TSTP Solution File: NUM740^4 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM740^4 : 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 : n029.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 13:55:55 EDT 2022
% Result : Theorem 78.02s 78.36s
% Output : Proof 78.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM740^4 : TPTP v8.1.0. Released v7.1.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 15:09:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 78.02/78.36 % SZS status Theorem
% 78.02/78.36 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 78.02/78.36 % Inferences: 3137
% 78.02/78.36 % SZS output start Proof
% 78.02/78.36 thf(ty_n_eq, type, n_eq : ($i>$i>$o)).
% 78.02/78.36 thf(ty_nat, type, nat : $i).
% 78.02/78.36 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)).
% 78.02/78.36 thf(ty_eigen__1, type, eigen__1 : $i).
% 78.02/78.36 thf(ty_eigen__0, type, eigen__0 : $i).
% 78.02/78.36 thf(ty_l_or, type, l_or : ($o>$o>$o)).
% 78.02/78.36 thf(ty_moref, type, moref : ($i>$i>$o)).
% 78.02/78.36 thf(ty_lessf, type, lessf : ($i>$i>$o)).
% 78.02/78.36 thf(ty_pair1type, type, pair1type : ($i>$i)).
% 78.02/78.36 thf(ty_in, type, in : ($i>$i>$o)).
% 78.02/78.36 thf(sP1,plain,sP1 <=> ((n_eq @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 78.02/78.36 thf(sP2,plain,sP2 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 78.02/78.36 thf(sP3,plain,sP3 <=> (((n_eq @ eigen__1) @ eigen__0) => sP1),introduced(definition,[new_symbols(definition,[sP3])])).
% 78.02/78.36 thf(sP4,plain,sP4 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((lessf @ eigen__1) @ eigen__0) => ((moref @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 78.02/78.36 thf(sP5,plain,sP5 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP3),introduced(definition,[new_symbols(definition,[sP5])])).
% 78.02/78.36 thf(sP6,plain,sP6 <=> (sP2 => (sP1 => ((n_eq @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP6])])).
% 78.02/78.36 thf(sP7,plain,sP7 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ X1) @ X2) => ((lessf @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 78.02/78.36 thf(sP8,plain,sP8 <=> (sP2 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((lessf @ eigen__1) @ X1) => ((moref @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 78.02/78.36 thf(sP9,plain,sP9 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_eq @ X1) @ X2) => ((n_eq @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 78.02/78.36 thf(sP10,plain,sP10 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 78.02/78.36 thf(sP11,plain,sP11 <=> (sP2 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_eq @ eigen__1) @ X1) => ((n_eq @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 78.02/78.36 thf(sP12,plain,sP12 <=> (sP1 = ((n_eq @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP12])])).
% 78.02/78.36 thf(sP13,plain,sP13 <=> (((moref @ eigen__0) @ eigen__1) = ((lessf @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP13])])).
% 78.02/78.36 thf(sP14,plain,sP14 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ X1) => ((lessf @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP14])])).
% 78.02/78.36 thf(sP15,plain,sP15 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_eq @ eigen__0) @ X1) => ((n_eq @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 78.02/78.36 thf(sP16,plain,sP16 <=> ((l_or @ ((moref @ eigen__0) @ eigen__1)) @ sP1),introduced(definition,[new_symbols(definition,[sP16])])).
% 78.02/78.36 thf(sP17,plain,sP17 <=> (((lessf @ eigen__1) @ eigen__0) => ((moref @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP17])])).
% 78.02/78.36 thf(sP18,plain,sP18 <=> ((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP18])])).
% 78.02/78.36 thf(sP19,plain,sP19 <=> ((n_eq @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])).
% 78.02/78.36 thf(sP20,plain,sP20 <=> (sP10 => sP15),introduced(definition,[new_symbols(definition,[sP20])])).
% 78.02/78.36 thf(sP21,plain,sP21 <=> (((moref @ eigen__0) @ eigen__1) => ((lessf @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP21])])).
% 78.02/78.36 thf(sP22,plain,sP22 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_eq @ eigen__1) @ X1) => ((n_eq @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP22])])).
% 78.02/78.36 thf(sP23,plain,sP23 <=> (sP1 => sP19),introduced(definition,[new_symbols(definition,[sP23])])).
% 78.02/78.36 thf(sP24,plain,sP24 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((lessf @ X1) @ X2) => ((moref @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 78.02/78.36 thf(sP25,plain,sP25 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((lessf @ eigen__1) @ X1) => ((moref @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP25])])).
% 78.02/78.36 thf(sP26,plain,sP26 <=> (sP10 => sP14),introduced(definition,[new_symbols(definition,[sP26])])).
% 78.02/78.36 thf(sP27,plain,sP27 <=> (sP2 => sP21),introduced(definition,[new_symbols(definition,[sP27])])).
% 78.02/78.36 thf(sP28,plain,sP28 <=> ((lessf @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP28])])).
% 78.02/78.36 thf(sP29,plain,sP29 <=> ((moref @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP29])])).
% 78.02/78.36 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
% 78.02/78.36 thf(def_frac,definition,(frac = (pair1type @ nat))).
% 78.02/78.36 thf(def_moreq,definition,(moreq = (^[X1:$i]:(^[X2:$i]:((l_or @ ((moref @ X1) @ X2)) @ ((n_eq @ X1) @ X2)))))).
% 78.02/78.36 thf(def_lesseq,definition,(lesseq = (^[X1:$i]:(^[X2:$i]:((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)))))).
% 78.02/78.36 thf(satz48,conjecture,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((moref @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ X2) @ X1)) @ ((n_eq @ X2) @ X1)))))))).
% 78.02/78.36 thf(h0,negated_conjecture,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((moref @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ X2) @ X1)) @ ((n_eq @ X2) @ X1))))))))),inference(assume_negation,[status(cth)],[satz48])).
% 78.02/78.36 thf(h1,assumption,(~((sP10 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => ((l_or @ ((lessf @ X1) @ eigen__0)) @ ((n_eq @ X1) @ eigen__0)))))))),introduced(assumption,[])).
% 78.02/78.36 thf(h2,assumption,sP10,introduced(assumption,[])).
% 78.02/78.36 thf(h3,assumption,(~((![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => ((l_or @ ((lessf @ X1) @ eigen__0)) @ ((n_eq @ X1) @ eigen__0))))))),introduced(assumption,[])).
% 78.02/78.36 thf(h4,assumption,(~((sP2 => (sP16 => sP18)))),introduced(assumption,[])).
% 78.02/78.36 thf(h5,assumption,sP2,introduced(assumption,[])).
% 78.02/78.36 thf(h6,assumption,(~((sP16 => sP18))),introduced(assumption,[])).
% 78.02/78.36 thf(h7,assumption,sP16,introduced(assumption,[])).
% 78.02/78.36 thf(h8,assumption,(~(sP18)),introduced(assumption,[])).
% 78.02/78.36 thf(1,plain,((sP12 | ~(sP1)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(2,plain,((sP12 | sP1) | sP19),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(3,plain,((sP13 | ~(sP29)) | ~(sP28)),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(4,plain,((sP13 | sP29) | sP28),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(5,plain,(~(sP15) | sP6),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(6,plain,((~(sP6) | ~(sP2)) | sP23),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(7,plain,((~(sP23) | ~(sP1)) | sP19),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(8,plain,(~(sP14) | sP27),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(9,plain,((~(sP27) | ~(sP2)) | sP21),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(10,plain,((~(sP21) | ~(sP29)) | sP28),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(11,plain,(~(sP22) | sP5),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(12,plain,((~(sP5) | ~(sP10)) | sP3),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(13,plain,((~(sP3) | ~(sP19)) | sP1),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(14,plain,(~(sP25) | sP4),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(15,plain,((~(sP4) | ~(sP10)) | sP17),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(16,plain,((~(sP17) | ~(sP28)) | sP29),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(17,plain,(((~(sP16) | sP18) | ~(sP13)) | ~(sP12)),inference(mating_rule,[status(thm)],[])).
% 78.02/78.36 thf(18,plain,((~(sP20) | ~(sP10)) | sP15),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(19,plain,((~(sP26) | ~(sP10)) | sP14),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(20,plain,((~(sP11) | ~(sP2)) | sP22),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(21,plain,((~(sP8) | ~(sP2)) | sP25),inference(prop_rule,[status(thm)],[])).
% 78.02/78.36 thf(22,plain,(~(sP24) | sP8),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(23,plain,(~(sP7) | sP26),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(24,plain,(~(sP9) | sP20),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(25,plain,(~(sP9) | sP11),inference(all_rule,[status(thm)],[])).
% 78.02/78.36 thf(satz43,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((lessf @ X1) @ X2) => ((moref @ X2) @ X1))))))).
% 78.02/78.36 thf(26,plain,sP24,inference(preprocess,[status(thm)],[satz43]).
% 78.02/78.36 thf(satz42,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((moref @ X1) @ X2) => ((lessf @ X2) @ X1))))))).
% 78.02/78.36 thf(27,plain,sP7,inference(preprocess,[status(thm)],[satz42]).
% 78.02/78.36 thf(satz38,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((n_eq @ X1) @ X2) => ((n_eq @ X2) @ X1))))))).
% 78.02/78.36 thf(28,plain,sP9,inference(preprocess,[status(thm)],[satz38]).
% 78.02/78.36 thf(29,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h2,h5,h7,h8,26,27,28])).
% 78.02/78.36 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,29,h7,h8])).
% 78.02/78.36 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,30,h5,h6])).
% 78.02/78.36 thf(32,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,31,h4])).
% 78.02/78.36 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,32,h2,h3])).
% 78.02/78.36 thf(34,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,33,h1])).
% 78.02/78.36 thf(0,theorem,(![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((moref @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ X2) @ X1)) @ ((n_eq @ X2) @ X1))))))),inference(contra,[status(thm),contra(discharge,[h0])],[34,h0])).
% 78.02/78.36 % SZS output end Proof
%------------------------------------------------------------------------------