TSTP Solution File: NUM653^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM653^4 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 : Mon Jul 18 13:54:40 EDT 2022
% Result : Theorem 98.41s 98.66s
% Output : Proof 98.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM653^4 : TPTP v8.1.0. Released v7.1.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 00:47:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 98.41/98.66 % SZS status Theorem
% 98.41/98.66 % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 98.41/98.66 % Inferences: 49
% 98.41/98.66 % SZS output start Proof
% 98.41/98.66 thf(ty_moreis, type, moreis : ($i>$i>$o)).
% 98.41/98.66 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)).
% 98.41/98.66 thf(ty_eigen__1, type, eigen__1 : $i).
% 98.41/98.66 thf(ty_eigen__0, type, eigen__0 : $i).
% 98.41/98.66 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)).
% 98.41/98.66 thf(ty_l_or, type, l_or : ($o>$o>$o)).
% 98.41/98.66 thf(ty_emptyset, type, emptyset : $i).
% 98.41/98.66 thf(ty_n_some, type, n_some : (($i>$o)>$o)).
% 98.41/98.66 thf(ty_diffprop, type, diffprop : ($i>$i>$i>$o)).
% 98.41/98.66 thf(ty_omega, type, omega : $i).
% 98.41/98.66 thf(ty_imp, type, imp : ($o>$o>$o)).
% 98.41/98.66 thf(ty_n_is, type, n_is : ($i>$i>$o)).
% 98.41/98.66 thf(ty_in, type, in : ($i>$i>$o)).
% 98.41/98.66 thf(ty_iii, type, iii : ($i>$i>$o)).
% 98.41/98.66 thf(sP1,plain,sP1 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 98.41/98.66 thf(sP2,plain,sP2 <=> ((imp @ ((iii @ eigen__1) @ eigen__0)) @ $false),introduced(definition,[new_symbols(definition,[sP2])])).
% 98.41/98.66 thf(sP3,plain,sP3 <=> (sP1 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__1) @ X1) => (n_some @ ((diffprop @ X1) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 98.41/98.66 thf(sP4,plain,sP4 <=> (((iii @ eigen__1) @ eigen__0) = (n_some @ ((diffprop @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 98.41/98.66 thf(sP5,plain,sP5 <=> ($false = $false),introduced(definition,[new_symbols(definition,[sP5])])).
% 98.41/98.66 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((moreis @ eigen__1) @ X1) => ((imp @ ((iii @ eigen__1) @ X1)) @ $false)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 98.41/98.66 thf(sP7,plain,sP7 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((moreis @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 98.41/98.66 thf(sP8,plain,sP8 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((moreis @ X1) @ X2) => ((imp @ ((iii @ X1) @ X2)) @ $false)))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 98.41/98.66 thf(sP9,plain,sP9 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((moreis @ eigen__1) @ eigen__0) => sP2)),introduced(definition,[new_symbols(definition,[sP9])])).
% 98.41/98.66 thf(sP10,plain,sP10 <=> ((l_or @ ((iii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP10])])).
% 98.41/98.66 thf(sP11,plain,sP11 <=> (sP1 => ((n_some @ ((diffprop @ eigen__0) @ eigen__1)) => ((iii @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP11])])).
% 98.41/98.66 thf(sP12,plain,sP12 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ X2)) => ((iii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 98.41/98.66 thf(sP13,plain,sP13 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((moreis @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 98.41/98.66 thf(sP14,plain,sP14 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__1) @ X1) => (n_some @ ((diffprop @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 98.41/98.66 thf(sP15,plain,sP15 <=> $false,introduced(definition,[new_symbols(definition,[sP15])])).
% 98.41/98.66 thf(sP16,plain,sP16 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 98.41/98.66 thf(sP17,plain,sP17 <=> (sP10 => ((moreis @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP17])])).
% 98.41/98.66 thf(sP18,plain,sP18 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((moreis @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 98.41/98.66 thf(sP19,plain,sP19 <=> ((moreis @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])).
% 98.41/98.66 thf(sP20,plain,sP20 <=> (sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((iii @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 98.41/98.66 thf(sP21,plain,sP21 <=> (sP1 => sP6),introduced(definition,[new_symbols(definition,[sP21])])).
% 98.41/98.66 thf(sP22,plain,sP22 <=> ((iii @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP22])])).
% 98.41/98.66 thf(sP23,plain,sP23 <=> (sP19 => sP2),introduced(definition,[new_symbols(definition,[sP23])])).
% 98.41/98.66 thf(sP24,plain,sP24 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ X1) @ X2) => (n_some @ ((diffprop @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 98.41/98.66 thf(sP25,plain,sP25 <=> (n_some @ ((diffprop @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP25])])).
% 98.41/98.66 thf(sP26,plain,sP26 <=> (sP25 => sP22),introduced(definition,[new_symbols(definition,[sP26])])).
% 98.41/98.66 thf(sP27,plain,sP27 <=> (sP22 => sP25),introduced(definition,[new_symbols(definition,[sP27])])).
% 98.41/98.66 thf(sP28,plain,sP28 <=> (sP1 => sP17),introduced(definition,[new_symbols(definition,[sP28])])).
% 98.41/98.66 thf(sP29,plain,sP29 <=> (sP16 => sP27),introduced(definition,[new_symbols(definition,[sP29])])).
% 98.41/98.66 thf(sP30,plain,sP30 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((iii @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 98.41/98.66 thf(sP31,plain,sP31 <=> ((imp @ sP25) @ sP15),introduced(definition,[new_symbols(definition,[sP31])])).
% 98.41/98.66 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
% 98.41/98.66 thf(def_d_not,definition,(d_not = (^[X1:$o]:((imp @ X1) @ sP15)))).
% 98.41/98.66 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))).
% 98.41/98.66 thf(def_d_29_ii,definition,(d_29_ii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X1) @ X2)))))).
% 98.41/98.66 thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))).
% 98.41/98.66 thf(satz10d,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15))))))).
% 98.41/98.66 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15)))))))),inference(assume_negation,[status(cth)],[satz10d])).
% 98.41/98.66 thf(h1,assumption,(~((sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((imp @ (n_some @ ((diffprop @ eigen__0) @ X1))) @ sP15))))))),introduced(assumption,[])).
% 98.41/98.66 thf(h2,assumption,sP16,introduced(assumption,[])).
% 98.41/98.66 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((imp @ (n_some @ ((diffprop @ eigen__0) @ X1))) @ sP15)))))),introduced(assumption,[])).
% 98.41/98.66 thf(h4,assumption,(~((sP1 => (sP10 => sP31)))),introduced(assumption,[])).
% 98.41/98.66 thf(h5,assumption,sP1,introduced(assumption,[])).
% 98.41/98.66 thf(h6,assumption,(~((sP10 => sP31))),introduced(assumption,[])).
% 98.41/98.66 thf(h7,assumption,sP10,introduced(assumption,[])).
% 98.41/98.66 thf(h8,assumption,(~(sP31)),introduced(assumption,[])).
% 98.41/98.66 thf(1,plain,((~(sP20) | ~(sP16)) | sP30),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(2,plain,(~(sP30) | sP11),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(3,plain,((~(sP11) | ~(sP1)) | sP26),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(4,plain,((~(sP26) | ~(sP25)) | sP22),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(5,plain,((~(sP3) | ~(sP1)) | sP14),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(6,plain,(~(sP14) | sP29),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(7,plain,((~(sP29) | ~(sP16)) | sP27),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(8,plain,((~(sP27) | ~(sP22)) | sP25),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(9,plain,((sP4 | ~(sP22)) | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(10,plain,((sP4 | sP22) | sP25),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(11,plain,~(sP15),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(12,plain,((sP5 | sP15) | sP15),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(13,plain,(((~(sP2) | sP31) | ~(sP4)) | ~(sP5)),inference(mating_rule,[status(thm)],[])).
% 98.41/98.66 thf(14,plain,((~(sP21) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(15,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(16,plain,((~(sP9) | ~(sP16)) | sP23),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(17,plain,((~(sP23) | ~(sP19)) | sP2),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(18,plain,(~(sP12) | sP20),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(19,plain,(~(sP8) | sP21),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(20,plain,(~(sP24) | sP3),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(21,plain,(~(sP18) | sP7),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(22,plain,((~(sP7) | ~(sP16)) | sP13),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(23,plain,(~(sP13) | sP28),inference(all_rule,[status(thm)],[])).
% 98.41/98.66 thf(24,plain,((~(sP28) | ~(sP1)) | sP17),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(25,plain,((~(sP17) | ~(sP10)) | sP19),inference(prop_rule,[status(thm)],[])).
% 98.41/98.66 thf(satz10c,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((moreis @ X1) @ X2) => (d_not @ ((iii @ X1) @ X2)))))))).
% 98.41/98.66 thf(26,plain,sP8,inference(preprocess,[status(thm)],[satz10c]).
% 98.41/98.66 thf(satz14,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((lessis @ X1) @ X2) => ((moreis @ X2) @ X1))))))).
% 98.41/98.66 thf(27,plain,sP18,inference(preprocess,[status(thm)],[satz14]).
% 98.41/98.66 thf(satz12,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((iii @ X1) @ X2) => ((d_29_ii @ X2) @ X1))))))).
% 98.41/98.66 thf(28,plain,sP24,inference(preprocess,[status(thm)],[satz12]).
% 98.41/98.66 thf(satz11,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ X1) @ X2) => ((iii @ X2) @ X1))))))).
% 98.41/98.66 thf(29,plain,sP12,inference(preprocess,[status(thm)],[satz11]).
% 98.41/98.66 thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h2,h5,h7,h8,26,27,28,29])).
% 98.41/98.66 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,30,h7,h8])).
% 98.41/98.66 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,31,h5,h6])).
% 98.41/98.66 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,32,h4])).
% 98.41/98.66 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,33,h2,h3])).
% 98.41/98.66 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,34,h1])).
% 98.41/98.66 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((imp @ (n_some @ ((diffprop @ X1) @ X2))) @ sP15)))))),inference(contra,[status(thm),contra(discharge,[h0])],[35,h0])).
% 98.41/98.66 % SZS output end Proof
%------------------------------------------------------------------------------