%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP155^1 : 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 : n008.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 01:45:16 PM UTC 2025
% Result : Theorem 20.31s 20.58s
% Output : Proof 20.31s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_relation,type,
relation: set_Product_prod_a_a ).
thf(ty_y,type,
y: a ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_x,type,
x: a ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_finite_card_a,type,
finite_card_a: set_a > nat ).
thf(ty_carrier,type,
carrier: set_a ).
thf(ty_finite_finite_a,type,
finite_finite_a: set_a > $o ).
thf(ty_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ty_prefer1676310729than_a,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(sP1,plain,
( sP1
<=> ( member_a @ x @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a,X2: a] :
( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: set_a] :
( sP2
=> ( ( ord_less_eq_set_a @ X1 @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ X1 ) )
=> ( X1
= ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( member_a @ X1 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP8
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP2
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: set_a,X2: set_a] :
( ( finite_finite_a @ X1 )
=> ( ( ord_less_eq_set_a @ X2 @ X1 )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ X1 ) @ ( finite_card_a @ X2 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(conj_0,conjecture,
sP17 ).
thf(h0,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP12
| ~ sP18
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| sP17
| sP13
| ~ sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| ~ sP8
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP15
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
~ sP13,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP14
| sP8
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP10
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP16
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP19
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP5
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_211_card__seteq,axiom,
sP19 ).
thf(fact_15_fnt__carrier__fnt__nbt,axiom,
sP11 ).
thf(fact_4_nbt__nest,axiom,
sP5 ).
thf(fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,axiom,
sP18 ).
thf(fact_1_assms_I1_J,axiom,
sP1 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h0,fact_211_card__seteq,fact_15_fnt__carrier__fnt__nbt,fact_4_nbt__nest,fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,fact_1_assms_I1_J]) ).
thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : ITP155^1 : TPTP v9.2.0. Released v7.5.0.
% 0.05/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n008.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 : Wed Oct 8 18:07:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 20.31/20.58 % SZS status Theorem
% 20.31/20.58 % Mode: cade22sinegrackle2xfaf3
% 20.31/20.58 % Steps: 2310
% 20.31/20.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------