TSTP Solution File: ITP018^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP018^4 : 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 : n027.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 00:28:37 EDT 2022
% Result : Theorem 80.28s 78.64s
% Output : Proof 80.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 28
% Syntax : Number of formulae : 47 ( 20 unt; 18 typ; 0 def)
% Number of atoms : 329 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 11 avg)
% Number of connectives : 489 ( 14 ~; 6 |; 0 &; 466 @)
% ( 0 <=>; 2 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 22 con; 0-2 aty)
% Number of variables : 27 ( 0 ^ 27 !; 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_mono_2Ec_2Erealax_2Ereal__neg,type,
mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(ty_tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
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(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
! [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 ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [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 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Ebinary__ieee_2Eneg__ulp]) ).
thf(h1,assumption,
~ ! [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(assumption,[]) ).
thf(h2,assumption,
( 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(assumption,[]) ).
thf(nax1287,axiom,
( p1287
<= ( ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
file('<stdin>',nax1287) ).
thf(ax398,axiom,
~ p1287,
file('<stdin>',ax398) ).
thf(pax1284,axiom,
( p1284
=> ! [X1: d,X5: d,X3: u] :
( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X3 ) ) ) ) ) )
= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X3 ) ) ) ) ) ) ),
file('<stdin>',pax1284) ).
thf(ax401,axiom,
p1284,
file('<stdin>',ax401) ).
thf(pax1286,axiom,
( p1286
=> ! [X1: d,X5: d] :
( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
file('<stdin>',pax1286) ).
thf(ax399,axiom,
p1286,
file('<stdin>',ax399) ).
thf(c_0_6,plain,
( ( ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
| p1287 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1287])]) ).
thf(c_0_7,plain,
~ p1287,
inference(fof_simplification,[status(thm)],[ax398]) ).
thf(c_0_8,plain,
! [X2375: d,X2376: d,X2377: u] :
( ~ p1284
| ( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X2375 @ X2376 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X2375 @ X2376 ) @ X2377 ) ) ) ) ) )
= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X2375 @ X2376 ) @ X2377 ) ) ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1284])])]) ).
thf(c_0_9,plain,
( p1287
| ( ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
~ p1287,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1: d,X5: d,X2: u] :
( ( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X2 ) ) ) ) ) )
= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X2 ) ) ) ) ) )
| ~ p1284 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
p1284,
inference(split_conjunct,[status(thm)],[ax401]) ).
thf(c_0_13,plain,
! [X2365: d,X2366: d] :
( ~ p1286
| ( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X2365 @ X2366 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X2365 @ X2366 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X2365 @ X2366 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1286])])]) ).
thf(c_0_14,plain,
( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
!= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
inference(sr,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_15,plain,
! [X1: d,X5: d,X2: u] :
( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__negate_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X2 ) ) ) ) ) )
= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ X2 ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
thf(c_0_16,plain,
! [X1: d,X5: d] :
( ( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
| ~ p1286 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
p1286,
inference(split_conjunct,[status(thm)],[ax399]) ).
thf(c_0_18,plain,
( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ f__0 @ f__1 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
!= ( fmono_2Ec_2Erealax_2Ereal__neg @ ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ f__0 @ f__1 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
! [X1: d,X5: d] :
( ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( fs @ ( ftyop_2Ebinary__ieee_2Efloat @ X1 @ X5 ) @ ( fc_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
= ( fj_mono_2Etyop_2Erealax_2Ereal @ ( fs @ ftyop_2Erealax_2Ereal @ ( fc_2Ebinary__ieee_2Eulp_2E1 @ ( fs @ ( ftyop_2Ebool_2Eitself @ ( ftyop_2Epair_2Eprod @ X1 @ X5 ) ) @ fc_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_20,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h2,h1,h0])],]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,1,h2]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1]) ).
thf(0,theorem,
! [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 ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP018^4 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 21:16:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 80.28/78.64 % SZS status Theorem
% 80.28/78.64 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 80.28/78.64 % Inferences: 4
% 80.28/78.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------