TSTP Solution File: SYN377^7 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN377^7 : 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 : n024.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 11:43:15 EDT 2022
% Result : Theorem 105.03s 105.13s
% Output : Proof 105.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN377^7 : 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 : n024.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 15:25:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 105.03/105.13 % SZS status Theorem
% 105.03/105.13 % Mode: mode368
% 105.03/105.13 % Inferences: 13408
% 105.03/105.13 % SZS output start Proof
% 105.03/105.13 thf(ty_mu, type, mu : $tType).
% 105.03/105.13 thf(ty_eigen__14, type, eigen__14 : $i).
% 105.03/105.13 thf(ty_eigen__6, type, eigen__6 : $i).
% 105.03/105.13 thf(ty_eigen__12, type, eigen__12 : $i).
% 105.03/105.13 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 105.03/105.13 thf(ty_eigen__2, type, eigen__2 : $i).
% 105.03/105.13 thf(ty_eigen__89, type, eigen__89 : mu).
% 105.03/105.13 thf(ty_eigen__4, type, eigen__4 : $i).
% 105.03/105.13 thf(ty_eigen__5, type, eigen__5 : mu).
% 105.03/105.13 thf(ty_eigen__3, type, eigen__3 : $i).
% 105.03/105.13 thf(ty_eigen__8, type, eigen__8 : $i).
% 105.03/105.13 thf(ty_eigen__13, type, eigen__13 : $i).
% 105.03/105.13 thf(ty_big_p, type, big_p : (mu>$i>$o)).
% 105.03/105.13 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 105.03/105.13 thf(ty_eigen__18, type, eigen__18 : mu).
% 105.03/105.13 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 105.03/105.13 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 105.03/105.14 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 105.03/105.14 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__12) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 105.03/105.14 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))))))))))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__12])])).
% 105.03/105.14 thf(h1, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 105.03/105.14 thf(eigendef_eigen__18, definition, eigen__18 = (eps__1 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__14) => (~((![X2:$i]:(((rel_s4 @ eigen__14) @ X2) => ((big_p @ X1) @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__18])])).
% 105.03/105.14 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 105.03/105.14 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[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) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 105.03/105.14 thf(eigendef_eigen__13, definition, eigen__13 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__12) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__13])])).
% 105.03/105.14 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__3) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 105.03/105.14 thf(eigendef_eigen__89, definition, eigen__89 = (eps__1 @ (^[X1:mu]:(~((~(((exists_in_world @ X1) @ eigen__13))))))), introduced(definition,[new_symbols(definition,[eigen__89])])).
% 105.03/105.14 thf(eigendef_eigen__5, definition, eigen__5 = (eps__1 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__4) => (~(((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 105.03/105.14 thf(sP1,plain,sP1 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__4) => (~(((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__4) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 105.03/105.14 thf(sP2,plain,sP2 <=> (![X1:mu]:(![X2:$i]:(![X3:$i]:((~((((exists_in_world @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((exists_in_world @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 105.03/105.14 thf(sP3,plain,sP3 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__14) => (~((![X2:$i]:(((rel_s4 @ eigen__14) @ X2) => ((big_p @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 105.03/105.14 thf(sP4,plain,sP4 <=> (((exists_in_world @ eigen__5) @ eigen__6) => (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => ((big_p @ eigen__5) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 105.03/105.14 thf(sP5,plain,sP5 <=> (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 105.03/105.14 thf(sP6,plain,sP6 <=> ((rel_s4 @ eigen__6) @ eigen__6),introduced(definition,[new_symbols(definition,[sP6])])).
% 105.03/105.14 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_s4 @ eigen__13) @ X1) => ((big_p @ eigen__89) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 105.03/105.14 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))))))))))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))))))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 105.03/105.14 thf(sP9,plain,sP9 <=> ((exists_in_world @ eigen__5) @ eigen__6),introduced(definition,[new_symbols(definition,[sP9])])).
% 105.03/105.14 thf(sP10,plain,sP10 <=> ((rel_s4 @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP10])])).
% 105.03/105.14 thf(sP11,plain,sP11 <=> (![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__18) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 105.03/105.14 thf(sP12,plain,sP12 <=> (((exists_in_world @ eigen__5) @ eigen__8) => (~((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_p @ eigen__5) @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 105.03/105.14 thf(sP13,plain,sP13 <=> (((exists_in_world @ eigen__89) @ eigen__13) => (~(sP7))),introduced(definition,[new_symbols(definition,[sP13])])).
% 105.03/105.14 thf(sP14,plain,sP14 <=> (![X1:$i]:(~((![X2:mu]:(~(((exists_in_world @ X2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 105.03/105.14 thf(sP15,plain,sP15 <=> (![X1:$i]:((~((((exists_in_world @ eigen__5) @ eigen__4) => (~(((rel_s4 @ eigen__4) @ X1)))))) => ((exists_in_world @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP15])])).
% 105.03/105.14 thf(sP16,plain,sP16 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__6) => (![X2:$i]:(((rel_s4 @ eigen__6) @ X2) => ((big_p @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 105.03/105.14 thf(sP17,plain,sP17 <=> ((rel_s4 @ eigen__14) @ eigen__14),introduced(definition,[new_symbols(definition,[sP17])])).
% 105.03/105.14 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:((~((((exists_in_world @ eigen__5) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((exists_in_world @ eigen__5) @ X2)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 105.03/105.14 thf(sP19,plain,sP19 <=> (sP5 => (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => ((big_p @ eigen__5) @ X1)))),introduced(definition,[new_symbols(definition,[sP19])])).
% 105.03/105.14 thf(sP20,plain,sP20 <=> ((exists_in_world @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP20])])).
% 105.03/105.14 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__3) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP21])])).
% 105.03/105.14 thf(sP22,plain,sP22 <=> ((~((![X1:mu]:(((exists_in_world @ X1) @ eigen__8) => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_p @ X1) @ X2))))))))) => (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 105.03/105.14 thf(sP23,plain,sP23 <=> (sP11 => (~((![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__18) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP23])])).
% 105.03/105.14 thf(sP24,plain,sP24 <=> (((rel_s4 @ eigen__4) @ eigen__8) => ((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_p @ eigen__5) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 105.03/105.14 thf(sP25,plain,sP25 <=> (sP17 => ((![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => ((big_p @ eigen__18) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 105.03/105.14 thf(sP26,plain,sP26 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__8) => (~((![X2:$i]:(((rel_s4 @ eigen__8) @ X2) => ((big_p @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP26])])).
% 105.03/105.14 thf(sP27,plain,sP27 <=> ((rel_s4 @ eigen__4) @ eigen__6),introduced(definition,[new_symbols(definition,[sP27])])).
% 105.03/105.14 thf(sP28,plain,sP28 <=> (sP20 => (~(((rel_s4 @ eigen__4) @ eigen__8)))),introduced(definition,[new_symbols(definition,[sP28])])).
% 105.03/105.14 thf(sP29,plain,sP29 <=> ((~((sP20 => (~(sP27))))) => sP9),introduced(definition,[new_symbols(definition,[sP29])])).
% 105.03/105.14 thf(sP30,plain,sP30 <=> ((~(sP3)) => (![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP30])])).
% 105.03/105.14 thf(sP31,plain,sP31 <=> (((exists_in_world @ eigen__18) @ eigen__14) => (~((![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => ((big_p @ eigen__18) @ X1)))))),introduced(definition,[new_symbols(definition,[sP31])])).
% 105.03/105.14 thf(sP32,plain,sP32 <=> ((![X1:$i]:(((rel_s4 @ eigen__13) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))) => (~((![X1:mu]:(((exists_in_world @ X1) @ eigen__13) => (~((![X2:$i]:(((rel_s4 @ eigen__13) @ X2) => ((big_p @ X1) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP32])])).
% 105.03/105.14 thf(sP33,plain,sP33 <=> ((exists_in_world @ eigen__18) @ eigen__14),introduced(definition,[new_symbols(definition,[sP33])])).
% 105.03/105.14 thf(sP34,plain,sP34 <=> (((rel_s4 @ eigen__2) @ eigen__12) => ((![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))))))))))))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 105.03/105.14 thf(sP35,plain,sP35 <=> ((~(sP28)) => ((exists_in_world @ eigen__5) @ eigen__8)),introduced(definition,[new_symbols(definition,[sP35])])).
% 105.03/105.14 thf(sP36,plain,sP36 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__13) => (~((![X2:$i]:(((rel_s4 @ eigen__13) @ X2) => ((big_p @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP36])])).
% 105.03/105.14 thf(sP37,plain,sP37 <=> ((rel_s4 @ eigen__12) @ eigen__14),introduced(definition,[new_symbols(definition,[sP37])])).
% 105.03/105.14 thf(sP38,plain,sP38 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP38])])).
% 105.03/105.14 thf(sP39,plain,sP39 <=> (((rel_s4 @ eigen__13) @ eigen__13) => (![X1:mu]:(((exists_in_world @ X1) @ eigen__13) => (![X2:$i]:(((rel_s4 @ eigen__13) @ X2) => ((big_p @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP39])])).
% 105.03/105.14 thf(sP40,plain,sP40 <=> ((rel_s4 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP40])])).
% 105.03/105.14 thf(sP41,plain,sP41 <=> ((exists_in_world @ eigen__89) @ eigen__13),introduced(definition,[new_symbols(definition,[sP41])])).
% 105.03/105.14 thf(sP42,plain,sP42 <=> (![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP42])])).
% 105.03/105.14 thf(sP43,plain,sP43 <=> (sP37 => sP30),introduced(definition,[new_symbols(definition,[sP43])])).
% 105.03/105.14 thf(sP44,plain,sP44 <=> (sP40 => (~(((rel_s4 @ eigen__4) @ eigen__8)))),introduced(definition,[new_symbols(definition,[sP44])])).
% 105.03/105.14 thf(sP45,plain,sP45 <=> (sP10 => sP22),introduced(definition,[new_symbols(definition,[sP45])])).
% 105.03/105.14 thf(sP46,plain,sP46 <=> (((rel_s4 @ eigen__2) @ eigen__3) => ((~(((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))))))))))) => sP38)),introduced(definition,[new_symbols(definition,[sP46])])).
% 105.03/105.14 thf(sP47,plain,sP47 <=> (![X1:mu]:(~(((exists_in_world @ X1) @ eigen__13)))),introduced(definition,[new_symbols(definition,[sP47])])).
% 105.03/105.14 thf(sP48,plain,sP48 <=> (![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~(((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((big_p @ X2) @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP48])])).
% 105.03/105.14 thf(sP49,plain,sP49 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))))))))))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP49])])).
% 105.03/105.14 thf(sP50,plain,sP50 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__13) => (![X2:$i]:(((rel_s4 @ eigen__13) @ X2) => ((big_p @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP50])])).
% 105.03/105.14 thf(sP51,plain,sP51 <=> (sP27 => sP19),introduced(definition,[new_symbols(definition,[sP51])])).
% 105.03/105.14 thf(sP52,plain,sP52 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__14) => (~(((![X2:$i]:(((rel_s4 @ eigen__14) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ eigen__14) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((big_p @ X1) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP52])])).
% 105.03/105.14 thf(sP53,plain,sP53 <=> (![X1:$i]:(((rel_s4 @ eigen__14) @ X1) => ((big_p @ eigen__18) @ X1))),introduced(definition,[new_symbols(definition,[sP53])])).
% 105.03/105.14 thf(sP54,plain,sP54 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP54])])).
% 105.03/105.14 thf(sP55,plain,sP55 <=> ((rel_s4 @ eigen__4) @ eigen__8),introduced(definition,[new_symbols(definition,[sP55])])).
% 105.03/105.14 thf(sP56,plain,sP56 <=> (sP53 => sP42),introduced(definition,[new_symbols(definition,[sP56])])).
% 105.03/105.14 thf(sP57,plain,sP57 <=> (sP20 => (~(((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP57])])).
% 105.03/105.14 thf(sP58,plain,sP58 <=> (![X1:$i]:((~((sP40 => (~(((rel_s4 @ eigen__4) @ X1)))))) => ((rel_s4 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP58])])).
% 105.03/105.14 thf(sP59,plain,sP59 <=> (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP59])])).
% 105.03/105.14 thf(sP60,plain,sP60 <=> (sP54 => (~((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))))))))),introduced(definition,[new_symbols(definition,[sP60])])).
% 105.03/105.14 thf(sP61,plain,sP61 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP61])])).
% 105.03/105.14 thf(sP62,plain,sP62 <=> ((exists_in_world @ eigen__5) @ eigen__8),introduced(definition,[new_symbols(definition,[sP62])])).
% 105.03/105.14 thf(sP63,plain,sP63 <=> (sP59 => (~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP63])])).
% 105.03/105.14 thf(sP64,plain,sP64 <=> ((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_p @ eigen__5) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP64])])).
% 105.03/105.14 thf(sP65,plain,sP65 <=> (![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) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6)))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP65])])).
% 105.03/105.14 thf(sP66,plain,sP66 <=> (sP37 => sP52),introduced(definition,[new_symbols(definition,[sP66])])).
% 105.03/105.14 thf(sP67,plain,sP67 <=> (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((big_p @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP67])])).
% 105.03/105.14 thf(sP68,plain,sP68 <=> (sP6 => sP16),introduced(definition,[new_symbols(definition,[sP68])])).
% 105.03/105.14 thf(sP69,plain,sP69 <=> ((![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))))))))),introduced(definition,[new_symbols(definition,[sP69])])).
% 105.03/105.14 thf(sP70,plain,sP70 <=> (sP48 => (~(sP69))),introduced(definition,[new_symbols(definition,[sP70])])).
% 105.03/105.14 thf(sP71,plain,sP71 <=> (![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP71])])).
% 105.03/105.14 thf(sP72,plain,sP72 <=> (![X1:$i]:(((rel_s4 @ eigen__12) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP72])])).
% 105.03/105.14 thf(sP73,plain,sP73 <=> (![X1:$i]:(((rel_s4 @ eigen__13) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP73])])).
% 105.03/105.14 thf(sP74,plain,sP74 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))) => (~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~(((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7)))))))))) => (~((![X4:$i]:(((rel_s4 @ X2) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (![X6:mu]:(((exists_in_world @ X6) @ X5) => (![X7:$i]:(((rel_s4 @ X5) @ X7) => ((big_p @ X6) @ X7))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((big_p @ X3) @ X5)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP74])])).
% 105.03/105.14 thf(sP75,plain,sP75 <=> (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => ((big_p @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP75])])).
% 105.03/105.14 thf(sP76,plain,sP76 <=> (sP41 => sP7),introduced(definition,[new_symbols(definition,[sP76])])).
% 105.03/105.14 thf(sP77,plain,sP77 <=> ((~(sP60)) => sP38),introduced(definition,[new_symbols(definition,[sP77])])).
% 105.03/105.14 thf(sP78,plain,sP78 <=> (((rel_s4 @ eigen__12) @ eigen__13) => sP32),introduced(definition,[new_symbols(definition,[sP78])])).
% 105.03/105.14 thf(sP79,plain,sP79 <=> (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => ((big_p @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP79])])).
% 105.03/105.14 thf(sP80,plain,sP80 <=> ((rel_s4 @ eigen__13) @ eigen__13),introduced(definition,[new_symbols(definition,[sP80])])).
% 105.03/105.14 thf(sP81,plain,sP81 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP81])])).
% 105.03/105.14 thf(sP82,plain,sP82 <=> (sP20 => (~(sP27))),introduced(definition,[new_symbols(definition,[sP82])])).
% 105.03/105.14 thf(sP83,plain,sP83 <=> (sP33 => (~(sP23))),introduced(definition,[new_symbols(definition,[sP83])])).
% 105.03/105.14 thf(sP84,plain,sP84 <=> (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => ((big_p @ X3) @ X4))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((big_p @ eigen__5) @ X2)))))),introduced(definition,[new_symbols(definition,[sP84])])).
% 105.03/105.14 thf(sP85,plain,sP85 <=> (sP40 => sP1),introduced(definition,[new_symbols(definition,[sP85])])).
% 105.03/105.14 thf(sP86,plain,sP86 <=> ((~(sP44)) => sP10),introduced(definition,[new_symbols(definition,[sP86])])).
% 105.03/105.14 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 105.03/105.14 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 105.03/105.14 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 105.03/105.14 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 105.03/105.14 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 105.03/105.14 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 105.03/105.14 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 105.03/105.14 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 105.03/105.14 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 105.03/105.14 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 105.03/105.14 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 105.03/105.14 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 105.03/105.14 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 105.03/105.14 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 105.03/105.14 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 105.03/105.14 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 105.03/105.14 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 105.03/105.14 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 105.03/105.14 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 105.03/105.14 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 105.03/105.14 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 105.03/105.14 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 105.03/105.14 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 105.03/105.14 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 105.03/105.14 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))))))))).
% 105.03/105.14 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 105.03/105.14 thf(def_mvalid,definition,(mvalid = (!!))).
% 105.03/105.14 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 105.03/105.14 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 105.03/105.14 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 105.03/105.14 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 105.03/105.14 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 105.03/105.14 thf(x2128,conjecture,(![X1:$i]:(~(((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))))))))))))).
% 105.03/105.14 thf(h2,negated_conjecture,(~(sP65)),inference(assume_negation,[status(cth)],[x2128])).
% 105.03/105.14 thf(1,plain,(~(sP36) | sP13),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(2,plain,((~(sP13) | ~(sP41)) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(3,plain,(~(sP50) | sP76),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(4,plain,((~(sP76) | ~(sP41)) | sP7),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(5,plain,(~(sP58) | sP86),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(6,plain,((~(sP86) | sP44) | sP10),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(7,plain,((~(sP44) | ~(sP40)) | ~(sP55)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(8,plain,(~(sP21) | sP58),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(9,plain,(sP47 | sP41),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__89])).
% 105.03/105.14 thf(10,plain,(~(sP15) | sP29),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(11,plain,((~(sP29) | sP82) | sP9),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(12,plain,((~(sP82) | ~(sP20)) | ~(sP27)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(13,plain,(~(sP15) | sP35),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(14,plain,((~(sP35) | sP28) | sP62),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(15,plain,((~(sP28) | ~(sP20)) | ~(sP55)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(16,plain,(~(sP18) | sP15),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(17,plain,(~(sP11) | sP25),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(18,plain,((~(sP25) | ~(sP17)) | sP56),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(19,plain,((~(sP56) | ~(sP53)) | sP42),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(20,plain,((~(sP39) | ~(sP80)) | sP50),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(21,plain,(sP23 | sP11),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(22,plain,(~(sP52) | sP83),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(23,plain,((~(sP83) | ~(sP33)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(24,plain,(~(sP81) | sP17),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(25,plain,(sP31 | sP53),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(26,plain,(sP31 | sP33),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(27,plain,(~(sP61) | sP21),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(28,plain,(~(sP26) | sP12),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(29,plain,((~(sP12) | ~(sP62)) | ~(sP67)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(30,plain,(~(sP54) | sP45),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(31,plain,((~(sP45) | ~(sP10)) | sP22),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(32,plain,((~(sP22) | sP26) | sP75),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(33,plain,(~(sP48) | sP66),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(34,plain,((~(sP66) | ~(sP37)) | sP52),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(35,plain,(sP3 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18])).
% 105.03/105.14 thf(36,plain,(sP30 | ~(sP42)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(37,plain,(sP30 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(38,plain,(sP43 | ~(sP30)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(39,plain,(sP43 | sP37),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(40,plain,(sP71 | ~(sP43)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14])).
% 105.03/105.14 thf(41,plain,(~(sP73) | sP39),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(42,plain,(~(sP14) | ~(sP47)),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(43,plain,(~(sP81) | sP80),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(44,plain,(sP32 | sP36),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(45,plain,(sP32 | sP73),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(46,plain,(sP78 | ~(sP32)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(47,plain,(sP72 | ~(sP78)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13])).
% 105.03/105.14 thf(48,plain,((~(sP69) | ~(sP71)) | ~(sP72)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(49,plain,(sP70 | sP69),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(50,plain,(sP70 | sP48),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(51,plain,(sP34 | ~(sP70)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(52,plain,(sP49 | ~(sP34)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])).
% 105.03/105.14 thf(53,plain,(sP60 | sP54),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(54,plain,(sP64 | ~(sP75)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(55,plain,(sP64 | sP67),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(56,plain,(sP24 | ~(sP64)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(57,plain,(sP24 | sP55),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(58,plain,(sP59 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 105.03/105.14 thf(59,plain,(~(sP2) | sP18),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(60,plain,(~(sP5) | sP68),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(61,plain,((~(sP68) | ~(sP6)) | sP16),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(62,plain,(~(sP16) | sP4),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(63,plain,((~(sP4) | ~(sP9)) | sP79),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(64,plain,(~(sP81) | sP6),inference(all_rule,[status(thm)],[])).
% 105.03/105.14 thf(65,plain,(sP19 | ~(sP79)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(66,plain,(sP19 | sP5),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(67,plain,(sP51 | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(68,plain,(sP51 | sP27),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(69,plain,(sP84 | ~(sP51)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 105.03/105.14 thf(70,plain,((~(sP63) | ~(sP59)) | ~(sP84)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(71,plain,(sP57 | sP63),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(72,plain,(sP57 | sP20),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(73,plain,(sP1 | ~(sP57)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5])).
% 105.03/105.14 thf(74,plain,(sP85 | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(75,plain,(sP85 | sP40),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(76,plain,(sP38 | ~(sP85)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])).
% 105.03/105.14 thf(77,plain,(sP77 | ~(sP38)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(78,plain,(sP77 | ~(sP60)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(79,plain,(sP46 | ~(sP77)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(80,plain,(sP74 | ~(sP46)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 105.03/105.14 thf(81,plain,((~(sP8) | ~(sP49)) | ~(sP74)),inference(prop_rule,[status(thm)],[])).
% 105.03/105.14 thf(82,plain,(sP65 | sP8),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 105.03/105.14 thf(nonempty_ax,axiom,sP14).
% 105.03/105.14 thf(a1,axiom,(mreflexive @ rel_s4)).
% 105.03/105.14 thf(83,plain,sP81,inference(preprocess,[status(thm)],[a1]).
% 105.03/105.14 thf(a2,axiom,(mtransitive @ rel_s4)).
% 105.03/105.14 thf(84,plain,sP61,inference(preprocess,[status(thm)],[a2]).
% 105.03/105.14 thf(cumulative_ax,axiom,sP2).
% 105.03/105.14 thf(85,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,nonempty_ax,83,84,cumulative_ax,h2])).
% 105.03/105.14 thf(86,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[85,h1])).
% 105.03/105.14 thf(87,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[86,h0])).
% 105.03/105.14 thf(0,theorem,(![X1:$i]:(~(((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5)))))))))))))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6)))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (![X6:$i]:(((rel_s4 @ X4) @ X6) => ((big_p @ X5) @ X6))))))))))) => (~((![X4:mu]:(((exists_in_world @ X4) @ X3) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((big_p @ X4) @ X5))))))))))))))))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (![X4:mu]:(((exists_in_world @ X4) @ X3) => (~(((~((~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8)))))))))))))) => (~((![X5:$i]:(((rel_s4 @ X3) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (![X7:mu]:(((exists_in_world @ X7) @ X6) => (![X8:$i]:(((rel_s4 @ X6) @ X8) => ((big_p @ X7) @ X8))))))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((big_p @ X4) @ X6)))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[85,h2])).
% 105.03/105.14 % SZS output end Proof
%------------------------------------------------------------------------------