TSTP Solution File: ITP169^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP169^1 : 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 : n021.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 00:29:21 EDT 2022
% Result : Theorem 1.02s 1.40s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 39
% Syntax : Number of formulae : 44 ( 9 unt; 27 typ; 1 def)
% Number of atoms : 70 ( 31 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 324 ( 83 ~; 4 |; 0 &; 189 @)
% ( 5 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 16 con; 0-4 aty)
% Number of variables : 5 ( 1 ^ 4 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_view_e774982825t_unit,type,
view_e774982825t_unit: $tType ).
thf(ty_real_int,type,
real_int: $tType ).
thf(ty_traffic,type,
traffic: $tType ).
thf(ty_nat_int,type,
nat_int: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_cars,type,
cars: $tType ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_eigen__2,type,
eigen__2: view_e774982825t_unit ).
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_v,type,
v: view_e774982825t_unit ).
thf(ty_res,type,
res: traffic > cars > nat_int ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_regular_regular,type,
regular_regular: cars > traffic > cars > real ).
thf(ty_ts,type,
ts: traffic ).
thf(ty_ord_le461438217t_unit,type,
ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(ty_e,type,
e: cars ).
thf(ty_ts3,type,
ts3: traffic ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_restrict,type,
restrict: view_e774982825t_unit > ( cars > nat_int ) > cars > nat_int ).
thf(ty_lan_Product_unit,type,
lan_Product_unit: view_e774982825t_unit > nat_int ).
thf(ty_c,type,
c: cars ).
thf(ty_one_one_nat,type,
one_one_nat: nat ).
thf(ty_len,type,
len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
thf(ty_real_length,type,
real_length: real_int > real ).
thf(ty_ext_Product_unit,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(h0,assumption,
! [X1: view_e774982825t_unit > $o,X2: view_e774982825t_unit] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [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 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ eigen__2 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__2 ) ) ) )
=> ( ( len @ regular_regular @ eigen__2 @ ts @ c )
!= ( ext_Product_unit @ eigen__2 ) ) )
=> ( ( restrict @ eigen__2 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ eigen__2 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__2 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__2 ) ) ) )
=> ( ( len @ regular_regular @ eigen__2 @ ts @ e )
!= ( ext_Product_unit @ eigen__2 ) ) )
=> ( ( restrict @ eigen__2 @ ( res @ ts ) @ e )
!= ( lan_Product_unit @ eigen__2 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__2 ) )
!= one_one_nat ) )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [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 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ord_le461438217t_unit @ eigen__2 @ ( move @ ts3 @ ts @ v ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__2 ) ) ) )
=> ( ( len @ regular_regular @ eigen__2 @ ts @ c )
!= ( ext_Product_unit @ eigen__2 ) ) )
=> ( ( restrict @ eigen__2 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ eigen__2 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__2 ) )
!= one_one_nat ) )
=> ~ ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ eigen__2 ) ) ) )
=> ( ( len @ regular_regular @ eigen__2 @ ts @ e )
!= ( ext_Product_unit @ eigen__2 ) ) )
=> ( ( restrict @ eigen__2 @ ( res @ ts ) @ e )
!= ( lan_Product_unit @ eigen__2 ) ) )
=> ( ( nat_card @ ( lan_Product_unit @ eigen__2 ) )
!= one_one_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(conj_1,conjecture,
sP5 ).
thf(h1,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(1,plain,
( ~ sP2
| sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
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,
~ sP3 ).
thf(conj_0,axiom,
sP1 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,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,conj_0,h1]) ).
thf(5,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[4,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h1])],[4,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP169^1 : 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
% 0.13/0.35 % Computer : n021.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 : 600
% 0.13/0.35 % DateTime : Fri Jun 3 11:11:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.02/1.40 % SZS status Theorem
% 1.02/1.40 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 1.02/1.40 % Inferences: 2052
% 1.02/1.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------