TSTP Solution File: SYO445^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO445^1 : 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 : n028.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 19:32:07 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO445^1 : 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 : n028.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 : Fri Jul 8 19:59:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: mode213
% 0.20/0.40 % Inferences: 113
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 thf(ty_p, type, p : ($i>$o)).
% 0.20/0.40 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.20/0.40 thf(ty_q, type, q : ($i>$o)).
% 0.20/0.40 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.20/0.40 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.20/0.40 thf(ty_eigen__4, type, eigen__4 : $i).
% 0.20/0.40 thf(ty_eigen__5, type, eigen__5 : $i).
% 0.20/0.40 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.20/0.40 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)).
% 0.20/0.40 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.20/0.40 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((rel_s5 @ eigen__4) @ X1) => (~((q @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 0.20/0.40 thf(sP1,plain,sP1 <=> (p @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.40 thf(sP2,plain,sP2 <=> ((~((((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__2)))))) => ((rel_s5 @ eigen__3) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.40 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.40 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((~((p @ X1))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.40 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.40 thf(sP6,plain,sP6 <=> (p @ eigen__4),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.40 thf(sP7,plain,sP7 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.40 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.40 thf(sP9,plain,sP9 <=> (((rel_s5 @ eigen__4) @ eigen__5) => (~((q @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.40 thf(sP10,plain,sP10 <=> (![X1:$i]:((~((((rel_s5 @ eigen__0) @ eigen__4) => (~(((rel_s5 @ eigen__4) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.20/0.40 thf(sP11,plain,sP11 <=> (((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.20/0.40 thf(sP12,plain,sP12 <=> ((rel_s5 @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.20/0.40 thf(sP13,plain,sP13 <=> ((~(sP6)) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.20/0.40 thf(sP14,plain,sP14 <=> (((rel_s5 @ eigen__0) @ eigen__3) => ((rel_s5 @ eigen__3) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.20/0.40 thf(sP15,plain,sP15 <=> ((~((((rel_s5 @ eigen__0) @ eigen__4) => (~(((rel_s5 @ eigen__4) @ eigen__5)))))) => sP12),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.20/0.40 thf(sP16,plain,sP16 <=> (((rel_s5 @ eigen__0) @ eigen__4) => (~(((rel_s5 @ eigen__4) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.20/0.40 thf(sP17,plain,sP17 <=> ((rel_s5 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.20/0.40 thf(sP18,plain,sP18 <=> ((rel_s5 @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.20/0.40 thf(sP19,plain,sP19 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.20/0.40 thf(sP20,plain,sP20 <=> (sP12 => (~((q @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.20/0.40 thf(sP21,plain,sP21 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.20/0.40 thf(sP22,plain,sP22 <=> (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.20/0.40 thf(sP23,plain,sP23 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.20/0.40 thf(sP24,plain,sP24 <=> (q @ eigen__5),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.20/0.40 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((q @ X1))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.20/0.40 thf(sP26,plain,sP26 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.20/0.40 thf(sP27,plain,sP27 <=> (sP26 => sP1),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.20/0.40 thf(sP28,plain,sP28 <=> (q @ eigen__2),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.20/0.40 thf(sP29,plain,sP29 <=> ((rel_s5 @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.20/0.40 thf(sP30,plain,sP30 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__3) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.20/0.40 thf(sP31,plain,sP31 <=> (((rel_s5 @ eigen__3) @ eigen__2) => (~(sP28))),introduced(definition,[new_symbols(definition,[sP31])])).
% 0.20/0.40 thf(sP32,plain,sP32 <=> ((rel_s5 @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP32])])).
% 0.20/0.40 thf(sP33,plain,sP33 <=> (![X1:$i]:((~((sP18 => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP33])])).
% 0.20/0.40 thf(sP34,plain,sP34 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP34])])).
% 0.20/0.40 thf(sP35,plain,sP35 <=> (sP17 => sP13),introduced(definition,[new_symbols(definition,[sP35])])).
% 0.20/0.40 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.20/0.40 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.20/0.40 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.20/0.40 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.20/0.40 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.20/0.40 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.20/0.40 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.20/0.40 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.20/0.40 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.20/0.40 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.20/0.40 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.20/0.40 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.20/0.40 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.20/0.40 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.20/0.40 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.20/0.40 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.20/0.40 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.20/0.40 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.20/0.40 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.20/0.40 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.20/0.40 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.20/0.40 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.20/0.40 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)))))))).
% 0.20/0.40 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.20/0.40 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.20/0.40 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.20/0.40 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.20/0.40 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.20/0.40 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.20/0.40 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.20/0.40 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.20/0.40 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))).
% 0.20/0.40 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))).
% 0.20/0.40 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3))))))))))))))) => (~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3)))))))))))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))))))))).
% 0.20/0.40 thf(h1,negated_conjecture,(~((![X1:$i]:(~(((((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3))))))))))) => (~(((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3)))))))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2))))))))))))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.20/0.40 thf(h2,assumption,((((~(sP34)) => (~(sP25))) => sP4) => (~((sP4 => ((~(sP34)) => (~(sP25))))))),introduced(assumption,[])).
% 0.20/0.40 thf(h3,assumption,(~((((~(sP34)) => (~(sP25))) => sP4))),introduced(assumption,[])).
% 0.20/0.40 thf(h4,assumption,(~((sP4 => ((~(sP34)) => (~(sP25)))))),introduced(assumption,[])).
% 0.20/0.40 thf(h5,assumption,((~(sP34)) => (~(sP25))),introduced(assumption,[])).
% 0.20/0.40 thf(h6,assumption,(~(sP4)),introduced(assumption,[])).
% 0.20/0.40 thf(h7,assumption,sP34,introduced(assumption,[])).
% 0.20/0.40 thf(h8,assumption,(~(sP25)),introduced(assumption,[])).
% 0.20/0.40 thf(h9,assumption,(~((sP26 => ((~(sP1)) => (~((![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (~((q @ X1))))))))))),introduced(assumption,[])).
% 0.20/0.40 thf(h10,assumption,sP26,introduced(assumption,[])).
% 0.20/0.40 thf(h11,assumption,(~(((~(sP1)) => (~((![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (~((q @ X1)))))))))),introduced(assumption,[])).
% 0.20/0.40 thf(h12,assumption,(~(sP1)),introduced(assumption,[])).
% 0.20/0.40 thf(h13,assumption,(![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (~((q @ X1))))),introduced(assumption,[])).
% 0.20/0.40 thf(1,plain,(~(sP34) | sP27),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(2,plain,((~(sP27) | ~(sP26)) | sP1),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(3,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h5,h6,h3,h2,h1,h0])],[1,2,h7,h10,h12])).
% 0.20/0.40 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,3,h12,h13])).
% 0.20/0.40 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11])).
% 0.20/0.40 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h6,5,h9])).
% 0.20/0.40 thf(h14,assumption,(~((sP21 => (~(sP28))))),introduced(assumption,[])).
% 0.20/0.40 thf(h15,assumption,sP21,introduced(assumption,[])).
% 0.20/0.40 thf(h16,assumption,sP28,introduced(assumption,[])).
% 0.20/0.40 thf(h17,assumption,(~((sP23 => ((~((p @ eigen__3))) => (~(sP22)))))),introduced(assumption,[])).
% 0.20/0.40 thf(h18,assumption,sP23,introduced(assumption,[])).
% 0.20/0.40 thf(h19,assumption,(~(((~((p @ eigen__3))) => (~(sP22))))),introduced(assumption,[])).
% 0.20/0.40 thf(h20,assumption,(~((p @ eigen__3))),introduced(assumption,[])).
% 0.20/0.40 thf(h21,assumption,sP22,introduced(assumption,[])).
% 0.20/0.40 thf(7,plain,(~(sP7) | sP3),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(8,plain,(~(sP3) | sP14),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(9,plain,((~(sP14) | ~(sP23)) | sP18),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(10,plain,(~(sP19) | sP30),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(11,plain,(~(sP30) | sP33),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(12,plain,(~(sP33) | sP2),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(13,plain,((~(sP2) | sP11) | sP32),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(14,plain,((~(sP11) | ~(sP18)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(15,plain,(~(sP22) | sP31),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(16,plain,((~(sP31) | ~(sP32)) | ~(sP28)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(a2,axiom,(mtransitive @ rel_s5)).
% 0.20/0.40 thf(17,plain,sP19,inference(preprocess,[status(thm)],[a2]).
% 0.20/0.40 thf(a3,axiom,(msymmetric @ rel_s5)).
% 0.20/0.40 thf(18,plain,sP7,inference(preprocess,[status(thm)],[a3]).
% 0.20/0.40 thf(19,plain,$false,inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h19,h17,h15,h16,h14,h8,h5,h6,h3,h2,h1,h0])],[7,8,9,10,11,12,13,14,15,16,17,18,h15,h16,h18,h21])).
% 0.20/0.40 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h8,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,19,h20,h21])).
% 0.20/0.40 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h8,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,20,h18,h19])).
% 0.20/0.40 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h8,h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__3)],[h6,21,h17])).
% 0.20/0.40 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h8,h5,h6,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,22,h15,h16])).
% 0.20/0.40 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__2)],[h8,23,h14])).
% 0.20/0.40 thf(25,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,6,24,h7,h8])).
% 0.20/0.40 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,25,h5,h6])).
% 0.20/0.40 thf(h22,assumption,sP4,introduced(assumption,[])).
% 0.20/0.40 thf(h23,assumption,(~(((~(sP34)) => (~(sP25))))),introduced(assumption,[])).
% 0.20/0.40 thf(h24,assumption,(~(sP34)),introduced(assumption,[])).
% 0.20/0.40 thf(h25,assumption,sP25,introduced(assumption,[])).
% 0.20/0.40 thf(h26,assumption,(~((sP17 => sP6))),introduced(assumption,[])).
% 0.20/0.40 thf(h27,assumption,sP17,introduced(assumption,[])).
% 0.20/0.40 thf(h28,assumption,(~(sP6)),introduced(assumption,[])).
% 0.20/0.40 thf(27,plain,(~(sP25) | sP20),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(28,plain,((~(sP20) | ~(sP12)) | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(29,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(30,plain,((~(sP15) | sP16) | sP12),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(31,plain,((~(sP16) | ~(sP17)) | ~(sP29)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(32,plain,(sP9 | sP24),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(33,plain,(sP9 | sP29),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(34,plain,(sP8 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])).
% 0.20/0.40 thf(35,plain,(~(sP19) | sP5),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(36,plain,(~(sP5) | sP10),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(37,plain,(~(sP4) | sP35),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(38,plain,((~(sP35) | ~(sP17)) | sP13),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(39,plain,((~(sP13) | sP6) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(40,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h22,h23,h4,h2,h1,h0])],[27,28,29,30,31,32,33,34,35,36,37,38,39,17,h22,h27,h28,h25])).
% 0.20/0.40 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h22,h23,h4,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,40,h27,h28])).
% 0.20/0.40 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h22,h23,h4,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__4)],[h24,41,h26])).
% 0.20/0.40 thf(43,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h23,h4,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,42,h24,h25])).
% 0.20/0.40 thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h4,43,h22,h23])).
% 0.20/0.40 thf(45,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,26,44,h3,h4])).
% 0.20/0.40 thf(46,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,45,h2])).
% 0.20/0.40 thf(47,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[46,h0])).
% 0.20/0.40 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2)))))))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3))))))))))))))) => (~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((p @ X2))) => (~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((q @ X3)))))))))))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (p @ X2))))) => (~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((q @ X2))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[46,h1])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------