TSTP Solution File: SEV096^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV096^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 : 600s
% DateTime : Tue Jul 19 18:04:50 EDT 2022
% Result : Theorem 0.51s 0.72s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 51 ( 14 unt; 9 typ; 2 def)
% Number of atoms : 146 ( 2 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 458 ( 154 ~; 9 |; 0 &; 203 @)
% ( 9 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 92 ( 2 ^ 90 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_cS,type,
cS: b > b > $o ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(ty_z,type,
z: a ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_f,type,
f: a > b > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( f @ eigen__8 @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ eigen__8 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( f @ z @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ z @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ~ ( f @ z @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ z @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ~ ( f @ eigen__8 @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ eigen__8 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( f @ eigen__8 @ eigen__0 )
=> ~ ( cR @ z @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cR @ z @ z ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( f @ eigen__8 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
~ ! [X2: a] :
( ~ ( f @ X1 @ eigen__0 )
=> ~ ( ~ ( f @ X2 @ eigen__0 )
=> ~ ( cR @ X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( f @ z @ eigen__0 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP6
=> ~ ( ~ ( f @ eigen__12 @ eigen__0 )
=> ~ ( cR @ eigen__8 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM552E_pme,conjecture,
( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ sP2 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [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: b] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ sP2 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [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: b] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM552E_pme]) ).
thf(h2,assumption,
~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [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: b] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [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(h7,assumption,
~ ! [X1: b] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(3,plain,
( ~ sP7
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP1
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(7,plain,
( ~ sP7
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h5,h12]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__0)],[h7,9,h12]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,10,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h3,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,13,h4,h5]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,14,h2,h3]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ sP2 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [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: b] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SEV096^5 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.08 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 600
% 0.09/0.27 % DateTime : Tue Jun 28 14:53:12 EDT 2022
% 0.09/0.27 % CPUTime :
% 0.51/0.72 % SZS status Theorem
% 0.51/0.72 % Mode: mode213
% 0.51/0.72 % Inferences: 6306
% 0.51/0.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------