TSTP Solution File: GEG019^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GEG019^1 : 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 02:41:38 EDT 2022
% Result : Theorem 9.93s 10.20s
% Output : Proof 9.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEG019^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 05:06:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.93/10.20 % SZS status Theorem
% 9.93/10.20 % Mode: mode515
% 9.93/10.20 % Inferences: 214
% 9.93/10.20 % SZS output start Proof
% 9.93/10.20 thf(ty_reg, type, reg : $tType).
% 9.93/10.20 thf(ty_a, type, a : ($i>$i>$o)).
% 9.93/10.20 thf(ty_eigen__2, type, eigen__2 : reg).
% 9.93/10.20 thf(ty_spain, type, spain : reg).
% 9.93/10.20 thf(ty_catalunya, type, catalunya : reg).
% 9.93/10.20 thf(ty_eigen__1, type, eigen__1 : $i).
% 9.93/10.20 thf(ty_paris, type, paris : reg).
% 9.93/10.20 thf(ty_eigen__0, type, eigen__0 : $i).
% 9.93/10.20 thf(ty_eigen__4, type, eigen__4 : reg).
% 9.93/10.20 thf(ty_eigen__5, type, eigen__5 : reg).
% 9.93/10.20 thf(ty_eigen__3, type, eigen__3 : reg).
% 9.93/10.20 thf(ty_eigen__17, type, eigen__17 : reg).
% 9.93/10.20 thf(ty_france, type, france : reg).
% 9.93/10.20 thf(ty_c, type, c : (reg>reg>$o)).
% 9.93/10.20 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 9.93/10.20 thf(eigendef_eigen__17, definition, eigen__17 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__3) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__17])])).
% 9.93/10.20 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__4) => ((c @ X1) @ spain)))))), introduced(definition,[new_symbols(definition,[eigen__5])])).
% 9.93/10.20 thf(sP1,plain,sP1 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP1])])).
% 9.93/10.20 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ france))) => (![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 9.93/10.20 thf(sP3,plain,sP3 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 9.93/10.20 thf(sP4,plain,sP4 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ spain))) => (![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ catalunya)))))) => (![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))))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 9.93/10.20 thf(sP5,plain,sP5 <=> (((c @ eigen__5) @ eigen__4) => ((c @ eigen__5) @ catalunya)),introduced(definition,[new_symbols(definition,[sP5])])).
% 9.93/10.20 thf(sP6,plain,sP6 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP6])])).
% 9.93/10.20 thf(sP7,plain,sP7 <=> ((~(((![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,[sP7])])).
% 9.93/10.20 thf(sP8,plain,sP8 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 9.93/10.20 thf(sP9,plain,sP9 <=> (((c @ eigen__5) @ catalunya) => ((c @ eigen__5) @ spain)),introduced(definition,[new_symbols(definition,[sP9])])).
% 9.93/10.20 thf(sP10,plain,sP10 <=> (((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,[sP10])])).
% 9.93/10.20 thf(sP11,plain,sP11 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP11])])).
% 9.93/10.20 thf(sP12,plain,sP12 <=> (((c @ eigen__17) @ eigen__3) => ((c @ eigen__17) @ france)),introduced(definition,[new_symbols(definition,[sP12])])).
% 9.93/10.20 thf(sP13,plain,sP13 <=> ((c @ eigen__17) @ eigen__3),introduced(definition,[new_symbols(definition,[sP13])])).
% 9.93/10.20 thf(sP14,plain,sP14 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP14])])).
% 9.93/10.20 thf(sP15,plain,sP15 <=> (((c @ eigen__17) @ paris) => ((c @ eigen__17) @ france)),introduced(definition,[new_symbols(definition,[sP15])])).
% 9.93/10.20 thf(sP16,plain,sP16 <=> ((c @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP16])])).
% 9.93/10.20 thf(sP17,plain,sP17 <=> ((c @ eigen__5) @ spain),introduced(definition,[new_symbols(definition,[sP17])])).
% 9.93/10.20 thf(sP18,plain,sP18 <=> (sP16 => sP17),introduced(definition,[new_symbols(definition,[sP18])])).
% 9.93/10.20 thf(sP19,plain,sP19 <=> ((c @ eigen__5) @ catalunya),introduced(definition,[new_symbols(definition,[sP19])])).
% 9.93/10.20 thf(sP20,plain,sP20 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP7))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 9.93/10.20 thf(sP21,plain,sP21 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP21])])).
% 9.93/10.20 thf(sP22,plain,sP22 <=> ((c @ eigen__17) @ france),introduced(definition,[new_symbols(definition,[sP22])])).
% 9.93/10.20 thf(sP23,plain,sP23 <=> (sP6 => (~(sP11))),introduced(definition,[new_symbols(definition,[sP23])])).
% 9.93/10.20 thf(sP24,plain,sP24 <=> ((~((sP21 => (![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,[sP24])])).
% 9.93/10.20 thf(sP25,plain,sP25 <=> (sP21 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP25])])).
% 9.93/10.20 thf(sP26,plain,sP26 <=> ((![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__2))) => (~((![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ spain)))))),introduced(definition,[new_symbols(definition,[sP26])])).
% 9.93/10.20 thf(sP27,plain,sP27 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP27])])).
% 9.93/10.20 thf(sP28,plain,sP28 <=> ((c @ eigen__17) @ paris),introduced(definition,[new_symbols(definition,[sP28])])).
% 9.93/10.20 thf(sP29,plain,sP29 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP24)))),introduced(definition,[new_symbols(definition,[sP29])])).
% 9.93/10.20 thf(sP30,plain,sP30 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))))))),introduced(definition,[new_symbols(definition,[sP30])])).
% 9.93/10.20 thf(sP31,plain,sP31 <=> (sP14 => (~(sP7))),introduced(definition,[new_symbols(definition,[sP31])])).
% 9.93/10.20 thf(sP32,plain,sP32 <=> (sP13 => sP28),introduced(definition,[new_symbols(definition,[sP32])])).
% 9.93/10.20 thf(sP33,plain,sP33 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP33])])).
% 9.93/10.20 thf(sP34,plain,sP34 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP34])])).
% 9.93/10.20 thf(sP35,plain,sP35 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP35])])).
% 9.93/10.20 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 9.93/10.20 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 9.93/10.20 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 9.93/10.20 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 9.93/10.20 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 9.93/10.20 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 9.93/10.20 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 9.93/10.20 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 9.93/10.20 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 9.93/10.20 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 9.93/10.20 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 9.93/10.20 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 9.93/10.20 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 9.93/10.20 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 9.93/10.20 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 9.93/10.20 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 9.93/10.20 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 9.93/10.20 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 9.93/10.20 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 9.93/10.20 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 9.93/10.20 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 9.93/10.20 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 9.93/10.20 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 9.93/10.20 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 9.93/10.20 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 9.93/10.20 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 9.93/10.20 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 9.93/10.20 thf(def_mvalid,definition,(mvalid = (!!))).
% 9.93/10.20 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 9.93/10.20 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 9.93/10.20 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 9.93/10.20 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))).
% 9.93/10.20 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))).
% 9.93/10.20 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))).
% 9.93/10.20 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))).
% 9.93/10.20 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))).
% 9.93/10.20 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))).
% 9.93/10.20 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))).
% 9.93/10.20 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))).
% 9.93/10.20 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))).
% 9.93/10.20 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))))) => (~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))))) => (~(((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))) => (~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))))))).
% 9.93/10.20 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))))) => (![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))) => (~(((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))) => (![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france))))))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 9.93/10.20 thf(h2,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (![X2:reg]:((~(((~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))) => (~(((~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))))))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h3,assumption,(~((sP14 => (![X1:reg]:((~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))) => (~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h4,assumption,sP14,introduced(assumption,[])).
% 9.93/10.20 thf(h5,assumption,(~((![X1:reg]:((~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))) => (~(((~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h6,assumption,(~(((~(((~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))) => (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))) => (~(((~(sP30)) => sP3)))))),introduced(assumption,[])).
% 9.93/10.20 thf(h7,assumption,(~(((~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))) => (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h8,assumption,((~(sP30)) => sP3),introduced(assumption,[])).
% 9.93/10.20 thf(h9,assumption,(~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h10,assumption,(~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))))))))),introduced(assumption,[])).
% 9.93/10.20 thf(h11,assumption,(~((sP6 => (~(sP34))))),introduced(assumption,[])).
% 9.93/10.20 thf(h12,assumption,sP6,introduced(assumption,[])).
% 9.93/10.20 thf(h13,assumption,sP34,introduced(assumption,[])).
% 9.93/10.20 thf(h14,assumption,(~((sP27 => (~(sP1))))),introduced(assumption,[])).
% 9.93/10.20 thf(h15,assumption,sP27,introduced(assumption,[])).
% 9.93/10.20 thf(h16,assumption,sP1,introduced(assumption,[])).
% 9.93/10.20 thf(h17,assumption,sP30,introduced(assumption,[])).
% 9.93/10.20 thf(h18,assumption,sP3,introduced(assumption,[])).
% 9.93/10.20 thf(1,plain,(~(sP35) | sP9),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(2,plain,((~(sP9) | ~(sP19)) | sP17),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(3,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(4,plain,((~(sP5) | ~(sP16)) | sP19),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(5,plain,(sP18 | ~(sP17)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(6,plain,(sP18 | sP16),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(7,plain,(sP8 | sP35),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(8,plain,(sP7 | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(9,plain,(~(sP20) | sP4),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(10,plain,(~(sP4) | sP31),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(11,plain,((~(sP31) | ~(sP14)) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(12,plain,(sP33 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])).
% 9.93/10.20 thf(13,plain,(~(sP30) | sP26),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(14,plain,((~(sP26) | ~(sP27)) | ~(sP33)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))).
% 9.93/10.20 thf(15,plain,sP20,inference(preprocess,[status(thm)],[ax1]).
% 9.93/10.20 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4,h15,h16,h17])).
% 9.93/10.20 thf(17,plain,(~(sP21) | sP15),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(18,plain,((~(sP15) | ~(sP28)) | sP22),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(19,plain,(~(sP34) | sP32),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(20,plain,((~(sP32) | ~(sP13)) | sP28),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(21,plain,(sP12 | ~(sP22)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(22,plain,(sP12 | sP13),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(23,plain,(sP25 | sP21),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(24,plain,(sP24 | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(25,plain,(sP11 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17])).
% 9.93/10.20 thf(26,plain,(~(sP2) | sP29),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(27,plain,(~(sP29) | sP10),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(28,plain,((~(sP10) | ~(sP14)) | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(29,plain,(~(sP3) | sP23),inference(all_rule,[status(thm)],[])).
% 9.93/10.20 thf(30,plain,((~(sP23) | ~(sP6)) | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 9.93/10.20 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))).
% 9.93/10.20 thf(31,plain,sP2,inference(preprocess,[status(thm)],[ax3]).
% 9.93/10.20 thf(32,plain,$false,inference(prop_unsat,[status(thm),assumptions([h18,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h4,h12,h13,h18])).
% 9.93/10.20 thf(33,plain,$false,inference(tab_imp,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h18])],[h8,16,32,h17,h18])).
% 9.93/10.20 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,33,h15,h16])).
% 9.93/10.20 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h10,34,h14])).
% 9.93/10.20 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,35,h12,h13])).
% 9.93/10.20 thf(37,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h9,36,h11])).
% 9.93/10.20 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,37,h9,h10])).
% 9.93/10.20 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,38,h7,h8])).
% 9.93/10.20 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,39,h6])).
% 9.93/10.20 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,40,h4,h5])).
% 9.93/10.20 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,41,h3])).
% 9.93/10.20 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,42,h2])).
% 9.93/10.20 thf(44,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[43,h0])).
% 9.93/10.20 thf(0,theorem,(![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]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))))) => (~(((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))) => (~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[43,h1])).
% 9.93/10.20 % SZS output end Proof
%------------------------------------------------------------------------------