%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP056^1 : 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 : 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 Oct 9 01:44:55 PM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_c1059388851t_unit,type,
list_c1059388851t_unit: $tType ).
thf(ty_nth_co1649820636t_unit,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(ty_one_one_nat,type,
one_one_nat: nat ).
thf(ty_nil_co1338500125t_unit,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(ty_size_s1406904903t_unit,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(ty_n,type,
n: nat ).
thf(ty_last_c571238084t_unit,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(ty_fe,type,
fe: nat > list_c1059388851t_unit ).
thf(ty_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: list_c1059388851t_unit] :
( ( X1 != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ X1 )
= ( nth_co1649820636t_unit @ X1 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X1 ) @ one_one_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( fe @ n )
!= nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ ( fe @ n ) )
= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( fe @ n )
= nil_co1338500125t_unit ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( last_c571238084t_unit @ ( fe @ n ) )
= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_0,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP2
| sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_1_LastIsLastIndex,axiom,
sP1 ).
thf(fact_0_FeNNotEmpty,axiom,
~ sP3 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,fact_1_LastIsLastIndex,fact_0_FeNNotEmpty]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP056^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n029.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 : Wed Oct 8 18:06:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22sinegrackle2x6978
% 0.19/0.43 % Steps: 68
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------