%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP079^1 : 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 : n031.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 01:44:59 PM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_val,type,
val: $tType ).
thf(ty_set_val,type,
set_val: $tType ).
thf(ty_ord_less_eq_set_val,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(ty_member_val,type,
member_val: val > set_val > $o ).
thf(ty_p,type,
p: set_val ).
thf(ty_scc,type,
scc: set_val ).
thf(sP1,plain,
( sP1
<=> ! [X1: set_val] :
( ( ord_less_eq_set_val @ X1 )
= ( ^ [X2: set_val] :
! [X3: val] :
( ( member_val @ X3 @ X1 )
=> ( member_val @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ord_less_eq_set_val @ scc @ p ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
= ( ! [X1: val] :
( ( member_val @ X1 @ scc )
=> ( member_val @ X1 @ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: set_val] :
( ( ord_less_eq_set_val @ scc @ X1 )
= ( ! [X2: val] :
( ( member_val @ X2 @ scc )
=> ( member_val @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ord_less_eq_set_val @ scc )
= ( ^ [X1: set_val] :
! [X2: val] :
( ( member_val @ X2 @ scc )
=> ( member_val @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: val] :
( ( member_val @ X1 @ scc )
=> ( member_val @ X1 @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ord_less_eq_set_val
= ( ^ [X1: set_val,X2: set_val] :
! [X3: val] :
( ( member_val @ X3 @ X1 )
=> ( member_val @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(conj_0,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP3
| sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP7
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_18_subset__eq,axiom,
sP7 ).
thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
sP6 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_18_subset__eq,fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP079^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n031.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 8 17:55:08 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % Mode: cade22sinegrackle2x6978
% 0.19/0.45 % Steps: 181
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------