TSTP Solution File: ITP050^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP050^1 : 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 : n026.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 04:01:44 EDT 2023
% Result : Theorem 23.89s 24.18s
% Output : Proof 23.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 72
% Syntax : Number of formulae : 77 ( 12 unt; 16 typ; 1 def)
% Number of atoms : 155 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 260 ( 29 ~; 28 |; 0 &; 150 @)
% ( 27 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 35 con; 0-4 aty)
% Number of variables : 32 ( 5 ^; 27 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_P559422087at_nat,type,
list_P559422087at_nat: $tType ).
thf(ty_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(ty_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_e_a,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(ty_ord_le841296385at_nat,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ty_eigen__9,type,
eigen__9: product_prod_nat_nat ).
thf(ty_member701585322at_nat,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(ty_s,type,
s: nat ).
thf(ty_set_Pr2131844118at_nat,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(ty_edges,type,
edges: set_Pr1986765409at_nat ).
thf(ty_isShortestPath_a,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(ty_t,type,
t: nat ).
thf(ty_p,type,
p: list_P559422087at_nat ).
thf(ty_isPath_a,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(ty_c,type,
c: product_prod_nat_nat > a ).
thf(h0,assumption,
! [X1: product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: product_prod_nat_nat] :
~ ( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: list_P559422087at_nat,X3: nat,X4: product_prod_nat_nat] :
( ( isPath_a @ c @ X1 @ X2 @ X3 )
=> ( ( member701585322at_nat @ X4 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X4 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ord_le841296385at_nat @ edges )
= ( ^ [X1: set_Pr1986765409at_nat] :
! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ edges )
=> ( member701585322at_nat @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: list_P559422087at_nat,X2: nat] :
( ( isShortestPath_a @ c @ s @ X1 @ X2 )
=> ( isPath_a @ c @ s @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( isShortestPath_a @ c @ s @ p @ t )
=> ( isPath_a @ c @ s @ p @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: product_prod_nat_nat] :
( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( e_a @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( isShortestPath_a @ c @ s @ p @ X1 )
=> ( isPath_a @ c @ s @ p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat,X2: product_prod_nat_nat] :
( ( isPath_a @ c @ s @ p @ X1 )
=> ( ( member701585322at_nat @ X2 @ ( set_Pr2131844118at_nat @ p ) )
=> ( member701585322at_nat @ X2 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( member701585322at_nat @ eigen__9 @ edges )
=> ( member701585322at_nat @ eigen__9 @ ( set_Pr2131844118at_nat @ p ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ edges @ X1 )
= ( ! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ edges )
=> ( member701585322at_nat @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( isPath_a @ c @ s @ p @ t ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ X1 )
= ( ^ [X2: set_Pr1986765409at_nat] :
! [X3: product_prod_nat_nat] :
( ( member701585322at_nat @ X3 @ X1 )
=> ( member701585322at_nat @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP1
= ( ! [X1: product_prod_nat_nat] :
( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ord_le841296385at_nat
= ( ^ [X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
! [X3: product_prod_nat_nat] :
( ( member701585322at_nat @ X3 @ X1 )
=> ( member701585322at_nat @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP12
=> ( ( member701585322at_nat @ eigen__9 @ ( set_Pr2131844118at_nat @ p ) )
=> ( member701585322at_nat @ eigen__9 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( isShortestPath_a @ c @ s @ p @ t ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: product_prod_nat_nat] :
( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( member701585322at_nat @ eigen__9 @ ( set_Pr2131844118at_nat @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( isShortestPath_a @ c @ X1 @ X2 @ X3 )
=> ( isPath_a @ c @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( member701585322at_nat @ eigen__9 @ ( e_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: product_prod_nat_nat] :
( sP12
=> ( ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) )
=> ( member701585322at_nat @ X1 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( member701585322at_nat @ eigen__9 @ edges )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP19
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: list_P559422087at_nat,X2: nat,X3: product_prod_nat_nat] :
( ( isPath_a @ c @ s @ X1 @ X2 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X1 ) )
=> ( member701585322at_nat @ X3 @ ( e_a @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( member701585322at_nat @ eigen__9 @ edges ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(conj_0,conjecture,
sP22 ).
thf(h1,negated_conjecture,
~ sP22,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP16
| ~ sP12
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP25
| ~ sP19
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| ~ sP27
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP23
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP22
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| ~ sP1
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP24
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| ~ sP17
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP6
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(14,plain,
( ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP9
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP26
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP15
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP20
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP2
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_130_subset__eq,axiom,
sP15 ).
thf(fact_19_shortestPath__is__path,axiom,
sP20 ).
thf(fact_18_isPath__edgeset,axiom,
sP2 ).
thf(fact_1_SP__EDGES,axiom,
sP1 ).
thf(fact_0_SP,axiom,
sP17 ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h1,fact_130_subset__eq,fact_19_shortestPath__is__path,fact_18_isPath__edgeset,fact_1_SP__EDGES,fact_0_SP]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
sP22,
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP050^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun Aug 27 14:52:19 EDT 2023
% 0.14/0.34 % CPUTime :
% 23.89/24.18 % SZS status Theorem
% 23.89/24.18 % Mode: cade22sinegrackle2xfaf3
% 23.89/24.18 % Steps: 99344
% 23.89/24.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------