%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP145^1 : 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 : n021.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 01:45:13 PM UTC 2025
% Result : Theorem 20.81s 21.01s
% Output : Proof 20.81s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_Pr1165141447_state,type,
set_Pr1165141447_state: $tType ).
thf(ty_produc2041926651_state,type,
produc2041926651_state: $tType ).
thf(ty_produc410756839_state,type,
produc410756839_state: $tType ).
thf(ty_cons_com,type,
cons_com: com > list_com > list_com ).
thf(ty_transi1302705790_state,type,
transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_pHoare259243666_exec1,type,
pHoare259243666_exec1: set_Pr1165141447_state ).
thf(ty_nil_com,type,
nil_com: list_com ).
thf(ty_n,type,
n: nat ).
thf(ty_s,type,
s: state ).
thf(ty_c,type,
c: com ).
thf(ty_member1069318160_state,type,
member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
thf(ty_produc1204172211_state,type,
produc1204172211_state: list_com > state > produc2041926651_state ).
thf(ty_transi1726587420_state,type,
transi1726587420_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(ty_produc1909270103_state,type,
produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
thf(ty_f,type,
f: nat > produc2041926651_state ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state,X3: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ X2 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X3 ) @ ( transi1302705790_state @ X2 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X3 ) @ ( transi1726587420_state @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1302705790_state @ X1 ) )
= ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1726587420_state @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s )
= ( f @ zero_zero_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ X1 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X2 ) @ X1 )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X2 ) @ ( transi1726587420_state @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
= ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1302705790_state @ X1 ) )
= ( ~ sP4
=> ~ ( ~ sP4
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1726587420_state @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: produc410756839_state,X2: set_Pr1165141447_state] :
( ( member1069318160_state @ X1 @ X2 )
=> ( member1069318160_state @ X1 @ ( transi1726587420_state @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1726587420_state @ X2 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1302705790_state @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP13
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1726587420_state @ X3 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: produc2041926651_state] :
( sP13
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ X1 ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state,X4: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ X3 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X4 ) @ ( transi1302705790_state @ X3 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X1 @ X4 ) @ ( transi1726587420_state @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ X1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1302705790_state @ X2 ) )
= ( ( ( f @ zero_zero_nat )
!= X1 )
=> ~ ( ( ( f @ zero_zero_nat )
!= X1 )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1726587420_state @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
=> ( sP8
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ X1 )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state,X4: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ X3 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X4 ) @ X3 )
=> ( member1069318160_state @ ( produc1909270103_state @ X1 @ X4 ) @ ( transi1726587420_state @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state,X4: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1726587420_state @ X3 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X2 @ X4 ) @ ( transi1302705790_state @ X3 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X1 @ X4 ) @ ( transi1726587420_state @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ X1 )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1726587420_state @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( ( ( f @ zero_zero_nat )
!= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X1 ) @ ( f @ ( suc @ X1 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP23
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state,X3: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ X2 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X3 ) @ X2 )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X3 ) @ ( transi1726587420_state @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state,X3: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1726587420_state @ X2 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X3 ) @ ( transi1302705790_state @ X2 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X3 ) @ ( transi1726587420_state @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1726587420_state @ X1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: produc2041926651_state,X2: produc2041926651_state,X3: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ X3 ) )
= ( ( X1 != X2 )
=> ~ ( ( X1 != X2 )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1726587420_state @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP4
=> ~ ( ~ sP4
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ zero_zero_nat ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP8
=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP2
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
= ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( f @ zero_zero_nat )
= ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: set_Pr1165141447_state] :
( ( transi1726587420_state @ ( transi1302705790_state @ X1 ) )
= ( transi1302705790_state @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1302705790_state @ X2 ) )
= ( ( ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s )
!= X1 )
=> ~ ( ( ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s )
!= X1 )
=> ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1726587420_state @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP20
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ X1 )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X2 ) @ ( transi1302705790_state @ X1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X2 ) @ ( transi1726587420_state @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP48
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: set_Pr1165141447_state,X2: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( f @ n ) ) @ ( transi1726587420_state @ X1 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ X2 ) @ ( transi1302705790_state @ X1 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X2 ) @ ( transi1726587420_state @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP30 = sP42 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ X1 ) @ ( transi1302705790_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ X1 ) @ ( transi1726587420_state @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ zero_zero_nat ) @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: produc2041926651_state,X2: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ X1 ) @ ( transi1726587420_state @ X2 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ ( f @ n ) @ X1 ) @ ( transi1302705790_state @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(conj_4,conjecture,
sP22 ).
thf(h0,negated_conjecture,
~ sP22,
inference(assume_negation,[status(cth)],[conj_4]) ).
thf(1,plain,
( ~ sP43
| ~ sP8
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP36
| sP8
| ~ sP45
| sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP55
| ~ sP48
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| ~ sP14
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP51
| sP22
| ~ sP45
| sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP42
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP26
| ~ sP30
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP33
| ~ sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP16
| ~ sP13
| sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP47
| ~ sP59
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP21
| ~ sP50
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP7
| ~ sP34
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP53
| ~ sP20
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP37
| ~ sP23
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP57
| sP30
| ~ sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP27
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP10
| sP59
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP18
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP58
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
~ sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP24
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP24
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP28
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP44
| ~ sP2
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP40
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP11
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP6
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP56
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP54
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP60
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP32
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP15
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP52
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP38
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP25
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP39
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP1
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP35
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP17
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP12
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP17
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP41
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP29
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP41
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP31
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP19
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP46
| sP4 ),
inference(symeq,[status(thm)],[]) ).
thf(50,plain,
( ~ sP49
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(conj_3,axiom,
sP2 ).
thf(conj_2,axiom,
sP35 ).
thf(conj_1,axiom,
sP46 ).
thf(fact_100_rtrancl__into__trancl2,axiom,
sP19 ).
thf(fact_96_trancl__rtrancl__trancl,axiom,
sP31 ).
thf(fact_75_r__r__into__trancl,axiom,
sP29 ).
thf(fact_37_r__into__trancl_H,axiom,
sP12 ).
thf(fact_31_rtrancl__eq__or__trancl,axiom,
sP41 ).
thf(fact_29_trancl__into__rtrancl,axiom,
sP17 ).
thf(fact_7_rtrancl__trancl__absorb,axiom,
sP49 ).
thf(51,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,h0,conj_3,conj_2,conj_1,fact_100_rtrancl__into__trancl2,fact_96_trancl__rtrancl__trancl,fact_75_r__r__into__trancl,fact_37_r__into__trancl_H,fact_31_rtrancl__eq__or__trancl,fact_29_trancl__into__rtrancl,fact_7_rtrancl__trancl__absorb]) ).
thf(0,theorem,
sP22,
inference(contra,[status(thm),contra(discharge,[h0])],[51,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP145^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n021.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 : 300
% 0.12/0.34 % DateTime : Wed Oct 8 18:26:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 20.81/21.01 % SZS status Theorem
% 20.81/21.01 % Mode: cade22sinegrackle2xfaf3
% 20.81/21.01 % Steps: 7949
% 20.81/21.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------