%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP225^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : Sat Feb 28 09:29:51 AM UTC 2026
% Result : Theorem 1.00s 1.69s
% Output : Proof 1.00s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_m,type,
m: nat ).
thf(ty_na,type,
na: nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(sP1,plain,
( sP1
<=> ( ( ord_less_nat @ zero_zero_nat @ m )
= ( ~ ! [X1: nat] :
( m
!= ( suc @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( m
!= ( suc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( m
= ( suc @ na ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ord_less_nat @ zero_zero_nat @ m ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( ord_less_nat @ zero_zero_nat @ X1 )
= ( ~ ! [X2: nat] :
( X1
!= ( suc @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(conj_0,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP2
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_79_gr0__conv__Suc,axiom,
sP5 ).
thf(fact_4__C3_Ohyps_C_I3_J,axiom,
sP3 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,h0,fact_79_gr0__conv__Suc,fact_4__C3_Ohyps_C_I3_J]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP225^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.30 % Computer : n027.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Thu Feb 26 09:48:37 EST 2026
% 0.12/0.30 % CPUTime :
% 1.00/1.69 % SZS status Theorem
% 1.00/1.69 % Mode: cade22sinegrackle2x6978
% 1.00/1.69 % Steps: 16451
% 1.00/1.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------