TSTP Solution File: ITP104^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP104^1 : 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 : n015.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 04:02:06 EDT 2023
% Result : Theorem 20.22s 20.80s
% Output : Proof 20.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_list_a,type,
list_a: $tType ).
thf(ty_listSl97544552lice_a,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(ty_size_size_list_a,type,
size_size_list_a: list_a > nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_listSl1174287072ice2_a,type,
listSl1174287072ice2_a: list_a > nat > list_list_a ).
thf(ty_xs,type,
xs: list_a ).
thf(ty_k,type,
k: nat ).
thf(ty_nth_list_a,type,
nth_list_a: list_list_a > nat > list_a ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_m,type,
m: nat ).
thf(sP1,plain,
( sP1
<=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m )
= ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ X1 ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ X1 ) @ m )
= ( nth_list_a @ ( listSl97544552lice_a @ xs @ X1 ) @ m ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) )
= k ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ X1 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ X1 ) @ m ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: list_a,X3: nat] :
( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X3 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X3 ) @ X1 ) )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m )
= ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: list_a,X2: nat] :
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X2 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X2 ) @ m ) )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) )
= ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat,X2: list_a,X3: nat] :
( ( ord_less_nat @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X2 ) @ X3 ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ X2 @ X3 ) @ X1 )
= ( nth_list_a @ ( listSl97544552lice_a @ X2 @ X3 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: list_a,X2: nat] :
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X2 ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ X1 @ X2 ) @ m )
= ( nth_list_a @ ( listSl97544552lice_a @ X1 @ X2 ) @ m ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_1,conjecture,
sP11 ).
thf(h0,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(1,plain,
( sP12
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP11
| ~ sP12
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP7 ),
inference(symeq,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(conj_0,axiom,
sP3 ).
thf(fact_30_list__slice__nth__length,axiom,
sP6 ).
thf(fact_19_list__slice2__list__slice__nth,axiom,
sP13 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,h0,conj_0,fact_30_list__slice__nth__length,fact_19_list__slice2__list__slice__nth]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n015.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 : 300
% 0.12/0.34 % DateTime : Sun Aug 27 11:51:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.22/20.80 % SZS status Theorem
% 20.22/20.80 % Mode: cade22sinegrackle2xfaf3
% 20.22/20.80 % Steps: 2535
% 20.22/20.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------