%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO221^5 : 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 : n021.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 03:25:10 PM UTC 2025
% Result : Theorem 1.12s 1.38s
% Output : Proof 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 35 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 83 ( 14 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 33 ~; 16 |; 0 &; 20 @)
% ( 14 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 19 con; 0-2 aty)
% Number of variables : 13 ( 1 ^; 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_b,type,
b: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( ( a = X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( cP @ a )
=> ( a = b ) )
=> ~ ( ~ ( ! [X1: $i] :
( ( cP @ X1 )
=> ( cP @ X1 ) )
=> ! [X1: $i] :
~ ( cP @ X1 ) )
=> ( cP @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ! [X1: $i] :
( ( a = X1 )
=> ( cP @ X1 ) )
=> ! [X1: $i] : ( a != X1 ) )
=> ( a = b ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( a = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( a = X1 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( cP @ a )
=> ( a = b ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( a = a ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cP @ a )
=> ( a = b ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ! [X1: $i] : ( a != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
~ ( ~ sP8
=> ~ ( ~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) )
=> ( X1 @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP @ a ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] : ( a != X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cBLEDSOE6,conjecture,
~ sP10 ).
thf(h1,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[cBLEDSOE6]) ).
thf(1,plain,
( ~ sP11
| sP2
| ~ sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( sP14
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP14
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
sP7,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP5
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(6,plain,
( ~ sP13
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| ~ sP5
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP1
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| sP9
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP8
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP10
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP10
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SYO221^5 : TPTP v9.2.0. Released v4.0.0.
% 0.13/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Oct 9 01:15:53 EDT 2025
% 0.15/0.36 % CPUTime :
% 1.12/1.38 % SZS status Theorem
% 1.12/1.38 % Mode: mode506
% 1.12/1.38 % Inferences: 78171
% 1.12/1.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------