%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP216^1 : 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 : n003.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 09:29:48 AM UTC 2026
% Result : Theorem 0.48s 0.85s
% Output : Proof 0.48s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_heap_T6362127782908069795rray_a,type,
heap_T6362127782908069795rray_a: $tType ).
thf(ty_heap_e7401611519738050253t_unit,type,
heap_e7401611519738050253t_unit: $tType ).
thf(ty_list_a,type,
list_a: $tType ).
thf(ty_heap_T5591663578999710211rray_a,type,
heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
thf(ty_xs,type,
xs: list_a ).
thf(ty_heap_T6932021131025641745rray_a,type,
heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o ).
thf(ty_array_of_list_a,type,
array_of_list_a: list_a > heap_T6362127782908069795rray_a ).
thf(ty_none_P2587165478634041381it_nat,type,
none_P2587165478634041381it_nat: option3216581401566546698it_nat ).
thf(ty_h,type,
h: heap_e7401611519738050253t_unit ).
thf(sP1,plain,
( sP1
<=> ! [X1: list_a,X2: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X1 ) @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= none_P2587165478634041381it_nat ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: heap_T6362127782908069795rray_a] :
( ( heap_T6932021131025641745rray_a @ X1 )
= ( ^ [X2: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ X1 @ X2 )
!= none_P2587165478634041381it_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: heap_e7401611519738050253t_unit] :
( ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ X1 )
= ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ X1 )
!= none_P2587165478634041381it_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ h )
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ h ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) )
= ( ^ [X1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ X1 )
!= none_P2587165478634041381it_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( heap_T6932021131025641745rray_a
= ( ^ [X1: heap_T6362127782908069795rray_a,X2: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ X1 @ X2 )
!= none_P2587165478634041381it_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ xs ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
~ sP2 ).
thf(h0,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP5
| ~ sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_45_success__of__listI,axiom,
sP1 ).
thf(fact_12_success__def,axiom,
sP8 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0,fact_45_success__of__listI,fact_12_success__def]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP216^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n003.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Feb 26 04:55:25 EST 2026
% 0.14/0.33 % CPUTime :
% 0.48/0.85 % SZS status Theorem
% 0.48/0.85 % Mode: cade22sinegrackle2x6978
% 0.48/0.85 % Steps: 209
% 0.48/0.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------