TSTP Solution File: SYN367^7 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN367^7 : TPTP v8.1.0. Released v5.5.0.
% 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 11:43:10 EDT 2022
% Result : Theorem 9.48s 9.91s
% Output : Proof 9.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN367^7 : TPTP v8.1.0. Released v5.5.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jul 11 19:38:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.48/9.91 % SZS status Theorem
% 9.48/9.91 % Mode: mode506
% 9.48/9.91 % Inferences: 61979
% 9.48/9.91 % SZS output start Proof
% 9.48/9.91 thf(ty_mu, type, mu : $tType).
% 9.48/9.91 thf(ty_p, type, p : ($i>$o)).
% 9.48/9.91 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 9.48/9.91 thf(ty_eigen__2, type, eigen__2 : $i).
% 9.48/9.91 thf(ty_eigen__15, type, eigen__15 : mu).
% 9.48/9.91 thf(ty_eigen__1, type, eigen__1 : $i).
% 9.48/9.91 thf(ty_eigen__0, type, eigen__0 : $i).
% 9.48/9.91 thf(ty_eigen__3, type, eigen__3 : mu).
% 9.48/9.91 thf(ty_eigen__10, type, eigen__10 : $i).
% 9.48/9.91 thf(ty_eigen__8, type, eigen__8 : $i).
% 9.48/9.91 thf(ty_eigen__20, type, eigen__20 : $i).
% 9.48/9.91 thf(ty_eigen__9, type, eigen__9 : mu).
% 9.48/9.91 thf(ty_big_q, type, big_q : (mu>$i>$o)).
% 9.48/9.91 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 9.48/9.91 thf(ty_big_r, type, big_r : (mu>$i>$o)).
% 9.48/9.91 thf(h0, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 9.48/9.91 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_r @ X1) @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 9.48/9.91 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 9.48/9.91 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (((![X4:$i]:(((rel_s4 @ X2) @ X4) => (p @ X4))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4)))))) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (p @ X5))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4))))))))))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 9.48/9.91 thf(eigendef_eigen__15, definition, eigen__15 = (eps__0 @ (^[X1:mu]:(~((~(((exists_in_world @ X1) @ eigen__1))))))), introduced(definition,[new_symbols(definition,[eigen__15])])).
% 9.48/9.91 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 9.48/9.91 thf(eigendef_eigen__10, definition, eigen__10 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__8) @ X1) => ((big_q @ eigen__9) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 9.48/9.91 thf(eigendef_eigen__8, definition, eigen__8 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3)))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 9.48/9.91 thf(eigendef_eigen__2, definition, eigen__2 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3)))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 9.48/9.91 thf(eigendef_eigen__20, definition, eigen__20 = (eps__1 @ (^[X1:$i]:(~((((rel_s4 @ eigen__10) @ X1) => (p @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__20])])).
% 9.48/9.91 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__8) => (![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_q @ X1) @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__9])])).
% 9.48/9.91 thf(sP1,plain,sP1 <=> (![X1:$i]:(~((![X2:mu]:(~(((exists_in_world @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 9.48/9.91 thf(sP2,plain,sP2 <=> (((rel_s4 @ eigen__1) @ eigen__20) => (p @ eigen__20)),introduced(definition,[new_symbols(definition,[sP2])])).
% 9.48/9.91 thf(sP3,plain,sP3 <=> (![X1:$i]:((~((((rel_s4 @ eigen__1) @ eigen__10) => (~(((rel_s4 @ eigen__10) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 9.48/9.91 thf(sP4,plain,sP4 <=> (((rel_s4 @ eigen__0) @ eigen__1) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (((![X3:$i]:(((rel_s4 @ X1) @ X3) => (p @ X3))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3)))))) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))))))))) => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 9.48/9.91 thf(sP5,plain,sP5 <=> ((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_q @ eigen__9) @ X1)))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 9.48/9.91 thf(sP6,plain,sP6 <=> ((rel_s4 @ eigen__1) @ eigen__10),introduced(definition,[new_symbols(definition,[sP6])])).
% 9.48/9.91 thf(sP7,plain,sP7 <=> (((rel_s4 @ eigen__1) @ eigen__8) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__8) => (((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_r @ X1) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 9.48/9.91 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (((![X3:$i]:(((rel_s4 @ X1) @ X3) => (p @ X3))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3)))))) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (p @ X4))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 9.48/9.91 thf(sP9,plain,sP9 <=> (![X1:mu]:(~(((exists_in_world @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 9.48/9.91 thf(sP10,plain,sP10 <=> (((rel_s4 @ eigen__1) @ eigen__8) => (~(((rel_s4 @ eigen__8) @ eigen__10)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 9.48/9.91 thf(sP11,plain,sP11 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 9.48/9.91 thf(sP12,plain,sP12 <=> (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 9.48/9.91 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_q @ eigen__9) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 9.48/9.91 thf(sP14,plain,sP14 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__1) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP14])])).
% 9.48/9.91 thf(sP15,plain,sP15 <=> (((rel_s4 @ eigen__1) @ eigen__2) => sP11),introduced(definition,[new_symbols(definition,[sP15])])).
% 9.48/9.91 thf(sP16,plain,sP16 <=> (![X1:$i]:((~((((rel_s4 @ eigen__1) @ eigen__8) => (~(((rel_s4 @ eigen__8) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP16])])).
% 9.48/9.91 thf(sP17,plain,sP17 <=> (((exists_in_world @ eigen__15) @ eigen__1) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_q @ eigen__15) @ X1)))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__15) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 9.48/9.91 thf(sP18,plain,sP18 <=> (sP5 => (~((sP12 => (~((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_r @ eigen__9) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 9.48/9.91 thf(sP19,plain,sP19 <=> (((exists_in_world @ eigen__9) @ eigen__8) => sP13),introduced(definition,[new_symbols(definition,[sP19])])).
% 9.48/9.91 thf(sP20,plain,sP20 <=> (((rel_s4 @ eigen__8) @ eigen__10) => ((big_q @ eigen__9) @ eigen__10)),introduced(definition,[new_symbols(definition,[sP20])])).
% 9.48/9.91 thf(sP21,plain,sP21 <=> ((~((sP6 => (~(((rel_s4 @ eigen__10) @ eigen__20)))))) => ((rel_s4 @ eigen__1) @ eigen__20)),introduced(definition,[new_symbols(definition,[sP21])])).
% 9.48/9.91 thf(sP22,plain,sP22 <=> ((rel_s4 @ eigen__1) @ eigen__20),introduced(definition,[new_symbols(definition,[sP22])])).
% 9.48/9.91 thf(sP23,plain,sP23 <=> ((rel_s4 @ eigen__10) @ eigen__20),introduced(definition,[new_symbols(definition,[sP23])])).
% 9.48/9.91 thf(sP24,plain,sP24 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (((![X4:$i]:(((rel_s4 @ X2) @ X4) => (p @ X4))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4)))))) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (p @ X5))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4))))))))))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_q @ X3) @ X4))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_r @ X3) @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 9.48/9.91 thf(sP25,plain,sP25 <=> (((rel_s4 @ eigen__1) @ eigen__1) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_r @ X1) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 9.48/9.91 thf(sP26,plain,sP26 <=> (sP23 => (p @ eigen__20)),introduced(definition,[new_symbols(definition,[sP26])])).
% 9.48/9.91 thf(sP27,plain,sP27 <=> (((exists_in_world @ eigen__3) @ eigen__2) => (((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_q @ eigen__3) @ X1)))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_r @ eigen__3) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 9.48/9.91 thf(sP28,plain,sP28 <=> (sP6 => (~(sP23))),introduced(definition,[new_symbols(definition,[sP28])])).
% 9.48/9.91 thf(sP29,plain,sP29 <=> ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_q @ eigen__15) @ X1)))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 9.48/9.91 thf(sP30,plain,sP30 <=> (((exists_in_world @ eigen__3) @ eigen__2) => (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_r @ eigen__3) @ X1)))),introduced(definition,[new_symbols(definition,[sP30])])).
% 9.48/9.91 thf(sP31,plain,sP31 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_r @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP31])])).
% 9.48/9.91 thf(sP32,plain,sP32 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__8) => (((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_q @ X1) @ X2)))))) => (~((sP12 => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP32])])).
% 9.48/9.91 thf(sP33,plain,sP33 <=> (((rel_s4 @ eigen__8) @ eigen__10) => (~((![X1:$i]:(((rel_s4 @ eigen__10) @ X1) => (p @ X1)))))),introduced(definition,[new_symbols(definition,[sP33])])).
% 9.48/9.91 thf(sP34,plain,sP34 <=> ((exists_in_world @ eigen__15) @ eigen__1),introduced(definition,[new_symbols(definition,[sP34])])).
% 9.48/9.91 thf(sP35,plain,sP35 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_r @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP35])])).
% 9.48/9.91 thf(sP36,plain,sP36 <=> (sP8 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => sP35)),introduced(definition,[new_symbols(definition,[sP36])])).
% 9.48/9.91 thf(sP37,plain,sP37 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP37])])).
% 9.48/9.91 thf(sP38,plain,sP38 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))))) => sP35),introduced(definition,[new_symbols(definition,[sP38])])).
% 9.48/9.91 thf(sP39,plain,sP39 <=> (![X1:$i]:(((rel_s4 @ eigen__10) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP39])])).
% 9.48/9.91 thf(sP40,plain,sP40 <=> (p @ eigen__20),introduced(definition,[new_symbols(definition,[sP40])])).
% 9.48/9.91 thf(sP41,plain,sP41 <=> ((sP37 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_q @ eigen__3) @ X1)))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~(sP31)))))),introduced(definition,[new_symbols(definition,[sP41])])).
% 9.48/9.91 thf(sP42,plain,sP42 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_q @ X1) @ X2)))))) => (~(((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((big_r @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP42])])).
% 9.48/9.91 thf(sP43,plain,sP43 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__2) => (![X2:$i]:(((rel_s4 @ eigen__2) @ X2) => ((big_r @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP43])])).
% 9.48/9.91 thf(sP44,plain,sP44 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP44])])).
% 9.48/9.91 thf(sP45,plain,sP45 <=> ((~(sP10)) => sP6),introduced(definition,[new_symbols(definition,[sP45])])).
% 9.48/9.91 thf(sP46,plain,sP46 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__8) => (![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_q @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP46])])).
% 9.48/9.91 thf(sP47,plain,sP47 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5)))))))))))),introduced(definition,[new_symbols(definition,[sP47])])).
% 9.48/9.91 thf(sP48,plain,sP48 <=> (((rel_s4 @ eigen__1) @ eigen__8) => sP46),introduced(definition,[new_symbols(definition,[sP48])])).
% 9.48/9.91 thf(sP49,plain,sP49 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP49])])).
% 9.48/9.91 thf(sP50,plain,sP50 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))),introduced(definition,[new_symbols(definition,[sP50])])).
% 9.48/9.91 thf(sP51,plain,sP51 <=> (sP29 => (~((sP50 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__15) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP51])])).
% 9.48/9.91 thf(sP52,plain,sP52 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_q @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP52])])).
% 9.48/9.91 thf(sP53,plain,sP53 <=> (sP50 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((big_r @ eigen__15) @ X1)))))),introduced(definition,[new_symbols(definition,[sP53])])).
% 9.48/9.91 thf(sP54,plain,sP54 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP54])])).
% 9.48/9.91 thf(sP55,plain,sP55 <=> ((exists_in_world @ eigen__9) @ eigen__8),introduced(definition,[new_symbols(definition,[sP55])])).
% 9.48/9.91 thf(sP56,plain,sP56 <=> (sP12 => (~((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_r @ eigen__9) @ X1)))))),introduced(definition,[new_symbols(definition,[sP56])])).
% 9.48/9.91 thf(sP57,plain,sP57 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP57])])).
% 9.48/9.91 thf(sP58,plain,sP58 <=> (sP57 => sP43),introduced(definition,[new_symbols(definition,[sP58])])).
% 9.48/9.91 thf(sP59,plain,sP59 <=> ((rel_s4 @ eigen__1) @ eigen__8),introduced(definition,[new_symbols(definition,[sP59])])).
% 9.48/9.91 thf(sP60,plain,sP60 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP60])])).
% 9.48/9.91 thf(sP61,plain,sP61 <=> (sP57 => (~(sP37))),introduced(definition,[new_symbols(definition,[sP61])])).
% 9.48/9.91 thf(sP62,plain,sP62 <=> (sP55 => sP18),introduced(definition,[new_symbols(definition,[sP62])])).
% 9.48/9.91 thf(sP63,plain,sP63 <=> (sP37 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((big_q @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP63])])).
% 9.48/9.91 thf(sP64,plain,sP64 <=> ((exists_in_world @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP64])])).
% 9.48/9.91 thf(sP65,plain,sP65 <=> ((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))))) => (~(sP31))),introduced(definition,[new_symbols(definition,[sP65])])).
% 9.48/9.91 thf(sP66,plain,sP66 <=> ((rel_s4 @ eigen__8) @ eigen__10),introduced(definition,[new_symbols(definition,[sP66])])).
% 9.48/9.91 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 9.48/9.91 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 9.48/9.91 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 9.48/9.91 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 9.48/9.91 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 9.48/9.91 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 9.48/9.91 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 9.48/9.91 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 9.48/9.91 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 9.48/9.91 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 9.48/9.91 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 9.48/9.91 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 9.48/9.91 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 9.48/9.91 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 9.48/9.91 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 9.48/9.91 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 9.48/9.91 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 9.48/9.91 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 9.48/9.91 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 9.48/9.91 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 9.48/9.91 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 9.48/9.91 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 9.48/9.91 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 9.48/9.91 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 9.48/9.91 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))))))))).
% 9.48/9.91 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 9.48/9.91 thf(def_mvalid,definition,(mvalid = (!!))).
% 9.48/9.91 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 9.48/9.91 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 9.48/9.91 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 9.48/9.91 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 9.48/9.91 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 9.48/9.91 thf(x2118,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => ((~((~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))))))) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))).
% 9.48/9.91 thf(h2,negated_conjecture,(~(sP47)),inference(assume_negation,[status(cth)],[x2118])).
% 9.48/9.91 thf(1,plain,(sP5 | sP13),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(2,plain,(~(sP12) | sP33),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(3,plain,((~(sP33) | ~(sP66)) | ~(sP39)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(4,plain,(~(sP3) | sP21),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(5,plain,((~(sP21) | sP28) | sP22),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(6,plain,((~(sP28) | ~(sP6)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(7,plain,(~(sP54) | sP2),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(8,plain,((~(sP2) | ~(sP22)) | sP40),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(9,plain,(sP26 | ~(sP40)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(10,plain,(sP26 | sP23),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(11,plain,(sP39 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__20])).
% 9.48/9.91 thf(12,plain,(~(sP16) | sP45),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(13,plain,((~(sP45) | sP10) | sP6),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(14,plain,((~(sP10) | ~(sP59)) | ~(sP66)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(15,plain,(sP56 | sP12),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(16,plain,((~(sP62) | ~(sP55)) | sP18),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(17,plain,((~(sP18) | ~(sP5)) | ~(sP56)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(18,plain,(~(sP32) | sP62),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(19,plain,(~(sP14) | sP16),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(20,plain,(~(sP8) | sP7),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(21,plain,((~(sP7) | ~(sP59)) | sP32),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(22,plain,(sP29 | sP54),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(23,plain,(sP53 | sP50),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(24,plain,(~(sP42) | sP17),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(25,plain,((~(sP17) | ~(sP34)) | sP51),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(26,plain,((~(sP51) | ~(sP29)) | ~(sP53)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(27,plain,(sP9 | sP34),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15])).
% 9.48/9.91 thf(28,plain,(~(sP14) | sP3),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(29,plain,(~(sP50) | sP61),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(30,plain,((~(sP61) | ~(sP57)) | ~(sP37)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(31,plain,(sP20 | sP66),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(32,plain,(sP13 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10])).
% 9.48/9.91 thf(33,plain,(sP19 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(34,plain,(sP19 | sP55),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(35,plain,(sP46 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])).
% 9.48/9.91 thf(36,plain,(sP48 | ~(sP46)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(37,plain,(sP48 | sP59),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(38,plain,((~(sP25) | ~(sP49)) | sP42),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(39,plain,(sP63 | sP37),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(40,plain,(sP65 | sP31),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(41,plain,(~(sP8) | sP25),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(42,plain,(~(sP11) | sP27),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(43,plain,((~(sP27) | ~(sP64)) | sP41),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(44,plain,((~(sP41) | ~(sP63)) | ~(sP65)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(45,plain,(~(sP8) | sP15),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(46,plain,((~(sP15) | ~(sP57)) | sP11),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(47,plain,(sP52 | ~(sP48)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8])).
% 9.48/9.91 thf(48,plain,(~(sP60) | sP14),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(49,plain,(~(sP44) | sP49),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(50,plain,(~(sP1) | ~(sP9)),inference(all_rule,[status(thm)],[])).
% 9.48/9.91 thf(51,plain,(sP30 | ~(sP31)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(52,plain,(sP30 | sP64),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(53,plain,(sP43 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 9.48/9.91 thf(54,plain,(sP58 | ~(sP43)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(55,plain,(sP58 | sP57),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(56,plain,(sP35 | ~(sP58)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2])).
% 9.48/9.91 thf(57,plain,(sP38 | ~(sP35)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(58,plain,(sP38 | ~(sP52)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(59,plain,(sP36 | ~(sP38)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(60,plain,(sP36 | sP8),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(61,plain,(sP4 | ~(sP36)),inference(prop_rule,[status(thm)],[])).
% 9.48/9.91 thf(62,plain,(sP24 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])).
% 9.48/9.91 thf(63,plain,(sP47 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])).
% 9.48/9.91 thf(a2,axiom,(mtransitive @ rel_s4)).
% 9.48/9.91 thf(64,plain,sP60,inference(preprocess,[status(thm)],[a2]).
% 9.48/9.91 thf(a1,axiom,(mreflexive @ rel_s4)).
% 9.48/9.91 thf(65,plain,sP44,inference(preprocess,[status(thm)],[a1]).
% 9.48/9.91 thf(nonempty_ax,axiom,sP1).
% 9.48/9.91 thf(66,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,nonempty_ax,h2])).
% 9.48/9.91 thf(67,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[66,h1])).
% 9.48/9.91 thf(68,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[67,h0])).
% 9.48/9.91 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => ((~((~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (p @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5)))))))))) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (p @ X6))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5))))))))))))))))) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_q @ X4) @ X5))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_r @ X4) @ X5)))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[66,h2])).
% 9.48/9.91 % SZS output end Proof
%------------------------------------------------------------------------------