%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR150^3 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 01:22:56 PM UTC 2025
% Result : Theorem 21.09s 21.32s
% Output : Proof 21.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_lList_THFTYPE_i,type,
lList_THFTYPE_i: $i ).
thf(ty_lOrganism_THFTYPE_i,type,
lOrganism_THFTYPE_i: $i ).
thf(ty_lCardinalityFn_THFTYPE_IIioIiI,type,
lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
thf(ty_lListOrderFn_THFTYPE_IiiiI,type,
lListOrderFn_THFTYPE_IiiiI: $i > $i > $i ).
thf(ty_instance_THFTYPE_IiioI,type,
instance_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lt_THFTYPE_IiioI,type,
lt_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_grandchild_THFTYPE_IiioI,type,
grandchild_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lJohn_THFTYPE_i,type,
lJohn_THFTYPE_i: $i ).
thf(ty_ltet_THFTYPE_IiioI,type,
ltet_THFTYPE_IiioI: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ltet_THFTYPE_IiioI @ X1
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) ) )
= ( ( X1
!= ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) ) )
=> ( lt_THFTYPE_IiioI @ X1
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ( ~ ( ( instance_THFTYPE_IiioI @ X1 @ lList_THFTYPE_i )
=> ~ ( instance_THFTYPE_IiioI @ lOrganism_THFTYPE_i @ lList_THFTYPE_i ) )
=> ~ ! [X2: $i] :
( ( lListOrderFn_THFTYPE_IiiiI @ X1 @ X2 )
= ( lListOrderFn_THFTYPE_IiiiI @ lOrganism_THFTYPE_i @ X2 ) ) )
=> ( X1 = lOrganism_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( instance_THFTYPE_IiioI @ X2 @ lList_THFTYPE_i )
=> ~ ( instance_THFTYPE_IiioI @ X1 @ lList_THFTYPE_i ) )
=> ~ ! [X3: $i] :
( ( lListOrderFn_THFTYPE_IiiiI @ X2 @ X3 )
= ( lListOrderFn_THFTYPE_IiiiI @ X1 @ X3 ) ) )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( ltet_THFTYPE_IiioI @ X2 @ X1 )
= ( ( X2 != X1 )
=> ( lt_THFTYPE_IiioI @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(con,conjecture,
~ sP2 ).
thf(h0,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP1
| sP8
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| ~ sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax1848,axiom,
sP6 ).
thf(ax1390,axiom,
sP5 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,ax1848,ax1390]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : CSR150^3 : TPTP v9.2.0. Released v5.3.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n023.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 16:56:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 21.09/21.32 % SZS status Theorem
% 21.09/21.32 % Mode: cade22sinegrackle2xfaf3
% 21.09/21.32 % Steps: 6706
% 21.09/21.32 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------