%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP196^1 : 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 01:45:24 PM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_poly_real,type,
list_poly_real: $tType ).
thf(ty_nil_poly_real,type,
nil_poly_real: list_poly_real ).
thf(ty_sturm_891428828rm_seq,type,
sturm_891428828rm_seq: list_poly_real > $o ).
thf(sP1,plain,
( sP1
<=> ( sturm_891428828rm_seq @ nil_poly_real ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: list_poly_real] :
( ( sturm_891428828rm_seq @ X1 )
=> ( X1 != nil_poly_real ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(conj_0,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_0_quasi__sturm__seq_Ops__not__Nil,axiom,
sP2 ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0,fact_0_quasi__sturm__seq_Ops__not__Nil]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP196^1 : TPTP v9.2.0. Released v7.5.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:46:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22sinegrackle2x6978
% 0.20/0.42 % Steps: 9
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------