TSTP Solution File: SYO449^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO449^1 : 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 : n021.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 19:32:08 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO449^1 : 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
% 0.12/0.33 % Computer : n021.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 18:05:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: mode213
% 0.20/0.46 % Inferences: 1254
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 thf(ty_p, type, p : ($i>$o)).
% 0.20/0.46 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.20/0.46 thf(ty_q, type, q : ($i>$o)).
% 0.20/0.46 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.20/0.46 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.20/0.46 thf(ty_eigen__4, type, eigen__4 : $i).
% 0.20/0.46 thf(ty_eigen__5, type, eigen__5 : $i).
% 0.20/0.46 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.20/0.46 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)).
% 0.20/0.46 thf(sP1,plain,sP1 <=> ((rel_s5 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.46 thf(sP2,plain,sP2 <=> ((rel_s5 @ eigen__1) @ eigen__4),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.46 thf(sP3,plain,sP3 <=> ((rel_s5 @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.46 thf(sP4,plain,sP4 <=> (((rel_s5 @ eigen__3) @ eigen__2) => (~((p @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.46 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.46 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__5) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__5) @ X2)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.46 thf(sP7,plain,sP7 <=> (![X1:$i]:((~((((rel_s5 @ eigen__5) @ eigen__1) => (~(((rel_s5 @ eigen__1) @ X1)))))) => ((rel_s5 @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.46 thf(sP8,plain,sP8 <=> (((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.46 thf(sP9,plain,sP9 <=> ((rel_s5 @ eigen__5) @ eigen__1),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.46 thf(sP10,plain,sP10 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.20/0.46 thf(sP11,plain,sP11 <=> ((p @ eigen__5) => (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (q @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.20/0.46 thf(sP12,plain,sP12 <=> (((rel_s5 @ eigen__1) @ eigen__5) => sP11),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.20/0.46 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (q @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.20/0.46 thf(sP14,plain,sP14 <=> ((rel_s5 @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.20/0.46 thf(sP15,plain,sP15 <=> (sP2 => (~(((rel_s5 @ eigen__4) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.20/0.46 thf(sP16,plain,sP16 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => ((p @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.20/0.46 thf(sP17,plain,sP17 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => ((rel_s5 @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.20/0.46 thf(sP18,plain,sP18 <=> (((rel_s5 @ eigen__1) @ eigen__5) => sP9),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.20/0.46 thf(sP19,plain,sP19 <=> (q @ eigen__4),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.20/0.46 thf(sP20,plain,sP20 <=> (((rel_s5 @ eigen__1) @ eigen__2) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.20/0.46 thf(sP21,plain,sP21 <=> ((rel_s5 @ eigen__1) @ eigen__5),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.20/0.46 thf(sP22,plain,sP22 <=> (![X1:$i]:((~((((rel_s5 @ eigen__3) @ eigen__0) => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.20/0.46 thf(sP23,plain,sP23 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__3) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.20/0.46 thf(sP24,plain,sP24 <=> ((~((sP9 => (~(sP2))))) => sP3),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.20/0.46 thf(sP25,plain,sP25 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.20/0.46 thf(sP26,plain,sP26 <=> (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.20/0.46 thf(sP27,plain,sP27 <=> (![X1:$i]:((~((((rel_s5 @ eigen__1) @ eigen__2) => (~(((rel_s5 @ eigen__2) @ X1)))))) => ((rel_s5 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.20/0.46 thf(sP28,plain,sP28 <=> (((rel_s5 @ eigen__1) @ eigen__3) => ((~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((p @ X1))))))) => (q @ eigen__3))),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.20/0.46 thf(sP29,plain,sP29 <=> ((rel_s5 @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.20/0.46 thf(sP30,plain,sP30 <=> (((rel_s5 @ eigen__0) @ eigen__2) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.20/0.46 thf(sP31,plain,sP31 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP31])])).
% 0.20/0.46 thf(sP32,plain,sP32 <=> ((~(sP20)) => ((rel_s5 @ eigen__1) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP32])])).
% 0.20/0.46 thf(sP33,plain,sP33 <=> ((~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((p @ X1))))))) => (q @ eigen__3)),introduced(definition,[new_symbols(definition,[sP33])])).
% 0.20/0.46 thf(sP34,plain,sP34 <=> (p @ eigen__2),introduced(definition,[new_symbols(definition,[sP34])])).
% 0.20/0.46 thf(sP35,plain,sP35 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP35])])).
% 0.20/0.46 thf(sP36,plain,sP36 <=> (q @ eigen__3),introduced(definition,[new_symbols(definition,[sP36])])).
% 0.20/0.46 thf(sP37,plain,sP37 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP37])])).
% 0.20/0.46 thf(sP38,plain,sP38 <=> ((~(sP15)) => sP21),introduced(definition,[new_symbols(definition,[sP38])])).
% 0.20/0.46 thf(sP39,plain,sP39 <=> (p @ eigen__5),introduced(definition,[new_symbols(definition,[sP39])])).
% 0.20/0.46 thf(sP40,plain,sP40 <=> (sP25 => (~(((rel_s5 @ eigen__1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP40])])).
% 0.20/0.46 thf(sP41,plain,sP41 <=> (sP9 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP41])])).
% 0.20/0.46 thf(sP42,plain,sP42 <=> ((~(sP8)) => sP14),introduced(definition,[new_symbols(definition,[sP42])])).
% 0.20/0.46 thf(sP43,plain,sP43 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP43])])).
% 0.20/0.46 thf(sP44,plain,sP44 <=> ((~(sP30)) => sP10),introduced(definition,[new_symbols(definition,[sP44])])).
% 0.20/0.46 thf(sP45,plain,sP45 <=> (![X1:$i]:((~((sP2 => (~(((rel_s5 @ eigen__4) @ X1)))))) => ((rel_s5 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP45])])).
% 0.20/0.46 thf(sP46,plain,sP46 <=> (sP10 => ((rel_s5 @ eigen__3) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP46])])).
% 0.20/0.46 thf(sP47,plain,sP47 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__1) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP47])])).
% 0.20/0.46 thf(sP48,plain,sP48 <=> ((~(sP40)) => sP35),introduced(definition,[new_symbols(definition,[sP48])])).
% 0.20/0.46 thf(sP49,plain,sP49 <=> (sP3 => sP19),introduced(definition,[new_symbols(definition,[sP49])])).
% 0.20/0.46 thf(sP50,plain,sP50 <=> ((rel_s5 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP50])])).
% 0.20/0.46 thf(sP51,plain,sP51 <=> ((rel_s5 @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP51])])).
% 0.20/0.46 thf(sP52,plain,sP52 <=> (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP52])])).
% 0.20/0.46 thf(sP53,plain,sP53 <=> (![X1:$i]:((~((sP35 => (~(((rel_s5 @ eigen__2) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP53])])).
% 0.20/0.46 thf(sP54,plain,sP54 <=> ((rel_s5 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP54])])).
% 0.20/0.46 thf(sP55,plain,sP55 <=> (![X1:$i]:((~((sP25 => (~(((rel_s5 @ eigen__1) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP55])])).
% 0.20/0.46 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.20/0.46 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.20/0.46 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.20/0.46 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.20/0.46 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.20/0.46 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.20/0.46 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.20/0.46 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.20/0.46 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.20/0.46 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.20/0.46 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.20/0.46 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.20/0.46 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.20/0.46 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.20/0.46 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.20/0.46 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.20/0.46 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.20/0.46 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.20/0.46 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.20/0.46 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.20/0.46 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.20/0.46 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.20/0.46 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)))))))).
% 0.20/0.46 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.20/0.46 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.20/0.46 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.20/0.46 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.20/0.46 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.20/0.46 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.20/0.46 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.20/0.46 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.20/0.46 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))).
% 0.20/0.46 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))).
% 0.20/0.46 thf(prove,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))))))) => (q @ X3)))))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((p @ X3))))) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4))))))))))) => (~(((~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((p @ X3))))) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4)))))))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))))))) => (q @ X3)))))))))))))).
% 0.20/0.46 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))) => (q @ X3)))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((p @ X3) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4))))))) => (~(((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((p @ X3) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4)))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))) => (q @ X3))))))))))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.20/0.46 thf(h1,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((p @ X3))))))) => (q @ X2)))) => (![X2:$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) => ((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => (~((p @ X3))))))) => (q @ X2)))))))))))))),introduced(assumption,[])).
% 0.20/0.46 thf(h2,assumption,(~((sP25 => (~(((sP13 => sP16) => (~((sP16 => sP13))))))))),introduced(assumption,[])).
% 0.20/0.46 thf(h3,assumption,sP25,introduced(assumption,[])).
% 0.20/0.46 thf(h4,assumption,((sP13 => sP16) => (~((sP16 => sP13)))),introduced(assumption,[])).
% 0.20/0.46 thf(h5,assumption,(~((sP13 => sP16))),introduced(assumption,[])).
% 0.20/0.46 thf(h6,assumption,(~((sP16 => sP13))),introduced(assumption,[])).
% 0.20/0.46 thf(h7,assumption,sP13,introduced(assumption,[])).
% 0.20/0.46 thf(h8,assumption,(~(sP16)),introduced(assumption,[])).
% 0.20/0.46 thf(h9,assumption,(~((sP54 => (sP34 => (![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (q @ X1))))))),introduced(assumption,[])).
% 0.20/0.46 thf(h10,assumption,sP54,introduced(assumption,[])).
% 0.20/0.46 thf(h11,assumption,(~((sP34 => (![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (q @ X1)))))),introduced(assumption,[])).
% 0.20/0.46 thf(h12,assumption,sP34,introduced(assumption,[])).
% 0.20/0.46 thf(h13,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__2) @ X1) => (q @ X1))))),introduced(assumption,[])).
% 0.20/0.46 thf(h14,assumption,(~((sP1 => sP36))),introduced(assumption,[])).
% 0.20/0.46 thf(h15,assumption,sP1,introduced(assumption,[])).
% 0.20/0.46 thf(h16,assumption,(~(sP36)),introduced(assumption,[])).
% 0.20/0.46 thf(1,plain,(~(sP5) | sP31),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(2,plain,(~(sP31) | sP46),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(3,plain,((~(sP46) | ~(sP10)) | sP51),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(4,plain,(~(sP37) | sP53),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(5,plain,(~(sP53) | sP44),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(6,plain,((~(sP44) | sP30) | sP10),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(7,plain,((~(sP30) | ~(sP35)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(8,plain,(~(sP22) | sP42),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(9,plain,((~(sP42) | sP8) | sP14),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(10,plain,((~(sP8) | ~(sP51)) | ~(sP35)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(11,plain,(~(sP23) | sP22),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(12,plain,(~(sP43) | sP37),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(13,plain,(~(sP37) | sP55),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(14,plain,(~(sP55) | sP48),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(15,plain,((~(sP48) | sP40) | sP35),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(16,plain,((~(sP40) | ~(sP25)) | ~(sP54)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(17,plain,(~(sP27) | sP32),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(18,plain,((~(sP32) | sP20) | sP50),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(19,plain,((~(sP20) | ~(sP54)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(20,plain,(~(sP43) | sP23),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(21,plain,(~(sP43) | sP47),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(22,plain,(~(sP47) | sP27),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(23,plain,(~(sP52) | sP4),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(24,plain,((~(sP4) | ~(sP14)) | ~(sP34)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(25,plain,(~(sP13) | sP28),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(26,plain,((~(sP28) | ~(sP50)) | sP33),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(27,plain,((~(sP33) | sP52) | sP36),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(a2,axiom,(mtransitive @ rel_s5)).
% 0.20/0.46 thf(28,plain,sP43,inference(preprocess,[status(thm)],[a2]).
% 0.20/0.46 thf(a3,axiom,(msymmetric @ rel_s5)).
% 0.20/0.46 thf(29,plain,sP5,inference(preprocess,[status(thm)],[a3]).
% 0.20/0.46 thf(30,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,h3,h7,h10,h12,h15,h16])).
% 0.20/0.46 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h7,h8,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,30,h15,h16])).
% 0.20/0.46 thf(32,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,31,h14])).
% 0.20/0.46 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,32,h12,h13])).
% 0.20/0.46 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,33,h10,h11])).
% 0.20/0.46 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,34,h9])).
% 0.20/0.46 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,35,h7,h8])).
% 0.20/0.46 thf(h17,assumption,sP16,introduced(assumption,[])).
% 0.20/0.46 thf(h18,assumption,(~(sP13)),introduced(assumption,[])).
% 0.20/0.46 thf(h19,assumption,(~((sP2 => ((~((![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (~((p @ X1))))))) => sP19)))),introduced(assumption,[])).
% 0.20/0.46 thf(h20,assumption,sP2,introduced(assumption,[])).
% 0.20/0.46 thf(h21,assumption,(~(((~((![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (~((p @ X1))))))) => sP19))),introduced(assumption,[])).
% 0.20/0.46 thf(h22,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__4) @ X1) => (~((p @ X1))))))),introduced(assumption,[])).
% 0.20/0.46 thf(h23,assumption,(~(sP19)),introduced(assumption,[])).
% 0.20/0.46 thf(h24,assumption,(~((sP29 => (~(sP39))))),introduced(assumption,[])).
% 0.20/0.46 thf(h25,assumption,sP29,introduced(assumption,[])).
% 0.20/0.46 thf(h26,assumption,sP39,introduced(assumption,[])).
% 0.20/0.46 thf(37,plain,(~(sP17) | sP18),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(38,plain,((~(sP18) | ~(sP21)) | sP9),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(39,plain,(~(sP5) | sP17),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(40,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(41,plain,(~(sP7) | sP24),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(42,plain,((~(sP24) | sP41) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(43,plain,((~(sP41) | ~(sP9)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(44,plain,(~(sP43) | sP6),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(45,plain,(~(sP26) | sP49),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(46,plain,((~(sP49) | ~(sP3)) | sP19),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(47,plain,(~(sP16) | sP12),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(48,plain,((~(sP12) | ~(sP21)) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(49,plain,((~(sP11) | ~(sP39)) | sP26),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(50,plain,(~(sP43) | sP47),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(51,plain,(~(sP47) | sP45),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(52,plain,(~(sP45) | sP38),inference(all_rule,[status(thm)],[])).
% 0.20/0.46 thf(53,plain,((~(sP38) | sP15) | sP21),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(54,plain,((~(sP15) | ~(sP2)) | ~(sP29)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.46 thf(55,plain,$false,inference(prop_unsat,[status(thm),assumptions([h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h6,h3,h4,h2,h1,h0])],[37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,28,29,h17,h20,h25,h26,h23])).
% 0.20/0.46 thf(56,plain,$false,inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h20,h21,h19,h17,h18,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,55,h25,h26])).
% 0.20/0.46 thf(57,plain,$false,inference(tab_negall,[status(thm),assumptions([h22,h23,h20,h21,h19,h17,h18,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__5)],[h22,56,h24])).
% 0.20/0.46 thf(58,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h17,h18,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,57,h22,h23])).
% 0.20/0.46 thf(59,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,58,h20,h21])).
% 0.20/0.46 thf(60,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h18,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h18,59,h19])).
% 0.20/0.46 thf(61,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h6,60,h17,h18])).
% 0.20/0.46 thf(62,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,36,61,h5,h6])).
% 0.20/0.46 thf(63,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,62,h3,h4])).
% 0.20/0.46 thf(64,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,63,h2])).
% 0.20/0.46 thf(65,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,64,h1])).
% 0.20/0.46 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))))))) => (q @ X3)))))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((p @ X3))))) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4))))))))))) => (~(((~((~((![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((p @ X3))))) => (![X4:$i]:(((rel_s5 @ X3) @ X4) => (q @ X4)))))))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => ((~((~((~((![X4:$i]:(((rel_s5 @ X3) @ X4) => (~((p @ X4))))))))))) => (q @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[65,h0])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------