TSTP Solution File: SYO543^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO543^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : Thu Jul 21 19:33:19 EDT 2022
% Result : Theorem 2.07s 2.27s
% Output : Proof 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 31
% Syntax : Number of formulae : 39 ( 12 unt; 3 typ; 3 def)
% Number of atoms : 109 ( 34 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 159 ( 71 ~; 14 |; 0 &; 20 @)
% ( 12 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 25 ( 14 ^ 11 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_epsii,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(h0,assumption,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $i] :
( ( epsii
@ ^ [X2: $i > $i] :
( ( eigen__0
=> ( X2 != X1 ) )
=> ~ ( ~ eigen__0
=> ( X2 != X1 ) ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $o] :
~ ! [X2: $i > $i] :
( ( epsii
@ ^ [X3: $i > $i] :
( ( X1
=> ( X3 != X2 ) )
=> ~ ( ~ X1
=> ( X3 != X2 ) ) ) )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $i] :
( ( epsii
@ ^ [X2: $i > $i] :
( ( eigen__0
=> ( X2 != X1 ) )
=> ~ ( ~ eigen__0
=> ( X2 != X1 ) ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0
=> ( ( epsii
@ ^ [X1: $i > $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__1 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0
=> ( eigen__1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( eigen__1 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ~ ( ~ eigen__0
=> ( ( epsii
@ ^ [X1: $i > $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__1 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ eigen__0
=> ( ( epsii
@ ^ [X1: $i > $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__1 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( epsii
@ ^ [X1: $i > $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__1 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $o,X2: $i > $i] :
( ( epsii
@ ^ [X3: $i > $i] :
( ( X1
=> ( X3 != X2 ) )
=> ~ ( ~ X1
=> ( X3 != X2 ) ) ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP9
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $i] :
~ ( ( sP9
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP9
=> ( X1 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_if,definition,
( if
= ( ^ [X1: $o,X2: $i > $i,X3: $i > $i] :
( epsii
@ ^ [X4: $i > $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(conj,conjecture,
sP10 ).
thf(h2,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
( ~ sP7
| ~ sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP5,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP3
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP2
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| ~ sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ~ ! [X2: $i > $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ) ).
thf(10,plain,
( sP4
| sP12 ),
inference(choice_rule,[status(thm)],[choiceaxii]) ).
thf(11,plain,
( sP1
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(12,plain,
( sP10
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
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(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h2])],[13,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO543^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 8 19:13:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 2.07/2.27 % SZS status Theorem
% 2.07/2.27 % Mode: mode506
% 2.07/2.27 % Inferences: 36477
% 2.07/2.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------