%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : CSR145^1 : 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 : n001.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 01:24:04 PM UTC 2025
% Result : Theorem 1.07s 1.29s
% Output : Proof 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 52
% Syntax : Number of formulae : 57 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 148 ( 19 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 182 ( 43 ~; 24 |; 0 &; 64 @)
% ( 25 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 31 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 38 ( 9 ^; 29 !; 0 ?; 38 :)
% 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_wife_THFTYPE_IiioI,type,
wife_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] :
~ ~ $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
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
=> ! [X1: $o] :
( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= X1 )
=> ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [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,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [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,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( !! @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i ) )
=> ! [X1: $i > $i > $o] :
( ( husband_THFTYPE_IiioI = X1 )
=> ~ ( !! @ ( X1 @ lChris_THFTYPE_i ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= sP4 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 )
= ( wife_THFTYPE_IiioI @ X1 @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ sP2 ) )
=> ~ ! [X1: $i] : ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ( husband_THFTYPE_IiioI @ X1 @ X2 )
= ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
=> ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [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,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $i > $o] :
( ( X1 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
=> ( X1
= ( ^ [X2: $i,X3: $i] : ~ sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] :
( ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= X1 )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $i > $o,X2: ( $i > $i > $o ) > $o] :
( ( X2 @ X1 )
=> ! [X3: $i > $i > $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
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] : ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( !! @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: ( $i > $i > $o ) > $o] :
( ( X1 @ husband_THFTYPE_IiioI )
=> ! [X2: $i > $i > $o] :
( ( husband_THFTYPE_IiioI = X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP1
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(con,conjecture,
~ sP15 ).
thf(h1,negated_conjecture,
sP15,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP9
| ~ sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP17
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP10
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP25
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP23
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( sP20
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(12,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP13
| ~ sP23
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP11
| ~ sP21
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP19
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP8
| sP22
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP24
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP18
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
sP6,
inference(eq_ind,[status(thm)],[]) ).
thf(20,plain,
~ sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
sP18,
inference(eq_ind,[status(thm)],[]) ).
thf(ax_003,axiom,
sP4 ).
thf(ax_002,axiom,
~ sP22 ).
thf(ax_001,axiom,
sP14 ).
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_003,ax_002,ax_001,ax,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
~ sP15,
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CSR145^1 : TPTP v9.2.0. Released v4.1.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n001.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 16:57:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 1.07/1.29 % SZS status Theorem
% 1.07/1.29 % Mode: mode506
% 1.07/1.29 % Inferences: 8275
% 1.07/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------