TSTP Solution File: GEG005^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GEG005^1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Sat Jul 16 02:41:36 EDT 2022
% Result : Theorem 26.27s 26.48s
% Output : Proof 26.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEG005^1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 7 05:17:50 EDT 2022
% 0.11/0.32 % CPUTime :
% 26.27/26.48 % SZS status Theorem
% 26.27/26.48 % Mode: mode454
% 26.27/26.48 % Inferences: 4971
% 26.27/26.48 % SZS output start Proof
% 26.27/26.48 thf(ty_reg, type, reg : $tType).
% 26.27/26.48 thf(ty_a, type, a : ($i>$i>$o)).
% 26.27/26.48 thf(ty_fool, type, fool : ($i>$i>$o)).
% 26.27/26.48 thf(ty_eigen__14, type, eigen__14 : reg).
% 26.27/26.48 thf(ty_spain, type, spain : reg).
% 26.27/26.48 thf(ty_catalunya, type, catalunya : reg).
% 26.27/26.48 thf(ty_eigen__25, type, eigen__25 : reg).
% 26.27/26.48 thf(ty_eigen__1, type, eigen__1 : $i).
% 26.27/26.48 thf(ty_paris, type, paris : reg).
% 26.27/26.48 thf(ty_eigen__0, type, eigen__0 : $i).
% 26.27/26.48 thf(ty_eigen__3, type, eigen__3 : reg).
% 26.27/26.48 thf(ty_eigen__8, type, eigen__8 : $i).
% 26.27/26.48 thf(ty_france, type, france : reg).
% 26.27/26.48 thf(ty_c, type, c : (reg>reg>$o)).
% 26.27/26.48 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 26.27/26.48 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 26.27/26.48 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 26.27/26.48 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~((((a @ eigen__0) @ X1) => ((~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))) => (![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ paris)))))) => (![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ catalunya))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 26.27/26.48 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 26.27/26.48 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => ((~(((~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))))) => (![X3:reg]:(((c @ X3) @ catalunya) => ((c @ X3) @ paris)))))) => (![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ catalunya)))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 26.27/26.48 thf(eigendef_eigen__8, definition, eigen__8 = (eps__1 @ (^[X1:$i]:(~((((fool @ eigen__0) @ X1) => ((~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))) => (![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ paris)))))) => (![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ catalunya))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 26.27/26.48 thf(eigendef_eigen__25, definition, eigen__25 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__14) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__25])])).
% 26.27/26.48 thf(sP1,plain,sP1 <=> (((a @ eigen__0) @ eigen__1) => (~(((~(((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 26.27/26.48 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ france))) => (![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 26.27/26.48 thf(sP3,plain,sP3 <=> ((![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ catalunya))) => (~((![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 26.27/26.48 thf(sP4,plain,sP4 <=> ((![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ spain))) => (~((![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ france)))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 26.27/26.48 thf(sP5,plain,sP5 <=> (![X1:reg]:(((c @ eigen__3) @ X1) => ((c @ X1) @ eigen__3))),introduced(definition,[new_symbols(definition,[sP5])])).
% 26.27/26.48 thf(sP6,plain,sP6 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => ((~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))) => (![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ paris)))))) => (![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ catalunya)))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 26.27/26.48 thf(sP7,plain,sP7 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 26.27/26.48 thf(sP8,plain,sP8 <=> ((c @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP8])])).
% 26.27/26.48 thf(sP9,plain,sP9 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP9])])).
% 26.27/26.48 thf(sP10,plain,sP10 <=> ((~((((c @ spain) @ paris) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))))) => (((c @ spain) @ france) => (~(sP7)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 26.27/26.48 thf(sP11,plain,sP11 <=> ((c @ spain) @ paris),introduced(definition,[new_symbols(definition,[sP11])])).
% 26.27/26.48 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((a @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 26.27/26.48 thf(sP13,plain,sP13 <=> ((c @ eigen__25) @ france),introduced(definition,[new_symbols(definition,[sP13])])).
% 26.27/26.48 thf(sP14,plain,sP14 <=> (((a @ eigen__0) @ eigen__1) => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 26.27/26.48 thf(sP15,plain,sP15 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP15])])).
% 26.27/26.48 thf(sP16,plain,sP16 <=> ((c @ spain) @ eigen__3),introduced(definition,[new_symbols(definition,[sP16])])).
% 26.27/26.48 thf(sP17,plain,sP17 <=> ((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP17])])).
% 26.27/26.48 thf(sP18,plain,sP18 <=> ((fool @ eigen__0) @ eigen__8),introduced(definition,[new_symbols(definition,[sP18])])).
% 26.27/26.48 thf(sP19,plain,sP19 <=> (sP18 => ((~(((~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))) => (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ paris)))))) => (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ catalunya))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 26.27/26.48 thf(sP20,plain,sP20 <=> (![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP20])])).
% 26.27/26.48 thf(sP21,plain,sP21 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP21])])).
% 26.27/26.48 thf(sP22,plain,sP22 <=> (((c @ eigen__25) @ paris) => sP13),introduced(definition,[new_symbols(definition,[sP22])])).
% 26.27/26.48 thf(sP23,plain,sP23 <=> (((a @ eigen__0) @ eigen__1) => ((~(((~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))) => (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ paris)))))) => (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ catalunya))))),introduced(definition,[new_symbols(definition,[sP23])])).
% 26.27/26.48 thf(sP24,plain,sP24 <=> ((~(((~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))) => (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ paris)))))) => (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP24])])).
% 26.27/26.48 thf(sP25,plain,sP25 <=> (![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP25])])).
% 26.27/26.48 thf(sP26,plain,sP26 <=> (((c @ eigen__25) @ eigen__14) => ((c @ eigen__25) @ paris)),introduced(definition,[new_symbols(definition,[sP26])])).
% 26.27/26.48 thf(sP27,plain,sP27 <=> ((~((sP21 => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 26.27/26.48 thf(sP28,plain,sP28 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP28])])).
% 26.27/26.48 thf(sP29,plain,sP29 <=> (((c @ eigen__3) @ spain) => sP16),introduced(definition,[new_symbols(definition,[sP29])])).
% 26.27/26.48 thf(sP30,plain,sP30 <=> (![X1:reg]:((c @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP30])])).
% 26.27/26.48 thf(sP31,plain,sP31 <=> ((~(sP17)) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP31])])).
% 26.27/26.48 thf(sP32,plain,sP32 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP32])])).
% 26.27/26.48 thf(sP33,plain,sP33 <=> (sP11 => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP33])])).
% 26.27/26.48 thf(sP34,plain,sP34 <=> ((![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ spain))) => (~(sP25))),introduced(definition,[new_symbols(definition,[sP34])])).
% 26.27/26.48 thf(sP35,plain,sP35 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP27)))),introduced(definition,[new_symbols(definition,[sP35])])).
% 26.27/26.48 thf(sP36,plain,sP36 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__0) @ X2) => (X1 @ X2))) => (![X2:$i]:(((a @ eigen__0) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP36])])).
% 26.27/26.48 thf(sP37,plain,sP37 <=> ((~(sP32)) => (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP37])])).
% 26.27/26.48 thf(sP38,plain,sP38 <=> ((c @ eigen__3) @ catalunya),introduced(definition,[new_symbols(definition,[sP38])])).
% 26.27/26.48 thf(sP39,plain,sP39 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (~((((c @ spain) @ france) => (~(sP7)))))))),introduced(definition,[new_symbols(definition,[sP39])])).
% 26.27/26.48 thf(sP40,plain,sP40 <=> (sP18 => (~((((c @ spain) @ france) => (~(sP7)))))),introduced(definition,[new_symbols(definition,[sP40])])).
% 26.27/26.48 thf(sP41,plain,sP41 <=> ((c @ eigen__3) @ spain),introduced(definition,[new_symbols(definition,[sP41])])).
% 26.27/26.48 thf(sP42,plain,sP42 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP31)))),introduced(definition,[new_symbols(definition,[sP42])])).
% 26.27/26.48 thf(sP43,plain,sP43 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => sP24))),introduced(definition,[new_symbols(definition,[sP43])])).
% 26.27/26.48 thf(sP44,plain,sP44 <=> (sP38 => sP41),introduced(definition,[new_symbols(definition,[sP44])])).
% 26.27/26.48 thf(sP45,plain,sP45 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP45])])).
% 26.27/26.48 thf(sP46,plain,sP46 <=> ((c @ eigen__25) @ eigen__14),introduced(definition,[new_symbols(definition,[sP46])])).
% 26.27/26.48 thf(sP47,plain,sP47 <=> (sP46 => sP13),introduced(definition,[new_symbols(definition,[sP47])])).
% 26.27/26.48 thf(sP48,plain,sP48 <=> ((c @ eigen__25) @ paris),introduced(definition,[new_symbols(definition,[sP48])])).
% 26.27/26.48 thf(sP49,plain,sP49 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (~((((c @ spain) @ france) => (~(sP7))))))),introduced(definition,[new_symbols(definition,[sP49])])).
% 26.27/26.48 thf(sP50,plain,sP50 <=> (![X1:reg]:(![X2:reg]:(((c @ X1) @ X2) => ((c @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP50])])).
% 26.27/26.48 thf(sP51,plain,sP51 <=> (sP8 => sP38),introduced(definition,[new_symbols(definition,[sP51])])).
% 26.27/26.48 thf(sP52,plain,sP52 <=> (((c @ spain) @ france) => (~(sP7))),introduced(definition,[new_symbols(definition,[sP52])])).
% 26.27/26.48 thf(sP53,plain,sP53 <=> (sP16 => sP11),introduced(definition,[new_symbols(definition,[sP53])])).
% 26.27/26.48 thf(sP54,plain,sP54 <=> ((![X1:$i]:(((fool @ eigen__0) @ X1) => sP24)) => sP6),introduced(definition,[new_symbols(definition,[sP54])])).
% 26.27/26.48 thf(sP55,plain,sP55 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => sP24)),introduced(definition,[new_symbols(definition,[sP55])])).
% 26.27/26.48 thf(sP56,plain,sP56 <=> (![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))),introduced(definition,[new_symbols(definition,[sP56])])).
% 26.27/26.48 thf(sP57,plain,sP57 <=> (![X1:reg]:(((c @ X1) @ eigen__14) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP57])])).
% 26.27/26.48 thf(sP58,plain,sP58 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP27))))),introduced(definition,[new_symbols(definition,[sP58])])).
% 26.27/26.48 thf(sP59,plain,sP59 <=> (sP21 => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP59])])).
% 26.27/26.48 thf(sP60,plain,sP60 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP60])])).
% 26.27/26.48 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 26.27/26.48 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 26.27/26.48 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 26.27/26.48 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 26.27/26.48 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 26.27/26.48 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 26.27/26.48 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 26.27/26.48 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 26.27/26.48 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 26.27/26.48 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 26.27/26.48 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 26.27/26.48 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 26.27/26.48 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 26.27/26.48 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 26.27/26.48 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 26.27/26.48 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 26.27/26.48 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 26.27/26.48 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 26.27/26.48 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 26.27/26.48 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 26.27/26.48 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 26.27/26.48 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 26.27/26.48 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 26.27/26.48 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 26.27/26.48 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 26.27/26.48 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))))))))).
% 26.27/26.48 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 26.27/26.48 thf(def_mvalid,definition,(mvalid = (!!))).
% 26.27/26.48 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 26.27/26.48 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 26.27/26.48 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 26.27/26.48 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))).
% 26.27/26.48 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))).
% 26.27/26.48 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))).
% 26.27/26.48 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))).
% 26.27/26.48 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))).
% 26.27/26.48 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))).
% 26.27/26.48 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))).
% 26.27/26.48 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))).
% 26.27/26.48 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))).
% 26.27/26.48 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((~(sP24)))))))).
% 26.27/26.48 thf(h2,negated_conjecture,(~(sP43)),inference(assume_negation,[status(cth)],[con])).
% 26.27/26.48 thf(1,plain,((~(sP51) | ~(sP8)) | sP38),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(2,plain,(~(sP28) | sP22),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(3,plain,((~(sP22) | ~(sP48)) | sP13),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(4,plain,(~(sP25) | sP26),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(5,plain,((~(sP26) | ~(sP46)) | sP48),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(6,plain,((~(sP44) | ~(sP38)) | sP41),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(7,plain,(~(sP30) | sP8),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(8,plain,(~(sP9) | sP51),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(9,plain,(~(sP21) | sP44),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(10,plain,(sP47 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(11,plain,(sP47 | sP46),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(12,plain,(~(sP5) | sP29),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(13,plain,((~(sP29) | ~(sP41)) | sP16),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(14,plain,(sP20 | ~(sP47)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__25])).
% 26.27/26.48 thf(15,plain,(~(sP15) | sP53),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(16,plain,((~(sP53) | ~(sP16)) | sP11),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(17,plain,(~(sP7) | sP4),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(18,plain,((~(sP4) | ~(sP57)) | ~(sP20)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(19,plain,(sP34 | sP25),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(20,plain,(sP34 | sP57),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(21,plain,(sP45 | ~(sP34)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14])).
% 26.27/26.48 thf(22,plain,(~(sP50) | sP5),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(23,plain,(~(sP39) | sP49),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(24,plain,(~(sP49) | sP40),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(25,plain,((~(sP40) | ~(sP18)) | ~(sP52)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(26,plain,(sP19 | sP18),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(27,plain,(sP55 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8])).
% 26.27/26.48 thf(28,plain,(sP59 | sP21),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(29,plain,(sP27 | ~(sP59)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(30,plain,(~(sP56) | sP10),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(31,plain,((~(sP10) | sP33) | sP52),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(32,plain,((~(sP33) | ~(sP11)) | ~(sP45)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(33,plain,(sP52 | sP7),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(34,plain,(sP17 | sP28),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(35,plain,(sP31 | sP56),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(36,plain,(sP31 | ~(sP17)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(37,plain,(sP3 | sP15),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(38,plain,(sP3 | sP9),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(39,plain,(sP32 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 26.27/26.48 thf(40,plain,(sP37 | ~(sP32)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(41,plain,(sP24 | ~(sP37)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(42,plain,(~(sP2) | sP42),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(43,plain,(~(sP42) | sP14),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(44,plain,((~(sP14) | ~(sP60)) | ~(sP31)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(45,plain,(~(sP58) | sP35),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(46,plain,(~(sP35) | sP1),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(47,plain,((~(sP1) | ~(sP60)) | ~(sP27)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(48,plain,(sP23 | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(49,plain,(sP23 | sP60),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(50,plain,(sP6 | ~(sP23)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])).
% 26.27/26.48 thf(51,plain,(~(sP12) | sP36),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(52,plain,(~(sP36) | sP54),inference(all_rule,[status(thm)],[])).
% 26.27/26.48 thf(53,plain,((~(sP54) | ~(sP55)) | sP6),inference(prop_rule,[status(thm)],[])).
% 26.27/26.48 thf(54,plain,(sP43 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])).
% 26.27/26.48 thf(c_reflexive,axiom,sP30).
% 26.27/26.48 thf(c_symmetric,axiom,sP50).
% 26.27/26.48 thf(i_axiom_for_fool_a,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ ((mbox @ a) @ X1)))))).
% 26.27/26.48 thf(55,plain,sP12,inference(preprocess,[status(thm)],[i_axiom_for_fool_a]).
% 26.27/26.48 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))).
% 26.27/26.48 thf(56,plain,sP58,inference(preprocess,[status(thm)],[ax1]).
% 26.27/26.48 thf(ax2,axiom,(mvalid @ ((mbox @ fool) @ (^[X1:$i]:((ec @ spain) @ france))))).
% 26.27/26.48 thf(57,plain,sP39,inference(preprocess,[status(thm)],[ax2]).
% 26.27/26.48 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))).
% 26.27/26.48 thf(58,plain,sP2,inference(preprocess,[status(thm)],[ax3]).
% 26.27/26.48 thf(59,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,c_reflexive,c_symmetric,55,56,57,58,h2])).
% 26.27/26.48 thf(60,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[59,h1])).
% 26.27/26.48 thf(61,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[60,h0])).
% 26.27/26.48 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((~(sP24))))))),inference(contra,[status(thm),contra(discharge,[h2])],[59,h2])).
% 26.27/26.48 % SZS output end Proof
%------------------------------------------------------------------------------