TSTP Solution File: ITP019^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP019^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 Aug 31 04:01:19 EDT 2023
% Result : Theorem 2.35s 2.53s
% Output : Proof 2.35s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_tp__ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
thf(ty_tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).
thf(ty_fo__c_2Enum_2E0,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
thf(ty_c_2Ecomplex_2Ecomplex__of__num,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(ty_eigen__0,type,
eigen__0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
thf(ty_surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
thf(ty_inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,type,
inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_inj__ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(ty_c_2Ecomplex_2Ecomplex__inv,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(sP1,plain,
( sP1
<=> ( ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ eigen__0 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( eigen__0
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ eigen__0 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X1 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( X1
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
! [X1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X1
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X1 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X1
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X1 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
thf(h1,assumption,
~ ( ~ sP3
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h3,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
sP4 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,h2,h3,conj_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: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X1
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X1 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : ITP019^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.07 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.06/0.25 % Computer : n011.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Sun Aug 27 12:53:54 EDT 2023
% 0.06/0.26 % CPUTime :
% 2.35/2.53 % SZS status Theorem
% 2.35/2.53 % Mode: cade22grackle2xfee4
% 2.35/2.53 % Steps: 94921
% 2.35/2.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------