%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP122^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 01:45:08 PM UTC 2025
% Result : Theorem 44.16s 44.31s
% Output : Proof 44.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_c,type,
c: a ).
thf(ty_less_eq,type,
less_eq: a > a > $o ).
thf(ty_a2,type,
a2: a ).
thf(ty_b,type,
b: a ).
thf(ty_sup,type,
sup: a > a > a ).
thf(ty_modula1936294176_aux_a,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(ty_inf,type,
inf: a > a > a ).
thf(ty_modula1373251614_aux_a,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(ty_modula17988509_aux_a,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(ty_modula1144073633_aux_a,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(sP1,plain,
( sP1
<=> ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ c @ X1 @ X2 ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ X1 @ X2 ) )
=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ X1 @ X2 ) @ ( modula1373251614_aux_a @ inf @ sup @ c @ X1 @ X2 ) )
= ( modula1144073633_aux_a @ inf @ sup @ c @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ X1 )
= ( modula1144073633_aux_a @ inf @ sup @ X1 @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula1373251614_aux_a @ inf @ sup @ c @ a2 @ b ) )
= ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ X1 )
= ( modula1144073633_aux_a @ inf @ sup @ a2 @ X1 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ c @ a2 @ X1 ) @ ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ X1 ) )
=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ X1 ) @ ( modula1373251614_aux_a @ inf @ sup @ c @ a2 @ X1 ) )
= ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a,X2: a,X3: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3 ) @ ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3 ) )
=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3 ) @ ( modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3 ) )
= ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ X1 @ X2 )
= ( modula1936294176_aux_a @ inf @ sup @ X2 @ a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a,X3: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3 )
= ( modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula1373251614_aux_a @ inf @ sup @ c @ a2 @ b ) )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a,X3: a] :
( ( modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3 )
= ( modula17988509_aux_a @ inf @ sup @ X2 @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( modula1373251614_aux_a @ inf @ sup @ c @ a2 @ X1 )
= ( modula17988509_aux_a @ inf @ sup @ a2 @ X1 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a,X3: a] :
( ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ X1 )
= ( modula1936294176_aux_a @ inf @ sup @ X1 @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a,X3: a] :
( ( modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3 )
= ( modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) )
= ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ a2 @ X1 @ X2 )
= ( modula1144073633_aux_a @ inf @ sup @ X2 @ a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP6
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b )
= ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a] :
( ( modula1373251614_aux_a @ inf @ sup @ c @ X1 @ X2 )
= ( modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( modula1373251614_aux_a @ inf @ sup @ c @ a2 @ b )
= ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
= ( modula1936294176_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
= ( sup @ ( modula17988509_aux_a @ inf @ sup @ c @ a2 @ b ) @ ( modula17988509_aux_a @ inf @ sup @ a2 @ b @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c )
= ( modula1144073633_aux_a @ inf @ sup @ c @ a2 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a,X2: a] :
( ( modula1144073633_aux_a @ inf @ sup @ c @ X1 @ X2 )
= ( modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> $false ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(conj_1,conjecture,
sP17 ).
thf(h0,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(1,plain,
( ~ sP1
| sP6
| ~ sP25
| ~ sP23 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP24
| ~ sP20
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( sP11
| ~ sP22
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
~ sP27,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP19
| ~ sP6
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP15
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP3
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP13
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP5
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP10
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP26
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP21
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP14
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP24
| sP17 ),
inference(symeq,[status(thm)],[]) ).
thf(fact_87_local_Od__b__c__a,axiom,
sP16 ).
thf(fact_93_local_Oe__b__c__a,axiom,
sP10 ).
thf(fact_94_local_Oe__c__a__b,axiom,
sP14 ).
thf(fact_132_local_Ob__a,axiom,
sP12 ).
thf(fact_135_a__join__b__eq__e,axiom,
sP8 ).
thf(conj_0,axiom,
sP1 ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,fact_87_local_Od__b__c__a,fact_93_local_Oe__b__c__a,fact_94_local_Oe__c__a__b,fact_132_local_Ob__a,fact_135_a__join__b__eq__e,conj_0,h0]) ).
thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : ITP122^1 : TPTP v9.2.0. Released v7.5.0.
% 0.12/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Wed Oct 8 18:36:23 EDT 2025
% 0.12/0.37 % CPUTime :
% 44.16/44.31 % SZS status Theorem
% 44.16/44.31 % Mode: cade22sinegrackle2x26c3
% 44.16/44.31 % Steps: 3006608
% 44.16/44.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------