%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP036^1 : 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 : n001.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 01:44:51 PM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_produc640052711real_c,type,
produc640052711real_c: $tType ).
thf(ty_hp_a_b_c,type,
hp_a_b_c: $tType ).
thf(ty_set_Pr754230471real_c,type,
set_Pr754230471real_c: $tType ).
thf(ty_set_Sum_sum_c_c,type,
set_Sum_sum_c_c: $tType ).
thf(ty_produc190496183real_c,type,
produc190496183real_c: $tType ).
thf(ty_denota231621370t_unit,type,
denota231621370t_unit: $tType ).
thf(ty_finite1398487019real_c,type,
finite1398487019real_c: $tType ).
thf(ty_eigen__1,type,
eigen__1: produc190496183real_c ).
thf(ty_choice_a_b_c,type,
choice_a_b_c: hp_a_b_c > hp_a_b_c > hp_a_b_c ).
thf(ty_eigen__0,type,
eigen__0: produc190496183real_c ).
thf(ty_static_MBV_a_b_c,type,
static_MBV_a_b_c: hp_a_b_c > set_Sum_sum_c_c ).
thf(ty_sup_su1349021703um_c_c,type,
sup_su1349021703um_c_c: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c ).
thf(ty_a,type,
a: hp_a_b_c ).
thf(ty_b,type,
b: hp_a_b_c ).
thf(ty_nu_2,type,
nu_2: finite1398487019real_c ).
thf(ty_mu3,type,
mu3: finite1398487019real_c ).
thf(ty_produc1687028567real_c,type,
produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
thf(ty_mu,type,
mu: produc190496183real_c ).
thf(ty_member346808080real_c,type,
member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
thf(ty_nu_12,type,
nu_12: finite1398487019real_c ).
thf(ty_denota904684656_a_b_c,type,
denota904684656_a_b_c: denota231621370t_unit > hp_a_b_c > set_Pr754230471real_c ).
thf(ty_nu_22,type,
nu_22: finite1398487019real_c ).
thf(ty_mu2,type,
mu2: finite1398487019real_c ).
thf(ty_i,type,
i: denota231621370t_unit ).
thf(ty_j,type,
j: denota231621370t_unit ).
thf(ty_denota1997846518gree_c,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(ty_produc394644079real_c,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(ty_v,type,
v: set_Sum_sum_c_c ).
thf(ty_nu_1,type,
nu_1: finite1398487019real_c ).
thf(sP1,plain,
( sP1
<=> ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: produc190496183real_c] :
( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X1 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
=> ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X1 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(conj_0,conjecture,
~ sP4 ).
thf(h0,negated_conjecture,
sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ eigen__1 ) @ ( denota904684656_a_b_c @ j @ b ) )
=> ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ eigen__1 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ eigen__1 ) @ ( denota904684656_a_b_c @ j @ b ),
introduced(assumption,[]) ).
thf(h5,assumption,
denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ eigen__1 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ),
introduced(assumption,[]) ).
thf(fact_22_False,axiom,
~ sP2 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h5,h3,h1,h0])],[h1,fact_22_False]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,1,h4,h5]) ).
thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: produc190496183real_c] :
( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ X1 ) @ ( denota904684656_a_b_c @ j @ b ) )
=> ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ X1 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,2,h3]) ).
thf(h6,assumption,
~ ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ eigen__0 ) @ ( denota904684656_a_b_c @ j @ b ) )
=> ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ eigen__0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ eigen__0 ) @ ( denota904684656_a_b_c @ j @ b ),
introduced(assumption,[]) ).
thf(h8,assumption,
denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ eigen__0 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ),
introduced(assumption,[]) ).
thf(4,plain,
( ~ sP3
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_3_agree_H,axiom,
sP1 ).
thf(fact_2_prog__sem_H,axiom,
sP5 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h2,h0])],[4,5,h0,fact_3_agree_H,fact_2_prog__sem_H]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,7,h6]) ).
thf(fact_88_eitherSem,axiom,
( ~ sP2
=> ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ) ) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_88_eitherSem,3,8,h1,h2]) ).
thf(0,theorem,
~ sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP036^1 : TPTP v9.2.0. Released v7.5.0.
% 0.06/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 18:03:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22sinegrackle2x6978
% 0.19/0.43 % Steps: 51
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------