TSTP Solution File: ITP180^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP180^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : 600s
% DateTime : Sun Jul 17 00:29:24 EDT 2022
% Result : Theorem 2.53s 2.74s
% Output : Proof 2.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP180^1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.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 : 600
% 0.13/0.34 % DateTime : Fri Jun 3 09:31:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.53/2.74 % SZS status Theorem
% 2.53/2.74 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.53/2.74 % Inferences: 4
% 2.53/2.74 % SZS output start Proof
% 2.53/2.74 thf(ty_product_prod_V_V, type, product_prod_V_V : $tType).
% 2.53/2.74 thf(ty_produc778275879_V_nat, type, produc778275879_V_nat : $tType).
% 2.53/2.74 thf(ty_labele2115946735nt_V_V, type, labele2115946735nt_V_V : $tType).
% 2.53/2.74 thf(ty_v, type, v : $tType).
% 2.53/2.74 thf(ty_set_V, type, set_V : $tType).
% 2.53/2.74 thf(ty_standard_Constant_V, type, standard_Constant_V : $tType).
% 2.53/2.74 thf(ty_set_Product_prod_V_V, type, set_Product_prod_V_V : $tType).
% 2.53/2.74 thf(ty_set_V2, type, set_V2 : $tType).
% 2.53/2.74 thf(ty_v2, type, v2 : $tType).
% 2.53/2.74 thf(ty_h, type, h : (v>v)).
% 2.53/2.74 thf(ty_labele1134902411nt_V_V, type, labele1134902411nt_V_V : (labele2115946735nt_V_V>set_V)).
% 2.53/2.74 thf(ty_eigen__2, type, eigen__2 : v).
% 2.53/2.74 thf(ty_member_V, type, member_V : (v2>set_V2>$o)).
% 2.53/2.74 thf(ty_getRel1432786916nt_V_V, type, getRel1432786916nt_V_V : (standard_Constant_V>labele2115946735nt_V_V>set_Product_prod_V_V)).
% 2.53/2.74 thf(ty_eigen__1, type, eigen__1 : (v2>v)).
% 2.53/2.74 thf(ty_eigen__0, type, eigen__0 : (v2>v)).
% 2.53/2.74 thf(ty_mainta197426964_nat_V, type, mainta197426964_nat_V : (produc778275879_V_nat>labele2115946735nt_V_V>$o)).
% 2.53/2.74 thf(ty_eigen__4, type, eigen__4 : (v2>v)).
% 2.53/2.74 thf(ty_eigen__5, type, eigen__5 : v).
% 2.53/2.74 thf(ty_product_Pair_V_V2, type, product_Pair_V_V2 : (v>v>product_prod_V_V)).
% 2.53/2.74 thf(ty_eigen__3, type, eigen__3 : (v2>v)).
% 2.53/2.74 thf(ty_member2015049524od_V_V, type, member2015049524od_V_V : (product_prod_V_V>set_Product_prod_V_V>$o)).
% 2.53/2.74 thf(ty_standa1319953089tant_V, type, standa1319953089tant_V : produc778275879_V_nat).
% 2.53/2.74 thf(ty_member_V2, type, member_V2 : (v>set_V>$o)).
% 2.53/2.74 thf(ty_bNF_Gr_V_V2, type, bNF_Gr_V_V2 : (set_V>(v>v)>set_Product_prod_V_V)).
% 2.53/2.74 thf(ty_c, type, c : set_V2).
% 2.53/2.74 thf(ty_bot_bot_set_V2, type, bot_bot_set_V2 : set_V).
% 2.53/2.74 thf(ty_map_gr907434255tant_V, type, map_gr907434255tant_V : (set_Product_prod_V_V>labele2115946735nt_V_V>labele2115946735nt_V_V)).
% 2.53/2.74 thf(ty_g, type, g : labele2115946735nt_V_V).
% 2.53/2.74 thf(ty_standard_S_Const_V, type, standard_S_Const_V : (v2>standard_Constant_V)).
% 2.53/2.74 thf(sP1,plain,sP1 <=> ((mainta197426964_nat_V @ standa1319953089tant_V) @ g),introduced(definition,[new_symbols(definition,[sP1])])).
% 2.53/2.74 thf(conj_0,conjecture,((member2015049524od_V_V @ ((product_Pair_V_V2 @ (m @ xa)) @ (m @ xa))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ y)) @ g))).
% 2.53/2.74 thf(h0,negated_conjecture,(~(((member2015049524od_V_V @ ((product_Pair_V_V2 @ (m @ xa)) @ (m @ xa))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ y)) @ g)))),inference(assume_negation,[status(cth)],[conj_0])).
% 2.53/2.74 thf(h1,assumption,sP1,introduced(assumption,[])).
% 2.53/2.74 thf(h2,assumption,(~(((labele1134902411nt_V_V @ g) = bot_bot_set_V2))),introduced(assumption,[])).
% 2.53/2.74 thf(h3,assumption,(~(sP1)),introduced(assumption,[])).
% 2.53/2.74 thf(h4,assumption,((labele1134902411nt_V_V @ g) = bot_bot_set_V2),introduced(assumption,[])).
% 2.53/2.74 thf(h5,assumption,(![X1:v2]:(((member_V @ X1) @ c) => ((member2015049524od_V_V @ ((product_Pair_V_V2 @ (eigen__0 @ X1)) @ (eigen__0 @ X1))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ X1)) @ ((map_gr907434255tant_V @ ((bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g)) @ h)) @ g))))),introduced(assumption,[])).
% 2.53/2.74 thf(h6,assumption,(![X1:v2]:(((member_V @ X1) @ c) => ((member2015049524od_V_V @ ((product_Pair_V_V2 @ (eigen__1 @ X1)) @ (eigen__1 @ X1))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ X1)) @ ((map_gr907434255tant_V @ ((bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g)) @ h)) @ g))))),introduced(assumption,[])).
% 2.53/2.74 thf(h7,assumption,((member_V2 @ eigen__2) @ (labele1134902411nt_V_V @ g)),introduced(assumption,[])).
% 2.53/2.74 thf(pax28, axiom, (p28=>![X67:v, X68:v, X69:standard_Constant_V, X70:labele2115946735nt_V_V, X71:labele2115946735nt_V_V]:(fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X67 @ X68) @ (fgetRel1432786916nt_V_V @ X69 @ X70)=>(fgraph_1808119_V_V_V @ X70 @ X71 @ (fid_on_V2 @ (flabele1134902411nt_V_V @ X70))=>fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X67 @ X68) @ (fgetRel1432786916nt_V_V @ X69 @ X71)))), file('<stdin>', pax28)).
% 2.53/2.74 thf(pax19, axiom, (p19=>![X91:product_prod_V_V]:~(![X95:v, X96:v]:~((X91)=(fproduct_Pair_V_V2 @ X95 @ X96)))), file('<stdin>', pax19)).
% 2.53/2.74 thf(ax55, axiom, p28, file('<stdin>', ax55)).
% 2.53/2.74 thf(ax64, axiom, p19, file('<stdin>', ax64)).
% 2.53/2.74 thf(pax8, axiom, (p8=>fgraph_1808119_V_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg) @ fg @ (fid_on_V2 @ (flabele1134902411nt_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg)))), file('<stdin>', pax8)).
% 2.53/2.74 thf(ax75, axiom, p8, file('<stdin>', ax75)).
% 2.53/2.74 thf(pax6, axiom, (p6=>fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg))), file('<stdin>', pax6)).
% 2.53/2.74 thf(nax77, axiom, (p77<=fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ fg)), file('<stdin>', nax77)).
% 2.53/2.74 thf(ax6, axiom, ~(p77), file('<stdin>', ax6)).
% 2.53/2.74 thf(ax77, axiom, p6, file('<stdin>', ax77)).
% 2.53/2.74 thf(c_0_10, plain, ![X355:v, X356:v, X357:standard_Constant_V, X358:labele2115946735nt_V_V, X359:labele2115946735nt_V_V]:(~p28|(~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X355 @ X356) @ (fgetRel1432786916nt_V_V @ X357 @ X358)|(~fgraph_1808119_V_V_V @ X358 @ X359 @ (fid_on_V2 @ (flabele1134902411nt_V_V @ X358))|fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X355 @ X356) @ (fgetRel1432786916nt_V_V @ X357 @ X359)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax28])])])).
% 2.53/2.74 thf(c_0_11, plain, ![X449:product_prod_V_V]:(~p19|(X449)=(fproduct_Pair_V_V2 @ (esk174_1 @ X449) @ (esk175_1 @ X449))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax19])])])])])).
% 2.53/2.74 thf(c_0_12, plain, ![X1:v, X2:v, X45:standard_Constant_V, X7:labele2115946735nt_V_V, X4:labele2115946735nt_V_V]:(fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X1 @ X2) @ (fgetRel1432786916nt_V_V @ X45 @ X7)|~p28|~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X1 @ X2) @ (fgetRel1432786916nt_V_V @ X45 @ X4)|~fgraph_1808119_V_V_V @ X4 @ X7 @ (fid_on_V2 @ (flabele1134902411nt_V_V @ X4))), inference(split_conjunct,[status(thm)],[c_0_10])).
% 2.53/2.74 thf(c_0_13, plain, p28, inference(split_conjunct,[status(thm)],[ax55])).
% 2.53/2.74 thf(c_0_14, plain, ![X19:product_prod_V_V]:((X19)=(fproduct_Pair_V_V2 @ (esk174_1 @ X19) @ (esk175_1 @ X19))|~p19), inference(split_conjunct,[status(thm)],[c_0_11])).
% 2.53/2.74 thf(c_0_15, plain, p19, inference(split_conjunct,[status(thm)],[ax64])).
% 2.53/2.74 thf(c_0_16, plain, (~p8|fgraph_1808119_V_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg) @ fg @ (fid_on_V2 @ (flabele1134902411nt_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg)))), inference(fof_nnf,[status(thm)],[pax8])).
% 2.53/2.74 thf(c_0_17, plain, ![X1:v, X2:v, X4:labele2115946735nt_V_V, X45:standard_Constant_V, X7:labele2115946735nt_V_V]:(fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X1 @ X2) @ (fgetRel1432786916nt_V_V @ X45 @ X4)|~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ X1 @ X2) @ (fgetRel1432786916nt_V_V @ X45 @ X7)|~fgraph_1808119_V_V_V @ X7 @ X4 @ (fid_on_V2 @ (flabele1134902411nt_V_V @ X7))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 2.53/2.74 thf(c_0_18, plain, ![X19:product_prod_V_V]:(fproduct_Pair_V_V2 @ (esk174_1 @ X19) @ (esk175_1 @ X19))=(X19), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 2.53/2.74 thf(c_0_19, plain, (fgraph_1808119_V_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg) @ fg @ (fid_on_V2 @ (flabele1134902411nt_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg)))|~p8), inference(split_conjunct,[status(thm)],[c_0_16])).
% 2.53/2.74 thf(c_0_20, plain, p8, inference(split_conjunct,[status(thm)],[ax75])).
% 2.53/2.74 thf(c_0_21, plain, (~p6|fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg))), inference(fof_nnf,[status(thm)],[pax6])).
% 2.53/2.74 thf(c_0_22, plain, (~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ fg)|p77), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax77])])).
% 2.53/2.74 thf(c_0_23, plain, ~p77, inference(fof_simplification,[status(thm)],[ax6])).
% 2.53/2.74 thf(c_0_24, plain, ![X4:labele2115946735nt_V_V, X45:standard_Constant_V, X19:product_prod_V_V, X7:labele2115946735nt_V_V]:(fmember2015049524od_V_V @ X19 @ (fgetRel1432786916nt_V_V @ X45 @ X4)|~fgraph_1808119_V_V_V @ X7 @ X4 @ (fid_on_V2 @ (flabele1134902411nt_V_V @ X7))|~fmember2015049524od_V_V @ X19 @ (fgetRel1432786916nt_V_V @ X45 @ X7)), inference(spm,[status(thm)],[c_0_17, c_0_18])).
% 2.53/2.74 thf(c_0_25, plain, fgraph_1808119_V_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg) @ fg @ (fid_on_V2 @ (flabele1134902411nt_V_V @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 2.53/2.74 thf(c_0_26, plain, (fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg))|~p6), inference(split_conjunct,[status(thm)],[c_0_21])).
% 2.53/2.74 thf(c_0_27, plain, p6, inference(split_conjunct,[status(thm)],[ax77])).
% 2.53/2.74 thf(c_0_28, plain, (p77|~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ fg)), inference(split_conjunct,[status(thm)],[c_0_22])).
% 2.53/2.74 thf(c_0_29, plain, ~p77, inference(split_conjunct,[status(thm)],[c_0_23])).
% 2.53/2.74 thf(c_0_30, plain, ![X19:product_prod_V_V, X45:standard_Constant_V]:(fmember2015049524od_V_V @ X19 @ (fgetRel1432786916nt_V_V @ X45 @ fg)|~fmember2015049524od_V_V @ X19 @ (fgetRel1432786916nt_V_V @ X45 @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 2.53/2.74 thf(c_0_31, plain, fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ (fmap_gr907434255tant_V @ (fbNF_Gr_V_V2 @ (flabele1134902411nt_V_V @ fg) @ fh) @ fg)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 2.53/2.74 thf(c_0_32, plain, ~fmember2015049524od_V_V @ (fproduct_Pair_V_V2 @ (fm @ fxa) @ (fm @ fxa)) @ (fgetRel1432786916nt_V_V @ (fstandard_S_Const_V @ fy) @ fg), inference(sr,[status(thm)],[c_0_28, c_0_29])).
% 2.53/2.74 thf(c_0_33, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32]), ['proof']).
% 2.53/2.74 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h7,h6,h5,h1,h2,h0])],[])).
% 2.53/2.74 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:v]:(~(((member_V2 @ X1) @ (labele1134902411nt_V_V @ g)))))))).
% 2.53/2.74 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h5,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h7])).
% 2.53/2.74 thf(fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,(~((![X1:v2>v]:(~((![X2:v2]:(((member_V @ X2) @ c) => ((member2015049524od_V_V @ ((product_Pair_V_V2 @ (X1 @ X2)) @ (X1 @ X2))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ X2)) @ ((map_gr907434255tant_V @ ((bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g)) @ h)) @ g))))))))))).
% 2.53/2.74 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,2,h6])).
% 2.53/2.74 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,3,h5])).
% 2.53/2.74 thf(h8,assumption,(![X1:v2]:(((member_V @ X1) @ c) => ((member2015049524od_V_V @ ((product_Pair_V_V2 @ (eigen__3 @ X1)) @ (eigen__3 @ X1))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ X1)) @ ((map_gr907434255tant_V @ ((bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g)) @ h)) @ g))))),introduced(assumption,[])).
% 2.53/2.74 thf(h9,assumption,(![X1:v2]:(((member_V @ X1) @ c) => ((member2015049524od_V_V @ ((product_Pair_V_V2 @ (eigen__4 @ X1)) @ (eigen__4 @ X1))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ X1)) @ ((map_gr907434255tant_V @ ((bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g)) @ h)) @ g))))),introduced(assumption,[])).
% 2.53/2.74 thf(h10,assumption,((member_V2 @ eigen__5) @ (labele1134902411nt_V_V @ g)),introduced(assumption,[])).
% 2.53/2.74 thf(fact_84_ne,axiom,sP1).
% 2.53/2.74 thf(5,plain,$false,inference(tab_conflict,[status(thm),assumptions([h10,h9,h8,h3,h4,h0])],[fact_84_ne,h3])).
% 2.53/2.74 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h8,h3,h4,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,5,h10])).
% 2.53/2.74 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h3,h4,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,6,h9])).
% 2.53/2.74 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,7,h8])).
% 2.53/2.74 thf(fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062,axiom,(sP1 = (~(((labele1134902411nt_V_V @ g) = bot_bot_set_V2))))).
% 2.53/2.74 thf(9,plain,$false,inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062,4,8,h1,h2,h3,h4])).
% 2.53/2.74 thf(0,theorem,((member2015049524od_V_V @ ((product_Pair_V_V2 @ (m @ xa)) @ (m @ xa))) @ ((getRel1432786916nt_V_V @ (standard_S_Const_V @ y)) @ g)),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])).
% 2.53/2.74 % SZS output end Proof
%------------------------------------------------------------------------------