%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP006^2 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : 300s
% DateTime : Thu Oct 9 01:46:24 PM UTC 2025
% Result : Theorem 197.23s 195.77s
% Output : Proof 197.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 99
% Syntax : Number of formulae : 110 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 546 ( 53 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 1758 ( 170 ~; 58 |; 0 &;1234 @)
% ( 48 <=>; 248 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 67 usr; 58 con; 0-2 aty)
% Number of variables : 166 ( 6 ^; 160 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_del,type,
del: $tType ).
thf(ty_c_2EquantHeuristics_2EGUESS__FORALL__POINT,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT: del > del > $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_mem,type,
mem: $i > del > $o ).
thf(ty_eigen__2,type,
eigen__2: del ).
thf(ty_c_2EquantHeuristics_2EGUESS__EXISTS__GAP,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP: del > del > $i ).
thf(ty_c_2EquantHeuristics_2EGUESS__FORALL,type,
c_2EquantHeuristics_2EGUESS__FORALL: del > del > $i ).
thf(ty_c_2EquantHeuristics_2EGUESS__EXISTS,type,
c_2EquantHeuristics_2EGUESS__EXISTS: del > del > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: del ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_bool,type,
bool: del ).
thf(ty_c_2EquantHeuristics_2EGUESS__EXISTS__POINT,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT: del > del > $i ).
thf(ty_c_2EquantHeuristics_2EGUESS__FORALL__GAP,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP: del > del > $i ).
thf(ty_arr,type,
arr: del > del > del ).
thf(h0,assumption,
! [X1: del > $o,X2: del] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: del] :
~ ! [X2: $i] :
( ( mem @ X2 @ ( arr @ X1 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X5: $i] :
( ( mem @ X5 @ eigen__2 )
=> ( ( p @ ( ap @ X4 @ X5 ) )
=> ( p @ ( ap @ X3 @ X5 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ eigen__2 ) @ X2 ) @ X3 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ eigen__2 ) @ X2 ) @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: $i] :
~ ( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X2: $i] :
( ( mem @ X2 @ eigen__2 )
=> ( ( p @ ( ap @ X1 @ X2 ) )
=> ( p @ ( ap @ eigen__5 @ X2 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: $i] :
~ ( ( mem @ X1 @ eigen__3 )
=> ~ ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: del] :
~ ! [X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X2 @ X1 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X1 @ bool ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ( ( p @ ( ap @ X5 @ X6 ) )
=> ( p @ ( ap @ X4 @ X6 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X2 @ X1 ) @ X3 ) @ X4 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X2 @ X1 ) @ X3 ) @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: $i] :
~ ( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X4: $i] :
( ( mem @ X4 @ eigen__2 )
=> ( ( p @ ( ap @ X3 @ X4 ) )
=> ( p @ ( ap @ X2 @ X4 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i] :
~ ( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ( p @ ( ap @ X2 @ X3 ) )
=> ( p @ ( ap @ X1 @ X3 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ~ ( ~ ( ~ ( ~ ( ~ ( ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS @ X1 @ X2 ) @ X3 ) @ X4 ) )
= ( ! [X5: $i] :
( ( mem @ X5 @ X2 )
=> ( ( p @ ( ap @ X4 @ X5 ) )
=> ~ ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ~ ( p @ ( ap @ X4 @ ( ap @ X3 @ X6 ) ) ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL @ X1 @ X2 ) @ X3 ) @ X4 ) )
!= ( ! [X5: $i] :
( ( mem @ X5 @ X2 )
=> ( ~ ( p @ ( ap @ X4 @ X5 ) )
=> ~ ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ( p @ ( ap @ X4 @ ( ap @ X3 @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ X2 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ ( arr @ X2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ X1 @ X2 ) @ X5 ) @ X6 ) )
= ( ! [X7: $i] :
( ( mem @ X7 @ X1 )
=> ( p @ ( ap @ X6 @ ( ap @ X5 @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ X2 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ ( arr @ X2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ X2 ) @ X5 ) @ X6 ) )
= ( ! [X7: $i] :
( ( mem @ X7 @ X1 )
=> ~ ( p @ ( ap @ X6 @ ( ap @ X5 @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ X2 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ ( arr @ X2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ X1 @ X2 ) @ X5 ) @ X6 ) )
= ( ! [X7: $i] :
( ( mem @ X7 @ X2 )
=> ( ( p @ ( ap @ X6 @ X7 ) )
=> ~ ! [X8: $i] :
( ( mem @ X8 @ X1 )
=> ( X7
!= ( ap @ X5 @ X8 ) ) ) ) ) ) ) ) ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ X2 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ ( arr @ X2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ X1 @ X2 ) @ X5 ) @ X6 ) )
= ( ! [X7: $i] :
( ( mem @ X7 @ X2 )
=> ( ~ ( p @ ( ap @ X6 @ X7 ) )
=> ~ ! [X8: $i] :
( ( mem @ X8 @ X1 )
=> ( X7
!= ( ap @ X5 @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( p @ ( ap @ eigen__5 @ ( ap @ eigen__4 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mem @ eigen__6 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__6 ) )
= ( ! [X1: $i] :
( ( mem @ X1 @ eigen__3 )
=> ~ ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mem @ eigen__12 @ eigen__3 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( mem @ X1 @ eigen__3 )
=> ~ ( p @ ( ap @ eigen__5 @ ( ap @ eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mem @ eigen__5 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
= sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( mem @ X1 @ eigen__2 )
=> ( ( p @ ( ap @ eigen__6 @ X1 ) )
=> ( p @ ( ap @ eigen__5 @ X1 ) ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__6 ) )
= ( ! [X1: $i] :
( ( mem @ X1 @ eigen__3 )
=> ~ ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( mem @ eigen__12 @ eigen__3 )
=> ( mem @ ( ap @ eigen__4 @ eigen__12 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ~ ( ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
= ( ! [X1: $i] :
( ( mem @ X1 @ eigen__2 )
=> ( ( p @ ( ap @ eigen__5 @ X1 ) )
=> ~ sP6 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
!= ( ! [X1: $i] :
( ( mem @ X1 @ eigen__2 )
=> ( ~ ( p @ ( ap @ eigen__5 @ X1 ) )
=> ~ ! [X2: $i] :
( ( mem @ X2 @ eigen__3 )
=> ( p @ ( ap @ eigen__5 @ ( ap @ eigen__4 @ X2 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ( p @ ( ap @ X2 @ ( ap @ X1 @ X3 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ~ ( p @ ( ap @ X2 @ ( ap @ X1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( mem @ ( ap @ eigen__4 @ eigen__12 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ X1 )
=> ( mem @ ( ap @ X3 @ X4 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( mem @ X1 @ eigen__2 )
=> ( ( p @ ( ap @ eigen__6 @ X1 ) )
=> ( p @ ( ap @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( mem @ X1 @ eigen__3 )
=> ( mem @ ( ap @ eigen__4 @ X1 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( mem @ eigen__12 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ~ ( ~ ( ~ ( ~ ( ~ ( ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) )
= ( ! [X2: $i] :
( ( mem @ X2 @ eigen__2 )
=> ( ( p @ ( ap @ X1 @ X2 ) )
=> ~ ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ~ ( p @ ( ap @ X1 @ ( ap @ eigen__4 @ X3 ) ) ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) )
!= ( ! [X2: $i] :
( ( mem @ X2 @ eigen__2 )
=> ( ~ ( p @ ( ap @ X1 @ X2 ) )
=> ~ ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ( p @ ( ap @ X1 @ ( ap @ eigen__4 @ X3 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ eigen__3 @ eigen__2 ) @ X2 ) @ X3 ) )
= ( ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ( p @ ( ap @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X2 ) @ X3 ) )
= ( ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ~ ( p @ ( ap @ X3 @ ( ap @ X2 @ X4 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ eigen__3 @ eigen__2 ) @ X2 ) @ X3 ) )
= ( ! [X4: $i] :
( ( mem @ X4 @ eigen__2 )
=> ( ( p @ ( ap @ X3 @ X4 ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ eigen__3 )
=> ( X4
!= ( ap @ X2 @ X5 ) ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ eigen__3 @ eigen__2 ) @ X2 ) @ X3 ) )
= ( ! [X4: $i] :
( ( mem @ X4 @ eigen__2 )
=> ( ~ ( p @ ( ap @ X3 @ X4 ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ eigen__3 )
=> ( X4
!= ( ap @ X2 @ X5 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ( p @ ( ap @ X2 @ X3 ) )
=> ( p @ ( ap @ X1 @ X3 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X2: $i] :
( ( mem @ X2 @ eigen__2 )
=> ( ( p @ ( ap @ X1 @ X2 ) )
=> ( p @ ( ap @ eigen__5 @ X2 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ~ sP11
=> ~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ( p @ ( ap @ X2 @ X3 ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ( X3
!= ( ap @ X1 @ X4 ) ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ~ ( p @ ( ap @ X2 @ X3 ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ( X3
!= ( ap @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP12
=> ( ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ eigen__12 ) ) )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( mem @ eigen__5 @ ( arr @ eigen__2 @ bool ) )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( mem @ eigen__5 @ ( arr @ eigen__2 @ bool ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( mem @ eigen__4 @ ( arr @ eigen__3 @ eigen__2 ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X4: $i] :
( ( mem @ X4 @ eigen__2 )
=> ( ( p @ ( ap @ X3 @ X4 ) )
=> ( p @ ( ap @ X2 @ X4 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP23
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( mem @ eigen__6 @ ( arr @ eigen__2 @ bool ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP26 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ X1 ) )
= ( ! [X2: $i] :
( ( mem @ X2 @ eigen__3 )
=> ~ ( p @ ( ap @ X1 @ ( ap @ eigen__4 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ eigen__4 ) @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( mem @ eigen__4 @ ( arr @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP16
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: del,X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ~ ( ~ ( ~ ( ~ ( ~ ( ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS @ eigen__3 @ X1 ) @ X2 ) @ X3 ) )
= ( ! [X4: $i] :
( ( mem @ X4 @ X1 )
=> ( ( p @ ( ap @ X3 @ X4 ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ eigen__3 )
=> ~ ( p @ ( ap @ X3 @ ( ap @ X2 @ X5 ) ) ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL @ eigen__3 @ X1 ) @ X2 ) @ X3 ) )
!= ( ! [X4: $i] :
( ( mem @ X4 @ X1 )
=> ( ~ ( p @ ( ap @ X3 @ X4 ) )
=> ~ ! [X5: $i] :
( ( mem @ X5 @ eigen__3 )
=> ( p @ ( ap @ X3 @ ( ap @ X2 @ X5 ) ) ) ) ) ) ) ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ eigen__3 @ X1 ) @ X4 ) @ X5 ) )
= ( ! [X6: $i] :
( ( mem @ X6 @ eigen__3 )
=> ( p @ ( ap @ X5 @ ( ap @ X4 @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ X1 ) @ X4 ) @ X5 ) )
= ( ! [X6: $i] :
( ( mem @ X6 @ eigen__3 )
=> ~ ( p @ ( ap @ X5 @ ( ap @ X4 @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ eigen__3 @ X1 ) @ X4 ) @ X5 ) )
= ( ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ( ( p @ ( ap @ X5 @ X6 ) )
=> ~ ! [X7: $i] :
( ( mem @ X7 @ eigen__3 )
=> ( X6
!= ( ap @ X4 @ X7 ) ) ) ) ) ) ) ) ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ eigen__3 @ X1 ) @ X4 ) @ X5 ) )
= ( ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ( ~ ( p @ ( ap @ X5 @ X6 ) )
=> ~ ! [X7: $i] :
( ( mem @ X7 @ eigen__3 )
=> ( X6
!= ( ap @ X4 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ~ ( p @ ( ap @ X2 @ ( ap @ X1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X2 @ X1 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X1 @ bool ) )
=> ! [X5: $i] :
( ( mem @ X5 @ ( arr @ X1 @ bool ) )
=> ( ! [X6: $i] :
( ( mem @ X6 @ X1 )
=> ( ( p @ ( ap @ X5 @ X6 ) )
=> ( p @ ( ap @ X4 @ X6 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X2 @ X1 ) @ X3 ) @ X4 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X2 @ X1 ) @ X3 ) @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP33
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ eigen__3 )
=> ( mem @ ( ap @ X1 @ X2 ) @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: del,X2: $i] :
( ( mem @ X2 @ ( arr @ X1 @ eigen__2 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__2 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__2 @ bool ) )
=> ( ! [X5: $i] :
( ( mem @ X5 @ eigen__2 )
=> ( ( p @ ( ap @ X4 @ X5 ) )
=> ( p @ ( ap @ X3 @ X5 ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ eigen__2 ) @ X2 ) @ X3 ) )
=> ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ X1 @ eigen__2 ) @ X2 ) @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP33
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP11
=> ~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ( p @ ( ap @ X2 @ X3 ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ( X3
!= ( ap @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__2 @ bool ) )
=> ~ ( ~ ( ~ ( ~ ( ~ ( ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ( p @ ( ap @ X2 @ X3 ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ~ ( p @ ( ap @ X2 @ ( ap @ X1 @ X4 ) ) ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL @ eigen__3 @ eigen__2 ) @ X1 ) @ X2 ) )
!= ( ! [X3: $i] :
( ( mem @ X3 @ eigen__2 )
=> ( ~ ( p @ ( ap @ X2 @ X3 ) )
=> ~ ! [X4: $i] :
( ( mem @ X4 @ eigen__3 )
=> ( p @ ( ap @ X2 @ ( ap @ X1 @ X4 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ eigen__3 @ eigen__2 ) @ X3 ) @ X4 ) )
= ( ! [X5: $i] :
( ( mem @ X5 @ eigen__3 )
=> ( p @ ( ap @ X4 @ ( ap @ X3 @ X5 ) ) ) ) ) ) ) ) )
=> ~ sP36 )
=> ~ ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ eigen__3 @ eigen__2 ) @ X3 ) @ X4 ) )
= ( ! [X5: $i] :
( ( mem @ X5 @ eigen__2 )
=> ( ( p @ ( ap @ X4 @ X5 ) )
=> ~ ! [X6: $i] :
( ( mem @ X6 @ eigen__3 )
=> ( X5
!= ( ap @ X3 @ X6 ) ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( mem @ X3 @ ( arr @ eigen__3 @ eigen__2 ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ eigen__2 @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ eigen__3 @ eigen__2 ) @ X3 ) @ X4 ) )
= ( ! [X5: $i] :
( ( mem @ X5 @ eigen__2 )
=> ( ~ ( p @ ( ap @ X4 @ X5 ) )
=> ~ ! [X6: $i] :
( ( mem @ X6 @ eigen__3 )
=> ( X5
!= ( ap @ X3 @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP33
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( mem @ X1 @ eigen__3 )
=> ~ ( p @ ( ap @ eigen__6 @ ( ap @ eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP29
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: del,X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__3 @ X1 ) )
=> ! [X3: $i] :
( ( mem @ X3 @ eigen__3 )
=> ( mem @ ( ap @ X2 @ X3 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP28
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
sP37 ).
thf(h2,negated_conjecture,
~ sP37,
inference(assume_negation,[status(cth)],[conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
thf(1,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| ~ sP16
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP47
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP39
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP24
| ~ sP33
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP5
| ~ sP16
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP30
| ~ sP26
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP21
| ~ sP12
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP48
| ~ sP28
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP34
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP34
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP45
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(16,plain,
( ~ sP9
| sP32
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP31
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP4
| ~ sP29
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP31
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP7
| ~ sP23
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP36
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP41
| ~ sP33
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP11
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP42
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP20
| ~ sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP17
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP27
| ~ sP23
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP35
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP43
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP38
| ~ sP33
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP2
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( sP1
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP1
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP8
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP46
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP46
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP19
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(39,plain,
( sP22
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP22
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP18
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(42,plain,
( sP44
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP44
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP25
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(45,plain,
( sP40
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(46,plain,
( sP37
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
sP2 ).
thf(ap_tp,axiom,
sP13 ).
thf(47,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,conj_thm_2EquantHeuristics_2EGUESS__REWRITES,ap_tp,h2]) ).
thf(48,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[47,h1]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[48,h0]) ).
thf(0,theorem,
sP37,
inference(contra,[status(thm),contra(discharge,[h2])],[47,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP006^2 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 18:00:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 197.23/195.77 % SZS status Theorem
% 197.23/195.77 % Mode: mode449:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 197.23/195.77 % Inferences: 1664
% 197.23/195.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------