%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP045^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 01:46:48 PM UTC 2025
% Result : Theorem 173.18s 173.06s
% Output : Proof 173.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_option1457017436_r_l_v,type,
option1457017436_r_l_v: $tType ).
thf(ty_l,type,
l: $tType ).
thf(ty_produc1156025366_r_l_v,type,
produc1156025366_r_l_v: $tType ).
thf(ty_cntxt_r_l_v,type,
cntxt_r_l_v: $tType ).
thf(ty_option_val_r_l_v,type,
option_val_r_l_v: $tType ).
thf(ty_produc1164766533_r_l_v,type,
produc1164766533_r_l_v: $tType ).
thf(ty_val_r_l_v,type,
val_r_l_v: $tType ).
thf(ty_expr_r_l_v,type,
expr_r_l_v: $tType ).
thf(ty_r,type,
r: $tType ).
thf(ty_r4,type,
r4: r ).
thf(ty_produc297528454_r_l_v,type,
produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
thf(ty_r3,type,
r3: r ).
thf(ty_s_1,type,
s_1: r > option1457017436_r_l_v ).
thf(ty_fun_up709272714_r_l_v,type,
fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
thf(ty_produc1834103605_r_l_v,type,
produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
thf(ty_e,type,
e: cntxt_r_l_v ).
thf(ty_e2,type,
e2: expr_r_l_v ).
thf(ty_r2,type,
r2: r ).
thf(ty_rid_r_l_v,type,
rid_r_l_v: r > val_r_l_v ).
thf(ty_tau,type,
tau: l > option_val_r_l_v ).
thf(ty_some_P1807977723_r_l_v,type,
some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
thf(ty_none_val_r_l_v,type,
none_val_r_l_v: option_val_r_l_v ).
thf(ty_plug_r_l_v,type,
plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(ty_combine_l_val_r_l_v,type,
combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
thf(ty_x,type,
x: produc1156025366_r_l_v ).
thf(ty_sigma,type,
sigma: l > option_val_r_l_v ).
thf(ty_vE_r_l_v,type,
vE_r_l_v: val_r_l_v > expr_r_l_v ).
thf(sP1,plain,
( sP1
<=> ( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: r > option1457017436_r_l_v,X2: option1457017436_r_l_v,X3: option1457017436_r_l_v] :
( ( r2 != r3 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X1 @ r2 @ X2 ) @ r3 @ X3 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X1 @ r3 @ X3 ) @ r2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( r2 = r4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) )
=> ! [X1: r > option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= X1 )
=> ( ( fun_up709272714_r_l_v @ X1 @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( r2 = r3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: option1457017436_r_l_v,X2: option1457017436_r_l_v] :
( ~ sP5
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ X1 ) @ r3 @ X2 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ X2 ) @ r2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: option1457017436_r_l_v,X2: option1457017436_r_l_v] :
( ~ sP3
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ X1 ) @ r4 @ X2 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4 @ X2 ) @ r2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: r > option1457017436_r_l_v,X2: ( r > option1457017436_r_l_v ) > $o] :
( ( X2 @ X1 )
=> ! [X3: r > option1457017436_r_l_v] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: r > option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= X1 )
=> ( ( fun_up709272714_r_l_v @ X1 @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: ( r > option1457017436_r_l_v ) > $o] :
( ( X1 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) )
=> ! [X2: r > option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP3
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: r > option1457017436_r_l_v,X2: option1457017436_r_l_v,X3: option1457017436_r_l_v] :
( ~ sP3
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X1 @ r2 @ X2 ) @ r4 @ X3 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X1 @ r4 @ X3 ) @ r2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP5
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: r,X2: r,X3: r > option1457017436_r_l_v,X4: option1457017436_r_l_v,X5: option1457017436_r_l_v] :
( ( X1 != X2 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X3 @ X1 @ X4 ) @ X2 @ X5 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X3 @ X2 @ X5 ) @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: r,X2: r > option1457017436_r_l_v,X3: option1457017436_r_l_v,X4: option1457017436_r_l_v] :
( ( r2 != X1 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ r2 @ X3 ) @ X1 @ X4 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X1 @ X4 ) @ r2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: option1457017436_r_l_v] :
( ~ sP5
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ X1 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ X1 ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: option1457017436_r_l_v] :
( ~ sP3
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4 @ X1 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r4 ) ) ) ) ) ) ) @ r4 @ X1 ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(conj_0,conjecture,
sP16 ).
thf(h0,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP18
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| sP5
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| ~ sP17
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| sP16
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP15
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP18
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP7
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP11
| sP3
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
sP8,
inference(eq_ind,[status(thm)],[]) ).
thf(fact_1_assms_I7_J,axiom,
~ sP3 ).
thf(fact_2_assms_I6_J,axiom,
~ sP5 ).
thf(fact_40_fun__upd__twist,axiom,
sP15 ).
thf(18,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,fact_1_assms_I7_J,fact_2_assms_I6_J,fact_40_fun__upd__twist,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP045^1 : TPTP v9.2.0. Released v7.5.0.
% 0.08/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Oct 8 18:26:08 EDT 2025
% 0.16/0.37 % CPUTime :
% 173.18/173.06 % SZS status Theorem
% 173.18/173.06 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 173.18/173.06 % Inferences: 874
% 173.18/173.06 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------