%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP083^1 : 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 : n025.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 01:45:00 PM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_val,type,
val: $tType ).
thf(ty_list_node,type,
list_node: $tType ).
thf(ty_set_val,type,
set_val: $tType ).
thf(ty_produc1432036078de_val,type,
produc1432036078de_val: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_node,type,
node: $tType ).
thf(ty_option_list_val,type,
option_list_val: $tType ).
thf(ty_phi_s,type,
phi_s: val ).
thf(ty_alpha_n,type,
alpha_n: g > list_node ).
thf(ty_phis,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(ty_inEdges,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(ty_member_val,type,
member_val: val > set_val > $o ).
thf(ty_uses,type,
uses: g > node > set_val ).
thf(ty_sSA_CF1517915011eD_val,type,
sSA_CF1517915011eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val ).
thf(ty_defs,type,
defs: g > node > set_val ).
thf(ty_sSA_CF1252180629de_val,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(ty_eigen__0,type,
eigen__0: val ).
thf(ty_g2,type,
g2: g ).
thf(sP1,plain,
( sP1
<=> ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ eigen__0 @ phi_s ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ eigen__0 @ X1 )
=> ( member_val @ X1 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: val,X2: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X1 @ X2 )
=> ( member_val @ X2 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: g,X2: val,X3: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X3 )
=> ( member_val @ X3 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP2
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_6_phiArg__in__allVars,axiom,
sP6 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h0,fact_6_phiArg__in__allVars,h1]) ).
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: val] :
~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X1 @ phi_s ) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,5,h1]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP083^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n025.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 18:46:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22sinegrackle2x6978
% 0.20/0.46 % Steps: 470
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------