TSTP Solution File: ITP179^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP179^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 04:02:45 EDT 2023
% Result : Theorem 122.07s 122.79s
% Output : Proof 122.07s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $tType ).
thf(ty_standard_Constant_a,type,
standard_Constant_a: $tType ).
thf(ty_set_Pr1647387645at_nat,type,
set_Pr1647387645at_nat: $tType ).
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_unival2092813468um_a_b,type,
unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).
thf(ty_restri1162247455um_a_b,type,
restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).
thf(ty_domain1368163076um_a_b,type,
domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).
thf(ty_ord_le192794300um_a_b,type,
ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(ty_g,type,
g: labele431970251um_a_b ).
thf(ty_bot_bo575978147um_a_b,type,
bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).
thf(ty_bot_bo810816657at_nat,type,
bot_bo810816657at_nat: set_Pr1647387645at_nat ).
thf(ty_labele16114835_a_nat,type,
labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).
thf(ty_image_256773707um_a_b,type,
image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).
thf(ty_produc1808556047um_a_b,type,
produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).
thf(ty_insert983991207um_a_b,type,
insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
thf(ty_insert271595217at_nat,type,
insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(ty_produc407553657at_nat,type,
produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).
thf(ty_edge_p1382426714tant_a,type,
edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_f,type,
f: set_Pr1174980151um_a_b ).
thf(ty_bot_bot_set_nat,type,
bot_bot_set_nat: set_nat ).
thf(ty_domain_nat_nat,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(ty_standard_S_Idt_a,type,
standard_S_Idt_a: standard_Constant_a ).
thf(ty_insert_nat,type,
insert_nat: nat > set_nat > set_nat ).
thf(ty_labele577278695um_a_b,type,
labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).
thf(ty_labele195203296_a_nat,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(ty_bot_bo2130386637at_nat,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(ty_v,type,
v: sum_sum_a_b ).
thf(ty_insert1625259895at_nat,type,
insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).
thf(ty_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(ty_labele1939049654um_a_b,type,
labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).
thf(ty_restri572569417_a_nat,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(ty_labele1810595089_a_nat,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(sP1,plain,
( sP1
<=> ( g
= ( restri1162247455um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ X1 ) )
= ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( insert_nat @ zero_zero_nat @ bot_bot_set_nat )
= ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ bot_bo2130386637at_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ~ ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) )
=> ~ sP1 )
=> ~ ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) ) )
=> ~ ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ bot_bo2130386637at_nat ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ bot_bo2130386637at_nat ) )
= ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat )
= ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( domain_nat_nat @ bot_bo2130386637at_nat )
= bot_bot_set_nat ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( bot_bot_set_nat
= ( domain_nat_nat @ bot_bo2130386637at_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: set_Pr1647387645at_nat,X2: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: nat,X2: set_nat] :
( ( insert_nat @ X1 @ ( insert_nat @ X1 @ X2 ) )
= ( insert_nat @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( insert_nat @ zero_zero_nat @ bot_bot_set_nat )
= ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ bot_bo2130386637at_nat ) )
= ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ bot_bo2130386637at_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( sP13
=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: nat,X2: nat,X3: set_Pr1986765409at_nat] :
( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X1 @ X2 ) @ X3 ) )
= ( insert_nat @ X1 @ ( domain_nat_nat @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: standard_Constant_a,X2: nat,X3: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X2 @ X3 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X2 @ X3 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: set_Pr1986765409at_nat] :
( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ X1 ) )
= ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( unival2092813468um_a_b @ f ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( insert_nat @ zero_zero_nat @ bot_bot_set_nat )
= ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP13
=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: set_Pr1647387645at_nat,X2: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ bot_bo2130386637at_nat ) )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP5
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: nat,X2: set_Pr1986765409at_nat] :
( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ X1 ) @ X2 ) )
= ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP28
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: set_nat] :
( ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ X1 ) )
= ( insert_nat @ zero_zero_nat @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( insert_nat @ zero_zero_nat @ ( domain_nat_nat @ bot_bo2130386637at_nat ) )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ bot_bo2130386637at_nat ) )
= ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> $false ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( domain1368163076um_a_b @ f )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(conj_0,conjecture,
~ sP38 ).
thf(h0,negated_conjecture,
sP38,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP43
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP22
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP19
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP32
| sP24
| ~ sP20 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP35
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP47
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP36
| ~ sP27
| ~ sP44 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP36
| sP3 ),
inference(symeq,[status(thm)],]) ).
thf(11,plain,
( ~ sP15
| sP16 ),
inference(symeq,[status(thm)],]) ).
thf(12,plain,
( sP33
| ~ sP16
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP33
| sP44 ),
inference(symeq,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| sP45
| ~ sP3
| ~ sP25 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP4
| sP7
| ~ sP33
| ~ sP47 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| sP13
| ~ sP45
| ~ sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP10
| sP27 ),
inference(symeq,[status(thm)],]) ).
thf(18,plain,
( ~ sP31
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP40
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP29
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP39
| ~ sP37
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP49
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP14
| sP42
| ~ sP39
| ~ sP49 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP30
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP26
| sP25 ),
inference(symeq,[status(thm)],]) ).
thf(28,plain,
( sP6
| ~ sP25
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP11
| sP18
| sP46
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP21
| sP12 ),
inference(symeq,[status(thm)],]) ).
thf(31,plain,
( ~ sP48
| sP23
| sP46
| ~ sP12
| sP46 ),
inference(mating_rule,[status(thm)],]) ).
thf(32,plain,
~ sP46,
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP34
| ~ sP13
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP28
| sP34
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP41
| sP28
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP5
| sP41
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP38
| sP5
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_252_insert__absorb2,axiom,
sP19 ).
thf(fact_137_labeled__graph_Osel_I1_J,axiom,
sP35 ).
thf(fact_135_labeled__graph_Osel_I2_J,axiom,
sP17 ).
thf(fact_29_Domain__empty,axiom,
sP15 ).
thf(fact_11_Domain__insert,axiom,
sP29 ).
thf(fact_9_u,axiom,
sP32 ).
thf(fact_7_graph__single,axiom,
sP30 ).
thf(fact_5_d,axiom,
sP4 ).
thf(fact_4_f,axiom,
sP20 ).
thf(fact_3_r,axiom,
sP11 ).
thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
sP48 ).
thf(fact_0_g,axiom,
sP1 ).
thf(38,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,fact_252_insert__absorb2,fact_137_labeled__graph_Osel_I1_J,fact_135_labeled__graph_Osel_I2_J,fact_29_Domain__empty,fact_11_Domain__insert,fact_9_u,fact_7_graph__single,fact_5_d,fact_4_f,fact_3_r,fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,fact_0_g,h0]) ).
thf(0,theorem,
~ sP38,
inference(contra,[status(thm),contra(discharge,[h0])],[38,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP179^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 14:58:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 122.07/122.79 % SZS status Theorem
% 122.07/122.79 % Mode: cade22sinegrackle2xec37
% 122.07/122.79 % Steps: 2280
% 122.07/122.79 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------