%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Oct 9 02:09:24 PM UTC 2025
% Result : Theorem 40.25s 40.45s
% Output : Proof 40.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_succ,type,
succ: $i > $i ).
thf(ty_m,type,
m: $i > $o ).
thf(ty_one,type,
one: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( m @ X1 )
=> ( m @ ( succ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( m @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ~ ( ( X1 @ one )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( succ @ X2 ) ) ) )
=> ! [X2: $i] : ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( m @ one )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( m @ one ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( m @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_m,definition,
( m
= ( ^ [X1: $i] :
( (~)
@ ( ( succ @ X1 )
= X1 ) ) ) ) ).
thf(m_is_all,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[m_is_all]) ).
thf(h1,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(induction,axiom,
sP3 ).
thf(m_is_one,axiom,
sP6 ).
thf(m_is_next,axiom,
sP1 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,induction,m_is_one,m_is_next,h1]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Oct 8 23:10:23 EDT 2025
% 0.16/0.36 % CPUTime :
% 40.25/40.45 % SZS status Theorem
% 40.25/40.45 % Mode: cade22grackle2x6987
% 40.25/40.45 % Steps: 40
% 40.25/40.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------