%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO538^1 : 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 : n020.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 03:25:58 PM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( ~ $false
=> ( ( eps
@ ^ [X1: $i] :
( ( $false
=> ( X1 != eigen__0 ) )
=> ~ ( ~ $false
=> ( X1 != eigen__1 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( ( $false
=> ( X1 != eigen__0 ) )
=> ~ ( ~ $false
=> ( X1 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( $false
=> ( ( eps
@ ^ [X1: $i] :
( ( $false
=> ( X1 != eigen__0 ) )
=> ~ ( ~ $false
=> ( X1 != eigen__1 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ~ $false
=> ( eigen__0 != eigen__0 ) )
=> ~ ( $false
=> ( eigen__0 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ $false
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( $false
=> ( eigen__1 != eigen__0 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( $false
=> ( ( eps
@ ^ [X1: $i] :
( ( ~ $false
=> ( X1 != eigen__0 ) )
=> ~ ( $false
=> ( X1 != eigen__1 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> $false ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ~ sP9
=> ( ( eps
@ ^ [X1: $i] :
( ( ~ sP9
=> ( X1 != eigen__0 ) )
=> ~ ( sP9
=> ( X1 != eigen__1 ) ) ) )
!= eigen__0 ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP9
=> ( eigen__0 != eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP9
=> ( ( eps
@ ^ [X1: $i] :
( ( ~ sP9
=> ( X1 != eigen__0 ) )
=> ~ ( sP9
=> ( X1 != eigen__1 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eps
@ ^ [X1: $i] :
( ( ~ sP9
=> ( X1 != eigen__0 ) )
=> ~ ( sP9
=> ( X1 != eigen__1 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
~ ( ( ~ sP9
=> ( X1 != eigen__0 ) )
=> ~ ( sP9
=> ( X1 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eps
@ ^ [X1: $i] :
( ( sP9
=> ( X1 != eigen__0 ) )
=> ~ ( ~ sP9
=> ( X1 != eigen__1 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(def_if,definition,
( if
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i] :
~ ( ( ( eps
@ ^ [X3: $i] :
( ( ~ sP9
=> ( X3 != X1 ) )
=> ~ ( ~ ~ sP9
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X3: $i] :
( ( sP9
=> ( X3 != X1 ) )
=> ~ ( ~ sP9
=> ( X3 != X2 ) ) ) )
!= X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
~ ( ( ( eps
@ ^ [X3: $i] :
( ( ~ sP9
=> ( X3 != X1 ) )
=> ~ ( sP9
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X3: $i] :
( ( sP9
=> ( X3 != X1 ) )
=> ~ ( ~ sP9
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $i] :
~ ( ( ( eps
@ ^ [X2: $i] :
( ( ~ sP9
=> ( X2 != eigen__0 ) )
=> ~ ( sP9
=> ( X2 != X1 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ( sP9
=> ( X2 != eigen__0 ) )
=> ~ ( ~ sP9
=> ( X2 != X1 ) ) ) )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( sP14
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP13
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| ~ sP13
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
sP16,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
~ sP9,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP11
| sP9
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP5
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP15
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(9,plain,
( sP10
| sP15 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h3]) ).
thf(11,plain,
( sP1
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP4
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP12
| ~ sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
~ sP9,
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP6
| sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP7
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP3
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP12
| sP3 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h1,h0])],[11,12,13,14,15,16,17,18,19,h4]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,10,20,h3,h4]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,21,h2]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
~ ( ( ( eps
@ ^ [X3: $i] :
( ( ~ sP9
=> ( X3 != X1 ) )
=> ~ ( ~ ~ sP9
=> ( X3 != X2 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X3: $i] :
( ( sP9
=> ( X3 != X1 ) )
=> ~ ( ~ sP9
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO538^1 : TPTP v9.2.0. Released v5.2.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n020.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 : Thu Oct 9 01:02:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % Mode: mode213
% 0.14/0.38 % Inferences: 64
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------