%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR150^1 : 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 : n005.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 01:22:55 PM UTC 2025
% Result : Theorem 63.65s 62.14s
% Output : Proof 63.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 57
% Syntax : Number of formulae : 64 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 170 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 236 ( 58 ~; 35 |; 0 &; 102 @)
% ( 26 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 33 con; 0-2 aty)
% Number of variables : 25 ( 7 ^; 18 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_grandchild_THFTYPE_IiioI,type,
grandchild_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_n3_THFTYPE_i,type,
n3_THFTYPE_i: $i ).
thf(ty_eigen__74,type,
eigen__74: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_lJohn_THFTYPE_i,type,
lJohn_THFTYPE_i: $i ).
thf(ty_eigen__66,type,
eigen__66: $i ).
thf(ty_ltet_THFTYPE_IiioI,type,
ltet_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_grandparent_THFTYPE_IiioI,type,
grandparent_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_parent_THFTYPE_IiioI,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lCardinalityFn_THFTYPE_IIioIiI,type,
lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
!= ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__66,definition,
( eigen__66
= ( eps__0
@ ^ [X1: $i] :
~ ( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__66])]) ).
thf(eigendef_eigen__74,definition,
( eigen__74
= ( eps__0
@ ^ [X1: $i] :
~ ( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__74])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( grandparent_THFTYPE_IiioI @ X1 @ X2 )
= ( ~ ! [X3: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ X3 )
=> ~ ( parent_THFTYPE_IiioI @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i )
= ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 )
= ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( grandchild_THFTYPE_IiioI @ eigen__1 @ X1 )
= ( ~ ! [X2: $i] :
( ( parent_THFTYPE_IiioI @ X2 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( parent_THFTYPE_IiioI @ eigen__74 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__66 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
= ( ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( parent_THFTYPE_IiioI @ eigen__66 @ eigen__1 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( parent_THFTYPE_IiioI @ eigen__66 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
= ( ~ ! [X2: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X2 )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ n3_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP14 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ltet_THFTYPE_IiioI @ ( lCardinalityFn_THFTYPE_IIioIiI @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) ) @ n3_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
= ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__74 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP21
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( lCardinalityFn_THFTYPE_IIioIiI @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) )
= ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP7
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ X2 )
= ( ~ ! [X3: $i] :
( ( parent_THFTYPE_IiioI @ X3 @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP8
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(con,conjecture,
~ sP20 ).
thf(h1,negated_conjecture,
sP20,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP26
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP24
| ~ sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP18
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP22
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP22
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP10
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__74]) ).
thf(8,plain,
( ~ sP3
| ~ sP14
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| sP14
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP11
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP11
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP18
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__66]) ).
thf(13,plain,
( ~ sP2
| ~ sP6
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP2
| sP6
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP25
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP17
| sP15
| sP4
| ~ sP23 ),
inference(mating_rule,[status(thm)],[]) ).
thf(21,plain,
( sP16
| ~ sP14
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP16
| sP14
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP19
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(24,plain,
( sP9
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP20
| ~ sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( sP23
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(ax_002,axiom,
sP25 ).
thf(ax_001,axiom,
sP17 ).
thf(ax,axiom,
sP1 ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,ax_002,ax_001,ax,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
~ sP20,
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR150^1 : TPTP v9.2.0. Released v4.1.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 17:09:53 EDT 2025
% 0.14/0.34 % CPUTime :
% 63.65/62.14 % SZS status Theorem
% 63.65/62.14 % Mode: cade22grackle2x34cb
% 63.65/62.14 % Steps: 9777
% 63.65/62.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------