TSTP Solution File: SYO063^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO063^4 : 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 : n023.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 19:29:57 EDT 2022
% Result : Theorem 260.00s 260.13s
% Output : Proof 260.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO063^4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.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 : Fri Jul 8 18:13:11 EDT 2022
% 0.19/0.33 % CPUTime :
% 260.00/260.13 % SZS status Theorem
% 260.00/260.13 % Mode: mode493
% 260.00/260.13 % Inferences: 2339
% 260.00/260.13 % SZS output start Proof
% 260.00/260.13 thf(ty_eigen__14, type, eigen__14 : $i).
% 260.00/260.13 thf(ty_p, type, p : ($i>$o)).
% 260.00/260.13 thf(ty_q, type, q : ($i>$o)).
% 260.00/260.13 thf(ty_s, type, s : ($i>$o)).
% 260.00/260.13 thf(ty_eigen__1, type, eigen__1 : $i).
% 260.00/260.13 thf(ty_eigen__0, type, eigen__0 : $i).
% 260.00/260.13 thf(ty_r, type, r : ($i>$o)).
% 260.00/260.13 thf(ty_eigen__3, type, eigen__3 : $i).
% 260.00/260.13 thf(ty_irel, type, irel : ($i>$i>$o)).
% 260.00/260.13 thf(ty_t, type, t : ($i>$o)).
% 260.00/260.13 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 260.00/260.13 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (t @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (r @ X3))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 260.00/260.13 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => (~((((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((irel @ X1) @ X2) => (t @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 260.00/260.13 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((irel @ X1) @ X2) => (~(((irel @ X2) @ X3)))))) => ((irel @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 260.00/260.13 thf(sP2,plain,sP2 <=> ((~((((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ eigen__3)))))) => ((irel @ eigen__0) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP2])])).
% 260.00/260.13 thf(sP3,plain,sP3 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (t @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (r @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 260.00/260.13 thf(sP4,plain,sP4 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (~((((![X3:$i]:(((irel @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (q @ X3)))) => (~(((![X3:$i]:(((irel @ X2) @ X3) => (t @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (r @ X3))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 260.00/260.13 thf(sP5,plain,sP5 <=> (((![X1:$i]:(((irel @ eigen__14) @ X1) => (p @ X1))) => (![X1:$i]:(((irel @ eigen__14) @ X1) => (q @ X1)))) => (~(((![X1:$i]:(((irel @ eigen__14) @ X1) => (t @ X1))) => (![X1:$i]:(((irel @ eigen__14) @ X1) => (r @ X1))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 260.00/260.13 thf(sP6,plain,sP6 <=> (((irel @ eigen__3) @ eigen__14) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP6])])).
% 260.00/260.13 thf(sP7,plain,sP7 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__0) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 260.00/260.13 thf(sP8,plain,sP8 <=> (![X1:$i]:(((irel @ eigen__14) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 260.00/260.13 thf(sP9,plain,sP9 <=> (((irel @ eigen__0) @ eigen__3) => (~((![X1:$i]:(((irel @ eigen__3) @ X1) => (~((((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((irel @ X1) @ X2) => (t @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2)))))))))))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 260.00/260.13 thf(sP10,plain,sP10 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 260.00/260.13 thf(sP11,plain,sP11 <=> (((irel @ eigen__3) @ eigen__14) => ((![X1:$i]:(((irel @ eigen__14) @ X1) => (t @ X1))) => (![X1:$i]:(((irel @ eigen__14) @ X1) => (r @ X1))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 260.00/260.13 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 260.00/260.13 thf(sP13,plain,sP13 <=> ((irel @ eigen__1) @ eigen__14),introduced(definition,[new_symbols(definition,[sP13])])).
% 260.00/260.13 thf(sP14,plain,sP14 <=> ((irel @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP14])])).
% 260.00/260.13 thf(sP15,plain,sP15 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP15])])).
% 260.00/260.13 thf(sP16,plain,sP16 <=> (((irel @ eigen__1) @ eigen__1) => (~(sP12))),introduced(definition,[new_symbols(definition,[sP16])])).
% 260.00/260.13 thf(sP17,plain,sP17 <=> (![X1:$i]:((~((sP15 => (~(((irel @ eigen__1) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 260.00/260.13 thf(sP18,plain,sP18 <=> ((![X1:$i]:(((irel @ eigen__14) @ X1) => (t @ X1))) => (![X1:$i]:(((irel @ eigen__14) @ X1) => (r @ X1)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 260.00/260.13 thf(sP19,plain,sP19 <=> (sP13 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP19])])).
% 260.00/260.13 thf(sP20,plain,sP20 <=> (s @ eigen__1),introduced(definition,[new_symbols(definition,[sP20])])).
% 260.00/260.13 thf(sP21,plain,sP21 <=> ((irel @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP21])])).
% 260.00/260.13 thf(sP22,plain,sP22 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__1) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP22])])).
% 260.00/260.13 thf(sP23,plain,sP23 <=> (sP15 => (~(((irel @ eigen__1) @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 260.00/260.13 thf(sP24,plain,sP24 <=> (((irel @ eigen__1) @ eigen__3) => (~(((irel @ eigen__3) @ eigen__14)))),introduced(definition,[new_symbols(definition,[sP24])])).
% 260.00/260.13 thf(sP25,plain,sP25 <=> ((!!) @ s),introduced(definition,[new_symbols(definition,[sP25])])).
% 260.00/260.13 thf(sP26,plain,sP26 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP26])])).
% 260.00/260.13 thf(sP27,plain,sP27 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (t @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2)))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 260.00/260.13 thf(sP28,plain,sP28 <=> ((~(sP24)) => sP13),introduced(definition,[new_symbols(definition,[sP28])])).
% 260.00/260.13 thf(sP29,plain,sP29 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (~((((![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((irel @ X1) @ X2) => (t @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (r @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 260.00/260.13 thf(sP30,plain,sP30 <=> (sP8 => (![X1:$i]:(((irel @ eigen__14) @ X1) => (q @ X1)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 260.00/260.13 thf(sP31,plain,sP31 <=> ((irel @ eigen__3) @ eigen__14),introduced(definition,[new_symbols(definition,[sP31])])).
% 260.00/260.13 thf(sP32,plain,sP32 <=> (((irel @ eigen__1) @ eigen__3) => (~(sP27))),introduced(definition,[new_symbols(definition,[sP32])])).
% 260.00/260.13 thf(sP33,plain,sP33 <=> (sP3 => sP12),introduced(definition,[new_symbols(definition,[sP33])])).
% 260.00/260.13 thf(sP34,plain,sP34 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => ((![X4:$i]:(((irel @ X3) @ X4) => (t @ X4))) => (![X4:$i]:(((irel @ X3) @ X4) => (r @ X4)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (p @ X2))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 260.00/260.13 thf(sP35,plain,sP35 <=> ((irel @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP35])])).
% 260.00/260.13 thf(sP36,plain,sP36 <=> (![X1:$i]:((~((sP35 => (~(((irel @ eigen__3) @ X1)))))) => ((irel @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP36])])).
% 260.00/260.13 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 260.00/260.13 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 260.00/260.13 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 260.00/260.13 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 260.00/260.13 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 260.00/260.13 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 260.00/260.13 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 260.00/260.13 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 260.00/260.13 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 260.00/260.13 thf(def_iand,definition,(iand = mand)).
% 260.00/260.13 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 260.00/260.13 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 260.00/260.13 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 260.00/260.13 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 260.00/260.13 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 260.00/260.13 thf(def_ivalid,definition,(ivalid = (!!))).
% 260.00/260.13 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 260.00/260.13 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 260.00/260.13 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 260.00/260.13 thf(con,conjecture,(![X1:$i]:((~((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (~((((~((~((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (q @ X4)))) => (~(((~((~((![X4:$i]:(((irel @ X3) @ X4) => (t @ X4))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (r @ X4))))))))))))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((~((![X3:$i]:(((irel @ X2) @ X3) => (~((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))))))))) => (~((~(((s @ X2) => (~((s @ X2)))))))))))))))).
% 260.00/260.13 thf(h1,negated_conjecture,(~((![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (~((((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))) => (![X4:$i]:(((irel @ X3) @ X4) => (q @ X4)))) => (~(((![X4:$i]:(((irel @ X3) @ X4) => (t @ X4))) => (![X4:$i]:(((irel @ X3) @ X4) => (r @ X4))))))))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((~((![X3:$i]:(((irel @ X2) @ X3) => (~((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))))))))) => ((s @ X2) => (~((s @ X2))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 260.00/260.13 thf(h2,assumption,(~((sP4 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (p @ X3))))))))) => ((s @ X1) => (~((s @ X1)))))))))))),introduced(assumption,[])).
% 260.00/260.13 thf(h3,assumption,sP4,introduced(assumption,[])).
% 260.00/260.13 thf(h4,assumption,(~((![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (p @ X3))))))))) => ((s @ X1) => (~((s @ X1))))))))))),introduced(assumption,[])).
% 260.00/260.13 thf(h5,assumption,(~((sP15 => (~(((~(sP10)) => (sP20 => (~(sP20))))))))),introduced(assumption,[])).
% 260.00/260.13 thf(h6,assumption,sP15,introduced(assumption,[])).
% 260.00/260.13 thf(h7,assumption,((~(sP10)) => (sP20 => (~(sP20)))),introduced(assumption,[])).
% 260.00/260.13 thf(h8,assumption,sP10,introduced(assumption,[])).
% 260.00/260.13 thf(h9,assumption,(sP20 => (~(sP20))),introduced(assumption,[])).
% 260.00/260.13 thf(1,plain,((~(sP19) | ~(sP13)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(2,plain,(~(sP10) | sP19),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(3,plain,(sP30 | sP8),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(4,plain,((~(sP5) | ~(sP30)) | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(5,plain,(~(sP27) | sP11),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(6,plain,((~(sP11) | ~(sP31)) | sP18),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(7,plain,(~(sP36) | sP28),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(8,plain,((~(sP28) | sP24) | sP13),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(9,plain,((~(sP24) | ~(sP35)) | ~(sP31)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(10,plain,(sP6 | sP5),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(11,plain,(sP6 | sP31),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(12,plain,(sP29 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14])).
% 260.00/260.13 thf(13,plain,((~(sP9) | ~(sP14)) | ~(sP29)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(14,plain,(~(sP4) | sP9),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(15,plain,(~(sP22) | sP36),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(16,plain,(~(sP17) | sP2),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(17,plain,((~(sP2) | sP23) | sP14),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(18,plain,((~(sP23) | ~(sP15)) | ~(sP35)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(19,plain,(sP32 | sP27),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(20,plain,(sP32 | sP35),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(21,plain,(sP3 | ~(sP32)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 260.00/260.13 thf(22,plain,(~(sP7) | sP17),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(23,plain,((~(sP33) | ~(sP3)) | sP12),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(24,plain,((~(sP16) | ~(sP21)) | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 260.00/260.13 thf(25,plain,(~(sP10) | sP16),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(26,plain,(~(sP34) | sP33),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(27,plain,(~(sP1) | sP22),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(28,plain,(~(sP1) | sP7),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(29,plain,(~(sP26) | sP21),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(axiom2,axiom,(ivalid @ ((iimplies @ (inot @ ((iimplies @ (iatom @ t)) @ (iatom @ r)))) @ (iatom @ p)))).
% 260.00/260.13 thf(30,plain,sP34,inference(preprocess,[status(thm)],[axiom2]).
% 260.00/260.13 thf(trans_axiom,axiom,sP1).
% 260.00/260.13 thf(refl_axiom,axiom,sP26).
% 260.00/260.13 thf(31,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h5,h3,h4,h2,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,h3,h6,h8,30,trans_axiom,refl_axiom])).
% 260.00/260.13 thf(h10,assumption,(~(sP20)),introduced(assumption,[])).
% 260.00/260.13 thf(32,plain,(~(sP25) | sP20),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(axiom1,axiom,(ivalid @ (iatom @ s))).
% 260.00/260.13 thf(33,plain,sP25,inference(preprocess,[status(thm)],[axiom1]).
% 260.00/260.13 thf(34,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[32,h10,33])).
% 260.00/260.13 thf(35,plain,(~(sP25) | sP20),inference(all_rule,[status(thm)],[])).
% 260.00/260.13 thf(36,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[35,h10,33])).
% 260.00/260.13 thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h10])],[h9,34,36,h10,h10])).
% 260.00/260.13 thf(38,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h7,31,37,h8,h9])).
% 260.00/260.13 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,38,h6,h7])).
% 260.00/260.13 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,39,h5])).
% 260.00/260.13 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,40,h3,h4])).
% 260.00/260.13 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,41,h2])).
% 260.00/260.13 thf(43,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[42,h0])).
% 260.00/260.13 thf(0,theorem,(![X1:$i]:((~((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (~((((~((~((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (q @ X4)))) => (~(((~((~((![X4:$i]:(((irel @ X3) @ X4) => (t @ X4))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (r @ X4))))))))))))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((~((![X3:$i]:(((irel @ X2) @ X3) => (~((![X4:$i]:(((irel @ X3) @ X4) => (p @ X4))))))))) => (~((~(((s @ X2) => (~((s @ X2))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[42,h1])).
% 260.00/260.13 % SZS output end Proof
%------------------------------------------------------------------------------