TSTP Solution File: ITP148^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP148^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 Aug 31 04:02:33 EDT 2023
% Result : Theorem 20.27s 20.58s
% Output : Proof 20.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_real,type,
real: $tType ).
thf(ty_complex,type,
complex: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_set_complex,type,
set_complex: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_path_pathfinish_a,type,
path_pathfinish_a: ( real > a ) > a ).
thf(ty_inj_on_a_complex,type,
inj_on_a_complex: ( a > complex ) > set_a > $o ).
thf(ty_comp_a_complex_real,type,
comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).
thf(ty_path_s36253918omplex,type,
path_s36253918omplex: ( real > complex ) > $o ).
thf(ty_top_top_set_complex,type,
top_top_set_complex: set_complex ).
thf(ty_eigen__0,type,
eigen__0: complex ).
thf(ty_path_p769714271omplex,type,
path_p769714271omplex: ( real > complex ) > complex ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_path_p797330068omplex,type,
path_p797330068omplex: ( real > complex ) > complex ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_bij_betw_a_complex,type,
bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).
thf(ty_real_V1477106445omplex,type,
real_V1477106445omplex: ( a > complex ) > $o ).
thf(ty_poinca1910941596x_of_a,type,
poinca1910941596x_of_a: a > complex ).
thf(ty_member_complex,type,
member_complex: complex > set_complex > $o ).
thf(ty_top_top_set_a,type,
top_top_set_a: set_a ).
thf(ty_path_arc_complex,type,
path_arc_complex: ( real > complex ) > $o ).
thf(ty_path_pathstart_a,type,
path_pathstart_a: ( real > a ) > a ).
thf(ty_c,type,
c: real > a ).
thf(ty_path_arc_a,type,
path_arc_a: ( real > a ) > $o ).
thf(sP1,plain,
( sP1
<=> ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_arc_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( path_arc_a @ c )
=> ( ( path_pathfinish_a @ c )
!= ( path_pathstart_a @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > complex,X2: real > a] :
( ( real_V1477106445omplex @ X1 )
=> ( ( inj_on_a_complex @ X1 @ top_top_set_a )
=> ( ( path_arc_complex @ ( comp_a_complex_real @ X1 @ X2 ) )
= ( path_arc_a @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: real > a] :
( ( real_V1477106445omplex @ poinca1910941596x_of_a )
=> ( sP3
=> ( ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ X1 ) )
= ( path_arc_a @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( real_V1477106445omplex @ poinca1910941596x_of_a )
=> ( sP3
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( path_arc_complex
= ( ^ [X1: real > complex] :
~ ( ( path_s36253918omplex @ X1 )
=> ( ( path_p769714271omplex @ X1 )
= ( path_p797330068omplex @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: real > complex] :
( ( path_arc_complex @ X1 )
= ( ~ ( ( path_s36253918omplex @ X1 )
=> ( ( path_p769714271omplex @ X1 )
= ( path_p797330068omplex @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP10
= ( ~ ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
=> sP1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: real > a] :
( ( path_arc_a @ X1 )
=> ( ( path_pathfinish_a @ X1 )
!= ( path_pathstart_a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( path_arc_a @ c ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > complex,X2: set_a,X3: set_complex] :
( ( bij_betw_a_complex @ X1 @ X2 @ X3 )
=> ( inj_on_a_complex @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: set_a,X2: set_complex] :
( ( bij_betw_a_complex @ poinca1910941596x_of_a @ X1 @ X2 )
=> ( inj_on_a_complex @ poinca1910941596x_of_a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: set_complex] :
( ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ X1 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( real_V1477106445omplex @ poinca1910941596x_of_a ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP19
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
member_complex @ eigen__0 @ top_top_set_complex,
introduced(assumption,[]) ).
thf(h2,assumption,
member_a @ eigen__1 @ top_top_set_a,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP10
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| ~ sP19
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| sP10
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP22
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP18
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| ~ sP16
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP15
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_337_bij__betw__imp__inj__on,axiom,
sP17 ).
thf(fact_250_complex__of__bij,axiom,
sP7 ).
thf(fact_236_arc__simple__path,axiom,
sP9 ).
thf(fact_222_arc__distinct__ends,axiom,
sP15 ).
thf(fact_214_arc__linear__image__eq,axiom,
sP5 ).
thf(fact_22_complex__of__linear,axiom,
sP22 ).
thf(fact_2_a1,axiom,
sP19 ).
thf(fact_0_assms_I2_J,axiom,
sP20 ).
thf(16,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,h0,fact_337_bij__betw__imp__inj__on,fact_250_complex__of__bij,fact_236_arc__simple__path,fact_222_arc__distinct__ends,fact_214_arc__linear__image__eq,fact_22_complex__of__linear,fact_2_a1,fact_0_assms_I2_J]) ).
thf(fact_227_UNIV__witness,axiom,
~ ! [X1: a] :
~ ( member_a @ X1 @ top_top_set_a ) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_227_UNIV__witness,16,h2]) ).
thf(fact_228_UNIV__witness,axiom,
~ ! [X1: complex] :
~ ( member_complex @ X1 @ top_top_set_complex ) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_228_UNIV__witness,17,h1]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP148^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 17:02:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.27/20.58 % SZS status Theorem
% 20.27/20.58 % Mode: cade22sinegrackle2xfaf3
% 20.27/20.58 % Steps: 1640
% 20.27/20.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------