TSTP Solution File: SYO064^4.002 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO064^4.002 : 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 : n020.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 19:29:58 EDT 2022
% Result : Theorem 1.98s 2.33s
% Output : Proof 1.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO064^4.002 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 : Fri Jul 8 18:23:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.33 % SZS status Theorem
% 1.98/2.33 % Mode: mode506
% 1.98/2.33 % Inferences: 40002
% 1.98/2.33 % SZS output start Proof
% 1.98/2.33 thf(ty_a, type, a : ($i>$o)).
% 1.98/2.33 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.98/2.33 thf(ty_a1, type, a1 : ($i>$o)).
% 1.98/2.33 thf(ty_a2, type, a2 : ($i>$o)).
% 1.98/2.33 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.98/2.33 thf(ty_b, type, b : ($i>$o)).
% 1.98/2.33 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.98/2.33 thf(ty_eigen__4, type, eigen__4 : $i).
% 1.98/2.33 thf(ty_b1, type, b1 : ($i>$o)).
% 1.98/2.33 thf(ty_irel, type, irel : ($i>$i>$o)).
% 1.98/2.33 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.98/2.33 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b1 @ X2) => (~((a2 @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 1.98/2.33 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~(((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b @ X3) => (~((a1 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((b1 @ X3) => (~((a2 @ X3)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.98/2.33 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 1.98/2.33 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 1.98/2.33 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.98/2.33 thf(sP2,plain,sP2 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b1 @ X2) => (~((a2 @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.98/2.33 thf(sP3,plain,sP3 <=> ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))))) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (a1 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.98/2.33 thf(sP4,plain,sP4 <=> (((irel @ eigen__1) @ eigen__1) => sP3),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.98/2.33 thf(sP5,plain,sP5 <=> (((irel @ eigen__0) @ eigen__1) => ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.98/2.33 thf(sP6,plain,sP6 <=> ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a1 @ X2)))))))) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.98/2.33 thf(sP7,plain,sP7 <=> (![X1:$i]:((~((((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.98/2.33 thf(sP8,plain,sP8 <=> (((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.98/2.33 thf(sP9,plain,sP9 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.98/2.33 thf(sP10,plain,sP10 <=> (((irel @ eigen__0) @ eigen__1) => sP6),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.98/2.33 thf(sP11,plain,sP11 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (b1 @ X4))))) => (![X4:$i]:(((irel @ X3) @ X4) => (a1 @ X4)))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (b1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.98/2.33 thf(sP12,plain,sP12 <=> (b @ eigen__4),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.98/2.33 thf(sP13,plain,sP13 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.98/2.33 thf(sP14,plain,sP14 <=> (a1 @ eigen__4),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.98/2.33 thf(sP15,plain,sP15 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a @ X2)))))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.98/2.33 thf(sP16,plain,sP16 <=> ((irel @ eigen__1) @ eigen__4),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.98/2.33 thf(sP17,plain,sP17 <=> ((irel @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.98/2.33 thf(sP18,plain,sP18 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.98/2.33 thf(sP19,plain,sP19 <=> (sP16 => (~((sP12 => (~(sP14)))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.98/2.33 thf(sP20,plain,sP20 <=> ((irel @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.98/2.33 thf(sP21,plain,sP21 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.98/2.33 thf(sP22,plain,sP22 <=> ((b1 @ eigen__2) => (~((a2 @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.98/2.33 thf(sP23,plain,sP23 <=> (a2 @ eigen__2),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.98/2.33 thf(sP24,plain,sP24 <=> (sP17 => sP12),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.98/2.33 thf(sP25,plain,sP25 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b1 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a1 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.98/2.33 thf(sP26,plain,sP26 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP26])])).
% 1.98/2.33 thf(sP27,plain,sP27 <=> (sP12 => (~(sP14))),introduced(definition,[new_symbols(definition,[sP27])])).
% 1.98/2.33 thf(sP28,plain,sP28 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b1 @ X2) => (~((a2 @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP28])])).
% 1.98/2.33 thf(sP29,plain,sP29 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP29])])).
% 1.98/2.33 thf(sP30,plain,sP30 <=> (sP16 => sP14),introduced(definition,[new_symbols(definition,[sP30])])).
% 1.98/2.33 thf(sP31,plain,sP31 <=> ((irel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP31])])).
% 1.98/2.33 thf(sP32,plain,sP32 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((irel @ X1) @ X2) => (~(((irel @ X2) @ X3)))))) => ((irel @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP32])])).
% 1.98/2.33 thf(sP33,plain,sP33 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b @ X3) => (~((a1 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((b1 @ X3) => (~((a2 @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP33])])).
% 1.98/2.33 thf(sP34,plain,sP34 <=> (sP31 => (b1 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP34])])).
% 1.98/2.33 thf(sP35,plain,sP35 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP35])])).
% 1.98/2.33 thf(sP36,plain,sP36 <=> (sP21 => sP13),introduced(definition,[new_symbols(definition,[sP36])])).
% 1.98/2.33 thf(sP37,plain,sP37 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))),introduced(definition,[new_symbols(definition,[sP37])])).
% 1.98/2.33 thf(sP38,plain,sP38 <=> ((~(sP26)) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1))))))))),introduced(definition,[new_symbols(definition,[sP38])])).
% 1.98/2.33 thf(sP39,plain,sP39 <=> ((~(sP8)) => sP17),introduced(definition,[new_symbols(definition,[sP39])])).
% 1.98/2.33 thf(sP40,plain,sP40 <=> (sP31 => (~(sP22))),introduced(definition,[new_symbols(definition,[sP40])])).
% 1.98/2.33 thf(sP41,plain,sP41 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))),introduced(definition,[new_symbols(definition,[sP41])])).
% 1.98/2.33 thf(sP42,plain,sP42 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP42])])).
% 1.98/2.33 thf(sP43,plain,sP43 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b1 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a1 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP43])])).
% 1.98/2.33 thf(sP44,plain,sP44 <=> ((!!) @ a2),introduced(definition,[new_symbols(definition,[sP44])])).
% 1.98/2.33 thf(sP45,plain,sP45 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__0) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP45])])).
% 1.98/2.33 thf(sP46,plain,sP46 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (a1 @ X1))),introduced(definition,[new_symbols(definition,[sP46])])).
% 1.98/2.33 thf(sP47,plain,sP47 <=> (b1 @ eigen__2),introduced(definition,[new_symbols(definition,[sP47])])).
% 1.98/2.33 thf(sP48,plain,sP48 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a @ X2)))))),introduced(definition,[new_symbols(definition,[sP48])])).
% 1.98/2.33 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.98/2.33 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.98/2.33 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.98/2.33 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.98/2.33 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 1.98/2.33 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 1.98/2.33 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 1.98/2.33 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 1.98/2.33 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 1.98/2.33 thf(def_iand,definition,(iand = mand)).
% 1.98/2.33 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.98/2.33 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.98/2.33 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 1.98/2.33 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 1.98/2.33 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 1.98/2.33 thf(def_ivalid,definition,(ivalid = (!!))).
% 1.98/2.33 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.98/2.33 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.98/2.33 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.98/2.33 thf(con,conjecture,sP33).
% 1.98/2.33 thf(h1,negated_conjecture,(~(sP33)),inference(assume_negation,[status(cth)],[con])).
% 1.98/2.33 thf(1,plain,((~(sP30) | ~(sP16)) | sP14),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(2,plain,(~(sP7) | sP39),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(3,plain,((~(sP39) | sP8) | sP17),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(4,plain,((~(sP8) | ~(sP29)) | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(5,plain,(~(sP46) | sP30),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(6,plain,(~(sP37) | sP24),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(7,plain,((~(sP24) | ~(sP17)) | sP12),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(8,plain,(~(sP45) | sP7),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(9,plain,((~(sP27) | ~(sP12)) | ~(sP14)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(10,plain,(sP19 | sP27),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(11,plain,(sP19 | sP16),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(12,plain,(~(sP48) | sP36),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(13,plain,((~(sP36) | ~(sP21)) | sP13),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(14,plain,(~(sP32) | sP45),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(15,plain,(~(sP1) | sP21),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(16,plain,(~(sP11) | sP25),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(17,plain,((~(sP25) | ~(sP37)) | sP43),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(18,plain,(~(sP43) | sP10),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(19,plain,((~(sP10) | ~(sP29)) | sP6),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(20,plain,(~(sP18) | sP15),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(21,plain,((~(sP15) | sP48) | sP37),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(22,plain,((~(sP13) | sP37) | sP35),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(23,plain,(sP26 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])).
% 1.98/2.33 thf(24,plain,(~(sP9) | sP4),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(25,plain,((~(sP4) | ~(sP20)) | sP3),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(26,plain,(~(sP1) | sP20),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(27,plain,((~(sP6) | sP9) | sP41),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(28,plain,((~(sP3) | sP41) | sP46),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(29,plain,(~(sP41) | sP34),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(30,plain,((~(sP34) | ~(sP31)) | sP47),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(31,plain,(~(sP44) | sP23),inference(all_rule,[status(thm)],[])).
% 1.98/2.33 thf(32,plain,((~(sP22) | ~(sP47)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(33,plain,(sP40 | sP22),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(34,plain,(sP40 | sP31),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(35,plain,(sP42 | ~(sP40)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 1.98/2.33 thf(36,plain,(sP38 | ~(sP42)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(37,plain,(sP38 | ~(sP26)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(38,plain,(sP5 | ~(sP38)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(39,plain,(sP5 | sP29),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(40,plain,(sP28 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 1.98/2.33 thf(41,plain,(sP2 | ~(sP28)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(42,plain,(sP2 | ~(sP35)),inference(prop_rule,[status(thm)],[])).
% 1.98/2.33 thf(43,plain,(sP33 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.98/2.33 thf(axiom3,axiom,(ivalid @ ((ior @ ((ior @ (iatom @ b)) @ (iatom @ a))) @ (iatom @ b)))).
% 1.98/2.33 thf(44,plain,sP18,inference(preprocess,[status(thm)],[axiom3]).
% 1.98/2.33 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ b)) @ ((ior @ ((ior @ (iatom @ b1)) @ (iatom @ a1))) @ (iatom @ b1))))).
% 1.98/2.33 thf(45,plain,sP11,inference(preprocess,[status(thm)],[axiom2]).
% 1.98/2.33 thf(axiom1,axiom,(ivalid @ (iatom @ a2))).
% 1.98/2.33 thf(46,plain,sP44,inference(preprocess,[status(thm)],[axiom1]).
% 1.98/2.33 thf(trans_axiom,axiom,sP32).
% 1.98/2.33 thf(refl_axiom,axiom,sP1).
% 1.98/2.33 thf(47,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,trans_axiom,refl_axiom,h1])).
% 1.98/2.33 thf(48,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[47,h0])).
% 1.98/2.33 thf(0,theorem,sP33,inference(contra,[status(thm),contra(discharge,[h1])],[47,h1])).
% 1.98/2.33 % SZS output end Proof
%------------------------------------------------------------------------------