TSTP Solution File: SEV434^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV434^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 Aug 31 19:34:33 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 62
% Syntax : Number of formulae : 74 ( 16 unt; 7 typ; 3 def)
% Number of atoms : 169 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 162 ( 61 ~; 39 |; 0 &; 25 @)
% ( 23 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 31 con; 0-2 aty)
% Number of variables : 22 ( 3 ^; 19 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__5,type,
eigen__5: $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_f,type,
f: $o > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( f @ eigen__4 )
= ( f @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o] :
( ( f @ X1 )
!= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ eigen__5 )
= ( f @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ eigen__5 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> eigen__5 ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o] :
( ( f @ X1 )
!= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( f @ sP7 )
= ( f @ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f @ sP9 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( f @ eigen__4 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> $false ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o] :
( ( f @ X1 )
!= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( f @ sP9 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
~ ! [X2: $o] :
( ( f @ X2 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( f @ sP17 )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( f @ sP9 )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP7 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(less3,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X2 = X3 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X2 = X3 ) ),
inference(assume_negation,[status(cth)],[less3]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 != X1 )
=> ( eigen__0 = X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ~ ( ~ sP22
=> ( eigen__0 = X1 ) )
=> ( eigen__1 = X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ sP22
=> sP18 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP22
=> sP18 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(1,plain,
( sP23
| ~ sP7
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP23
| sP7
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP5
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP12
| ~ sP5
| sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP20
| sP21
| ~ sP2
| sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| ~ sP17
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| sP17
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP13
| ~ sP7
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP13
| sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP10
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| sP16
| ~ sP10
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP20
| sP18
| ~ sP12
| ~ sP20 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(14,plain,
~ sP14,
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP11
| sP1
| ~ sP11
| ~ sP21 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP11
| sP22
| ~ sP16
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(17,plain,
( sP15
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(18,plain,
( ~ sP19
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP4
| sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(20,plain,
( ~ sP19
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP8
| sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(22,plain,
( ~ sP19
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(fsurj,axiom,
sP19 ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,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,h7,h8,h6,fsurj]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,23,h7,h8]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,24,h5,h6]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,25,h4]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,26,h3]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,27,h2]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X2 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[28,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV434^1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:06:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 % SZS status Theorem
% 0.20/0.63 % Mode: cade22grackle2xfee4
% 0.20/0.63 % Steps: 1962
% 0.20/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------