%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP153^1 : 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 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(ty_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_y,type,
y: a ).
thf(ty_carrier,type,
carrier: set_a ).
thf(ty_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(ty_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ty_relation,type,
relation: set_Product_prod_a_a ).
thf(ty_z,type,
z: a ).
thf(sP1,plain,
( sP1
<=> ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ relation ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ y @ z ) @ relation )
=> ( member_a @ y @ carrier ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( member_a @ z @ carrier ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ relation )
=> ( member_a @ X1 @ carrier ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member_a @ z @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ y @ X1 ) @ relation )
=> ( member_a @ y @ carrier ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member449909584od_a_a @ ( product_Pair_a_a @ y @ z ) @ relation ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ X1 ) @ relation )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( member_a @ y @ carrier ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
~ ( sP5
=> ~ sP9 ) ).
thf(h0,negated_conjecture,
( sP5
=> ~ sP9 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_8_not__outside,axiom,
sP4 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h0])],[1,2,3,h1,fact_8_not__outside,h3]) ).
thf(fact_0_assms,axiom,
~ ( sP1
=> ~ sP7 ) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h3,h4])],[fact_0_assms,4,h3,h4]) ).
thf(6,plain,
( ~ sP2
| ~ sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h0])],[6,7,8,h2,fact_8_not__outside,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h0]),tab_negimp(discharge,[h3,h4])],[fact_0_assms,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,5,10,h1,h2]) ).
thf(0,theorem,
~ ( sP5
=> ~ sP9 ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : ITP153^1 : TPTP v9.2.0. Released v7.5.0.
% 0.04/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 18:50:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % Mode: cade22sinegrackle2x6978
% 0.18/0.42 % Steps: 49
% 0.18/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------