TSTP Solution File: ITP019^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP019^4 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : 600s
% DateTime : Sun Jul 17 00:28:39 EDT 2022
% Result : Theorem 13.66s 13.71s
% Output : Proof 13.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 49
% Syntax : Number of formulae : 80 ( 30 unt; 17 typ; 0 def)
% Number of atoms : 202 ( 56 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 388 ( 88 ~; 8 |; 0 &; 229 @)
% ( 0 <=>; 62 =>; 1 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 13 con; 0-2 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% 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_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Earithmetic_2EEXP,type,
mono_2Ec_2Earithmetic_2EEXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(ty_eigen__1,type,
eigen__1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > 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_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
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(ty_mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(ty_mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Earithmetic_2EMOD,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(ty_mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(ty_mono_2Ec_2Earithmetic_2E_3C_3D,type,
mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
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,
~ ( ( eigen__0
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ eigen__0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
eigen__0
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ eigen__0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF ),
introduced(assumption,[]) ).
thf(h15,assumption,
! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ ( mono_2Ec_2Enum_2ESUC @ X2 ) )
= ( ( X1 != X2 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ~ ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ~ ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X2 ) )
=> ~ ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ X1 @ ( eigen__1 @ X1 @ X2 ) ) @ X2 )
=> ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X2 @ ( mono_2Ec_2Earithmetic_2EEXP @ X1 @ ( mono_2Ec_2Enum_2ESUC @ ( eigen__1 @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ X2 @ X1 ) @ X1 )
= ( mono_2Ec_2Earithmetic_2EMOD @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ X1 @ X2 ) @ X1 )
= ( mono_2Ec_2Earithmetic_2EMOD @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(pax493,axiom,
( p493
=> ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 ) )
= X1 ) ),
file('<stdin>',pax493) ).
thf(pax496,axiom,
( p496
=> ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ f__0 )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
file('<stdin>',pax496) ).
thf(ax14,axiom,
p493,
file('<stdin>',ax14) ).
thf(ax11,axiom,
p496,
file('<stdin>',ax11) ).
thf(pax491,axiom,
( p491
=> ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
file('<stdin>',pax491) ).
thf(nax497,axiom,
( p497
<= ( f__0
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
file('<stdin>',nax497) ).
thf(ax10,axiom,
~ p497,
file('<stdin>',ax10) ).
thf(ax16,axiom,
p491,
file('<stdin>',ax16) ).
thf(c_0_8,plain,
! [X205: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ~ p493
| ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ X205 ) )
= X205 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax493])])]) ).
thf(c_0_9,plain,
( ~ p496
| ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ f__0 )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
inference(fof_nnf,[status(thm)],[pax496]) ).
thf(c_0_10,plain,
! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 ) )
= X1 )
| ~ p493 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
p493,
inference(split_conjunct,[status(thm)],[ax14]) ).
thf(c_0_12,plain,
( ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ f__0 )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
| ~ p496 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
p496,
inference(split_conjunct,[status(thm)],[ax11]) ).
thf(c_0_14,plain,
( ~ p491
| ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
inference(fof_nnf,[status(thm)],[pax491]) ).
thf(c_0_15,plain,
( ( f__0
!= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
| p497 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax497])]) ).
thf(c_0_16,plain,
~ p497,
inference(fof_simplification,[status(thm)],[ax10]) ).
thf(c_0_17,plain,
! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_18,plain,
( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ f__0 )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
thf(c_0_19,plain,
( ( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
| ~ p491 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
p491,
inference(split_conjunct,[status(thm)],[ax16]) ).
thf(c_0_21,plain,
( p497
| ( f__0
!= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,plain,
~ p497,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,plain,
( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
= f__0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_24,plain,
( ( fmono_2Ec_2Ecomplex_2Ecomplex__inv @ ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) )
= ( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_25,plain,
( fmono_2Ec_2Ecomplex_2Ecomplex__of__num @ fmono_2Ec_2Enum_2E0 )
!= f__0,
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],]) ).
thf(thm_2Earithmetic_2EADD__MODULUS,axiom,
~ ( ! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ X2 @ X1 ) @ X1 )
= ( mono_2Ec_2Earithmetic_2EMOD @ X2 @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ X1 @ X2 ) @ X1 )
= ( mono_2Ec_2Earithmetic_2EMOD @ X2 @ X1 ) ) ) ) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[thm_2Earithmetic_2EADD__MODULUS,1,h17,h18]) ).
thf(thm_2Elogroot_2ELOG__exists,axiom,
~ ! [X1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
~ ! [X2: mono_2Etyop_2Enum_2Enum,X3: mono_2Etyop_2Enum_2Enum] :
( ~ ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X2 )
=> ~ ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X3 ) )
=> ~ ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ X2 @ ( X1 @ X2 @ X3 ) ) @ X3 )
=> ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X3 @ ( mono_2Ec_2Earithmetic_2EEXP @ X2 @ ( mono_2Ec_2Enum_2ESUC @ ( X1 @ X2 @ X3 ) ) ) ) ) ) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__1)],[thm_2Elogroot_2ELOG__exists,2,h16]) ).
thf(thm_2Ecardinal_2ELT,axiom,
~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ ( mono_2Ec_2Enum_2ESUC @ X2 ) )
= ( ( X1 != X2 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2 ) ) ) ) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[thm_2Ecardinal_2ELT,3,h14,h15]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,4,h12,h13]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,5,h10,h11]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,6,h8,h9]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,7,h6,h7]) ).
thf(thm_2Ecardinal_2ELE__1,axiom,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( X1 != mono_2Ec_2Enum_2E0 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X1 ) ) )
=> ~ ! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X1 )
=> ( X1 != mono_2Ec_2Enum_2E0 ) ) ) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[thm_2Ecardinal_2ELE__1,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,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])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP019^4 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 08:02:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 13.66/13.71 % SZS status Theorem
% 13.66/13.71 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 13.66/13.71 % Inferences: 2
% 13.66/13.71 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------