%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR138^2 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 01:22:49 PM UTC 2025
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_lBill_THFTYPE_i,type,
lBill_THFTYPE_i: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_parent_THFTYPE_IiioI,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lMary_THFTYPE_i,type,
lMary_THFTYPE_i: $i ).
thf(ty_lAnna_THFTYPE_i,type,
lAnna_THFTYPE_i: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_likes_THFTYPE_IiioI,type,
likes_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(sP1,plain,
( sP1
<=> ( parent_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( likes_THFTYPE_IiioI @ eigen__4 )
= ( ^ [X1: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ eigen__0 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( parent_THFTYPE_IiioI @ eigen__0 )
= ( ^ [X1: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( likes_THFTYPE_IiioI @ X1 )
= ( ^ [X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( parent_THFTYPE_IiioI @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ~ ( ( likes_THFTYPE_IiioI @ X1 @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ lAnna_THFTYPE_i ) )
=> ( likes_THFTYPE_IiioI
= ( ^ [X2: $i,X3: $i] : ~ $false ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( likes_THFTYPE_IiioI @ eigen__4 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( likes_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $i > $o,X2: $i] :
( ~ ( ~ ( ( X1 @ X2 @ lBill_THFTYPE_i )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ lAnna_THFTYPE_i ) )
=> ( X1
= ( ^ [X3: $i,X4: $i] : ~ $false ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP6 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( likes_THFTYPE_IiioI @ eigen__4 @ eigen__5 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( likes_THFTYPE_IiioI @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ~ ( sP8
=> ~ ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) )
=> sP10 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> $false ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i] :
( ~ ( ~ ( ( X2 @ X3 @ lBill_THFTYPE_i )
=> ~ ( X1 @ X3 @ lAnna_THFTYPE_i ) )
=> ( X2
= ( ^ [X4: $i,X5: $i] : ~ sP16 ) ) )
=> ( X1
= ( ^ [X4: $i,X5: $i] : ~ sP16 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 )
= ( ^ [X2: $i] : ~ sP16 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP8
=> ~ sP17 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP8
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(con,conjecture,
~ sP18 ).
thf(h0,negated_conjecture,
sP18,
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( !! @ ( parent_THFTYPE_IiioI @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( !! @ ( parent_THFTYPE_IiioI @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( parent_THFTYPE_IiioI @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( !! @ ( likes_THFTYPE_IiioI @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( !! @ ( likes_THFTYPE_IiioI @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( likes_THFTYPE_IiioI @ eigen__6 @ eigen__7 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP21
| ~ sP8
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP20
| sP21
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| sP14
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP15
| sP20
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| sP6
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
~ sP16,
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP4
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP19
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP18
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax_035,axiom,
sP8 ).
thf(ax,axiom,
sP17 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h0,ax_035,h2,h6,ax]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__7)],[h7,18,h8]) ).
thf(ax_005,axiom,
~ ! [X1: $i,X2: $i] : ( likes_THFTYPE_IiioI @ X1 @ X2 ) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__6)],[ax_005,19,h7]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__5)],[h5,20,h6]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__4)],[ax_005,21,h5]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,22,h4]) ).
thf(ax_029,axiom,
~ ! [X1: $i,X2: $i] : ( parent_THFTYPE_IiioI @ X1 @ X2 ) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[ax_029,23,h3]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,24,h2]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[ax_029,25,h1]) ).
thf(0,theorem,
~ sP18,
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : CSR138^2 : TPTP v9.2.0. Released v4.1.0.
% 0.08/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 17:02:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % Mode: cade22sinegrackle2x6978
% 0.21/0.50 % Steps: 1167
% 0.21/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------