%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP010^5 : 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 : n015.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 01:44:33 PM UTC 2025
% Result : Theorem 1.20s 1.38s
% Output : Proof 1.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_tp__ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
thf(ty_del,type,
del: $tType ).
thf(ty_c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND: del > $i ).
thf(ty_fo__c_2Earithmetic_2EZERO,type,
fo__c_2Earithmetic_2EZERO: tp__ty_2Enum_2Enum ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: $i ).
thf(ty_fo__c_2Enum_2E0,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
thf(ty_c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: $i ).
thf(ty_mem,type,
mem: $i > del > $o ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: $i ).
thf(ty_c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: $i ).
thf(ty_ty_2Enum_2Enum,type,
ty_2Enum_2Enum: del ).
thf(ty_c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: $i ).
thf(ty_c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: $i ).
thf(ty_surj__ty_2Enum_2Enum,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
thf(ty_c_2Enum_2ESUC,type,
c_2Enum_2ESUC: $i ).
thf(ty_c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_inj__ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(ty_c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: $i ).
thf(ty_c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: $i ).
thf(ty_arr,type,
arr: del > del > del ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[conj_thm_2Ecardinal_2ECARD__NOT__LE]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( ( X1 != X2 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( mem @ eigen__0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
=> ~ ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ ( ap @ eigen__0 @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ eigen__0 @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
mem @ eigen__0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
=> ~ ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ ( ap @ eigen__0 @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ eigen__0 @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( X1 = fo__c_2Enum_2E0 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( ( X1
!= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= fo__c_2Enum_2E0 ),
introduced(assumption,[]) ).
thf(h25,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= fo__c_2Enum_2E0 ),
introduced(assumption,[]) ).
thf(h27,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= X1 ),
introduced(assumption,[]) ).
thf(h29,assumption,
! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,h0]) ).
thf(ax_thm_2Earithmetic_2EADD,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= X1 )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[ax_thm_2Earithmetic_2EADD,2,h28,h29]) ).
thf(ax_thm_2Earithmetic_2ESUB,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= fo__c_2Enum_2E0 )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h26,h27])],[ax_thm_2Earithmetic_2ESUB,3,h26,h27]) ).
thf(ax_thm_2Earithmetic_2EMULT,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
= fo__c_2Enum_2E0 )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[ax_thm_2Earithmetic_2EMULT,4,h24,h25]) ).
thf(ax_thm_2Earithmetic_2EEXP,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[ax_thm_2Earithmetic_2EEXP,5,h22,h23]) ).
thf(conj_thm_2Earithmetic_2ELE,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( X1 = fo__c_2Enum_2E0 ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( ( X1
!= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[conj_thm_2Earithmetic_2ELE,6,h20,h21]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h16,7,h18,h19]) ).
thf(conj_thm_2Enumeral_2Enumeral__suc,axiom,
~ ( ~ ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) ) ) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[conj_thm_2Enumeral_2Enumeral__suc,8,h16,h17]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,9,h14,h15]) ).
thf(conj_thm_2Elogroot_2ELOG__exists,axiom,
~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
=> ~ ! [X2: tp__ty_2Enum_2Enum,X3: tp__ty_2Enum_2Enum] :
( ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X3 ) ) ) )
=> ~ ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( ap @ ( ap @ X1 @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( inj__ty_2Enum_2Enum @ X3 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X3 ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X3 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ X1 @ ( inj__ty_2Enum_2Enum @ X2 ) ) @ ( inj__ty_2Enum_2Enum @ X3 ) ) ) ) ) ) ) ) ) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__0)],[conj_thm_2Elogroot_2ELOG__exists,10,h13]) ).
thf(conj_thm_2Ecardinal_2ELT,axiom,
~ ( ! [X1: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) )
= ( ( X1 != X2 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ) ) ) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[conj_thm_2Ecardinal_2ELT,11,h11,h12]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,12,h9,h10]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,15,h3,h4]) ).
thf(conj_thm_2Ecardinal_2ELE__1,axiom,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( X1 != fo__c_2Enum_2E0 )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ) )
=> ~ ! [X1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) )
=> ( X1 != fo__c_2Enum_2E0 ) ) ) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[conj_thm_2Ecardinal_2ELE__1,16,h1,h2]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP010^5 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.10/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 18:35:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.20/1.38 % SZS status Theorem
% 1.20/1.38 % Mode: cade22sinegrackle2x6978
% 1.20/1.38 % Steps: 1
% 1.20/1.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------