TSTP Solution File: ITP147^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP147^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 00:29:17 EDT 2022
% Result : Theorem 51.43s 51.63s
% Output : Proof 51.43s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_p,type,
p: a ).
thf(ty_abs_abs_real,type,
abs_abs_real: real > real ).
thf(ty_line_open_segment_a,type,
line_open_segment_a: a > a > set_a ).
thf(ty_elemen154694473ball_a,type,
elemen154694473ball_a: a > real > set_a ).
thf(ty_thesisa,type,
thesisa: $o ).
thf(ty_eigen__1,type,
eigen__1: a > real ).
thf(ty_a2,type,
a2: a ).
thf(ty_b,type,
b: a ).
thf(ty_eigen__0,type,
eigen__0: real ).
thf(ty_auto_ll_on_flow0_a,type,
auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_topolo1710226732a_real,type,
topolo1710226732a_real: set_a > ( a > real ) > $o ).
thf(ty_one_one_real,type,
one_one_real: real ).
thf(ty_f,type,
f: a > a ).
thf(ty_x,type,
x: set_a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( member_a @ X1 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X1 @ ( eigen__1 @ X1 ) ) @ ( line_open_segment_a @ a2 @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ord_less_real @ zero_zero_real @ eigen__0 )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ eigen__1 )
=> ( ( ( eigen__1 @ p )
= zero_zero_real )
=> ( ! [X1: a] :
( ( member_a @ X1 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( eigen__1 @ X1 ) ) @ one_one_real ) )
=> ( sP1
=> thesisa ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( member_a @ X1 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( eigen__1 @ X1 ) ) @ one_one_real ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( eigen__1 @ p )
= zero_zero_real )
=> ( sP4
=> ( sP1
=> thesisa ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > real] :
( ( ord_less_real @ zero_zero_real @ eigen__0 )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ X1 )
=> ( ( ( X1 @ p )
= zero_zero_real )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( X1 @ X2 ) ) @ one_one_real ) )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( X1 @ X2 ) ) @ ( line_open_segment_a @ a2 @ b ) ) )
=> thesisa ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: real,X2: a > real] :
( ( ord_less_real @ zero_zero_real @ X1 )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ X1 ) @ X2 )
=> ( ( ( X2 @ p )
= zero_zero_real )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( elemen154694473ball_a @ p @ X1 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( X2 @ X3 ) ) @ one_one_real ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( elemen154694473ball_a @ p @ X1 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ ( X2 @ X3 ) ) @ ( line_open_segment_a @ a2 @ b ) ) )
=> thesisa ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> thesisa ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ord_less_real @ zero_zero_real @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> thesisa ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__1 @ p )
= zero_zero_real ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_1,conjecture,
sP12 ).
thf(h0,negated_conjecture,
~ sP12,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h1,assumption,
~ ( sP11
=> ! [X1: a > real] :
( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ X1 )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( X1 @ X2 ) ) @ ( line_open_segment_a @ a2 @ b ) ) )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( X1 @ X2 ) ) @ one_one_real ) )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ X1 )
=> ( ( X1 @ p )
!= zero_zero_real ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP11,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a > real] :
( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ X1 )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X2 @ ( X1 @ X2 ) ) @ ( line_open_segment_a @ a2 @ b ) ) )
=> ( ! [X2: a] :
( ( member_a @ X2 @ ( elemen154694473ball_a @ p @ eigen__0 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( X1 @ X2 ) ) @ one_one_real ) )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ eigen__0 ) @ X1 )
=> ( ( X1 @ p )
!= zero_zero_real ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP3
=> ( sP1
=> ( sP4
=> ( sP3
=> ~ sP13 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ( sP4
=> ( sP3
=> ~ sP13 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP4
=> ( sP3
=> ~ sP13 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP3
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP11
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| ~ sP3
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP13
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_4_that,axiom,
sP7 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h11,h9,h10,h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h0,fact_4_that,h2,h7,h9,h5,h11]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h11])],[h10,8,h5,h11]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,9,h9,h10]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,10,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,11,h5,h6]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,12,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).
thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: real] :
( ( ord_less_real @ zero_zero_real @ X1 )
=> ! [X2: a > real] :
( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ X1 ) @ X2 )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( elemen154694473ball_a @ p @ X1 ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X3 @ ( X2 @ X3 ) ) @ ( line_open_segment_a @ a2 @ b ) ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( elemen154694473ball_a @ p @ X1 ) )
=> ( ord_less_real @ ( abs_abs_real @ ( X2 @ X3 ) ) @ one_one_real ) )
=> ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ X1 ) @ X2 )
=> ( ( X2 @ p )
!= zero_zero_real ) ) ) ) ) ) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,14,h1]) ).
thf(0,theorem,
sP12,
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP147^1 : TPTP v8.1.0. Released 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 : n020.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 21:51:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 51.43/51.63 % SZS status Theorem
% 51.43/51.63 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 51.43/51.63 % Inferences: 230
% 51.43/51.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------