TSTP Solution File: SYO463^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO463^5 : 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 : n027.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 19:32:32 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO463^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 01:10:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % Mode: mode213
% 0.14/0.39 % Inferences: 146
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 thf(ty_p, type, p : ($i>$o)).
% 0.14/0.39 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.14/0.39 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.14/0.39 thf(ty_q, type, q : ($i>$o)).
% 0.14/0.39 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.14/0.39 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.14/0.39 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.14/0.39 thf(sP1,plain,sP1 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.14/0.39 thf(sP2,plain,sP2 <=> (((p @ eigen__2) => (q @ eigen__2)) => (~(((q @ eigen__2) => (p @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.14/0.39 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__0) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.14/0.39 thf(sP4,plain,sP4 <=> ((q @ eigen__3) => (p @ eigen__3)),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.14/0.39 thf(sP5,plain,sP5 <=> (q @ eigen__3),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.14/0.39 thf(sP6,plain,sP6 <=> ((~((((rel_s4 @ eigen__0) @ eigen__1) => (~(sP1))))) => ((rel_s4 @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.14/0.39 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((((p @ X1) => (q @ X1)) => (~(((q @ X1) => (p @ X1))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.14/0.39 thf(sP8,plain,sP8 <=> (((rel_s4 @ eigen__0) @ eigen__2) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.14/0.39 thf(sP9,plain,sP9 <=> (((p @ eigen__3) => sP5) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.14/0.39 thf(sP10,plain,sP10 <=> (((rel_s4 @ eigen__1) @ eigen__3) => sP5),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.14/0.39 thf(sP11,plain,sP11 <=> ((p @ eigen__2) => (q @ eigen__2)),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.14/0.39 thf(sP12,plain,sP12 <=> (((rel_s4 @ eigen__0) @ eigen__3) => (~(sP9))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.14/0.39 thf(sP13,plain,sP13 <=> (![X1:$i]:((~((((rel_s4 @ eigen__0) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ X1)))))) => ((rel_s4 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.14/0.39 thf(sP14,plain,sP14 <=> ((rel_s4 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.14/0.39 thf(sP15,plain,sP15 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.14/0.39 thf(sP16,plain,sP16 <=> (((rel_s4 @ eigen__0) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.14/0.39 thf(sP17,plain,sP17 <=> ((~(sP16)) => sP14),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.14/0.39 thf(sP18,plain,sP18 <=> (((rel_s4 @ eigen__0) @ eigen__1) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.14/0.39 thf(sP19,plain,sP19 <=> ((rel_s4 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.14/0.39 thf(sP20,plain,sP20 <=> (sP1 => (p @ eigen__2)),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.14/0.39 thf(sP21,plain,sP21 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.14/0.39 thf(sP22,plain,sP22 <=> (q @ eigen__2),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.14/0.39 thf(sP23,plain,sP23 <=> (p @ eigen__2),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.14/0.39 thf(sP24,plain,sP24 <=> ((rel_s4 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.14/0.39 thf(sP25,plain,sP25 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.14/0.39 thf(sP26,plain,sP26 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.14/0.39 thf(sP27,plain,sP27 <=> (p @ eigen__3),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.14/0.39 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.14/0.39 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.14/0.39 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.14/0.39 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.14/0.39 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.14/0.39 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.14/0.39 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.14/0.39 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.14/0.39 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.14/0.39 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.14/0.39 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.14/0.39 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.14/0.39 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.14/0.39 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.14/0.39 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.14/0.39 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.14/0.39 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.14/0.39 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.14/0.39 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.14/0.39 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.14/0.39 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.14/0.39 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.14/0.39 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 0.14/0.39 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.14/0.39 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.14/0.39 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.14/0.39 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.14/0.39 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.14/0.39 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.14/0.39 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.14/0.39 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.14/0.39 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.14/0.39 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.14/0.39 thf(prove,conjecture,(![X1:$i]:((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((p @ X2))))) => (q @ X2)))))) => (~(((~((~((q @ X2))))) => (p @ X2))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3)))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3)))))))))))))).
% 0.14/0.39 thf(h0,negated_conjecture,(~((![X1:$i]:((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((((p @ X2) => (q @ X2)) => (~(((q @ X2) => (p @ X2))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3)))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))))))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.14/0.39 thf(h1,assumption,(~((sP7 => (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2)))))))))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h2,assumption,sP7,introduced(assumption,[])).
% 0.14/0.39 thf(h3,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h4,assumption,(~((sP25 => (~(((sP21 => sP26) => (~((sP26 => sP21))))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h5,assumption,sP25,introduced(assumption,[])).
% 0.14/0.39 thf(h6,assumption,((sP21 => sP26) => (~((sP26 => sP21)))),introduced(assumption,[])).
% 0.14/0.39 thf(h7,assumption,(~((sP21 => sP26))),introduced(assumption,[])).
% 0.14/0.39 thf(h8,assumption,(~((sP26 => sP21))),introduced(assumption,[])).
% 0.14/0.39 thf(h9,assumption,sP21,introduced(assumption,[])).
% 0.14/0.39 thf(h10,assumption,(~(sP26)),introduced(assumption,[])).
% 0.14/0.39 thf(h11,assumption,(~((sP1 => sP22))),introduced(assumption,[])).
% 0.14/0.39 thf(h12,assumption,sP1,introduced(assumption,[])).
% 0.14/0.39 thf(h13,assumption,(~(sP22)),introduced(assumption,[])).
% 0.14/0.39 thf(1,plain,((~(sP11) | ~(sP23)) | sP22),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(2,plain,(sP2 | sP11),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(3,plain,(~(sP7) | sP8),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(4,plain,((~(sP8) | ~(sP24)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(5,plain,(~(sP15) | sP3),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(6,plain,(~(sP3) | sP13),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(7,plain,(~(sP13) | sP6),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(8,plain,((~(sP6) | sP18) | sP24),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(9,plain,((~(sP18) | ~(sP25)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(10,plain,(~(sP21) | sP20),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(11,plain,((~(sP20) | ~(sP1)) | sP23),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(a2,axiom,(mtransitive @ rel_s4)).
% 0.14/0.39 thf(12,plain,sP15,inference(preprocess,[status(thm)],[a2]).
% 0.14/0.39 thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h5,h9,h12,h13])).
% 0.14/0.39 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,13,h12,h13])).
% 0.14/0.39 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,14,h11])).
% 0.14/0.39 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,15,h9,h10])).
% 0.14/0.39 thf(h14,assumption,sP26,introduced(assumption,[])).
% 0.14/0.39 thf(h15,assumption,(~(sP21)),introduced(assumption,[])).
% 0.14/0.39 thf(h16,assumption,(~((sP19 => sP27))),introduced(assumption,[])).
% 0.14/0.39 thf(h17,assumption,sP19,introduced(assumption,[])).
% 0.14/0.39 thf(h18,assumption,(~(sP27)),introduced(assumption,[])).
% 0.14/0.39 thf(17,plain,((~(sP4) | ~(sP5)) | sP27),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(18,plain,(sP9 | sP4),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(19,plain,(~(sP7) | sP12),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(20,plain,((~(sP12) | ~(sP14)) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(21,plain,(~(sP26) | sP10),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(22,plain,((~(sP10) | ~(sP19)) | sP5),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(23,plain,(~(sP15) | sP3),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(24,plain,(~(sP3) | sP13),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(25,plain,(~(sP13) | sP17),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(26,plain,((~(sP17) | sP16) | sP14),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(27,plain,((~(sP16) | ~(sP25)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(28,plain,$false,inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h8,h5,h6,h4,h2,h3,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,12,h2,h5,h14,h17,h18])).
% 0.14/0.39 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,28,h17,h18])).
% 0.14/0.39 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h15,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,29,h16])).
% 0.14/0.39 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h8,30,h14,h15])).
% 0.14/0.39 thf(32,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,16,31,h7,h8])).
% 0.14/0.39 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,32,h5,h6])).
% 0.14/0.39 thf(34,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,33,h4])).
% 0.14/0.39 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,34,h2,h3])).
% 0.14/0.39 thf(36,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,35,h1])).
% 0.14/0.39 thf(0,theorem,(![X1:$i]:((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((p @ X2))))) => (q @ X2)))))) => (~(((~((~((q @ X2))))) => (p @ X2))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3)))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[36,h0])).
% 0.14/0.39 % SZS output end Proof
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