TSTP Solution File: GEG011^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GEG011^1 : 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 : n027.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 02:41:37 EDT 2022
% Result : Theorem 9.79s 10.25s
% Output : Proof 9.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEG011^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 05:13:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.79/10.25 % SZS status Theorem
% 9.79/10.25 % Mode: mode515
% 9.79/10.25 % Inferences: 960
% 9.79/10.25 % SZS output start Proof
% 9.79/10.25 thf(ty_reg, type, reg : $tType).
% 9.79/10.25 thf(ty_a, type, a : ($i>$i>$o)).
% 9.79/10.25 thf(ty_eigen__2, type, eigen__2 : reg).
% 9.79/10.25 thf(ty_spain, type, spain : reg).
% 9.79/10.25 thf(ty_catalunya, type, catalunya : reg).
% 9.79/10.25 thf(ty_eigen__1, type, eigen__1 : $i).
% 9.79/10.25 thf(ty_paris, type, paris : reg).
% 9.79/10.25 thf(ty_eigen__0, type, eigen__0 : $i).
% 9.79/10.25 thf(ty_eigen__4, type, eigen__4 : reg).
% 9.79/10.25 thf(ty_eigen__5, type, eigen__5 : reg).
% 9.79/10.25 thf(ty_eigen__3, type, eigen__3 : reg).
% 9.79/10.25 thf(ty_eigen__20, type, eigen__20 : reg).
% 9.79/10.25 thf(ty_france, type, france : reg).
% 9.79/10.25 thf(ty_c, type, c : (reg>reg>$o)).
% 9.79/10.25 thf(sP1,plain,sP1 <=> ((c @ eigen__5) @ paris),introduced(definition,[new_symbols(definition,[sP1])])).
% 9.79/10.25 thf(sP2,plain,sP2 <=> ((c @ eigen__20) @ spain),introduced(definition,[new_symbols(definition,[sP2])])).
% 9.79/10.25 thf(sP3,plain,sP3 <=> ((c @ eigen__20) @ catalunya),introduced(definition,[new_symbols(definition,[sP3])])).
% 9.79/10.25 thf(sP4,plain,sP4 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP4])])).
% 9.79/10.25 thf(sP5,plain,sP5 <=> (((c @ eigen__5) @ france) => ((c @ eigen__5) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP5])])).
% 9.79/10.25 thf(sP6,plain,sP6 <=> (((c @ eigen__4) @ eigen__2) => ((c @ eigen__4) @ catalunya)),introduced(definition,[new_symbols(definition,[sP6])])).
% 9.79/10.25 thf(sP7,plain,sP7 <=> ((c @ eigen__4) @ catalunya),introduced(definition,[new_symbols(definition,[sP7])])).
% 9.79/10.25 thf(sP8,plain,sP8 <=> ((c @ eigen__4) @ eigen__2),introduced(definition,[new_symbols(definition,[sP8])])).
% 9.79/10.25 thf(sP9,plain,sP9 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP9])])).
% 9.79/10.25 thf(sP10,plain,sP10 <=> ((~((sP9 => (![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])])).
% 9.79/10.25 thf(sP11,plain,sP11 <=> (sP2 => ((c @ eigen__20) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP11])])).
% 9.79/10.25 thf(sP12,plain,sP12 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP12])])).
% 9.79/10.25 thf(sP13,plain,sP13 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP13])])).
% 9.79/10.25 thf(sP14,plain,sP14 <=> (sP3 => sP2),introduced(definition,[new_symbols(definition,[sP14])])).
% 9.79/10.25 thf(sP15,plain,sP15 <=> (((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,[sP15])])).
% 9.79/10.25 thf(sP16,plain,sP16 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 9.79/10.25 thf(sP17,plain,sP17 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP17])])).
% 9.79/10.25 thf(sP18,plain,sP18 <=> (sP7 => ((c @ eigen__4) @ spain)),introduced(definition,[new_symbols(definition,[sP18])])).
% 9.79/10.25 thf(sP19,plain,sP19 <=> (sP1 => ((c @ eigen__5) @ france)),introduced(definition,[new_symbols(definition,[sP19])])).
% 9.79/10.25 thf(sP20,plain,sP20 <=> ((c @ eigen__5) @ france),introduced(definition,[new_symbols(definition,[sP20])])).
% 9.79/10.25 thf(sP21,plain,sP21 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(sP16)) => (![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,[sP21])])).
% 9.79/10.25 thf(sP22,plain,sP22 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP22])])).
% 9.79/10.25 thf(sP23,plain,sP23 <=> (sP9 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 9.79/10.25 thf(sP24,plain,sP24 <=> (((c @ eigen__3) @ eigen__2) => ((c @ eigen__3) @ paris)),introduced(definition,[new_symbols(definition,[sP24])])).
% 9.79/10.25 thf(sP25,plain,sP25 <=> ((c @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP25])])).
% 9.79/10.25 thf(sP26,plain,sP26 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP26])])).
% 9.79/10.25 thf(sP27,plain,sP27 <=> (((c @ eigen__3) @ paris) => ((c @ eigen__3) @ france)),introduced(definition,[new_symbols(definition,[sP27])])).
% 9.79/10.25 thf(sP28,plain,sP28 <=> ((c @ eigen__5) @ eigen__2),introduced(definition,[new_symbols(definition,[sP28])])).
% 9.79/10.25 thf(sP29,plain,sP29 <=> ((c @ eigen__3) @ france),introduced(definition,[new_symbols(definition,[sP29])])).
% 9.79/10.25 thf(sP30,plain,sP30 <=> ((~(sP16)) => (![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,[sP30])])).
% 9.79/10.25 thf(sP31,plain,sP31 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP10))))),introduced(definition,[new_symbols(definition,[sP31])])).
% 9.79/10.25 thf(sP32,plain,sP32 <=> ((c @ eigen__20) @ eigen__2),introduced(definition,[new_symbols(definition,[sP32])])).
% 9.79/10.25 thf(sP33,plain,sP33 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP30))))),introduced(definition,[new_symbols(definition,[sP33])])).
% 9.79/10.25 thf(sP34,plain,sP34 <=> ((c @ eigen__3) @ paris),introduced(definition,[new_symbols(definition,[sP34])])).
% 9.79/10.25 thf(sP35,plain,sP35 <=> ((c @ eigen__4) @ spain),introduced(definition,[new_symbols(definition,[sP35])])).
% 9.79/10.25 thf(sP36,plain,sP36 <=> (sP26 => (~(sP10))),introduced(definition,[new_symbols(definition,[sP36])])).
% 9.79/10.25 thf(sP37,plain,sP37 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP10)))),introduced(definition,[new_symbols(definition,[sP37])])).
% 9.79/10.25 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 9.79/10.25 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 9.79/10.25 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 9.79/10.25 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 9.79/10.25 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 9.79/10.25 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 9.79/10.25 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 9.79/10.25 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 9.79/10.25 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 9.79/10.25 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 9.79/10.25 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 9.79/10.25 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 9.79/10.25 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 9.79/10.25 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 9.79/10.25 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 9.79/10.25 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 9.79/10.25 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 9.79/10.25 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 9.79/10.25 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 9.79/10.25 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 9.79/10.25 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 9.79/10.25 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 9.79/10.25 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)))))))).
% 9.79/10.25 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 9.79/10.25 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 9.79/10.25 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 9.79/10.25 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 9.79/10.25 thf(def_mvalid,definition,(mvalid = (!!))).
% 9.79/10.25 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 9.79/10.25 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 9.79/10.25 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 9.79/10.25 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))).
% 9.79/10.25 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))).
% 9.79/10.25 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))).
% 9.79/10.25 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))).
% 9.79/10.25 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))).
% 9.79/10.25 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))).
% 9.79/10.25 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))).
% 9.79/10.25 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))).
% 9.79/10.25 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))).
% 9.79/10.25 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))) => (~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => (~((~(((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya))))))))))))))))).
% 9.79/10.25 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))) => ((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))) => (~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => ((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 9.79/10.25 thf(h1,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (![X2:reg]:((~(((~(((~(((![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))) => (~((![X3:reg]:((~((((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))) => ((~(((![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))) => (~((![X3:reg]:((~((((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2)))))))))))))))))) => (~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))) => ((![X3:reg]:(((c @ X3) @ catalunya) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h2,assumption,(~((sP26 => (![X1:reg]:((~(((~(((~(((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => (~((![X2:reg]:((~((((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))) => (~((![X2:reg]:((~((((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1)))))))))))))))))) => (~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))) => ((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h3,assumption,sP26,introduced(assumption,[])).
% 9.79/10.25 thf(h4,assumption,(~((![X1:reg]:((~(((~(((~(((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => (~((![X2:reg]:((~((((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))) => (~((![X2:reg]:((~((((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1)))))))))))))))))) => (~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))) => ((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h5,assumption,(~(((~(((~(((~((sP4 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))) => (~((![X1:reg]:((~((((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))))) => ((~((sP17 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain)))))) => (~((![X1:reg]:((~((((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))))))))) => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ eigen__2))) => sP13))) => ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))) => sP12))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h6,assumption,(~(((~(((~((sP4 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))) => (~((![X1:reg]:((~((((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))))) => ((~((sP17 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain)))))) => (~((![X1:reg]:((~((((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h7,assumption,((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ eigen__2))) => sP13))) => ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))) => sP12)),introduced(assumption,[])).
% 9.79/10.25 thf(h8,assumption,(~(((~((sP4 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))) => (~((![X1:reg]:((~((((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h9,assumption,(~(((~((sP17 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain)))))) => (~((![X1:reg]:((~((((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h10,assumption,(~((sP4 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))),introduced(assumption,[])).
% 9.79/10.25 thf(h11,assumption,(![X1:reg]:((~((((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h12,assumption,sP4,introduced(assumption,[])).
% 9.79/10.25 thf(h13,assumption,(~((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france))))),introduced(assumption,[])).
% 9.79/10.25 thf(h14,assumption,(~((sP25 => sP29))),introduced(assumption,[])).
% 9.79/10.25 thf(h15,assumption,sP25,introduced(assumption,[])).
% 9.79/10.25 thf(h16,assumption,(~(sP29)),introduced(assumption,[])).
% 9.79/10.25 thf(h17,assumption,(~((sP17 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain)))))),introduced(assumption,[])).
% 9.79/10.25 thf(h18,assumption,(![X1:reg]:((~((((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))),introduced(assumption,[])).
% 9.79/10.25 thf(h19,assumption,sP17,introduced(assumption,[])).
% 9.79/10.25 thf(h20,assumption,(~((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain))))),introduced(assumption,[])).
% 9.79/10.25 thf(h21,assumption,(~((sP8 => sP35))),introduced(assumption,[])).
% 9.79/10.25 thf(h22,assumption,sP8,introduced(assumption,[])).
% 9.79/10.25 thf(h23,assumption,(~(sP35)),introduced(assumption,[])).
% 9.79/10.25 thf(h24,assumption,((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ eigen__2))) => sP13),introduced(assumption,[])).
% 9.79/10.25 thf(h25,assumption,((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))) => sP12),introduced(assumption,[])).
% 9.79/10.25 thf(h26,assumption,(~((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ eigen__2))))),introduced(assumption,[])).
% 9.79/10.25 thf(h27,assumption,sP13,introduced(assumption,[])).
% 9.79/10.25 thf(h28,assumption,(~((sP1 => sP28))),introduced(assumption,[])).
% 9.79/10.25 thf(h29,assumption,sP1,introduced(assumption,[])).
% 9.79/10.25 thf(h30,assumption,(~(sP28)),introduced(assumption,[])).
% 9.79/10.25 thf(1,plain,(~(sP9) | sP19),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(2,plain,((~(sP19) | ~(sP1)) | sP20),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(3,plain,(sP23 | sP9),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(4,plain,(sP10 | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(5,plain,(~(sP31) | sP37),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(6,plain,(~(sP37) | sP36),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(7,plain,((~(sP36) | ~(sP26)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(8,plain,(~(sP4) | sP5),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(9,plain,((~(sP5) | ~(sP20)) | sP28),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))).
% 9.79/10.25 thf(10,plain,sP31,inference(preprocess,[status(thm)],[ax3]).
% 9.79/10.25 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h29,h30,h28,h26,h24,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h3,h12,h29,h30])).
% 9.79/10.25 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h28,h26,h24,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,11,h29,h30])).
% 9.79/10.25 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h26,h24,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__5)],[h26,12,h28])).
% 9.79/10.25 thf(14,plain,(~(sP9) | sP27),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(15,plain,((~(sP27) | ~(sP34)) | sP29),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(16,plain,(sP23 | sP9),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(17,plain,(sP10 | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(18,plain,(~(sP31) | sP37),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(19,plain,(~(sP37) | sP36),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(20,plain,((~(sP36) | ~(sP26)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(21,plain,(~(sP13) | sP24),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(22,plain,((~(sP24) | ~(sP25)) | sP34),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(23,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h24,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[14,15,16,17,18,19,20,21,22,10,h3,h15,h16,h27])).
% 9.79/10.25 thf(24,plain,$false,inference(tab_imp,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[h24,13,23,h26,h27])).
% 9.79/10.25 thf(h31,assumption,(~((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))))),introduced(assumption,[])).
% 9.79/10.25 thf(h32,assumption,sP12,introduced(assumption,[])).
% 9.79/10.25 thf(h33,assumption,(~((sP3 => sP32))),introduced(assumption,[])).
% 9.79/10.25 thf(h34,assumption,sP3,introduced(assumption,[])).
% 9.79/10.25 thf(h35,assumption,(~(sP32)),introduced(assumption,[])).
% 9.79/10.25 thf(25,plain,(~(sP22) | sP14),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(26,plain,((~(sP14) | ~(sP3)) | sP2),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(27,plain,(sP16 | sP22),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(28,plain,(sP30 | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(29,plain,(~(sP33) | sP21),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(30,plain,(~(sP21) | sP15),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(31,plain,((~(sP15) | ~(sP26)) | ~(sP30)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(32,plain,(~(sP17) | sP11),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(33,plain,((~(sP11) | ~(sP2)) | sP32),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))).
% 9.79/10.25 thf(34,plain,sP33,inference(preprocess,[status(thm)],[ax1]).
% 9.79/10.25 thf(35,plain,$false,inference(prop_unsat,[status(thm),assumptions([h34,h35,h33,h31,h25,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[25,26,27,28,29,30,31,32,33,34,h3,h19,h34,h35])).
% 9.79/10.25 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h33,h31,h25,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,35,h34,h35])).
% 9.79/10.25 thf(37,plain,$false,inference(tab_negall,[status(thm),assumptions([h31,h25,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__20)],[h31,36,h33])).
% 9.79/10.25 thf(38,plain,(~(sP22) | sP18),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(39,plain,((~(sP18) | ~(sP7)) | sP35),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(40,plain,(sP16 | sP22),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(41,plain,(sP30 | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(42,plain,(~(sP33) | sP21),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(43,plain,(~(sP21) | sP15),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(44,plain,((~(sP15) | ~(sP26)) | ~(sP30)),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(45,plain,(~(sP12) | sP6),inference(all_rule,[status(thm)],[])).
% 9.79/10.25 thf(46,plain,((~(sP6) | ~(sP8)) | sP7),inference(prop_rule,[status(thm)],[])).
% 9.79/10.25 thf(47,plain,$false,inference(prop_unsat,[status(thm),assumptions([h32,h25,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[38,39,40,41,42,43,44,45,46,34,h3,h22,h23,h32])).
% 9.79/10.25 thf(48,plain,$false,inference(tab_imp,[status(thm),assumptions([h25,h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h31]),tab_imp(discharge,[h32])],[h25,37,47,h31,h32])).
% 9.79/10.25 thf(49,plain,$false,inference(tab_imp,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h25])],[h7,24,48,h24,h25])).
% 9.79/10.25 thf(50,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,49,h22,h23])).
% 9.79/10.25 thf(51,plain,$false,inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__4)],[h20,50,h21])).
% 9.79/10.25 thf(52,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,51,h19,h20])).
% 9.79/10.25 thf(53,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h9,52,h17,h18])).
% 9.79/10.25 thf(54,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,53,h15,h16])).
% 9.79/10.25 thf(55,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,54,h14])).
% 9.79/10.25 thf(56,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,55,h12,h13])).
% 9.79/10.25 thf(57,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,56,h10,h11])).
% 9.79/10.25 thf(58,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,57,h8,h9])).
% 9.79/10.25 thf(59,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,58,h6,h7])).
% 9.79/10.25 thf(60,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,59,h5])).
% 9.79/10.25 thf(61,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,60,h3,h4])).
% 9.79/10.25 thf(62,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,61,h2])).
% 9.79/10.25 thf(63,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,62,h1])).
% 9.79/10.25 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))) => (~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => (~((~(((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[63,h0])).
% 9.79/10.25 % SZS output end Proof
%------------------------------------------------------------------------------