [X4: b] :
~ ! [X5: b] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o,X5: b] :
( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__4
@ @+[X1: b] : ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: b] :
~ ( eigen__4 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cX5310_SUB,conjecture,
sP3 ).
thf(h1,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[cX5310_SUB]) ).
thf(1,plain,
( sP5
| sP6 ),
inference(choice_rule,[status(thm)],[]) ).
thf(2,plain,
( sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP4
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(5,plain,
( ~ sP2
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL738^5 : 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
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 6 01:39:23 UTC 2026
% 0.11/0.36 % CPUTime :
% 17.76/18.21 % SZS status Theorem
% 17.76/18.21 % Mode: mode466
% 17.76/18.21 % Inferences: 74609
% 17.76/18.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------