%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP036^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 01:46:46 PM UTC 2025
% Result : Theorem 2.60s 2.84s
% Output : Proof 2.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP036^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36 % Computer : n019.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 18:03:23 EDT 2025
% 0.13/0.36 % CPUTime :
% 2.60/2.84 % SZS status Theorem
% 2.60/2.84 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.60/2.84 % Inferences: 1
% 2.60/2.84 % SZS output start Proof
% 2.60/2.84 thf(ty_finite1398487019real_c, type, finite1398487019real_c : $tType).
% 2.60/2.84 thf(ty_hp_a_b_c, type, hp_a_b_c : $tType).
% 2.60/2.84 thf(ty_set_Sum_sum_c_c, type, set_Sum_sum_c_c : $tType).
% 2.60/2.84 thf(ty_produc640052711real_c, type, produc640052711real_c : $tType).
% 2.60/2.84 thf(ty_set_Pr754230471real_c, type, set_Pr754230471real_c : $tType).
% 2.60/2.84 thf(ty_denota231621370t_unit, type, denota231621370t_unit : $tType).
% 2.60/2.84 thf(ty_produc190496183real_c, type, produc190496183real_c : $tType).
% 2.60/2.84 thf(ty_a, type, a : hp_a_b_c).
% 2.60/2.84 thf(ty_denota1997846518gree_c, type, denota1997846518gree_c : (produc190496183real_c>produc190496183real_c>set_Sum_sum_c_c>$o)).
% 2.60/2.84 thf(ty_mu2, type, mu2 : finite1398487019real_c).
% 2.60/2.84 thf(ty_nu_12, type, nu_12 : finite1398487019real_c).
% 2.60/2.84 thf(ty_v, type, v : set_Sum_sum_c_c).
% 2.60/2.84 thf(ty_static_MBV_a_b_c, type, static_MBV_a_b_c : (hp_a_b_c>set_Sum_sum_c_c)).
% 2.60/2.84 thf(ty_eigen__1, type, eigen__1 : produc190496183real_c).
% 2.60/2.84 thf(ty_eigen__0, type, eigen__0 : produc190496183real_c).
% 2.60/2.84 thf(ty_b, type, b : hp_a_b_c).
% 2.60/2.84 thf(ty_j, type, j : denota231621370t_unit).
% 2.60/2.84 thf(ty_nu_2, type, nu_2 : finite1398487019real_c).
% 2.60/2.84 thf(ty_produc394644079real_c, type, produc394644079real_c : (finite1398487019real_c>finite1398487019real_c>produc190496183real_c)).
% 2.60/2.84 thf(ty_i, type, i : denota231621370t_unit).
% 2.60/2.84 thf(ty_produc1687028567real_c, type, produc1687028567real_c : (produc190496183real_c>produc190496183real_c>produc640052711real_c)).
% 2.60/2.84 thf(ty_member346808080real_c, type, member346808080real_c : (produc640052711real_c>set_Pr754230471real_c>$o)).
% 2.60/2.84 thf(ty_nu_1, type, nu_1 : finite1398487019real_c).
% 2.60/2.84 thf(ty_denota904684656_a_b_c, type, denota904684656_a_b_c : (denota231621370t_unit>hp_a_b_c>set_Pr754230471real_c)).
% 2.60/2.84 thf(ty_nu_22, type, nu_22 : finite1398487019real_c).
% 2.60/2.84 thf(ty_mu3, type, mu3 : finite1398487019real_c).
% 2.60/2.84 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)).
% 2.60/2.84 thf(sP1,plain,sP1 <=> ((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,[sP1])])).
% 2.60/2.84 thf(conj_0,conjecture,(~((![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))))))))).
% 2.60/2.84 thf(h0,negated_conjecture,(![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)))))),inference(assume_negation,[status(cth)],[conj_0])).
% 2.60/2.84 thf(h1,assumption,sP1,introduced(assumption,[])).
% 2.60/2.84 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,[])).
% 2.60/2.84 thf(h3,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,[])).
% 2.60/2.84 thf(h4,assumption,((member346808080real_c @ ((produc1687028567real_c @ ((produc394644079real_c @ nu_22) @ nu_2)) @ eigen__0)) @ ((denota904684656_a_b_c @ j) @ b)),introduced(assumption,[])).
% 2.60/2.84 thf(h5,assumption,(((denota1997846518gree_c @ ((produc394644079real_c @ mu3) @ mu2)) @ eigen__0) @ ((sup_su1349021703um_c_c @ (static_MBV_a_b_c @ b)) @ v)),introduced(assumption,[])).
% 2.60/2.84 thf(fact_22_False,axiom,(~(sP1))).
% 2.60/2.84 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h5,h3,h1,h0])],[h1,fact_22_False])).
% 2.60/2.84 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,1,h4,h5])).
% 2.60/2.84 thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:produc190496183real_c]:(((member346808080real_c @ ((produc1687028567real_c @ ((produc394644079real_c @ nu_22) @ nu_2)) @ X1)) @ ((denota904684656_a_b_c @ j) @ b)) => (~((((denota1997846518gree_c @ ((produc394644079real_c @ mu3) @ mu2)) @ X1) @ ((sup_su1349021703um_c_c @ (static_MBV_a_b_c @ b)) @ v))))))))).
% 2.60/2.84 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),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_062,2,h3])).
% 2.60/2.84 thf(h6,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,[])).
% 2.60/2.84 thf(h7,assumption,((member346808080real_c @ ((produc1687028567real_c @ ((produc394644079real_c @ nu_22) @ nu_2)) @ eigen__1)) @ ((denota904684656_a_b_c @ j) @ b)),introduced(assumption,[])).
% 2.60/2.84 thf(h8,assumption,(((denota1997846518gree_c @ ((produc394644079real_c @ mu3) @ mu2)) @ eigen__1) @ ((sup_su1349021703um_c_c @ (static_MBV_a_b_c @ b)) @ v)),introduced(assumption,[])).
% 2.60/2.84 thf(pax83, axiom, (p83=>![X1:produc190496183real_c]:(fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ X1) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))=>~(fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ X1 @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)))), file('<stdin>', pax83)).
% 2.60/2.84 thf(pax2, axiom, (p2=>fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ fmu @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)), file('<stdin>', pax2)).
% 2.60/2.84 thf(pax1, axiom, (p1=>fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ fmu) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))), file('<stdin>', pax1)).
% 2.60/2.84 thf(ax0, axiom, p83, file('<stdin>', ax0)).
% 2.60/2.84 thf(ax79, axiom, p2, file('<stdin>', ax79)).
% 2.60/2.84 thf(ax80, axiom, p1, file('<stdin>', ax80)).
% 2.60/2.84 thf(c_0_6, plain, ![X70:produc190496183real_c]:(~p83|(~fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ X70) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))|~fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ X70 @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax83])])])])).
% 2.60/2.84 thf(c_0_7, plain, (~p2|fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ fmu @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)), inference(fof_nnf,[status(thm)],[pax2])).
% 2.60/2.84 thf(c_0_8, plain, (~p1|fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ fmu) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))), inference(fof_nnf,[status(thm)],[pax1])).
% 2.60/2.84 thf(c_0_9, plain, ![X1:produc190496183real_c]:(~p83|~fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ X1) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))|~fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ X1 @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 2.60/2.84 thf(c_0_10, plain, p83, inference(split_conjunct,[status(thm)],[ax0])).
% 2.60/2.84 thf(c_0_11, plain, (fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ fmu @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)|~p2), inference(split_conjunct,[status(thm)],[c_0_7])).
% 2.60/2.84 thf(c_0_12, plain, p2, inference(split_conjunct,[status(thm)],[ax79])).
% 2.60/2.84 thf(c_0_13, plain, (fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ fmu) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))|~p1), inference(split_conjunct,[status(thm)],[c_0_8])).
% 2.60/2.84 thf(c_0_14, plain, p1, inference(split_conjunct,[status(thm)],[ax80])).
% 2.60/2.84 thf(c_0_15, plain, ![X1:produc190496183real_c]:(~fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ X1) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb))|~fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ X1 @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])])).
% 2.60/2.84 thf(c_0_16, plain, fdenota1997846518gree_c @ (fproduc394644079real_c @ fmu3 @ fmu2) @ fmu @ (fsup_su1349021703um_c_c @ (fstatic_MBV_a_b_c @ (fchoice_a_b_c @ fa @ fb)) @ fv), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])).
% 2.60/2.84 thf(c_0_17, plain, fmember346808080real_c @ (fproduc1687028567real_c @ (fproduc394644079real_c @ fnu_22 @ fnu_2) @ fmu) @ (fdenota904684656_a_b_c @ fj @ (fchoice_a_b_c @ fa @ fb)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])).
% 2.60/2.84 thf(c_0_18, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])]), ['proof']).
% 2.60/2.84 thf(4,plain,$false,inference(eprover,[status(thm),assumptions([h7,h8,h6,h2,h0])],[])).
% 2.60/2.84 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8])).
% 2.60/2.84 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h6]),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_062,5,h6])).
% 2.60/2.84 thf(fact_88_eitherSem,axiom,((~(sP1)) => ((member346808080real_c @ ((produc1687028567real_c @ ((produc394644079real_c @ nu_12) @ nu_1)) @ ((produc394644079real_c @ mu3) @ mu2))) @ ((denota904684656_a_b_c @ i) @ b)))).
% 2.60/2.84 thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_88_eitherSem,3,6,h1,h2])).
% 2.60/2.84 thf(0,theorem,(~((![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)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])).
% 2.60/2.84 % SZS output end Proof
%------------------------------------------------------------------------------