TSTP Solution File: SEU912^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU912^5 : 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 : n025.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 14:10:48 EDT 2022
% Result : Theorem 50.03s 50.21s
% Output : Proof 50.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 171
% Syntax : Number of formulae : 186 ( 20 unt; 16 typ; 8 def)
% Number of atoms : 781 ( 46 equ; 0 cnn)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 2135 ( 574 ~; 95 |; 0 &; 781 @)
% ( 75 <=>; 610 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 249 ( 249 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 81 con; 0-2 aty)
% Number of variables : 439 ( 84 ^ 355 !; 0 ?; 439 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__7,type,
eigen__7: b > $o ).
thf(ty_cC,type,
cC: ( c > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: c > $o ).
thf(ty_eigen__26,type,
eigen__26: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_eigen__10,type,
eigen__10: b ).
thf(ty_cB,type,
cB: ( b > $o ) > $o ).
thf(ty_cA,type,
cA: ( a > $o ) > $o ).
thf(ty_eigen__22,type,
eigen__22: a > $o ).
thf(ty_g,type,
g: ( b > $o ) > c > $o ).
thf(ty_f,type,
f: ( a > $o ) > b > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cA @ X1 )
=> ( cC @ ( g @ ( f @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ( cA @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( c > $o ) > $o,X2: c > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: c > $o] :
~ ( ~ ( ! [X2: ( c > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: c] : $false )
=> ~ ! [X3: c > $o] :
( ( X2 @ X3 )
=> ! [X4: c] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: c] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: c] :
( ( X1 @ X2 )
=> ~ ! [X3: c > $o] :
( ( cC @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: c] :
( ( X1 @ X5 )
=> ( g @ ( f @ X4 ) @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__2
@ ^ [X1: b] :
~ ( ( eigen__7 @ X1 )
=> ~ ! [X2: b > $o] :
( ( cB @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__6 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( f @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__22 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(h3,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__3
@ ^ [X1: b > $o] :
~ ( ~ ( ! [X2: ( b > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: b] : $false )
=> ~ ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: b] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: b] :
( ( X1 @ X2 )
=> ( f @ eigen__6 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( g @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cB @ ( f @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ~ ( ! [X2: ( b > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: b] : $false )
=> ~ ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: b] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: b] :
( ( X1 @ X2 )
=> ~ ! [X3: b > $o] :
( ( cB @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: b > $o] :
( ( cB @ X1 )
=> ( cC @ ( g @ X1 ) ) ) )
=> ~ ! [X1: c > $o] :
( ~ ( ! [X2: ( c > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: c] : $false )
=> ~ ! [X3: c > $o] :
( ( X2 @ X3 )
=> ! [X4: c] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: c] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: c] :
( ( X1 @ X2 )
=> ~ ! [X3: c > $o] :
( ( cC @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ X2 @ X3 ) ) )
=> ( cB @ X2 ) )
=> ~ ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ X2 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ~ ( ! [X4: ( b > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: b] : $false )
=> ~ ! [X5: b > $o] :
( ( X4 @ X5 )
=> ! [X6: b] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: b] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: b] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: b > $o] :
( ~ ( ( cB @ X4 )
=> ~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cB @ X4 )
=> ~ ! [X5: c] :
( ( X1 @ X5 )
=> ( g @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: ( c > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: c] : $false )
=> ~ ! [X2: c > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( X1
@ ^ [X4: c] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__0 ) )
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: c > $o] :
( ( cC @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
=> ~ ( ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) )
=> ( cB @ X1 ) )
=> ~ ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ~ ( ! [X3: ( b > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: b] : $false )
=> ~ ! [X4: b > $o] :
( ( X3 @ X4 )
=> ! [X5: b] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: b] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: b] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ~ ( ( cB @ X3 )
=> ~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cB @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ X3 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cC @ ( g @ ( f @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cB @ ( f @ eigen__26 ) )
=> ~ ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__26 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: c > $o] :
( ~ ( ! [X2: ( c > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: c] : $false )
=> ~ ! [X3: c > $o] :
( ( X2 @ X3 )
=> ! [X4: c] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: c] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: c] :
( ( X1 @ X2 )
=> ~ ! [X3: c > $o] :
( ( cC @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: c] :
( ( X1 @ X5 )
=> ( g @ ( f @ X4 ) @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cB @ ( f @ eigen__6 ) )
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__6 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__7 @ eigen__10 )
=> ( f @ eigen__6 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ! [X1: ( c > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: c] : $false )
=> ~ ! [X2: c > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( X1
@ ^ [X4: c] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__0 ) )
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: c > $o] :
( ( cC @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
=> ~ ( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( f @ X1 @ X2 ) ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( f @ X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: b] :
( ( eigen__7 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__22 @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__22 ) )
=> ~ ! [X1: a] :
( ( eigen__22 @ X1 )
=> ( eigen__6 @ X1 ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__22 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cB @ ( f @ eigen__3 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__6 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( f @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: ( b > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: b] : $false )
=> ~ ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( X1
@ ^ [X4: b] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__7 ) )
=> ~ ! [X1: b] :
( ( eigen__7 @ X1 )
=> ~ ! [X2: b > $o] :
( ( cB @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: c > $o] :
( ~ ( ! [X2: ( c > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: c] : $false )
=> ~ ! [X3: c > $o] :
( ( X2 @ X3 )
=> ! [X4: c] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: c] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: c] :
( ( X1 @ X2 )
=> ~ ! [X3: c > $o] :
( ( cC @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ X2 @ X3 ) ) )
=> ( cB @ X2 ) )
=> ~ ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( X1 @ X3 )
=> ( g @ X2 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ~ ( ! [X4: ( b > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: b] : $false )
=> ~ ! [X5: b > $o] :
( ( X4 @ X5 )
=> ! [X6: b] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: b] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: b] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: b > $o] :
( ~ ( ( cB @ X4 )
=> ~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cB @ X4 )
=> ~ ! [X5: c] :
( ( X1 @ X5 )
=> ( g @ X4 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__7 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( eigen__22 @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__22 ) )
=> ~ ! [X1: a] :
( ( eigen__22 @ X1 )
=> ( eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: b > $o] :
( ~ ( ! [X2: ( b > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: b] : $false )
=> ~ ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: b] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: b] :
( ( X1 @ X2 )
=> ( f @ eigen__6 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ~ ( ( cB @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cB @ X2 )
=> ~ ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( g @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cA @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cA @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ! [X1: ( b > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: b] : $false )
=> ~ ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( X1
@ ^ [X4: b] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__7 ) )
=> ~ ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__6 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cA @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cB @ ( f @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP18
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP22
=> ~ ( f @ eigen__6 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cC @ ( g @ ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP19
=> ~ ! [X1: a] :
( ( eigen__22 @ X1 )
=> ( eigen__26 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__6 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( f @ X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: b] :
( ( eigen__7 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( sP21
=> ~ sP27 )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__6 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP6
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( cB @ ( f @ eigen__26 ) )
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__26 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ( cA @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) )
=> ( cB @ X1 ) )
=> ~ ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ~ ( ! [X3: ( b > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: b] : $false )
=> ~ ! [X4: b > $o] :
( ( X3 @ X4 )
=> ! [X5: b] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: b] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: b] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ~ ( ( cB @ X3 )
=> ~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cB @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ X3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__26 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__22 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( f @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ! [X1: ( c > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: c] : $false )
=> ~ ! [X2: c > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( X1
@ ^ [X4: c] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__0 ) )
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: c > $o] :
( ( cC @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( f @ eigen__6 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: b > $o] :
( ( cB @ X1 )
=> ( cC @ ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( eigen__22 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a > $o] :
( ( cA @ X1 )
=> ( cB @ ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( cB @ ( f @ eigen__26 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP13
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( cA @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__6 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: c] :
( ( eigen__0 @ X3 )
=> ( g @ ( f @ X2 ) @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__26 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ! [X1: ( b > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: b] : $false )
=> ~ ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( X1
@ ^ [X4: b] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__7 ) )
=> ~ ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP19
=> sP41 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ ( sP43
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__1 ) @ X1 ) ) )
=> sP43 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP25
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP21
=> ~ ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ~ ( ! [X3: ( b > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: b] : $false )
=> ~ ! [X4: b > $o] :
( ( X3 @ X4 )
=> ! [X5: b] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: b] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: b] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ~ ( ( cB @ X3 )
=> ~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cB @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: b > $o] :
( ~ ( ( cB @ X1 )
=> ~ ! [X2: b] :
( ( eigen__7 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cB @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP1
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: ( b > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: b] : $false )
=> ~ ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b] :
( ( eigen__7 @ X3 )
=> ( X1
@ ^ [X4: b] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ sP26
=> ~ ( sP19
=> ~ sP34 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ sP50
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: b] :
( ( eigen__7 @ X1 )
=> ~ ! [X2: b > $o] :
( ( cB @ X2 )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP40
=> ~ ! [X1: b > $o] :
( ~ ( ! [X2: ( b > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: b] : $false )
=> ~ ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: b] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: b] :
( ( X1 @ X2 )
=> ~ ! [X3: b > $o] :
( ( cB @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP16
=> ~ sP35 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP4
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: b > $o] :
( ~ ( ! [X2: ( b > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: b] : $false )
=> ~ ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: b] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: b] :
( ( X1 @ X2 )
=> ~ ! [X3: b > $o] :
( ( cB @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
=> ~ ( ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ( cA @ X2 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: b] :
( ( X1 @ X3 )
=> ( f @ X2 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ sP26
=> ~ ( sP19
=> ~ sP45 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP18
=> ( cB @ ( f @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: b > $o] :
( ( cB @ X1 )
=> ~ ( X1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP21
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP19
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: b] :
( ( eigen__7 @ X1 )
=> ( f @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP19
=> ~ sP34 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP32
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( cB @ ( f @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( sP21
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ~ sP58
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP43
=> ~ ! [X1: c] :
( ( eigen__0 @ X1 )
=> ( g @ ( f @ eigen__1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP15
=> ~ sP64 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: c] :
( ( eigen__0 @ X2 )
=> ( g @ ( f @ X1 ) @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: c] :
( ( eigen__0 @ X4 )
=> ( g @ ( f @ X3 ) @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(cDOMTHM9_pme,conjecture,
sP53 ).
thf(h4,negated_conjecture,
~ sP53,
inference(assume_negation,[status(cth)],[cDOMTHM9_pme]) ).
thf(1,plain,
( sP31
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP52
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP60
| sP4
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| ~ sP41
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP66
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP40
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP47
| ~ sP19
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP35
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP62
| sP26
| ~ sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP68
| ~ sP19
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP26
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP55
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP55
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP39
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).
thf(15,plain,
( ~ sP44
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| sP16
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP59
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP59
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP12
| ~ sP59 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__22]) ).
thf(20,plain,
( ~ sP28
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP56
| sP50
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP50
| ~ sP21
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP9
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP73
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP64
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP24
| ~ sP22
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP67
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP7
| ~ sP15
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP74
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP74
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP57
| ~ sP74 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__10]) ).
thf(32,plain,
( ~ sP61
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP42
| sP13
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP13
| ~ sP54
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP46
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP46
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP20
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP20
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP17
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__7]) ).
thf(40,plain,
( ~ sP51
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP30
| sP6
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP6
| ~ sP22
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP40
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP71
| ~ sP21
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP65
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP65
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP29
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP29
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP75
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(50,plain,
( ~ sP38
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP11
| ~ sP70
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP40
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP63
| ~ sP18
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP23
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP23
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP25
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(57,plain,
( sP48
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP48
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP33
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP32
| ~ sP48 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(61,plain,
( ~ sP14
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP2
| sP36
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP69
| ~ sP32
| ~ sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP8
| sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( sP8
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( sP58
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( sP58
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP5
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(69,plain,
( sP72
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP72
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP49
| ~ sP25
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP1
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP1
| ~ sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP53
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( sP53
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,h4]) ).
thf(77,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[76,h3]) ).
thf(78,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h1,h0]),eigenvar_choice(discharge,[h2])],[77,h2]) ).
thf(79,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h0]),eigenvar_choice(discharge,[h1])],[78,h1]) ).
thf(80,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4]),eigenvar_choice(discharge,[h0])],[79,h0]) ).
thf(0,theorem,
sP53,
inference(contra,[status(thm),contra(discharge,[h4])],[76,h4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU912^5 : 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
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 11:09:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 50.03/50.21 % SZS status Theorem
% 50.03/50.21 % Mode: mode371
% 50.03/50.21 % Inferences: 597
% 50.03/50.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------