%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : CSR150^2 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 01:24:06 PM UTC 2025
% Result : Theorem 23.00s 23.08s
% Output : Proof 23.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 77 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 110 ( 17 ~; 9 |; 0 &; 70 @)
% ( 10 <=>; 4 =>; 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 : 19 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 22 ( 15 ^; 7 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_ltet_THFTYPE_IiioI,type,
ltet_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lCardinalityFn_THFTYPE_IIioIiI,type,
lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
thf(ty_grandchild_THFTYPE_IiioI,type,
grandchild_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lJohn_THFTYPE_i,type,
lJohn_THFTYPE_i: $i ).
thf(ty_lt_THFTYPE_IiioI,type,
lt_THFTYPE_IiioI: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i )
!= ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
= ( ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
!= ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) )
=> ( lt_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,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( grandchild_THFTYPE_IiioI @ eigen__2 @ lJohn_THFTYPE_i )
= ( grandchild_THFTYPE_IiioI @ eigen__2 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i )
= ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( 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,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP6 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( ltet_THFTYPE_IiioI @ X2 @ X1 )
= ( ( X2 != X1 )
=> ( lt_THFTYPE_IiioI @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( 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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(con,conjecture,
~ sP10 ).
thf(h1,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(5,plain,
( sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP9
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax_002,axiom,
sP8 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,ax_002,h1]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CSR150^2 : TPTP v9.2.0. Released v4.1.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 8 17:06:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 23.00/23.08 % SZS status Theorem
% 23.00/23.08 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 23.00/23.08 % Inferences: 3118
% 23.00/23.08 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------