TSTP Solution File: CSR144^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR144^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : Wed Aug 30 21:33:34 EDT 2023
% Result : Theorem 20.21s 20.53s
% Output : Proof 20.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 87
% Syntax : Number of formulae : 93 ( 13 unt; 9 typ; 2 def)
% Number of atoms : 253 ( 13 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 318 ( 79 ~; 63 |; 0 &; 131 @)
% ( 36 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 41 con; 0-2 aty)
% Number of variables : 28 ( 2 ^; 26 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_believes_THFTYPE_IiooI,type,
believes_THFTYPE_IiooI: $i > $o > $o ).
thf(ty_wife_THFTYPE_IiioI,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_husband_THFTYPE_IiioI,type,
husband_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lMax_THFTYPE_i,type,
lMax_THFTYPE_i: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_considers_THFTYPE_IiooI,type,
considers_THFTYPE_IiooI: $i > $o > $o ).
thf(ty_inverse_THFTYPE_IIiioIIiioIoI,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(ty_holdsDuring_THFTYPE_IiooI,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
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] :
~ ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( holdsDuring_THFTYPE_IiooI @ eigen__0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( husband_THFTYPE_IiioI @ X1 @ X2 )
= ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ $false )
= ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
= ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( holdsDuring_THFTYPE_IiooI @ eigen__0 @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
= sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
= ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X1 )
= ( wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 )
=> ~ ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( believes_THFTYPE_IiooI @ X1 @ ~ sP7 )
=> ~ ! [X2: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ ~ sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP12
= ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP7
= ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $o,X2: $i] :
( ( believes_THFTYPE_IiooI @ X2 @ X1 )
=> ~ ! [X3: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X3 @ ( considers_THFTYPE_IiooI @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( holdsDuring_THFTYPE_IiooI @ eigen__1 @ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( believes_THFTYPE_IiooI @ X1 @ sP7 )
=> ~ ! [X2: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( holdsDuring_THFTYPE_IiooI @ eigen__1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP10 = sP29 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ X1 @ wife_THFTYPE_IiioI )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
= ( wife_THFTYPE_IiioI @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ X1 @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ X2 @ X1 )
=> ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP2
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(con,conjecture,
~ sP23 ).
thf(h1,negated_conjecture,
sP23,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( sP14
| ~ sP33
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP21
| sP7
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP25
| sP27
| ~ sP6
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP3
| ~ sP30
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP29
| sP24
| ~ sP14
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP24
| sP29
| ~ sP21
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP29
| sP33
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP29
| sP10
| sP33
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| ~ sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| ~ sP24
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP6
| sP24
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP30
| ~ sP10
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP30
| sP10
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| ~ sP33
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| sP33
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP20
| sP13 ),
inference(symeq,[status(thm)],]) ).
thf(18,plain,
( sP8
| ~ sP12
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
~ sP7,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP16
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP15
| sP28
| ~ sP8
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP15
| sP2
| sP12
| sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP5
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP18
| sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(25,plain,
( sP32
| sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(26,plain,
( ~ sP35
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP17
| ~ sP28
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP36
| ~ sP2
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP31
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP19
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP26
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP34
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP22
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP22
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(ax,axiom,
sP9 ).
thf(ax_001,axiom,
sP34 ).
thf(ax_002,axiom,
sP22 ).
thf(ax_003,axiom,
sP1 ).
thf(37,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,ax,ax_001,ax_002,ax_003,h1]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
~ sP23,
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR144^1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 : 300
% 0.12/0.33 % DateTime : Mon Aug 28 08:52:26 EDT 2023
% 0.12/0.33 % CPUTime :
% 20.21/20.53 % SZS status Theorem
% 20.21/20.53 % Mode: cade22grackle2x798d
% 20.21/20.53 % Steps: 966
% 20.21/20.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------