%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP155^1 : 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 : n018.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 01:47:07 PM UTC 2025
% Result : Theorem 25.86s 26.04s
% Output : Proof 25.86s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_finite_finite_a,type,
finite_finite_a: set_a > $o ).
thf(ty_relation,type,
relation: set_Product_prod_a_a ).
thf(ty_finite_card_a,type,
finite_card_a: set_a > nat ).
thf(ty_prefer1676310729than_a,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(ty_y,type,
y: a ).
thf(ty_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ty_finite179568208od_a_a,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_carrier,type,
carrier: set_a ).
thf(ty_x,type,
x: a ).
thf(sP1,plain,
( sP1
<=> ( member_a @ x @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) )
=> ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: set_a] :
( ( ( prefer1676310729than_a @ y @ carrier @ relation )
= X1 )
=> ( ord_less_eq_set_a @ X1 @ ( prefer1676310729than_a @ y @ 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 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
=> ( sP6
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: set_a] :
( ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
=> ( ( 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,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP6
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( member_a @ X1 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP6
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( finite_finite_a @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: set_a,X2: set_a] :
( ( X1 = X2 )
=> ( ord_less_eq_set_a @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( 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,[sP20])]) ).
thf(conj_0,conjecture,
sP13 ).
thf(h0,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h2,assumption,
finite179568208od_a_a @ relation,
introduced(assumption,[]) ).
thf(fact_7__092_060open_062finite_Acarrier_092_060close_062,axiom,
sP15 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_7__092_060open_062finite_Acarrier_092_060close_062,h1]) ).
thf(2,plain,
( ~ sP17
| ~ sP1
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| ~ sP16
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| ~ sP6
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| ~ sP20
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP12
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| sP6
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP18
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP9
| ~ sP19
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_211_card__seteq,axiom,
sP8 ).
thf(fact_150_equalityD2,axiom,
sP18 ).
thf(fact_15_fnt__carrier__fnt__nbt,axiom,
sP12 ).
thf(fact_4_nbt__nest,axiom,
sP4 ).
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,
sP20 ).
thf(fact_1_assms_I1_J,axiom,
sP1 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h0])],[2,3,4,5,6,7,8,9,10,11,12,13,14,h0,fact_211_card__seteq,fact_150_equalityD2,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(fact_105_fnt__carrier__fnt__rel,axiom,
( sP15
=> ( finite179568208od_a_a @ relation ) ) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_105_fnt__carrier__fnt__rel,1,15,h1,h2]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP155^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n018.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 :
% 25.86/26.04 % SZS status Theorem
% 25.86/26.04 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 25.86/26.04 % Inferences: 183
% 25.86/26.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------