TSTP Solution File: CSR146^3 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : CSR146^3 : 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 : n009.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 23:14:31 EDT 2022
% Result : Theorem 1.99s 2.23s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 60
% Syntax : Number of formulae : 65 ( 14 unt; 8 typ; 1 def)
% Number of atoms : 149 ( 17 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 191 ( 39 ~; 24 |; 0 &; 78 @)
% ( 25 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 32 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 5 ^ 29 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_husband_THFTYPE_IiioI,type,
husband_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_lChris_THFTYPE_i,type,
lChris_THFTYPE_i: $i ).
thf(ty_inverse_THFTYPE_IIiioIIiioIoI,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(ty_lCorina_THFTYPE_i,type,
lCorina_THFTYPE_i: $i ).
thf(ty_lYearFn_THFTYPE_IiiI,type,
lYearFn_THFTYPE_IiiI: $i > $i ).
thf(ty_holdsDuring_THFTYPE_IiooI,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
thf(ty_wife_THFTYPE_IiioI,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_n2009_THFTYPE_i,type,
n2009_THFTYPE_i: $i ).
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] :
~ ~ $false ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( husband_THFTYPE_IiioI @ X1 @ X2 )
= ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( !! @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i ) )
=> ! [X1: $i > $i > $o] :
( ( husband_THFTYPE_IiioI = X1 )
=> ~ ( !! @ ( X1 @ lChris_THFTYPE_i ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] : ~ $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( $i > $i > $o ) > $o] :
( ( X1 @ husband_THFTYPE_IiioI )
=> ! [X2: $i > $i > $o] :
( ( husband_THFTYPE_IiioI = X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( !! @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o] :
( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= X1 )
=> ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $i > $o,X2: ( $i > $i > $o ) > $o] :
( ( X2 @ X1 )
=> ! [X3: $i > $i > $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [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,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o > $o] :
( ( X1 @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) )
=> ! [X2: $o] :
( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [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,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $i > $o] :
( ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( X1 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) )
=> ( X1
= ( ^ [X2: $i,X3: $i] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i > $i > $o] :
( ( husband_THFTYPE_IiioI = X1 )
=> ~ ( !! @ ( X1 @ lChris_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ( husband_THFTYPE_IiioI @ X1 @ X2 )
= ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP9
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 )
= ( wife_THFTYPE_IiioI @ X1 @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> $false ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP9
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(con,conjecture,
~ sP18 ).
thf(h1,negated_conjecture,
sP18,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP13
| ~ sP21
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP20
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP23
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP25
| sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP16
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(12,plain,
( ~ sP18
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP22
| ~ sP9
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP12
| ~ sP4
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP19
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP5
| sP8
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
sP3,
inference(eq_ind,[status(thm)],]) ).
thf(20,plain,
~ sP24,
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
sP14,
inference(eq_ind,[status(thm)],]) ).
thf(ax_004,axiom,
sP10 ).
thf(ax_003,axiom,
~ sP8 ).
thf(ax_001,axiom,
sP17 ).
thf(ax,axiom,
sP1 ).
thf(22,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,ax_004,ax_003,ax_001,ax,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
~ sP18,
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CSR146^3 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sat Jun 11 06:41:23 EDT 2022
% 0.14/0.33 % CPUTime :
% 1.99/2.23 % SZS status Theorem
% 1.99/2.23 % Mode: mode506
% 1.99/2.23 % Inferences: 8425
% 1.99/2.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------