TSTP Solution File: ITP018^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP018^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Sun Jul 17 00:28:36 EDT 2022
% Result : Theorem 1.95s 2.19s
% Output : Proof 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 58
% Syntax : Number of formulae : 64 ( 12 unt; 18 typ; 2 def)
% Number of atoms : 94 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 636 ( 25 ~; 18 |; 0 &; 562 @)
% ( 19 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 25 con; 0-2 aty)
% Number of variables : 27 ( 2 ^ 25 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_u,type,
u: $tType ).
thf(ty_d,type,
d: $tType ).
thf(ty_mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(ty_du,type,
du: $tType ).
thf(ty_c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(ty_tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(ty_mono_2Ec_2Erealax_2Ereal__neg,type,
mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(ty_s,type,
s: d > u > du ).
thf(ty_j_mono_2Etyop_2Erealax_2Ereal,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(ty_c_2Ebinary__ieee_2Eulp_2E1,type,
c_2Ebinary__ieee_2Eulp_2E1: du > u ).
thf(ty_tyop_2Ebinary__ieee_2Efloat,type,
tyop_2Ebinary__ieee_2Efloat: d > d > d ).
thf(ty_eigen__1,type,
eigen__1: d ).
thf(ty_eigen__0,type,
eigen__0: d ).
thf(ty_c_2Ebinary__ieee_2Efloat__negate_2E1,type,
c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).
thf(ty_tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: d > d ).
thf(ty_tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: d ).
thf(ty_c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
thf(ty_c_2Ebinary__ieee_2Efloat__plus__min_2E1,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).
thf(h0,assumption,
! [X1: d > $o,X2: d] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: d] :
~ ! [X2: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= X1 )
=> ( X1
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: d,X2: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP4
=> ! [X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= X1 )
=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ X1 )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( X2 @ X1 )
=> ! [X3: mono_2Etyop_2Erealax_2Ereal] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: d,X2: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ X2 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: d,X2: d,X3: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ X3 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: d,X2: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( X1 @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
=> ! [X2: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= X1 )
=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ X1 )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ eigen__0 @ eigen__1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ eigen__0 @ eigen__1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
sP14 ).
thf(h1,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[thm_2Ebinary__ieee_2Eneg__ulp]) ).
thf(1,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| ~ sP2
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP16
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| ~ sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP4
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP15
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
sP9,
inference(eq_ind,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
sP1,
inference(eq_sym,[status(thm)],]) ).
thf(16,plain,
( sP10
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(17,plain,
( sP14
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(thm_2Ebinary__ieee_2Eulp,axiom,
sP5 ).
thf(thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
sP13 ).
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,thm_2Ebinary__ieee_2Eulp,thm_2Ebinary__ieee_2Efloat__to__real__negate,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP018^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : Fri Jun 3 14:58:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.95/2.19 % SZS status Theorem
% 1.95/2.19 % Mode: mode506
% 1.95/2.19 % Inferences: 28
% 1.95/2.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------