TSTP Solution File: ITP169^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP169^1 : 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 : n029.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 04:02:42 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_real_int,type,
real_int: $tType ).
thf(ty_traffic,type,
traffic: $tType ).
thf(ty_nat_int,type,
nat_int: $tType ).
thf(ty_view_e774982825t_unit,type,
view_e774982825t_unit: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_cars,type,
cars: $tType ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_ext_Product_unit,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(ty_e,type,
e: cars ).
thf(ty_lan_Product_unit,type,
lan_Product_unit: view_e774982825t_unit > nat_int ).
thf(ty_ts,type,
ts: traffic ).
thf(ty_ts3,type,
ts3: traffic ).
thf(ty_v,type,
v: view_e774982825t_unit ).
thf(ty_restrict,type,
restrict: view_e774982825t_unit > ( cars > nat_int ) > cars > nat_int ).
thf(ty_c,type,
c: cars ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_res,type,
res: traffic > cars > nat_int ).
thf(ty_len,type,
len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
thf(ty_regular_regular,type,
regular_regular: cars > traffic > cars > real ).
thf(ty_ord_le461438217t_unit,type,
ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(ty_one_one_nat,type,
one_one_nat: nat ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_nat_card,type,
nat_card: nat_int > nat ).
thf(ty_move,type,
move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(ty_eigen__0,type,
eigen__0: view_e774982825t_unit ).
thf(ty_real_length,type,
real_length: real_int > real ).
thf(sP1,plain,
( sP1
<=> ( ( restrict @ eigen__0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( len @ regular_regular @ eigen__0 @ ts @ e )
= ( ext_Product_unit @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ eigen__0 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__0 ) ) ) )
=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
!= ( ext_Product_unit @ eigen__0 ) ) )
=> ~ sP1 )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__0 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__0 ) ) ) )
=> ~ sP2 )
=> ( ( restrict @ eigen__0 @ ( res @ ts ) @ e )
!= ( lan_Product_unit @ eigen__0 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__0 ) )
!= one_one_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ eigen__0 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__0 ) ) ) )
=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
!= ( ext_Product_unit @ eigen__0 ) ) )
=> ~ sP1 )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__0 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP4
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: view_e774982825t_unit] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ X1 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X1 ) ) ) )
=> ( ( len @ regular_regular @ X1 @ ts @ c )
!= ( ext_Product_unit @ X1 ) ) )
=> ( ( restrict @ X1 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X1 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ X1 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X1 ) ) ) )
=> ( ( len @ regular_regular @ X1 @ ts @ e )
!= ( ext_Product_unit @ X1 ) ) )
=> ( ( restrict @ X1 @ ( res @ ts ) @ e )
!= ( lan_Product_unit @ X1 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ X1 ) )
!= one_one_nat ) )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ord_le461438217t_unit @ eigen__0 @ ( move @ ts3 @ ts @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ~ ( sP8
=> ~ sP6 )
=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
!= ( ext_Product_unit @ eigen__0 ) ) )
=> ~ sP1 )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__0 ) )
!= one_one_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( nat_card @ ( lan_Product_unit @ eigen__0 ) )
= one_one_nat ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ~ ( sP8
=> ~ sP6 )
=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
!= ( ext_Product_unit @ eigen__0 ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( sP8
=> ~ sP6 )
=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
!= ( ext_Product_unit @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( len @ regular_regular @ eigen__0 @ ts @ c )
= ( ext_Product_unit @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP8
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP3
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( restrict @ eigen__0 @ ( res @ ts ) @ e )
= ( lan_Product_unit @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP5
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(conj_1,conjecture,
sP18 ).
thf(h0,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h1,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
sP16,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h9,assumption,
sP6,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h14,assumption,
sP13,
introduced(assumption,[]) ).
thf(h15,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP8
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP14
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| sP5
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP17
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP15
| sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(conj_0,axiom,
sP7 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h9,h13,h14,h11,h12,h10,h3,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h0,conj_0,h15,h9,h14,h12,h3,h7,h5]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h10,h3,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h9])],[h13,11,h15,h9]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h3,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,12,h13,h14]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h3,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,13,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h3])],[h8,14,h10,h3]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,15,h8,h9]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,17,h4,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,18,h2,h3]) ).
thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,axiom,
~ ! [X1: view_e774982825t_unit] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ X1 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X1 ) ) ) )
=> ( ( len @ regular_regular @ X1 @ ts @ c )
!= ( ext_Product_unit @ X1 ) ) )
=> ( ( restrict @ X1 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X1 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ X1 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X1 ) ) ) )
=> ( ( len @ regular_regular @ X1 @ ts @ e )
!= ( ext_Product_unit @ X1 ) ) )
=> ( ( restrict @ X1 @ ( res @ ts ) @ e )
!= ( lan_Product_unit @ X1 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ X1 ) )
!= one_one_nat ) ) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,19,h1]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP169^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 14:38:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % Mode: cade22sinegrackle2x6978
% 0.19/0.42 % Steps: 85
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------