TSTP Solution File: SEV080^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV080^5 : 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 : n022.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 19:32:33 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 30
% Syntax : Number of formulae : 37 ( 9 unt; 4 typ; 2 def)
% Number of atoms : 107 ( 39 equ; 1 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 174 ( 66 ~; 16 |; 0 &; 49 @)
% ( 11 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 16 con; 0-2 aty)
% Number of variables : 49 ( 19 ^; 30 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
( ( ^ [X3: a] :
~ ( ( eigen__0 @ X3 )
=> ( X1 != X3 ) ) )
!= ( ^ [X3: a] : ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) ) )
!= ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: a] :
( ( ^ [X3: a] :
~ ( ( eigen__0 @ X3 )
=> ( X1 != X3 ) ) )
!= ( ^ [X3: a] : ( X2 = X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) ) )
= ( ^ [X1: a] : ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ( eigen__2 != X2 ) ) )
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ( ( eigen__0 @ eigen__5 )
=> ( eigen__2 != eigen__5 ) ) )
= ( eigen__2 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__2 != X1 ) ) )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__2 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__5 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__0 @ ( X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: a] :
( ( ^ [X4: a] :
~ ( ( eigen__0 @ X4 )
=> ( X2
!= ( X1 @ X4 ) ) ) )
!= ( ^ [X4: a] : ( X3 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cEQP_1A_pme,conjecture,
! [X1: a > $o] :
~ ! [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( ^ [X5: a] :
~ ( ( X1 @ X5 )
=> ( X3
!= ( X2 @ X5 ) ) ) )
!= ( ^ [X5: a] : ( X4 = X5 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > $o] :
~ ! [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( ^ [X5: a] :
~ ( ( X1 @ X5 )
=> ( X3
!= ( X2 @ X5 ) ) ) )
!= ( ^ [X5: a] : ( X4 = X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cEQP_1A_pme]) ).
thf(h2,assumption,
! [X1: a > a] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__0 @ ( X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ! [X3: a] :
( ( ^ [X4: a] :
~ ( ( eigen__0 @ X4 )
=> ( X2
!= ( X1 @ X4 ) ) ) )
!= ( (=) @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP11
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP11
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP8
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP8
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(7,plain,
( sP2
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP7
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP1
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(12,plain,
( ~ sP9
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,13,h2]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
! [X1: a > $o] :
~ ! [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( ^ [X5: a] :
~ ( ( X1 @ X5 )
=> ( X3
!= ( X2 @ X5 ) ) ) )
!= ( ^ [X5: a] : ( X4 = X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV080^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.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 03:55:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.69 % SZS status Theorem
% 0.20/0.69 % Mode: cade22grackle2xfee4
% 0.20/0.69 % Steps: 10402
% 0.20/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------