TSTP Solution File: GEG009^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GEG009^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : 300s
% DateTime : Wed Aug 30 22:40:30 EDT 2023
% Result : Theorem 80.31s 80.81s
% Output : Proof 107.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEG009^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n013.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 : 300
% 0.12/0.33 % DateTime : Mon Aug 28 00:55:02 EDT 2023
% 0.12/0.33 % CPUTime :
% 80.31/80.81 % SZS status Theorem
% 80.31/80.81 % Mode: cade22grackle2x4fb9
% 80.31/80.81 % Steps: 7855
% 80.31/80.81 % SZS output start Proof
% 80.31/80.81 thf(ty_reg, type, reg : $tType).
% 80.31/80.81 thf(ty_spain, type, spain : reg).
% 80.31/80.81 thf(ty_catalunya, type, catalunya : reg).
% 80.31/80.81 thf(ty_paris, type, paris : reg).
% 80.31/80.81 thf(ty_a, type, a : ($i>$i>$o)).
% 80.31/80.81 thf(ty_c, type, c : (reg>reg>$o)).
% 80.31/80.81 thf(ty_france, type, france : reg).
% 80.31/80.81 thf(sP1,plain,sP1 <=> (![X1:reg]:(![X2:reg]:(((c @ X1) @ X2) => ((c @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 80.31/80.81 thf(sP2,plain,sP2 <=> (((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))))) => (~((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris)))))) => (~(((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))) => ((c @ X1) @ spain))) => (~((![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 80.31/80.81 thf(sP3,plain,sP3 <=> (((c @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))) @ france) => ((c @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))) @ paris)),introduced(definition,[new_symbols(definition,[sP3])])).
% 80.31/80.81 thf(sP4,plain,sP4 <=> ((a @ (@+[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))) => (~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3)))))))))))))))))) @ (@+[X1:$i]:(~((((a @ (@+[X2:$i]:(~((![X3:$i]:(((a @ X2) @ X3) => (~((![X4:reg]:((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris))))))) => (~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ spain) => ((c @ X5) @ X4)))))))))))))))))) @ X1) => (~((![X2:reg]:((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))) => (~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))) => (~((![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ X2))))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 80.31/80.81 thf(sP5,plain,sP5 <=> ((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))) => ((c @ X1) @ spain))) => (~((![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 80.31/80.81 thf(sP6,plain,sP6 <=> (((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) => ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ paris)),introduced(definition,[new_symbols(definition,[sP6])])).
% 80.31/80.81 thf(sP7,plain,sP7 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ catalunya),introduced(definition,[new_symbols(definition,[sP7])])).
% 80.31/80.81 thf(sP8,plain,sP8 <=> ((c @ paris) @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 80.31/80.81 thf(sP9,plain,sP9 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP9])])).
% 80.31/80.81 thf(sP10,plain,sP10 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 80.31/80.81 thf(sP11,plain,sP11 <=> (sP4 => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP3))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~(((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ paris))))))))))) => (((c @ X1) @ france) => (~(((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))) => ((c @ X2) @ france))))))))))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 80.31/80.81 thf(sP12,plain,sP12 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP12])])).
% 80.31/80.81 thf(sP13,plain,sP13 <=> ((c @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))) @ paris),introduced(definition,[new_symbols(definition,[sP13])])).
% 80.31/80.81 thf(sP14,plain,sP14 <=> (sP9 => (~(sP12))),introduced(definition,[new_symbols(definition,[sP14])])).
% 80.31/80.81 thf(sP15,plain,sP15 <=> (sP9 => (((c @ (@+[X1:reg]:(~((((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) @ spain) => ((c @ (@+[X1:reg]:(~((((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) @ catalunya))),introduced(definition,[new_symbols(definition,[sP15])])).
% 80.31/80.81 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(sP15)) => ((~((((c @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))))))))) @ catalunya) => (~((![X3:reg]:((((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ (@+[X5:reg]:(~(((~((((c @ X5) @ catalunya) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ catalunya)))))))))))) => (((c @ X5) @ spain) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ spain)))))))))))))))))))) @ X3) => ((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ (@+[X5:reg]:(~(((~((((c @ X5) @ catalunya) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ catalunya)))))))))))) => (((c @ X5) @ spain) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ spain)))))))))))))))))))) @ (@+[X4:reg]:(~(((~((((c @ X4) @ catalunya) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ catalunya)))))))))))) => (((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))))))) => (~((((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))) @ X3) => ((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))) @ catalunya))))))))))) => (((c @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))))))))) @ spain) => (~((![X3:reg]:((((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ (@+[X5:reg]:(~(((~((((c @ X5) @ catalunya) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ catalunya)))))))))))) => (((c @ X5) @ spain) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ spain)))))))))))))))))))) @ X3) => ((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ (@+[X5:reg]:(~(((~((((c @ X5) @ catalunya) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ catalunya)))))))))))) => (((c @ X5) @ spain) => (~((![X6:reg]:((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ X5))) => (~((![X7:reg]:(((c @ X7) @ X6) => ((c @ X7) @ spain)))))))))))))))))))) @ (@+[X4:reg]:(~(((~((((c @ X4) @ catalunya) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ catalunya)))))))))))) => (((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))))))) => (~((((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ spain)))))) @ X3) => ((c @ (@+[X4:reg]:(~((((c @ X4) @ X3) => ((c @ X4) @ spain)))))) @ spain)))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 80.31/80.81 thf(sP17,plain,sP17 <=> (![X1:reg]:(((c @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) @ X1) => ((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 80.31/80.81 thf(sP18,plain,sP18 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 80.31/80.81 thf(sP19,plain,sP19 <=> ((c @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))) @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 80.31/80.81 thf(sP20,plain,sP20 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 80.31/80.81 thf(sP21,plain,sP21 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ paris),introduced(definition,[new_symbols(definition,[sP21])])).
% 80.31/80.81 thf(sP22,plain,sP22 <=> ((~(sP15)) => ((~((((c @ (@+[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))))))))))))))) @ catalunya) => (~((![X1:reg]:((((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))))) @ X1) => ((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))))) @ (@+[X2:reg]:(~(((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))))))) => (~((((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))) @ X1) => ((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))) @ catalunya))))))))))) => (((c @ (@+[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))))))))))))))) @ spain) => (~((![X1:reg]:((((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))))) @ X1) => ((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~(((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))))) @ (@+[X2:reg]:(~(((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))))))) => (~((((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ spain)))))) @ X1) => ((c @ (@+[X2:reg]:(~((((c @ X2) @ X1) => ((c @ X2) @ spain)))))) @ spain))))))))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 80.31/80.81 thf(sP23,plain,sP23 <=> (((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ catalunya))) => (~((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris)))))) => (~(sP14))),introduced(definition,[new_symbols(definition,[sP23])])).
% 80.31/80.81 thf(sP24,plain,sP24 <=> (![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ (@+[X2:reg]:(~((((c @ X2) @ france) => ((c @ X2) @ paris)))))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 80.31/80.81 thf(sP25,plain,sP25 <=> (sP7 => ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ spain)),introduced(definition,[new_symbols(definition,[sP25])])).
% 80.31/80.81 thf(sP26,plain,sP26 <=> (![X1:$i]:(((a @ (@+[X2:$i]:(~((![X3:$i]:(((a @ X2) @ X3) => (~((![X4:reg]:((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris))))))) => (~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ spain) => ((c @ X5) @ X4)))))))))))))))))) @ X1) => (~(sP22)))),introduced(definition,[new_symbols(definition,[sP26])])).
% 80.31/80.81 thf(sP27,plain,sP27 <=> ((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ catalunya))) => (~((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 80.31/80.81 thf(sP28,plain,sP28 <=> (![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP28])])).
% 80.31/80.81 thf(sP29,plain,sP29 <=> (((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ spain) => ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris))))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 80.31/80.81 thf(sP30,plain,sP30 <=> (![X1:reg]:(((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ paris)))))) => (~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP30])])).
% 80.31/80.81 thf(sP31,plain,sP31 <=> (sP4 => (~(sP22))),introduced(definition,[new_symbols(definition,[sP31])])).
% 80.31/80.81 thf(sP32,plain,sP32 <=> ((c @ paris) @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ (@+[X3:reg]:(~((((c @ X3) @ france) => ((c @ X3) @ paris)))))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP32])])).
% 80.31/80.81 thf(sP33,plain,sP33 <=> (sP20 => sP7),introduced(definition,[new_symbols(definition,[sP33])])).
% 80.31/80.81 thf(sP34,plain,sP34 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ (@+[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 80.31/80.81 thf(sP35,plain,sP35 <=> (sP24 => (~((![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP35])])).
% 80.31/80.81 thf(sP36,plain,sP36 <=> (![X1:$i]:(((a @ (@+[X2:$i]:(~((![X3:$i]:(((a @ X2) @ X3) => (~((![X4:reg]:((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris))))))) => (~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ spain) => ((c @ X5) @ X4)))))))))))))))))) @ X1) => (~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ france))) => sP3))) => (~((![X2:reg]:((~((((c @ X2) @ paris) => (~(((![X3:reg]:(((c @ X3) @ (@+[X4:reg]:(~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ (@+[X4:reg]:(~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))) => ((c @ X3) @ paris))))))))))) => (((c @ X2) @ france) => (~(((![X3:reg]:(((c @ X3) @ (@+[X4:reg]:(~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ (@+[X4:reg]:(~(((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))) => ((c @ X3) @ france)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP36])])).
% 80.31/80.81 thf(sP37,plain,sP37 <=> (![X1:reg]:((c @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP37])])).
% 80.31/80.81 thf(sP38,plain,sP38 <=> (sP34 => sP19),introduced(definition,[new_symbols(definition,[sP38])])).
% 80.31/80.81 thf(sP39,plain,sP39 <=> ((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP3),introduced(definition,[new_symbols(definition,[sP39])])).
% 80.31/80.81 thf(sP40,plain,sP40 <=> (sP21 => sP32),introduced(definition,[new_symbols(definition,[sP40])])).
% 80.31/80.81 thf(sP41,plain,sP41 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(sP39)) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~(((![X4:reg]:(((c @ X4) @ (@+[X5:reg]:(~(((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris)))))))))) => ((c @ X4) @ X3))) => (~((![X4:reg]:(((c @ X4) @ (@+[X5:reg]:(~(((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris)))))))))) => ((c @ X4) @ paris))))))))))) => (((c @ X3) @ france) => (~(((![X4:reg]:(((c @ X4) @ (@+[X5:reg]:(~(((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))) => ((c @ X4) @ X3))) => (~((![X4:reg]:(((c @ X4) @ (@+[X5:reg]:(~(((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))) => ((c @ X4) @ france))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP41])])).
% 80.31/80.81 thf(sP42,plain,sP42 <=> (sP19 => sP13),introduced(definition,[new_symbols(definition,[sP42])])).
% 80.31/80.81 thf(sP43,plain,sP43 <=> (sP32 => sP8),introduced(definition,[new_symbols(definition,[sP43])])).
% 80.31/80.81 thf(sP44,plain,sP44 <=> (![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP44])])).
% 80.31/80.81 thf(sP45,plain,sP45 <=> (![X1:reg]:(((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP45])])).
% 80.31/80.81 thf(sP46,plain,sP46 <=> ((c @ (@+[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))) @ spain),introduced(definition,[new_symbols(definition,[sP46])])).
% 80.31/80.81 thf(sP47,plain,sP47 <=> (sP8 => sP13),introduced(definition,[new_symbols(definition,[sP47])])).
% 80.31/80.81 thf(sP48,plain,sP48 <=> ((~(sP39)) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~(((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))) => ((c @ X2) @ paris))))))))))) => (((c @ X1) @ france) => (~(((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ (@+[X3:reg]:(~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))) => ((c @ X2) @ france)))))))))))))),introduced(definition,[new_symbols(definition,[sP48])])).
% 80.31/80.81 thf(sP49,plain,sP49 <=> (((c @ (@+[X1:reg]:(~((((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) @ spain) => ((c @ (@+[X1:reg]:(~((((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) @ catalunya)),introduced(definition,[new_symbols(definition,[sP49])])).
% 80.31/80.81 thf(sP50,plain,sP50 <=> (![X1:reg]:(((c @ paris) @ X1) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP50])])).
% 80.31/80.81 thf(sP51,plain,sP51 <=> (![X1:reg]:(((c @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))) @ X1) => ((c @ X1) @ (@+[X2:reg]:(~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ (@+[X4:reg]:(~((((c @ X4) @ france) => ((c @ X4) @ paris)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))),introduced(definition,[new_symbols(definition,[sP51])])).
% 80.31/80.81 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 80.31/80.81 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 80.31/80.81 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 80.31/80.81 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 80.31/80.81 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 80.31/80.81 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 80.31/80.81 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 80.31/80.81 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 80.31/80.81 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 80.31/80.81 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 80.31/80.81 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 80.31/80.81 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 80.31/80.81 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 80.31/80.81 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 80.31/80.81 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 80.31/80.81 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 80.31/80.81 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 80.31/80.81 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 80.31/80.81 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 80.31/80.81 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 80.31/80.81 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X3) @ X4))) @ ((X1 @ X2) @ X4)))))))).
% 80.31/80.81 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((X1 @ X3) @ X4)))))))).
% 80.31/80.81 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (X3 = X4)))))))).
% 80.31/80.81 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:(((X1 @ X2) @ X3) & (![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X4)) @ (X3 = X4))))))))).
% 80.31/80.81 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X3)) @ (?[X5:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 80.31/80.81 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 80.31/80.81 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (?[X5:$i]:(((X1 @ X3) @ X5) & ((X1 @ X4) @ X5)))))))))).
% 80.31/80.81 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 80.31/80.81 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 80.31/80.81 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 80.31/80.81 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 80.31/80.81 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:((~) @ ((c @ X1) @ X2)))))).
% 80.31/80.81 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((c @ X3) @ X1)) @ ((c @ X3) @ X2))))))).
% 80.31/80.81 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(((p @ X1) @ X2) & ((p @ X2) @ X1)))))).
% 80.31/80.81 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(?[X3:reg]:(((p @ X3) @ X1) & ((p @ X3) @ X2))))))).
% 80.31/80.81 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:((((o @ X1) @ X2) & ((~) @ ((p @ X1) @ X2))) & ((~) @ ((p @ X2) @ X1))))))).
% 80.31/80.81 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(((c @ X1) @ X2) & ((~) @ ((o @ X1) @ X2))))))).
% 80.31/80.81 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(((p @ X1) @ X2) & ((~) @ ((p @ X2) @ X1))))))).
% 80.31/80.81 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(((pp @ X1) @ X2) & (?[X3:reg]:(((ec @ X3) @ X1) & ((ec @ X3) @ X2)))))))).
% 80.31/80.81 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(((pp @ X1) @ X2) & ((~) @ (?[X3:reg]:(((ec @ X3) @ X1) & ((ec @ X3) @ X2))))))))).
% 80.31/80.81 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))) => (~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3)))))))))))))))).
% 80.31/80.81 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))) => (~(((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))))))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 80.31/80.81 thf(h1,assumption,sP4,introduced(assumption,[])).
% 80.31/80.81 thf(h2,assumption,sP30,introduced(assumption,[])).
% 80.31/80.81 thf(1,plain,((~(sP40) | ~(sP21)) | sP32),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(2,plain,((~(sP38) | ~(sP34)) | sP19),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(3,plain,(~(sP51) | sP40),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(4,plain,((~(sP6) | ~(sP10)) | sP21),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(5,plain,(~(sP17) | sP38),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(6,plain,((~(sP33) | ~(sP20)) | sP7),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(7,plain,((~(sP25) | ~(sP7)) | sP46),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(8,plain,((~(sP29) | ~(sP46)) | sP34),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(9,plain,(~(sP37) | sP10),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(10,plain,(~(sP1) | sP51),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(11,plain,(~(sP45) | sP6),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(12,plain,(sP39 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(13,plain,(sP3 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(14,plain,(~(sP37) | sP20),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(15,plain,(~(sP1) | sP17),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(16,plain,(~(sP44) | sP33),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(17,plain,(~(sP9) | sP25),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(18,plain,(~(sP18) | sP29),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(19,plain,(sP48 | ~(sP39)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(20,plain,(sP15 | ~(sP49)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(21,plain,(sP15 | sP9),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(22,plain,(~(sP12) | sP49),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(23,plain,(sP22 | ~(sP15)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(24,plain,((~(sP43) | ~(sP32)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(25,plain,(sP5 | sP18),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(26,plain,((~(sP42) | ~(sP19)) | sP13),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(27,plain,(sP14 | sP12),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(28,plain,((~(sP11) | ~(sP4)) | ~(sP48)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(29,plain,((~(sP31) | ~(sP4)) | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(30,plain,((~(sP47) | ~(sP8)) | sP13),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(31,plain,(~(sP24) | sP43),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(32,plain,(sP35 | sP45),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(33,plain,(sP35 | sP24),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(34,plain,((~(sP2) | ~(sP35)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(35,plain,(~(sP28) | sP42),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(36,plain,(sP27 | sP28),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(37,plain,(sP27 | sP44),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(38,plain,((~(sP23) | ~(sP27)) | ~(sP14)),inference(prop_rule,[status(thm)],[])).
% 80.31/80.81 thf(39,plain,(~(sP36) | sP11),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(40,plain,(~(sP26) | sP31),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(41,plain,(~(sP50) | sP47),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(42,plain,(~(sP30) | sP2),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(43,plain,(~(sP30) | sP23),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(44,plain,(~(sP41) | sP36),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(45,plain,(~(sP16) | sP26),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 thf(46,plain,(~(sP1) | sP50),inference(all_rule,[status(thm)],[])).
% 80.31/80.81 1:903: Could not find hyp name
% 80.31/80.81 s = Pi:$i (\_:$i.Pi:$i (\_:$i.imp (a ^1 ^0) (imp (imp (imp (imp (Pi:reg (\_:reg.imp (c ^0 paris) (c ^0 france))) (imp (c (Sepsilon:reg (\_:reg.imp (imp (c ^0 france) (c ^0 paris)) False)) france) (c (Sepsilon:reg (\_:reg.imp (imp (c ^0 france) (c ^0 paris)) False)) paris))) False) (imp (Pi:reg (\_:reg.imp (imp (imp (c ^0 paris) (imp (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False)) False))) (c ^0 ^1))) (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False)) False))) (c ^0 paris))) False)) False)) False) (imp (c ^0 france) (imp (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 france))) False)) False))) (c ^0 ^1))) (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 france))) False)) False))) (c ^0 france))) False)) False)))) False)) False)))
% 80.31/80.81 hyp:
% 80.31/80.81 [832] h1: a (Sepsilon:$i (\_:$i.imp (Pi:$i (\_:$i.imp (a ^1 ^0) (imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^2))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False))) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))) False))) False)) (Sepsilon:$i (\_:$i.imp (imp (a (Sepsilon:$i (\_:$i.imp (Pi:$i (\_:$i.imp (a ^1 ^0) (imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^2))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False))) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))) False))) False)) ^0) (imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^2))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False))) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))) False)) False))
% 80.31/80.81 [851] h2: Pi:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False)) False))) (c ^0 ^1))) (imp (Pi:reg (\_:reg.imp (c ^0 (Sepsilon:reg (\_:reg.imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^3))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False)) False))) (c ^0 paris))) False)) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))
% 80.31/80.81 [854] h0: imp (Pi:$i (\_:$i.Pi:$i (\_:$i.imp (a ^1 ^0) (imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^2))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False))) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))) False)))) False
% 80.31/80.81 [819] h0: imp (Pi:$i (\_:$i.Pi:$i (\_:$i.imp (a ^1 ^0) (imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 ^2))) (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 paris))) False))) (imp (imp (Pi:reg (\_:reg.imp (c ^0 ^1) (c ^0 spain))) (imp (Pi:reg (\_:reg.imp (c ^0 spain) (c ^0 ^1))) False)) False))) False)))) False
% 80.31/80.81 % SZS status Error
% 80.31/80.81 Exception: Failure("Could not find hyp name")
% 107.91/108.31 % SZS status Theorem
% 107.91/108.31 % Mode: cade22grackle2xb9cd
% 107.91/108.31 % Steps: 119194
% 107.91/108.31 % SZS output start Proof
% 107.91/108.31 thf(ty_reg, type, reg : $tType).
% 107.91/108.31 thf(ty_spain, type, spain : reg).
% 107.91/108.31 thf(ty_catalunya, type, catalunya : reg).
% 107.91/108.31 thf(ty_paris, type, paris : reg).
% 107.91/108.31 thf(ty_a, type, a : ($i>$i>$o)).
% 107.91/108.31 thf(ty_c, type, c : (reg>reg>$o)).
% 107.91/108.31 thf(ty_eigen__11, type, eigen__11 : reg).
% 107.91/108.31 thf(ty_eigen__1, type, eigen__1 : $i).
% 107.91/108.31 thf(ty_france, type, france : reg).
% 107.91/108.31 thf(ty_eigen__83, type, eigen__83 : reg).
% 107.91/108.31 thf(ty_eigen__2, type, eigen__2 : reg).
% 107.91/108.31 thf(ty_eigen__0, type, eigen__0 : $i).
% 107.91/108.31 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 107.91/108.31 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ paris)))))), introduced(definition,[new_symbols(definition,[eigen__11])])).
% 107.91/108.31 thf(eigendef_eigen__83, definition, eigen__83 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__11))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__83])])).
% 107.91/108.31 thf(eigendef_eigen__2, definition, eigen__2 = (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__2])])).
% 107.91/108.31 thf(sP1,plain,sP1 <=> (![X1:reg]:(![X2:reg]:(((c @ X1) @ X2) => ((c @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 107.91/108.31 thf(sP2,plain,sP2 <=> (((c @ eigen__2) @ eigen__2) => ((c @ eigen__2) @ catalunya)),introduced(definition,[new_symbols(definition,[sP2])])).
% 107.91/108.31 thf(sP3,plain,sP3 <=> ((![X1:reg]:(((c @ X1) @ eigen__83) => ((c @ X1) @ eigen__11))) => (~((![X1:reg]:(((c @ X1) @ eigen__83) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 107.91/108.31 thf(sP4,plain,sP4 <=> (![X1:reg]:(((c @ X1) @ eigen__83) => ((c @ X1) @ eigen__11))),introduced(definition,[new_symbols(definition,[sP4])])).
% 107.91/108.31 thf(sP5,plain,sP5 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])).
% 107.91/108.31 thf(sP6,plain,sP6 <=> (((c @ eigen__11) @ eigen__2) => ((c @ eigen__11) @ paris)),introduced(definition,[new_symbols(definition,[sP6])])).
% 107.91/108.31 thf(sP7,plain,sP7 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__11))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 107.91/108.31 thf(sP8,plain,sP8 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP8])])).
% 107.91/108.31 thf(sP9,plain,sP9 <=> (sP5 => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP8))) => (~((![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,[sP9])])).
% 107.91/108.31 thf(sP10,plain,sP10 <=> (![X1:reg]:(((c @ eigen__2) @ X1) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP10])])).
% 107.91/108.31 thf(sP11,plain,sP11 <=> ((c @ eigen__11) @ paris),introduced(definition,[new_symbols(definition,[sP11])])).
% 107.91/108.31 thf(sP12,plain,sP12 <=> ((c @ eigen__2) @ spain),introduced(definition,[new_symbols(definition,[sP12])])).
% 107.91/108.31 thf(sP13,plain,sP13 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ france))) => sP8))) => (~((![X2:reg]:((~((((c @ X2) @ paris) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))))) => (((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 107.91/108.31 thf(sP14,plain,sP14 <=> (((c @ eigen__11) @ eigen__83) => sP11),introduced(definition,[new_symbols(definition,[sP14])])).
% 107.91/108.31 thf(sP15,plain,sP15 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP15])])).
% 107.91/108.31 thf(sP16,plain,sP16 <=> ((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP8))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 107.91/108.31 thf(sP17,plain,sP17 <=> (![X1:reg]:(((c @ eigen__83) @ X1) => ((c @ X1) @ eigen__83))),introduced(definition,[new_symbols(definition,[sP17])])).
% 107.91/108.31 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(sP15)) => (![X3:reg]:((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 107.91/108.31 thf(sP19,plain,sP19 <=> ((c @ eigen__11) @ eigen__2),introduced(definition,[new_symbols(definition,[sP19])])).
% 107.91/108.31 thf(sP20,plain,sP20 <=> ((c @ eigen__2) @ eigen__11),introduced(definition,[new_symbols(definition,[sP20])])).
% 107.91/108.31 thf(sP21,plain,sP21 <=> (((c @ eigen__83) @ eigen__83) => ((c @ eigen__83) @ eigen__11)),introduced(definition,[new_symbols(definition,[sP21])])).
% 107.91/108.31 thf(sP22,plain,sP22 <=> ((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))) => (~((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ paris)))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 107.91/108.31 thf(sP23,plain,sP23 <=> (![X1:reg]:(((c @ X1) @ eigen__83) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP23])])).
% 107.91/108.31 thf(sP24,plain,sP24 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP24])])).
% 107.91/108.31 thf(sP25,plain,sP25 <=> (sP5 => (~(((~(sP15)) => (![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,[sP25])])).
% 107.91/108.31 thf(sP26,plain,sP26 <=> (sP20 => sP19),introduced(definition,[new_symbols(definition,[sP26])])).
% 107.91/108.31 thf(sP27,plain,sP27 <=> (![X1:reg]:((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))) => (~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 107.91/108.31 thf(sP28,plain,sP28 <=> ((c @ eigen__83) @ eigen__83),introduced(definition,[new_symbols(definition,[sP28])])).
% 107.91/108.31 thf(sP29,plain,sP29 <=> ((![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) @ spain))) => (~(sP24)))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 107.91/108.31 thf(sP30,plain,sP30 <=> ((c @ eigen__2) @ catalunya),introduced(definition,[new_symbols(definition,[sP30])])).
% 107.91/108.31 thf(sP31,plain,sP31 <=> (((c @ eigen__11) @ france) => sP11),introduced(definition,[new_symbols(definition,[sP31])])).
% 107.91/108.31 thf(sP32,plain,sP32 <=> ((c @ eigen__11) @ eigen__83),introduced(definition,[new_symbols(definition,[sP32])])).
% 107.91/108.31 thf(sP33,plain,sP33 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (~(sP24))),introduced(definition,[new_symbols(definition,[sP33])])).
% 107.91/108.31 thf(sP34,plain,sP34 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP34])])).
% 107.91/108.31 thf(sP35,plain,sP35 <=> ((~(sP15)) => (![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,[sP35])])).
% 107.91/108.31 thf(sP36,plain,sP36 <=> ((![X1:reg]:(((c @ X1) @ eigen__11) => ((c @ X1) @ spain))) => (~((![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ eigen__11)))))),introduced(definition,[new_symbols(definition,[sP36])])).
% 107.91/108.31 thf(sP37,plain,sP37 <=> (((c @ eigen__83) @ eigen__11) => sP32),introduced(definition,[new_symbols(definition,[sP37])])).
% 107.91/108.31 thf(sP38,plain,sP38 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP38])])).
% 107.91/108.31 thf(sP39,plain,sP39 <=> ((c @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP39])])).
% 107.91/108.31 thf(sP40,plain,sP40 <=> (![X1:reg]:((c @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP40])])).
% 107.91/108.31 thf(sP41,plain,sP41 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP35)))),introduced(definition,[new_symbols(definition,[sP41])])).
% 107.91/108.31 thf(sP42,plain,sP42 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP16))))),introduced(definition,[new_symbols(definition,[sP42])])).
% 107.91/108.31 thf(sP43,plain,sP43 <=> ((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP8),introduced(definition,[new_symbols(definition,[sP43])])).
% 107.91/108.31 thf(sP44,plain,sP44 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP44])])).
% 107.91/108.31 thf(sP45,plain,sP45 <=> (sP7 => (~(sP36))),introduced(definition,[new_symbols(definition,[sP45])])).
% 107.91/108.31 thf(sP46,plain,sP46 <=> (sP12 => sP20),introduced(definition,[new_symbols(definition,[sP46])])).
% 107.91/108.31 thf(sP47,plain,sP47 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ eigen__11))),introduced(definition,[new_symbols(definition,[sP47])])).
% 107.91/108.31 thf(sP48,plain,sP48 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP48])])).
% 107.91/108.31 thf(sP49,plain,sP49 <=> ((c @ eigen__83) @ eigen__11),introduced(definition,[new_symbols(definition,[sP49])])).
% 107.91/108.31 thf(sP50,plain,sP50 <=> (sP30 => sP12),introduced(definition,[new_symbols(definition,[sP50])])).
% 107.91/108.31 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 107.91/108.31 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 107.91/108.31 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 107.91/108.31 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 107.91/108.31 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 107.91/108.31 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X1)) @ X2))))).
% 107.91/108.31 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 107.91/108.31 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 107.91/108.31 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 107.91/108.31 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 107.91/108.31 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 107.91/108.31 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 107.91/108.31 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 107.91/108.31 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:$true))).
% 107.91/108.31 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 107.91/108.31 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((~) @ ((X1 @ X3) @ X4)) | (X2 @ X4)))))))).
% 107.91/108.31 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 107.91/108.31 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 107.91/108.31 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((X1 @ X2) @ X3)) @ ((X1 @ X3) @ X2))))))).
% 107.91/108.31 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3)))))).
% 107.91/108.31 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X3) @ X4))) @ ((X1 @ X2) @ X4)))))))).
% 107.91/108.31 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((X1 @ X3) @ X4)))))))).
% 107.91/108.31 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (X3 = X4)))))))).
% 107.91/108.31 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(?[X3:$i]:(((X1 @ X2) @ X3) & (![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X4)) @ (X3 = X4))))))))).
% 107.91/108.31 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ ((X1 @ X2) @ X3)) @ (?[X5:$i]:(((X1 @ X2) @ X5) & ((X1 @ X5) @ X3)))))))))).
% 107.91/108.31 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ ((((X1 @ X3) @ X4) | (X3 = X4)) | ((X1 @ X4) @ X3))))))))).
% 107.91/108.31 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((X1 @ X2) @ X3) & ((X1 @ X2) @ X4))) @ (?[X5:$i]:(((X1 @ X3) @ X5) & ((X1 @ X4) @ X5)))))))))).
% 107.91/108.31 thf(def_mvalid,definition,(mvalid = (^[X1:$i>$o]:(![X2:$i]:(X1 @ X2))))).
% 107.91/108.31 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:((~) @ (X1 @ X2)))))).
% 107.91/108.31 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(?[X2:$i]:(X1 @ X2))))).
% 107.91/108.31 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(?[X2:$i]:((~) @ (X1 @ X2)))))).
% 107.91/108.31 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:((~) @ ((c @ X1) @ X2)))))).
% 107.91/108.31 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ ((c @ X3) @ X1)) @ ((c @ X3) @ X2))))))).
% 107.91/108.31 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(((p @ X1) @ X2) & ((p @ X2) @ X1)))))).
% 107.91/108.31 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(?[X3:reg]:(((p @ X3) @ X1) & ((p @ X3) @ X2))))))).
% 107.91/108.31 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:((((o @ X1) @ X2) & ((~) @ ((p @ X1) @ X2))) & ((~) @ ((p @ X2) @ X1))))))).
% 107.91/108.31 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(((c @ X1) @ X2) & ((~) @ ((o @ X1) @ X2))))))).
% 107.91/108.31 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(((p @ X1) @ X2) & ((~) @ ((p @ X2) @ X1))))))).
% 107.91/108.31 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(((pp @ X1) @ X2) & (?[X3:reg]:(((ec @ X3) @ X1) & ((ec @ X3) @ X2)))))))).
% 107.91/108.31 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(((pp @ X1) @ X2) & ((~) @ (?[X3:reg]:(((ec @ X3) @ X1) & ((ec @ X3) @ X2))))))))).
% 107.91/108.31 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP27)))))).
% 107.91/108.31 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP27))))))),inference(assume_negation,[status(cth)],[con])).
% 107.91/108.31 thf(h2,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP27)))))),introduced(assumption,[])).
% 107.91/108.31 thf(h3,assumption,(~((sP5 => (~(sP27))))),introduced(assumption,[])).
% 107.91/108.31 thf(h4,assumption,sP5,introduced(assumption,[])).
% 107.91/108.31 thf(h5,assumption,sP27,introduced(assumption,[])).
% 107.91/108.31 thf(1,plain,((~(sP37) | ~(sP49)) | sP32),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(2,plain,(~(sP17) | sP37),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(3,plain,((~(sP21) | ~(sP28)) | sP49),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(4,plain,(~(sP40) | sP28),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(5,plain,(~(sP1) | sP17),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(6,plain,(~(sP4) | sP21),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(7,plain,((~(sP46) | ~(sP12)) | sP20),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(8,plain,(~(sP47) | sP46),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(9,plain,(sP36 | sP47),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(10,plain,((~(sP45) | ~(sP7)) | ~(sP36)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(11,plain,((~(sP14) | ~(sP32)) | sP11),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(12,plain,(~(sP23) | sP14),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(13,plain,(sP3 | sP23),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(14,plain,(sP3 | sP4),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(15,plain,(sP7 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__83])).
% 107.91/108.31 thf(16,plain,((~(sP6) | ~(sP19)) | sP11),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(17,plain,((~(sP26) | ~(sP20)) | sP19),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(18,plain,(~(sP27) | sP45),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(19,plain,(~(sP34) | sP6),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(20,plain,(~(sP10) | sP26),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(21,plain,((~(sP50) | ~(sP30)) | sP12),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(22,plain,((~(sP2) | ~(sP39)) | sP30),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(23,plain,(~(sP40) | sP39),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(24,plain,(~(sP1) | sP10),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(25,plain,(~(sP48) | sP50),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(26,plain,(~(sP38) | sP2),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(27,plain,((~(sP9) | ~(sP5)) | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(28,plain,((~(sP25) | ~(sP5)) | ~(sP35)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(29,plain,(~(sP13) | sP9),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(30,plain,(~(sP41) | sP25),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(31,plain,(sP15 | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(32,plain,(sP15 | sP48),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(33,plain,(sP35 | ~(sP15)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(34,plain,(sP31 | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(35,plain,(sP8 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])).
% 107.91/108.31 thf(36,plain,(sP43 | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(37,plain,(sP16 | ~(sP43)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(38,plain,(~(sP18) | sP41),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(39,plain,(~(sP42) | sP13),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(40,plain,(sP22 | sP34),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(41,plain,(sP22 | sP38),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(42,plain,(sP33 | sP24),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(43,plain,(sP44 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 107.91/108.31 thf(44,plain,((~(sP29) | ~(sP44)) | ~(sP33)),inference(prop_rule,[status(thm)],[])).
% 107.91/108.31 thf(45,plain,(~(sP27) | sP29),inference(all_rule,[status(thm)],[])).
% 107.91/108.31 thf(ax3,axiom,sP42).
% 107.91/108.31 thf(ax1,axiom,sP18).
% 107.91/108.31 thf(c_symmetric,axiom,sP1).
% 107.91/108.31 thf(c_reflexive,axiom,sP40).
% 107.91/108.31 thf(46,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,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,h4,h5,ax3,ax1,c_symmetric,c_reflexive])).
% 107.91/108.31 thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,46,h4,h5])).
% 107.91/108.31 thf(48,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,47,h3])).
% 107.91/108.31 thf(49,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,48,h2])).
% 107.91/108.31 thf(50,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[49,h0])).
% 107.91/108.31 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP27))))),inference(contra,[status(thm),contra(discharge,[h1])],[49,h1])).
% 107.91/108.31 % SZS output end Proof
%------------------------------------------------------------------------------