%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP019^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 01:44:42 PM UTC 2025
% Result : Theorem 5.15s 5.27s
% Output : Proof 5.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(ty_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(ty_mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(ty_eigen__0,type,
eigen__0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(ty_mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(ty_mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(sP1,plain,
( sP1
<=> ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( X1
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ eigen__0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X1
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X1
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(assume_negation,[status(cth)],[thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
thf(h1,assumption,
~ ( ~ sP2
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
sP1 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,h2,h3,thm_2Ecomplex_2ECOMPLEX__INV__EQ__0]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,3,h2,h3]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).
thf(0,theorem,
! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( X1
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : ITP019^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.03/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.38 % Computer : n008.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Wed Oct 8 17:51:38 EDT 2025
% 0.14/0.38 % CPUTime :
% 5.15/5.27 % SZS status Theorem
% 5.15/5.27 % Mode: cade22grackle2xfee4
% 5.15/5.27 % Steps: 193149
% 5.15/5.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------