TSTP Solution File: CSR150^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : CSR150^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : 600s
% DateTime : Fri Jul 15 23:14:33 EDT 2022
% Result : Theorem 2.24s 2.49s
% Output : Proof 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 83
% Syntax : Number of formulae : 90 ( 14 unt; 10 typ; 3 def)
% Number of atoms : 236 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 365 ( 87 ~; 41 |; 0 &; 166 @)
% ( 35 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 42 con; 0-2 aty)
% Number of variables : 43 ( 7 ^ 36 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_parent_THFTYPE_IiioI,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $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_eigen__1,type,
eigen__1: $i ).
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_n3_THFTYPE_i,type,
n3_THFTYPE_i: $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__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
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
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 )
= ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( 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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__6 )
=> ~ ( parent_THFTYPE_IiioI @ eigen__6 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) )
!= ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) )
=> ! [X1: $o] :
( ( ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i )
= X1 )
=> ( ( ~ ! [X2: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X2 )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ eigen__1 ) ) )
!= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o > $o] :
( ( X1 @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 ) )
=> ! [X2: $o] :
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( 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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [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,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o > $o] :
( ( X1 @ ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) )
=> ! [X2: $o] :
( ( ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP6
=> ~ ( parent_THFTYPE_IiioI @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP3
=> ! [X1: $o] :
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 )
= X1 )
=> ( X1
!= ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( 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,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP9
=> ( ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) )
!= ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( parent_THFTYPE_IiioI @ eigen__6 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( parent_THFTYPE_IiioI @ eigen__2 @ eigen__1 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) )
= ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $o] :
( ( ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i )
= X1 )
=> ( ( ~ ! [X2: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X2 )
=> ~ ( parent_THFTYPE_IiioI @ X2 @ eigen__1 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i )
= ( ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $o] :
( ( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__1 )
= X1 )
=> ( X1
!= ( grandchild_THFTYPE_IiioI @ eigen__1 @ lJohn_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( parent_THFTYPE_IiioI @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [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,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
= ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ltet_THFTYPE_IiioI @ ( lCardinalityFn_THFTYPE_IIioIiI @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) ) @ n3_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X2: $i] : ( grandchild_THFTYPE_IiioI @ X2 @ lJohn_THFTYPE_i ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ n3_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 )
=> ~ ( parent_THFTYPE_IiioI @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP16
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP4
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( n3_THFTYPE_i = n3_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [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,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ~ sP29 )
= ( ~ ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ eigen__1 )
=> ~ ( parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(con,conjecture,
~ sP27 ).
thf(h1,negated_conjecture,
sP27,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP35
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP30
| ~ sP16
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP5
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP29
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(6,plain,
sP32,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP26
| sP28
| ~ sP14
| ~ sP32 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP29
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| ~ sP6
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP17
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP17
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP15
| ~ sP9
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP19
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP18
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP34
| sP29
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP34
| ~ sP29
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP35
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(19,plain,
( ~ sP33
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP23
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| ~ sP4
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP21
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP13
| sP3
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP8
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( sP24
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(30,plain,
( sP20
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP27
| ~ sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( sP14
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
sP2,
inference(eq_ind,[status(thm)],]) ).
thf(ax_002,axiom,
sP33 ).
thf(ax_001,axiom,
sP26 ).
thf(ax,axiom,
sP1 ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,ax_002,ax_001,ax,h1]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[34,h0]) ).
thf(0,theorem,
~ sP27,
inference(contra,[status(thm),contra(discharge,[h1])],[34,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR150^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 19:55:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.24/2.49 % SZS status Theorem
% 2.24/2.49 % Mode: mode506
% 2.24/2.49 % Inferences: 41881
% 2.24/2.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------