TSTP Solution File: SYO068^4.005 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO068^4.005 : TPTP v8.1.0. Released v4.0.0.
% 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 : Thu Jul 21 19:30:03 EDT 2022
% Result : Theorem 1.98s 2.22s
% Output : Proof 1.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO068^4.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 : Sat Jul 9 04:30:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.98/2.22 % SZS status Theorem
% 1.98/2.22 % Mode: mode506
% 1.98/2.22 % Inferences: 19607
% 1.98/2.22 % SZS output start Proof
% 1.98/2.22 thf(ty_eigen__6, type, eigen__6 : $i).
% 1.98/2.22 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.98/2.22 thf(ty_p3, type, p3 : ($i>$o)).
% 1.98/2.22 thf(ty_p4, type, p4 : ($i>$o)).
% 1.98/2.22 thf(ty_p2, type, p2 : ($i>$o)).
% 1.98/2.22 thf(ty_irel, type, irel : ($i>$i>$o)).
% 1.98/2.22 thf(ty_p0, type, p0 : ($i>$o)).
% 1.98/2.22 thf(ty_p5, type, p5 : ($i>$o)).
% 1.98/2.22 thf(ty_p1, type, p1 : ($i>$o)).
% 1.98/2.22 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.98/2.22 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p5 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 1.98/2.22 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.98/2.22 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.98/2.22 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.98/2.22 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.98/2.22 thf(sP4,plain,sP4 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.98/2.22 thf(sP5,plain,sP5 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.98/2.22 thf(sP6,plain,sP6 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.98/2.22 thf(sP7,plain,sP7 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.98/2.22 thf(sP8,plain,sP8 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.98/2.22 thf(sP9,plain,sP9 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.98/2.22 thf(sP10,plain,sP10 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.98/2.22 thf(sP11,plain,sP11 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.98/2.22 thf(sP12,plain,sP12 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.98/2.22 thf(sP13,plain,sP13 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.98/2.22 thf(sP14,plain,sP14 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.98/2.22 thf(sP15,plain,sP15 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.98/2.22 thf(sP16,plain,sP16 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.98/2.22 thf(sP17,plain,sP17 <=> (((irel @ eigen__0) @ eigen__0) => sP11),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.98/2.22 thf(sP18,plain,sP18 <=> (((irel @ eigen__0) @ eigen__0) => sP12),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.98/2.22 thf(sP19,plain,sP19 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.98/2.22 thf(sP20,plain,sP20 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.98/2.22 thf(sP21,plain,sP21 <=> (p5 @ eigen__6),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.98/2.22 thf(sP22,plain,sP22 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.98/2.22 thf(sP23,plain,sP23 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => sP6),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.98/2.22 thf(sP24,plain,sP24 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.98/2.22 thf(sP25,plain,sP25 <=> (sP14 => sP15),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.98/2.22 thf(sP26,plain,sP26 <=> (((irel @ eigen__0) @ eigen__0) => sP9),introduced(definition,[new_symbols(definition,[sP26])])).
% 1.98/2.22 thf(sP27,plain,sP27 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 1.98/2.22 thf(sP28,plain,sP28 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP28])])).
% 1.98/2.22 thf(sP29,plain,sP29 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))),introduced(definition,[new_symbols(definition,[sP29])])).
% 1.98/2.22 thf(sP30,plain,sP30 <=> (sP24 => sP4),introduced(definition,[new_symbols(definition,[sP30])])).
% 1.98/2.22 thf(sP31,plain,sP31 <=> (((irel @ eigen__0) @ eigen__6) => sP21),introduced(definition,[new_symbols(definition,[sP31])])).
% 1.98/2.22 thf(sP32,plain,sP32 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP32])])).
% 1.98/2.22 thf(sP33,plain,sP33 <=> (sP14 => sP22),introduced(definition,[new_symbols(definition,[sP33])])).
% 1.98/2.22 thf(sP34,plain,sP34 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 1.98/2.22 thf(sP35,plain,sP35 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP35])])).
% 1.98/2.22 thf(sP36,plain,sP36 <=> (sP16 => sP35),introduced(definition,[new_symbols(definition,[sP36])])).
% 1.98/2.22 thf(sP37,plain,sP37 <=> (sP28 => sP3),introduced(definition,[new_symbols(definition,[sP37])])).
% 1.98/2.22 thf(sP38,plain,sP38 <=> ((!!) @ p5),introduced(definition,[new_symbols(definition,[sP38])])).
% 1.98/2.22 thf(sP39,plain,sP39 <=> (sP22 => sP2),introduced(definition,[new_symbols(definition,[sP39])])).
% 1.98/2.22 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.98/2.22 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.98/2.22 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.98/2.22 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.98/2.22 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 1.98/2.22 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 1.98/2.22 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 1.98/2.22 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 1.98/2.22 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 1.98/2.22 thf(def_iand,definition,(iand = mand)).
% 1.98/2.22 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.98/2.22 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.98/2.22 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 1.98/2.22 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 1.98/2.22 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 1.98/2.22 thf(def_ivalid,definition,(ivalid = (!!))).
% 1.98/2.22 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.98/2.22 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.98/2.22 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.98/2.22 thf(con,conjecture,sP32).
% 1.98/2.22 thf(h1,negated_conjecture,(~(sP32)),inference(assume_negation,[status(cth)],[con])).
% 1.98/2.22 thf(1,plain,(~(sP38) | sP21),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(2,plain,(sP31 | ~(sP21)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(3,plain,(sP14 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 1.98/2.22 thf(4,plain,(~(sP19) | sP26),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(5,plain,((~(sP26) | ~(sP28)) | sP9),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(6,plain,((~(sP25) | ~(sP14)) | sP15),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(7,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(8,plain,((~(sP7) | ~(sP28)) | sP33),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(9,plain,((~(sP33) | ~(sP14)) | sP22),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(10,plain,((~(sP39) | ~(sP22)) | sP2),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(11,plain,(~(sP2) | sP8),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(12,plain,((~(sP8) | ~(sP28)) | sP10),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(13,plain,((~(sP10) | ~(sP22)) | sP29),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(14,plain,((~(sP23) | ~(sP29)) | sP6),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(15,plain,(~(sP6) | sP18),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(16,plain,((~(sP18) | ~(sP28)) | sP12),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(17,plain,((~(sP12) | ~(sP29)) | sP24),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(18,plain,((~(sP30) | ~(sP24)) | sP4),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(19,plain,(~(sP4) | sP17),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(20,plain,((~(sP17) | ~(sP28)) | sP11),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(21,plain,((~(sP11) | ~(sP24)) | sP16),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(22,plain,((~(sP36) | ~(sP16)) | sP35),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(23,plain,(~(sP35) | sP37),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(24,plain,((~(sP37) | ~(sP28)) | sP3),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(25,plain,((~(sP3) | ~(sP16)) | sP19),inference(prop_rule,[status(thm)],[])).
% 1.98/2.22 thf(26,plain,(~(sP1) | sP28),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(27,plain,(~(sP27) | sP25),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(28,plain,(~(sP34) | sP39),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(29,plain,(~(sP5) | sP23),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(30,plain,(~(sP20) | sP30),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(31,plain,(~(sP13) | sP36),inference(all_rule,[status(thm)],[])).
% 1.98/2.22 thf(32,plain,(sP32 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.98/2.22 thf(axiom6,axiom,(ivalid @ ((iimplies @ (iatom @ p5)) @ ((iimplies @ (iatom @ p5)) @ (iatom @ p4))))).
% 1.98/2.22 thf(33,plain,sP27,inference(preprocess,[status(thm)],[axiom6]).
% 1.98/2.22 thf(axiom5,axiom,(ivalid @ ((iimplies @ (iatom @ p4)) @ ((iimplies @ (iatom @ p4)) @ (iatom @ p3))))).
% 1.98/2.22 thf(34,plain,sP34,inference(preprocess,[status(thm)],[axiom5]).
% 1.98/2.22 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ p3)) @ ((iimplies @ (iatom @ p3)) @ (iatom @ p2))))).
% 1.98/2.22 thf(35,plain,sP5,inference(preprocess,[status(thm)],[axiom4]).
% 1.98/2.22 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ p2)) @ ((iimplies @ (iatom @ p2)) @ (iatom @ p1))))).
% 1.98/2.22 thf(36,plain,sP20,inference(preprocess,[status(thm)],[axiom3]).
% 1.98/2.22 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))).
% 1.98/2.22 thf(37,plain,sP13,inference(preprocess,[status(thm)],[axiom2]).
% 1.98/2.22 thf(axiom1,axiom,(ivalid @ (iatom @ p5))).
% 1.98/2.22 thf(38,plain,sP38,inference(preprocess,[status(thm)],[axiom1]).
% 1.98/2.22 thf(refl_axiom,axiom,sP1).
% 1.98/2.22 thf(39,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,refl_axiom,h1])).
% 1.98/2.22 thf(40,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[39,h0])).
% 1.98/2.22 thf(0,theorem,sP32,inference(contra,[status(thm),contra(discharge,[h1])],[39,h1])).
% 1.98/2.22 % SZS output end Proof
%------------------------------------------------------------------------------