TSTP Solution File: SYO360^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO360^5 : 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 : n016.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 19:31:37 EDT 2022
% Result : Theorem 1.96s 2.18s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 47 ( 9 unt; 6 typ; 1 def)
% Number of atoms : 83 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 134 ( 23 ~; 18 |; 0 &; 66 @)
% ( 17 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 17 ( 1 ^ 16 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_h,type,
h: a > a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_j,type,
j: a > a ).
thf(ty_g,type,
g: ( a > a ) > a > a ).
thf(ty_f,type,
f: ( a > a ) > a > a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
( ( f @ h @ X1 )
!= ( g @ j @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: a > a,X2: a] :
( ( f @ X1 @ X2 )
= ( g @ X1 @ X2 ) )
=> ~ ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( f @ j @ eigen__0 )
= ( g @ j @ eigen__0 ) )
=> ( ( f @ h @ eigen__0 )
!= ( f @ j @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( f @ h @ X1 )
= ( g @ j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( f @ j @ X1 )
= ( g @ j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ j @ eigen__0 )
= ( g @ j @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( h = j ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( X1
= ( g @ j @ eigen__0 ) )
=> ( ( f @ h @ eigen__0 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( f @ h @ eigen__0 )
!= ( g @ j @ eigen__0 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f @ h @ eigen__0 )
= ( g @ j @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( f @ h )
= ( g @ j ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP1
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ( X1 @ ( g @ j @ eigen__0 ) )
=> ! [X2: a] :
( ( X2
= ( g @ j @ eigen__0 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( f @ h @ eigen__0 )
= ( f @ j @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > a,X2: a] :
( ( f @ X1 @ X2 )
= ( g @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cEDEC1,conjecture,
sP13 ).
thf(h1,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[cEDEC1]) ).
thf(1,plain,
( sP7
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP15,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP16
| ~ sP7
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| ~ sP5
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP17
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP6,
inference(eq_ind_sym,[status(thm)],]) ).
thf(12,plain,
( sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP1
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP3
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(15,plain,
( sP12
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP13
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP13
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO360^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n016.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 08:32:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.18 % SZS status Theorem
% 1.96/2.18 % Mode: mode506
% 1.96/2.18 % Inferences: 56
% 1.96/2.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------