TSTP Solution File: NUM699^4 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM699^4 : 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 : n026.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 13:55:25 EDT 2022
% Result : Theorem 22.36s 22.58s
% Output : Proof 22.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM699^4 : TPTP v8.1.0. Released v7.1.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n026.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 : 600
% 0.12/0.34 % DateTime : Wed Jul 6 16:45:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 22.36/22.58 % SZS status Theorem
% 22.36/22.58 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 22.36/22.58 % Inferences: 340
% 22.36/22.58 % SZS output start Proof
% 22.36/22.58 thf(ty_moreis, type, moreis : ($i>$i>$o)).
% 22.36/22.58 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)).
% 22.36/22.58 thf(ty_d_29_ii, type, d_29_ii : ($i>$i>$o)).
% 22.36/22.58 thf(ty_eigen__1, type, eigen__1 : $i).
% 22.36/22.58 thf(ty_eigen__0, type, eigen__0 : $i).
% 22.36/22.58 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)).
% 22.36/22.58 thf(ty_l_or, type, l_or : ($o>$o>$o)).
% 22.36/22.58 thf(ty_emptyset, type, emptyset : $i).
% 22.36/22.58 thf(ty_n_some, type, n_some : (($i>$o)>$o)).
% 22.36/22.58 thf(ty_diffprop, type, diffprop : ($i>$i>$i>$o)).
% 22.36/22.58 thf(ty_omega, type, omega : $i).
% 22.36/22.58 thf(ty_n_is, type, n_is : ($i>$i>$o)).
% 22.36/22.58 thf(ty_in, type, in : ($i>$i>$o)).
% 22.36/22.58 thf(ty_d_Sing, type, d_Sing : ($i>$i)).
% 22.36/22.58 thf(ty_binunion, type, binunion : ($i>$i>$i)).
% 22.36/22.58 thf(sP1,plain,sP1 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((moreis @ eigen__0) @ X1) => ((l_or @ (n_some @ ((diffprop @ eigen__0) @ X1))) @ ((n_is @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 22.36/22.58 thf(sP2,plain,sP2 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ eigen__1)) => ((d_29_ii @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 22.36/22.58 thf(sP3,plain,sP3 <=> (((d_29_ii @ eigen__0) @ eigen__1) => ((moreis @ eigen__0) @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 22.36/22.58 thf(sP4,plain,sP4 <=> (![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)))))))) => (((d_29_ii @ X2) @ X1) => ((moreis @ X2) @ ((binunion @ X1) @ (d_Sing @ X1)))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 22.36/22.58 thf(sP5,plain,sP5 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((d_29_ii @ X1) @ eigen__1) => ((moreis @ X1) @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 22.36/22.58 thf(sP6,plain,sP6 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 22.36/22.58 thf(sP7,plain,sP7 <=> (sP6 => ((is_of @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 22.36/22.58 thf(sP8,plain,sP8 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 22.36/22.58 thf(sP9,plain,sP9 <=> (sP6 => sP5),introduced(definition,[new_symbols(definition,[sP9])])).
% 22.36/22.58 thf(sP10,plain,sP10 <=> (![X1:$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:$i]:(~((X4 = emptyset)))))))) => ((n_some @ ((diffprop @ X2) @ X1)) => ((d_29_ii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 22.36/22.58 thf(sP11,plain,sP11 <=> ((n_some @ ((diffprop @ eigen__0) @ eigen__1)) => ((d_29_ii @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP11])])).
% 22.36/22.58 thf(sP12,plain,sP12 <=> ((moreis @ eigen__0) @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 22.36/22.58 thf(sP13,plain,sP13 <=> ((l_or @ (n_some @ ((diffprop @ eigen__0) @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))))) @ ((n_is @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP13])])).
% 22.36/22.58 thf(sP14,plain,sP14 <=> (sP12 => sP13),introduced(definition,[new_symbols(definition,[sP14])])).
% 22.36/22.58 thf(sP15,plain,sP15 <=> (sP6 => sP2),introduced(definition,[new_symbols(definition,[sP15])])).
% 22.36/22.58 thf(sP16,plain,sP16 <=> (sP8 => sP3),introduced(definition,[new_symbols(definition,[sP16])])).
% 22.36/22.58 thf(sP17,plain,sP17 <=> (((is_of @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => sP14),introduced(definition,[new_symbols(definition,[sP17])])).
% 22.36/22.58 thf(sP18,plain,sP18 <=> ((d_29_ii @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP18])])).
% 22.36/22.58 thf(sP19,plain,sP19 <=> (n_some @ ((diffprop @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP19])])).
% 22.36/22.58 thf(sP20,plain,sP20 <=> ((is_of @ ((binunion @ eigen__1) @ (d_Sing @ eigen__1))) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 22.36/22.58 thf(sP21,plain,sP21 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((is_of @ ((binunion @ X1) @ (d_Sing @ X1))) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))))),introduced(definition,[new_symbols(definition,[sP21])])).
% 22.36/22.58 thf(sP22,plain,sP22 <=> (sP8 => sP11),introduced(definition,[new_symbols(definition,[sP22])])).
% 22.36/22.58 thf(sP23,plain,sP23 <=> (sP8 => sP1),introduced(definition,[new_symbols(definition,[sP23])])).
% 22.36/22.58 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)))))))) => (((moreis @ X1) @ X2) => ((l_or @ (n_some @ ((diffprop @ X1) @ X2))) @ ((n_is @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 22.36/22.58 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
% 22.36/22.58 thf(def_ordsucc,definition,(ordsucc = (^[X1:$i]:((binunion @ X1) @ (d_Sing @ X1))))).
% 22.36/22.58 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))).
% 22.36/22.58 thf(def_iii,definition,(iii = (^[X1:$i]:(^[X2:$i]:(n_some @ ((diffprop @ X2) @ X1)))))).
% 22.36/22.58 thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))).
% 22.36/22.58 thf(satz25c,conjecture,(![X1:$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:$i]:(~((X4 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ X2)) => ((l_or @ (n_some @ ((diffprop @ X1) @ ((binunion @ X2) @ (d_Sing @ X2))))) @ ((n_is @ ((binunion @ X2) @ (d_Sing @ X2))) @ X1)))))))).
% 22.36/22.58 thf(h0,negated_conjecture,(~((![X1:$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:$i]:(~((X4 = emptyset)))))))) => ((n_some @ ((diffprop @ X1) @ X2)) => ((l_or @ (n_some @ ((diffprop @ X1) @ ((binunion @ X2) @ (d_Sing @ X2))))) @ ((n_is @ ((binunion @ X2) @ (d_Sing @ X2))) @ X1))))))))),inference(assume_negation,[status(cth)],[satz25c])).
% 22.36/22.58 thf(h1,assumption,(~((sP8 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((l_or @ (n_some @ ((diffprop @ eigen__0) @ ((binunion @ X1) @ (d_Sing @ X1))))) @ ((n_is @ ((binunion @ X1) @ (d_Sing @ X1))) @ eigen__0)))))))),introduced(assumption,[])).
% 22.36/22.58 thf(h2,assumption,sP8,introduced(assumption,[])).
% 22.36/22.58 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((n_some @ ((diffprop @ eigen__0) @ X1)) => ((l_or @ (n_some @ ((diffprop @ eigen__0) @ ((binunion @ X1) @ (d_Sing @ X1))))) @ ((n_is @ ((binunion @ X1) @ (d_Sing @ X1))) @ eigen__0))))))),introduced(assumption,[])).
% 22.36/22.58 thf(h4,assumption,(~((sP6 => (sP19 => sP13)))),introduced(assumption,[])).
% 22.36/22.58 thf(h5,assumption,sP6,introduced(assumption,[])).
% 22.36/22.58 thf(h6,assumption,(~((sP19 => sP13))),introduced(assumption,[])).
% 22.36/22.58 thf(h7,assumption,sP19,introduced(assumption,[])).
% 22.36/22.58 thf(h8,assumption,(~(sP13)),introduced(assumption,[])).
% 22.36/22.58 thf(1,plain,((~(sP9) | ~(sP6)) | sP5),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(2,plain,(~(sP5) | sP16),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(3,plain,((~(sP16) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(4,plain,((~(sP3) | ~(sP18)) | sP12),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(5,plain,(~(sP21) | sP7),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(6,plain,((~(sP7) | ~(sP6)) | sP20),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(7,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(8,plain,((~(sP15) | ~(sP6)) | sP2),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(9,plain,(~(sP2) | sP22),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(10,plain,((~(sP22) | ~(sP8)) | sP11),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(11,plain,((~(sP11) | ~(sP19)) | sP18),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(12,plain,(~(sP24) | sP23),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(13,plain,((~(sP23) | ~(sP8)) | sP1),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(14,plain,(~(sP1) | sP17),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(15,plain,((~(sP17) | ~(sP20)) | sP14),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(16,plain,((~(sP14) | ~(sP12)) | sP13),inference(prop_rule,[status(thm)],[])).
% 22.36/22.58 thf(17,plain,(~(sP4) | sP9),inference(all_rule,[status(thm)],[])).
% 22.36/22.58 thf(satz25a,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ X2) @ X1) => ((moreis @ X2) @ (ordsucc @ X1)))))))).
% 22.36/22.58 thf(18,plain,sP4,inference(preprocess,[status(thm)],[satz25a]).
% 22.36/22.58 thf(satz13,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((moreis @ X1) @ X2) => ((lessis @ X2) @ X1))))))).
% 22.36/22.58 thf(19,plain,sP24,inference(preprocess,[status(thm)],[satz13]).
% 22.36/22.58 thf(satz12,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((iii @ X1) @ X2) => ((d_29_ii @ X2) @ X1))))))).
% 22.36/22.58 thf(20,plain,sP10,inference(preprocess,[status(thm)],[satz12]).
% 22.36/22.58 thf(suc_p,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((is_of @ (ordsucc @ X1)) @ (^[X2:$i]:((in @ X2) @ nat)))))).
% 22.36/22.58 thf(21,plain,sP21,inference(preprocess,[status(thm)],[suc_p]).
% 22.36/22.58 thf(22,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h2,h5,h7,h8,18,19,20,21])).
% 22.36/22.58 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,22,h7,h8])).
% 22.36/22.58 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,23,h5,h6])).
% 22.36/22.58 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,24,h4])).
% 22.36/22.58 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,25,h2,h3])).
% 22.36/22.58 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,26,h1])).
% 22.36/22.58 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)))))))) => ((n_some @ ((diffprop @ X1) @ X2)) => ((l_or @ (n_some @ ((diffprop @ X1) @ ((binunion @ X2) @ (d_Sing @ X2))))) @ ((n_is @ ((binunion @ X2) @ (d_Sing @ X2))) @ X1))))))),inference(contra,[status(thm),contra(discharge,[h0])],[27,h0])).
% 22.36/22.58 % SZS output end Proof
%------------------------------------------------------------------------------