%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV057^5 : 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 : n014.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 02:56:11 PM UTC 2025
% Result : Theorem 1.11s 1.42s
% Output : Proof 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 45
% Syntax : Number of formulae : 54 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 157 ( 42 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 248 ( 85 ~; 23 |; 0 &; 57 @)
% ( 21 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 27 con; 0-2 aty)
% Number of variables : 40 ( 4 ^; 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > $o] :
~ ~ ! [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ~ ( ( X1 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) )
=> ~ ! [X5: a] :
( ~ ( ( X1 @ X5 )
=> ( X3
!= ( X2 @ X5 ) ) )
=> ( X5 = X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
( ~ ( ( eigen__0 @ X2 )
=> ( X1 != X2 ) )
=> ~ ! [X3: a] :
( ~ ( ( eigen__0 @ X3 )
=> ( X1 != X3 ) )
=> ( X3 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) )
=> ( X1 = eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > a] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__0 @ ( X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: a] :
( ~ ( ( eigen__0 @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ! [X4: a] :
( ~ ( ( eigen__0 @ X4 )
=> ( X2
!= ( X1 @ X4 ) ) )
=> ( X4 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__2 = eigen__4 )
=> ( eigen__4 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
( ~ ( ( eigen__0 @ X2 )
=> ( X1 != X2 ) )
=> ~ ! [X3: a] :
( ~ ( ( eigen__0 @ X3 )
=> ( X1 != X3 ) )
=> ( X3 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> ~ ! [X1: a] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) )
=> ~ ! [X2: a] :
( ~ ( ( eigen__0 @ X2 )
=> ( eigen__2 != X2 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( eigen__0 @ eigen__4 )
=> ~ sP7 )
=> ( eigen__4 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( sP3
=> ( eigen__2 != eigen__2 ) )
=> ~ ! [X1: a] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) )
=> ( X1 = eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__4 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__0 @ X1 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a > $o] :
~ ! [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ~ ( ( X1 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) )
=> ~ ! [X5: a] :
( ~ ( ( X1 @ X5 )
=> ( X3
!= ( X2 @ X5 ) ) )
=> ( X5 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) )
=> ~ ! [X2: a] :
( ~ ( ( eigen__0 @ X2 )
=> ( eigen__2 != X2 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP3
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__0 @ eigen__4 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cEQP1_1A_pme,conjecture,
sP16 ).
thf(h2,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[cEQP1_1A_pme]) ).
thf(1,plain,
( sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP8
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP21
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| ~ sP7
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
sP2,
inference(eq_sym,[status(thm)],[]) ).
thf(8,plain,
( sP20
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(9,plain,
( sP10
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP10
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
sP14,
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP18
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(13,plain,
( ~ sP19
| ~ sP3
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP17
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( sP9
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP9
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP6
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(19,plain,
( ~ sP15
| ~ sP20
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP1
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( sP16
| sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h2]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[22,h1]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h2])],[22,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEV057^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 18:53:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.11/1.42 % SZS status Theorem
% 1.11/1.42 % Mode: mode506
% 1.11/1.42 % Inferences: 41957
% 1.11/1.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------