TSTP Solution File: SEU935^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU935^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 17:37:57 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 44
% Syntax : Number of formulae : 58 ( 18 unt; 8 typ; 4 def)
% Number of atoms : 103 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 172 ( 72 ~; 16 |; 0 &; 57 @)
% ( 14 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 50 ( 4 ^; 46 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(ty_eigen__1,type,
eigen__1: b > c ).
thf(ty_eigen__2,type,
eigen__2: c ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__0,type,
eigen__0: a > b ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b] :
( ( eigen__1 @ X1 )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__1
@ ^ [X1: a] :
( ( eigen__0 @ X1 )
!= ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a] :
( ( eigen__0 @ X1 )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: b] :
( ( eigen__1 @ X1 )
!= ( eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: c] :
~ ! [X2: b] :
( ( eigen__1 @ X2 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__15 )
= ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__1 @ eigen__3 )
= ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ eigen__3 )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__8 ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__3
= ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: b] :
( ( eigen__1 @ X1 )
!= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__8 )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
~ ! [X2: a] :
( ( eigen__0 @ X2 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( eigen__1 @ ( eigen__0 @ X1 ) )
!= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
!= ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
!= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: b] :
( ( eigen__1 @ X1 )
!= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__1 @ eigen__9 )
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cFN_THM_2_pme,conjecture,
! [X1: a > b,X2: b > c] :
( ~ ( ! [X3: b] :
~ ! [X4: a] :
( ( X1 @ X4 )
!= X3 )
=> ~ ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) )
=> ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: a > b,X2: b > c] :
( ~ ( ! [X3: b] :
~ ! [X4: a] :
( ( X1 @ X4 )
!= X3 )
=> ~ ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) )
=> ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 ) ),
inference(assume_negation,[status(cth)],[cFN_THM_2_pme]) ).
thf(h3,assumption,
~ ! [X1: b > c] :
( ~ ( sP9
=> ~ ! [X2: c] :
~ ! [X3: b] :
( ( X1 @ X3 )
!= X2 ) )
=> ! [X2: c] :
~ ! [X3: a] :
( ( X1 @ ( eigen__0 @ X3 ) )
!= X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP9
=> ~ sP1 )
=> ! [X1: c] :
~ ! [X2: a] :
( ( eigen__1 @ ( eigen__0 @ X2 ) )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP9
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: c] :
~ ! [X2: a] :
( ( eigen__1 @ ( eigen__0 @ X2 ) )
!= X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP6
| ~ sP8
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP5
| ~ sP3
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( sP11
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15]) ).
thf(5,plain,
( ~ sP9
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(8,plain,
( ~ sP1
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(10,plain,
( ~ sP9
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP13
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(12,plain,
( ~ sP1
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h7,h8,h9]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h6,13,h9]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,16,h4]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,17,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
! [X1: a > b,X2: b > c] :
( ~ ( ! [X3: b] :
~ ! [X4: a] :
( ( X1 @ X4 )
!= X3 )
=> ~ ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) )
=> ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[18,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU935^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 16:27:08 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.54 % SZS status Theorem
% 0.21/0.54 % Mode: cade22grackle2xfee4
% 0.21/0.54 % Steps: 1640
% 0.21/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------