%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV171^5 : 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 : n025.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 02:56:24 PM UTC 2025
% Result : Theorem 2.13s 2.44s
% Output : Proof 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 33 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 72 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 27 ~; 12 |; 0 &; 59 @)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 49 ( 26 ^; 23 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__17,type,
eigen__17: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a] :
~ ~ ! [X2: a,X3: a] :
( ( ^ [X4: a > a > a] : ( X4 @ X1 @ X1 ) )
!= ( ^ [X4: a > a > a] : ( X4 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: a] :
~ ( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__8 @ eigen__8 ) )
= ( ^ [X2: a > a > a] : ( X2 @ X1 @ X1 ) ) )
=> ( eigen__8 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
= ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__8 @ eigen__8 ) )
= ( ^ [X2: a > a > a] : ( X2 @ X1 @ X1 ) ) )
=> ( eigen__8 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( ^ [X1: a > a > a] : ( X1 @ eigen__8 @ eigen__8 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__17 @ eigen__17 ) ) )
=> ( eigen__8 = eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > a > a] :
( ( X1 @ eigen__8 @ eigen__8 )
= ( X1 @ eigen__17 @ eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__11 @ eigen__11 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__11 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
~ ! [X2: a,X3: a] :
( ( ^ [X4: a > a > a] : ( X4 @ X1 @ X1 ) )
!= ( ^ [X4: a > a > a] : ( X4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a] :
( ( ^ [X3: a > a > a] : ( X3 @ eigen__11 @ eigen__11 ) )
!= ( ^ [X3: a > a > a] : ( X3 @ eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: a,X2: a] :
( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
= ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
=> ( X1 = X2 ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] : ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > ( a > a > a ) > a] :
( ! [X2: a,X3: a] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ~ ! [X2: a] :
~ ! [X3: a,X4: a] :
( ( X1 @ X2 )
!= ( ^ [X5: a > a > a] : ( X5 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__8 = eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a,X2: a] :
( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
= ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__8 @ eigen__8 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__17 @ eigen__17 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cTHM33_pme,conjecture,
~ sP9 ).
thf(h1,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[cTHM33_pme]) ).
thf(1,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP2
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP2
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP1
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(7,plain,
( ~ sP8
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP5
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(10,plain,
( sP11
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(11,plain,
( ~ sP7
| ~ sP11
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV171^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 18:55:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.13/2.44 % SZS status Theorem
% 2.13/2.44 % Mode: mode506
% 2.13/2.44 % Inferences: 90859
% 2.13/2.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------