TSTP Solution File: SEV054^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV054^5 : 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 : n021.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 18:04:38 EDT 2022
% Result : Theorem 26.83s 26.22s
% Output : Proof 26.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 46
% Syntax : Number of formulae : 55 ( 14 unt; 4 typ; 3 def)
% Number of atoms : 158 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 449 ( 71 ~; 22 |; 0 &; 268 @)
% ( 19 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 23 con; 0-2 aty)
% Number of variables : 103 ( 24 ^ 79 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > a ).
thf(ty_eigen__1,type,
eigen__1: ( a > $o ) > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(h0,assumption,
! [X1: ( ( a > $o ) > a ) > $o,X2: ( a > $o ) > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: ( a > $o ) > a] :
~ ( ~ ( ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( eigen__0 @ X2 @ X4 ) )
=> ~ ! [X2: a > $o] :
~ ( ! [X3: a] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 @ ( X1 @ X2 ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) )
=> ( eigen__0 @ ( X1 @ X2 ) @ X3 ) ) ) )
=> ! [X2: a > a] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__0 @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X3: a] :
~ ( eigen__0 @ ( X2 @ X3 ) @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > a > $o] :
~ ! [X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > a] :
( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X4: a] :
~ ( X1 @ ( X3 @ X4 ) @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( a > a ) > $o,X2: a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__2
@ ^ [X1: a > a] :
~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X2: a] :
~ ( eigen__0 @ ( X1 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( a > $o ) > a] :
( ~ ( ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( eigen__0 @ X2 @ X4 ) )
=> ~ ! [X2: a > $o] :
~ ( ! [X3: a] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 @ ( X1 @ X2 ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) )
=> ( eigen__0 @ ( X1 @ X2 ) @ X3 ) ) ) )
=> ! [X2: a > a] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__0 @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X3: a] :
~ ( eigen__0 @ ( X2 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) )
=> ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
~ ( eigen__0 @ ( eigen__2 @ X1 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > a] :
( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X2: a] :
~ ( eigen__0 @ ( X1 @ X2 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) )
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
=> ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ! [X2: a] :
( ( eigen__0 @ X2 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( eigen__0
@ ( eigen__1
@ ^ [X2: a] : ( eigen__0 @ X2 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
=> ( eigen__0 @ X1
@ ( eigen__1
@ ^ [X2: a] : ( eigen__0 @ X2 @ X2 ) ) ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) )
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP3 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > a > $o,X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > a] :
( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X4: a] :
~ ( X1 @ ( X3 @ X4 ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
=> ( eigen__0 @ X1
@ ( eigen__1
@ ^ [X2: a] : ( eigen__0 @ X2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP15
=> ( eigen__0
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) )
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) )
@ ( eigen__1
@ ^ [X1: a] : ( eigen__0 @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a] :
( ( eigen__0
@ ( eigen__1
@ ^ [X2: a] : ( eigen__0 @ X2 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__2
@ ( eigen__1
@ ^ [X2: a] : ( eigen__0 @ X2 @ X2 ) ) )
@ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(cTHM403_pme,conjecture,
sP13 ).
thf(h3,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[cTHM403_pme]) ).
thf(1,plain,
( ~ sP4
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP11
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP19
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP17
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| ~ sP15
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP10
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( sP14
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP14
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP5
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2]) ).
thf(15,plain,
( sP18
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP12
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP1
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(19,plain,
( sP13
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h3]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[20,h2]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[21,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h3])],[20,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV054^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 : Tue Jun 28 04:50:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 26.83/26.22 % SZS status Theorem
% 26.83/26.22 % Mode: mode454
% 26.83/26.22 % Inferences: 35
% 26.83/26.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------