%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP105^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 Oct 9 01:45:04 PM UTC 2025
% Result : Theorem 20.78s 21.01s
% Output : Proof 20.78s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_a,type,
list_a: $tType ).
thf(ty_list_list_a,type,
list_list_a: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_listSl97544552lice_a,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(ty_nil_list_a,type,
nil_list_a: list_list_a ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_nil_a,type,
nil_a: list_a ).
thf(ty_size_s1427607542list_a,type,
size_s1427607542list_a: list_list_a > nat ).
thf(ty_k,type,
k: nat ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
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_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: list_a,X2: nat] :
( ( ord_less_nat @ ( size_size_list_a @ X1 ) @ X2 )
=> ( ( listSl97544552lice_a @ X1 @ X2 )
= nil_list_a ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( size_size_list_a @ nil_a ) @ X1 ) )
= ( ~ ( ( ord_less_eq_nat @ X1 @ ( size_size_list_a @ nil_a ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ nil_a @ k ) )
= ( divide_divide_nat @ ( size_size_list_a @ nil_a ) @ k ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( size_size_list_a @ nil_a ) @ k ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ ( listSl97544552lice_a @ nil_a @ k ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat,X2: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ X1 @ X2 ) )
= ( ~ ( ( ord_less_eq_nat @ X2 @ X1 )
=> ~ ( ord_less_nat @ zero_zero_nat @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: list_list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ X1 ) )
= ( X1 != nil_list_a ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ord_less_eq_nat @ k @ ( size_size_list_a @ nil_a ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ k ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ nil_a @ X1 ) )
= ( divide_divide_nat @ ( size_size_list_a @ nil_a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
= ( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ord_less_nat @ ( size_size_list_a @ nil_a ) @ k ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ord_less_nat @ zero_zero_nat @ k ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: nat] :
( ( ord_less_nat @ ( size_size_list_a @ nil_a ) @ X1 )
=> ( ( listSl97544552lice_a @ nil_a @ X1 )
= nil_list_a ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( size_size_list_a @ nil_a )
= zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: list_a,X2: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ X1 @ X2 ) )
= ( divide_divide_nat @ ( size_size_list_a @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( zero_zero_nat
= ( size_size_list_a @ nil_a ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP5 = ( ~ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(conj_0,conjecture,
sP16 ).
thf(h0,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP6
| sP5
| ~ sP3
| sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP13
| sP12
| sP4
| ~ sP19 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( sP9
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP20
| ~ sP5
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP17
| ~ sP12
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP11
| sP6
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP15
| sP19 ),
inference(symeq,[status(thm)],[]) ).
thf(15,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_316_div__greater__zero__iff,axiom,
sP7 ).
thf(fact_257_list__slice__length,axiom,
sP18 ).
thf(fact_57_list_Osize_I3_J,axiom,
sP15 ).
thf(fact_52_length__greater__0__conv,axiom,
sP8 ).
thf(fact_9_list__slice__less,axiom,
sP1 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h0,fact_316_div__greater__zero__iff,fact_257_list__slice__length,fact_57_list_Osize_I3_J,fact_52_length__greater__0__conv,fact_9_list__slice__less]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP105^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 17:51:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 20.78/21.01 % SZS status Theorem
% 20.78/21.01 % Mode: cade22sinegrackle2xfaf3
% 20.78/21.01 % Steps: 6154
% 20.78/21.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------