%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP157^1 : 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 : n029.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 0.20s 0.43s
% Output : Proof 0.20s
% 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_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(ty_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(ty_pr,type,
pr: set_Product_prod_a_a ).
thf(ty_z,type,
z: a ).
thf(ty_y,type,
y: a ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_prefer161218362good_a,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(ty_b,type,
b: set_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,X2: a,X3: set_a,X4: set_Product_prod_a_a] :
( ( member_a @ X1 @ ( prefer161218362good_a @ X2 @ X3 @ X4 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: set_Product_prod_a_a] :
( ( member_a @ z @ ( prefer161218362good_a @ y @ b @ X1 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: set_a,X2: set_Product_prod_a_a] :
( ( member_a @ z @ ( prefer161218362good_a @ y @ X1 @ X2 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: set_a,X3: set_Product_prod_a_a] :
( ( member_a @ z @ ( prefer161218362good_a @ X1 @ X2 @ X3 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ X1 ) @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(conj_0,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP6
| ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_8_at__lst__asgd__ge,axiom,
sP1 ).
thf(fact_0_assms,axiom,
sP5 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_8_at__lst__asgd__ge,fact_0_assms]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP157^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 18:23:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % Mode: cade22sinegrackle2x6978
% 0.20/0.43 % Steps: 120
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------