%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : CSR145^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 01:22:54 PM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_husband_THFTYPE_IiioI,type,
husband_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_wife_THFTYPE_IiioI,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(ty_inverse_THFTYPE_IIiioIIiioIoI,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(ty_lChris_THFTYPE_i,type,
lChris_THFTYPE_i: $i ).
thf(ty_lCorina_THFTYPE_i,type,
lCorina_THFTYPE_i: $i ).
thf(sP1,plain,
( sP1
<=> ! [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
=> ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ X1 )
= ( ^ [X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 )
= ( wife_THFTYPE_IiioI @ X1 @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
= ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $i > $o] :
( ( X1 @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
=> ( X1
= ( ^ [X2: $i,X3: $i] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( husband_THFTYPE_IiioI @ X1 @ X2 )
= ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i )
= ( ^ [X1: $i] : ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( husband_THFTYPE_IiioI
= ( ^ [X1: $i,X2: $i] : ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 )
= ( ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ eigen__0 )
= ( ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(con,conjecture,
~ sP6 ).
thf(h0,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP17
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP11
| ~ sP16
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| sP15
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
~ sP7,
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| ~ sP17
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax_003,axiom,
sP18 ).
thf(ax_001,axiom,
sP1 ).
thf(ax,axiom,
sP16 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h0,ax_003,h1,ax_001,ax]) ).
thf(ax_002,axiom,
~ ! [X1: $i] : ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 ) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[ax_002,15,h1]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CSR145^1 : TPTP v9.2.0. Released v4.1.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 16:57:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22grackle2xfee4
% 0.20/0.46 % Steps: 438
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------