%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV431^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 02:56:49 PM UTC 2025
% Result : Theorem 22.09s 22.30s
% Output : Proof 22.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 53 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 63 ( 14 ~; 8 |; 0 &; 28 @)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 16 ( 1 ^; 9 !; 0 ?; 16 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_f,type,
f: a > b ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
( ( @+[X2: a] :
( ( f @ X2 )
= ( f @ X1 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ( ( f @ X1 )
= ( f @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( @+[X1: a] :
( ( f @ X1 )
= ( f @ eigen__1 ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( @+[X2: a] :
( ( f @ X2 )
= ( f @ X1 ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( f @ X1 )
!= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ eigen__1 )
= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f
@ @+[X1: a] :
( ( f @ X1 )
= ( f @ eigen__1 ) ) )
= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ( f
@ @+[X2: a] :
( ( f @ X2 )
= ( f @ eigen__1 ) ) )
= ( f @ X1 ) )
=> ( ( @+[X2: a] :
( ( f @ X2 )
= ( f @ eigen__1 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b > a] :
~ ! [X2: a] :
( ( X1 @ ( f @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(invexists,conjecture,
~ sP8 ).
thf(h1,negated_conjecture,
sP8,
inference(assume_negation,[status(cth)],[invexists]) ).
thf(1,plain,
sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( sP6
| sP4 ),
inference(choice_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| ~ sP6
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP3
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP8
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(finj,axiom,
sP1 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,finj,h1]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
~ sP8,
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEV431^1 : TPTP v9.2.0. Released v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 19:06:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 22.09/22.30 % SZS status Theorem
% 22.09/22.30 % Mode: mode459
% 22.09/22.30 % Inferences: 422
% 22.09/22.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------