TSTP Solution File: SEV097^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV097^5 : 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 : n002.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 19:32:36 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 34
% Syntax : Number of formulae : 47 ( 16 unt; 9 typ; 2 def)
% Number of atoms : 129 ( 2 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 401 ( 128 ~; 5 |; 0 &; 184 @)
% ( 6 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 86 ( 2 ^; 84 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_f,type,
f: a > b > $o ).
thf(ty_cS,type,
cS: b > b > $o ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_z,type,
z: a ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: b] :
~ ~ ( f @ eigen__0 @ X1 ) ) ),
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__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ( f @ eigen__0 @ eigen__1 )
=> ~ ( ~ ( f @ X1 @ eigen__1 )
=> ~ ( cR @ eigen__0 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
~ ( f @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
~ ! [X2: a] :
( ~ ( f @ eigen__0 @ X1 )
=> ~ ( ~ ( f @ X2 @ X1 )
=> ~ ( cR @ eigen__0 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ~ sP3
=> ~ ( ~ ( f @ X1 @ eigen__1 )
=> ~ ( cR @ eigen__0 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> ~ ( ~ ( f @ eigen__6 @ eigen__1 )
=> ~ ( cR @ eigen__0 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cTHM552C_pme,conjecture,
( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ( ~ ( ~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) )
=> ! [X1: a] :
~ ! [X2: b] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ( ~ ( ~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) )
=> ! [X1: a] :
~ ! [X2: b] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM552C_pme]) ).
thf(h3,assumption,
~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) )
=> ! [X1: a] :
~ ! [X2: b] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a] : ( cR @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a] :
~ ! [X2: b] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP5,
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(3,plain,
( ~ sP2
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP1
| sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(5,plain,
( ~ sP5
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,h11,h13]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__0)],[h8,6,h13]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,7,h11,h12]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h4,9,h7,h8]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,10,h5,h6]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ( ~ ( ~ ( sP5
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) )
=> ! [X1: a] :
~ ! [X2: b] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[12,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV097^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n002.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 02:30:46 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 175
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------