%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP154^1 : 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 : n026.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 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_carrier,type,
carrier: set_a ).
thf(ty_relation,type,
relation: set_Product_prod_a_a ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
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(ty_x,type,
x: a ).
thf(ty_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ~ ( ( member_a @ x @ carrier )
=> ~ ( member_a @ X1 @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ x ) @ relation ) )
= ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ X1 ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ x ) @ relation ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ X1 ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( member_a @ x @ carrier )
=> ~ ( member_a @ x @ carrier ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP3
=> ( member449909584od_a_a @ ( product_Pair_a_a @ x @ x ) @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ x ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member_a @ x @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a,X2: a] :
( ~ ( ( member_a @ X1 @ carrier )
=> ~ ( member_a @ X2 @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ relation ) )
= ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ relation )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ relation ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ relation )
=> ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( member449909584od_a_a @ ( product_Pair_a_a @ x @ x ) @ relation ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
( ~ sP6
=> sP6 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP6
=> sP6 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP10
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP7
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP3
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_20_strict__not__refl__weak,axiom,
sP8 ).
thf(fact_7_no__better__subset__pref,axiom,
sP9 ).
thf(fact_1_assms_I2_J,axiom,
sP7 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h1,h0])],[1,2,3,4,5,6,7,h1,fact_20_strict__not__refl__weak,fact_7_no__better__subset__pref,fact_1_assms_I2_J]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h1])],[h0,8,h1,h1]) ).
thf(0,theorem,
( ~ sP6
=> sP6 ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.15 % Problem : ITP154^1 : TPTP v9.2.0. Released v7.5.0.
% 0.06/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8042.1875MB
% 0.12/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Wed Oct 8 17:50:08 EDT 2025
% 0.12/0.40 % CPUTime :
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 % Mode: cade22sinegrackle2x6978
% 0.19/0.50 % Steps: 66
% 0.19/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------