%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU874^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 02:42:04 PM UTC 2025
% Result : Theorem 71.11s 71.12s
% Output : Proof 71.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 51
% Syntax : Number of formulae : 61 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 180 ( 34 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 315 ( 81 ~; 30 |; 0 &; 102 @)
% ( 23 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 29 con; 0-2 aty)
% Number of variables : 81 ( 33 ^; 48 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cX,type,
cX: a > $o ).
thf(ty_eigen__85,type,
eigen__85: a ).
thf(ty_eigen__84,type,
eigen__84: ( a > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( cX @ X2 ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__85,definition,
( eigen__85
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__0 = X1 )
=> ( cX @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__85])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a] :
( ( cX @ X1 )
!= ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( cX @ X3 ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( ( a > $o ) > $o ) > $o,X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__84,definition,
( eigen__84
= ( eps__2
@ ^ [X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__0 = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( eigen__0 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__84])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( cX @ X2 ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__84
@ ^ [X1: a] : $false )
=> ! [X1: a] :
( ( eigen__0 = X1 )
=> ( eigen__84
@ ^ [X2: a] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( eigen__84
@ ^ [X1: a] : $false )
=> ~ ! [X1: a > $o] :
( ( eigen__84 @ X1 )
=> ! [X2: a] :
( ( eigen__0 = X2 )
=> ( eigen__84
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) )
=> ( eigen__84
@ ^ [X1: a] : ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__0 = X1 )
=> ( eigen__84
@ ^ [X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__0 = X1 )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__1 @ eigen__0 )
=> ( cX @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cX @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__84
@ ^ [X1: a] : ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > $o] :
( ( eigen__84 @ X1 )
=> ! [X2: a] :
( ( eigen__0 = X2 )
=> ( eigen__84
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__1 @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( cX @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__84
@ ^ [X1: a] : $false )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( cX @ X1 )
= ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( cX @ X3 ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__0 = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( eigen__0 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__84
@ ^ [X1: a] : $false ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cX
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( cX @ X3 ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP10
=> ~ ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cX @ eigen__85 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP13
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( cX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP7 = ( ~ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__0 = eigen__85 )
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 = eigen__85 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(cDOMLEMMA3_pme,conjecture,
sP15 ).
thf(h3,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[cDOMLEMMA3_pme]) ).
thf(1,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP17
| ~ sP23 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( sP22
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP22
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP5
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__85]) ).
thf(6,plain,
( ~ sP2
| ~ sP14
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( sP11
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP11
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP13
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__84]) ).
thf(13,plain,
( ~ sP19
| ~ sP13
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP1
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| ~ sP18
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP20
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( sP10
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP16
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP1
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(21,plain,
( sP21
| ~ sP7
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP21
| sP7
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP12
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(24,plain,
( sP15
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h3]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[25,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[26,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
sP15,
inference(contra,[status(thm),contra(discharge,[h3])],[25,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU874^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 21:14:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 71.11/71.12 % SZS status Theorem
% 71.11/71.12 % Mode: cade22grackle2x34cb
% 71.11/71.12 % Steps: 159029
% 71.11/71.12 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------