%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GEG009^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 : Thu Oct 9 01:27:38 PM UTC 2025
% Result : Theorem 109.29s 109.36s
% Output : Proof 109.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEG009^1 : TPTP v9.2.0. Released v4.1.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 12:30:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 109.29/109.36 % SZS status Theorem
% 109.29/109.36 % Mode: mode447
% 109.29/109.36 % Inferences: 49
% 109.29/109.36 % SZS output start Proof
% 109.29/109.36 thf(ty_reg, type, reg : $tType).
% 109.29/109.36 thf(ty_a, type, a : ($i>$i>$o)).
% 109.29/109.36 thf(ty_spain, type, spain : reg).
% 109.29/109.36 thf(ty_eigen__1, type, eigen__1 : $i).
% 109.29/109.36 thf(ty_paris, type, paris : reg).
% 109.29/109.36 thf(ty_eigen__0, type, eigen__0 : $i).
% 109.29/109.36 thf(ty_c, type, c : (reg>reg>$o)).
% 109.29/109.36 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 109.29/109.36 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 109.29/109.36 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 109.29/109.36 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 109.29/109.36 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 109.29/109.36 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 109.29/109.36 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 109.29/109.36 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 109.29/109.36 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 109.29/109.36 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 109.29/109.36 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 109.29/109.36 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 109.29/109.36 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 109.29/109.36 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 109.29/109.36 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 109.29/109.36 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 109.29/109.36 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 109.29/109.36 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 109.29/109.36 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 109.29/109.36 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 109.29/109.36 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 109.29/109.36 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 109.29/109.36 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)))))))).
% 109.29/109.36 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 109.29/109.36 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 109.29/109.36 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 109.29/109.36 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 109.29/109.36 thf(def_mvalid,definition,(mvalid = (!!))).
% 109.29/109.36 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 109.29/109.36 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 109.29/109.36 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 109.29/109.36 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))).
% 109.29/109.36 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))).
% 109.29/109.36 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))).
% 109.29/109.36 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))).
% 109.29/109.36 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))).
% 109.29/109.36 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))).
% 109.29/109.36 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))).
% 109.29/109.36 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))).
% 109.29/109.36 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))).
% 109.29/109.36 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)))))))))))))))).
% 109.29/109.36 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])).
% 109.29/109.36 thf(h1,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (~((![X2:reg]:((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))) => (~(((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))) => (~((![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ X2)))))))))))))))),introduced(assumption,[])).
% 109.29/109.36 thf(h2,assumption,(~((((a @ eigen__0) @ eigen__1) => (~((![X1:reg]:((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))) => (~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1))))))))))))))),introduced(assumption,[])).
% 109.29/109.36 thf(h3,assumption,((a @ eigen__0) @ eigen__1),introduced(assumption,[])).
% 109.29/109.36 thf(h4,assumption,(![X1:reg]:((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))) => (~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1)))))))))),introduced(assumption,[])).
% 109.29/109.36 thf(pax1, axiom, (p1=>![X12:reg]:(![X13:reg]:(![X4:reg]:(fc @ X4 @ X13=>fc @ X4 @ X12)=>~(![X4:reg]:(fc @ X4 @ X13=>fc @ X4 @ fparis)))=>~((![X13:reg]:(fc @ X13 @ X12=>fc @ X13 @ fspain)=>~(![X13:reg]:(fc @ X13 @ fspain=>fc @ X13 @ X12)))))), file('<stdin>', pax1)).
% 109.29/109.36 thf(pax10, axiom, (p10=>![X8:reg]:fc @ X8 @ X8), file('<stdin>', pax10)).
% 109.29/109.36 thf(pax5, axiom, (p5=>![X9:$i, X10:$i]:(fa @ X9 @ X10=>~((~((![X4:reg]:(fc @ X4 @ fcatalunya=>fc @ X4 @ fspain)=>![X4:reg]:(fc @ X4 @ fspain=>fc @ X4 @ fcatalunya)))=>![X4:reg]:(~((fc @ X4 @ fcatalunya=>~(![X7:reg]:(![X11:reg]:(fc @ X11 @ X7=>fc @ X11 @ X4)=>~(![X11:reg]:(fc @ X11 @ X7=>fc @ X11 @ fcatalunya))))))=>(fc @ X4 @ fspain=>~(![X7:reg]:(![X11:reg]:(fc @ X11 @ X7=>fc @ X11 @ X4)=>~(![X11:reg]:(fc @ X11 @ X7=>fc @ X11 @ fspain)))))))))), file('<stdin>', pax5)).
% 109.29/109.36 thf(pax2, axiom, (p2=>fa @ f__0 @ f__1), file('<stdin>', pax2)).
% 109.29/109.36 thf(ax100, axiom, p1, file('<stdin>', ax100)).
% 109.29/109.36 thf(ax91, axiom, p10, file('<stdin>', ax91)).
% 109.29/109.36 thf(ax96, axiom, p5, file('<stdin>', ax96)).
% 109.29/109.36 thf(ax99, axiom, p2, file('<stdin>', ax99)).
% 109.29/109.36 thf(pax9, axiom, (p9=>![X8:reg, X2:reg]:(fc @ X8 @ X2=>fc @ X2 @ X8)), file('<stdin>', pax9)).
% 109.29/109.36 thf(ax88, axiom, (~(p3)|p13), file('<stdin>', ax88)).
% 109.29/109.36 thf(ax68, axiom, (~(p1)|p34), file('<stdin>', ax68)).
% 109.29/109.36 thf(ax92, axiom, p9, file('<stdin>', ax92)).
% 109.29/109.36 thf(ax90, axiom, (~(p12)|~(p2)|~(p11)), file('<stdin>', ax90)).
% 109.29/109.36 thf(ax89, axiom, (~(p13)|p12), file('<stdin>', ax89)).
% 109.29/109.36 thf(ax98, axiom, p3, file('<stdin>', ax98)).
% 109.29/109.36 thf(pax34, axiom, (p34=>(![X5:reg]:(![X2:reg]:(fc @ X2 @ X5=>fc @ X2 @ f__2)=>~(![X2:reg]:(fc @ X2 @ X5=>fc @ X2 @ fparis)))=>~((![X5:reg]:(fc @ X5 @ f__2=>fc @ X5 @ fspain)=>~(![X5:reg]:(fc @ X5 @ fspain=>fc @ X5 @ f__2)))))), file('<stdin>', pax34)).
% 109.29/109.36 thf(pax84, axiom, (p84=>fc @ fspain @ fparis), file('<stdin>', pax84)).
% 109.29/109.36 thf(ax84, axiom, (p11|~(p17)), file('<stdin>', ax84)).
% 109.29/109.36 thf(nax84, axiom, (p84<=fc @ fspain @ fparis), file('<stdin>', nax84)).
% 109.29/109.36 thf(ax81, axiom, (p17|~(p20)), file('<stdin>', ax81)).
% 109.29/109.36 thf(ax76, axiom, (p20|~(p25)), file('<stdin>', ax76)).
% 109.29/109.36 thf(nax25, axiom, (p25<=(fc @ f__2 @ ffrance=>fc @ f__2 @ fparis)), file('<stdin>', nax25)).
% 109.29/109.36 thf(c_0_22, plain, ![X412:reg, X414:reg, X415:reg, X416:reg, X417:reg]:(((~fc @ X416 @ X412|fc @ X416 @ fspain|(~fc @ X414 @ (esk200_1 @ X412)|fc @ X414 @ X412)|~p1)&(~fc @ X417 @ fspain|fc @ X417 @ X412|(~fc @ X414 @ (esk200_1 @ X412)|fc @ X414 @ X412)|~p1))&((~fc @ X416 @ X412|fc @ X416 @ fspain|(~fc @ X415 @ (esk200_1 @ X412)|fc @ X415 @ fparis)|~p1)&(~fc @ X417 @ fspain|fc @ X417 @ X412|(~fc @ X415 @ (esk200_1 @ X412)|fc @ X415 @ fparis)|~p1))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])])])])).
% 109.29/109.36 thf(c_0_23, plain, ![X352:reg]:(~p10|fc @ X352 @ X352), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])])).
% 109.29/109.36 thf(c_0_24, plain, ![X358:$i, X359:$i, X360:reg, X363:reg, X366:reg]:(((~fc @ X360 @ fcatalunya|fc @ X360 @ fspain|~fa @ X358 @ X359|~p5)&((fc @ esk173_0 @ fspain|~fa @ X358 @ X359|~p5)&(~fc @ esk173_0 @ fcatalunya|~fa @ X358 @ X359|~p5)))&(((fc @ esk174_0 @ fcatalunya|~fa @ X358 @ X359|~p5)&(((fc @ (esk176_1 @ X363) @ X363|fc @ (esk175_1 @ X363) @ X363|~fa @ X358 @ X359|~p5)&(~fc @ (esk176_1 @ X363) @ fcatalunya|fc @ (esk175_1 @ X363) @ X363|~fa @ X358 @ X359|~p5))&((fc @ (esk176_1 @ X363) @ X363|~fc @ (esk175_1 @ X363) @ esk174_0|~fa @ X358 @ X359|~p5)&(~fc @ (esk176_1 @ X363) @ fcatalunya|~fc @ (esk175_1 @ X363) @ esk174_0|~fa @ X358 @ X359|~p5))))&((fc @ esk174_0 @ fspain|~fa @ X358 @ X359|~p5)&(((fc @ (esk178_1 @ X366) @ X366|fc @ (esk177_1 @ X366) @ X366|~fa @ X358 @ X359|~p5)&(~fc @ (esk178_1 @ X366) @ fspain|fc @ (esk177_1 @ X366) @ X366|~fa @ X358 @ X359|~p5))&((fc @ (esk178_1 @ X366) @ X366|~fc @ (esk177_1 @ X366) @ esk174_0|~fa @ X358 @ X359|~p5)&(~fc @ (esk178_1 @ X366) @ fspain|~fc @ (esk177_1 @ X366) @ esk174_0|~fa @ X358 @ X359|~p5)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])])])])])).
% 109.29/109.36 thf(c_0_25, plain, (~p2|fa @ f__0 @ f__1), inference(fof_nnf,[status(thm)],[pax2])).
% 109.29/109.36 thf(c_0_26, plain, ![X1:reg, X4:reg, X2:reg]:(fc @ X1 @ X2|fc @ X4 @ X2|~fc @ X1 @ fspain|~fc @ X4 @ (esk200_1 @ X2)|~p1), inference(split_conjunct,[status(thm)],[c_0_22])).
% 109.29/109.36 thf(c_0_27, plain, p1, inference(split_conjunct,[status(thm)],[ax100])).
% 109.29/109.36 thf(c_0_28, plain, ![X1:reg]:(fc @ X1 @ X1|~p10), inference(split_conjunct,[status(thm)],[c_0_23])).
% 109.29/109.36 thf(c_0_29, plain, p10, inference(split_conjunct,[status(thm)],[ax91])).
% 109.29/109.36 thf(c_0_30, plain, ![X3:$i, X6:$i]:(fc @ esk173_0 @ fspain|~fa @ X3 @ X6|~p5), inference(split_conjunct,[status(thm)],[c_0_24])).
% 109.29/109.36 thf(c_0_31, plain, p5, inference(split_conjunct,[status(thm)],[ax96])).
% 109.29/109.36 thf(c_0_32, plain, (fa @ f__0 @ f__1|~p2), inference(split_conjunct,[status(thm)],[c_0_25])).
% 109.29/109.36 thf(c_0_33, plain, p2, inference(split_conjunct,[status(thm)],[ax99])).
% 109.29/109.36 thf(c_0_34, plain, ![X4:reg, X2:reg, X1:reg]:(fc @ X1 @ X2|fc @ X4 @ X2|~fc @ X4 @ (esk200_1 @ X2)|~fc @ X1 @ fspain), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 109.29/109.36 thf(c_0_35, plain, ![X1:reg]:fc @ X1 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 109.29/109.36 thf(c_0_36, plain, ![X3:$i, X6:$i]:(fc @ esk173_0 @ fspain|~fa @ X3 @ X6), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 109.29/109.36 thf(c_0_37, plain, fa @ f__0 @ f__1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 109.29/109.36 thf(c_0_38, plain, ![X3:$i, X6:$i]:(~fc @ esk173_0 @ fcatalunya|~fa @ X3 @ X6|~p5), inference(split_conjunct,[status(thm)],[c_0_24])).
% 109.29/109.36 thf(c_0_39, plain, ![X1:reg, X3:$i, X6:$i]:(fc @ X1 @ fspain|~fc @ X1 @ fcatalunya|~fa @ X3 @ X6|~p5), inference(split_conjunct,[status(thm)],[c_0_24])).
% 109.29/109.36 thf(c_0_40, plain, ![X1:reg, X2:reg]:(fc @ (esk200_1 @ X1) @ X1|fc @ X2 @ X1|~fc @ X2 @ fspain), inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 109.29/109.36 thf(c_0_41, plain, fc @ esk173_0 @ fspain, inference(spm,[status(thm)],[c_0_36, c_0_37])).
% 109.29/109.36 thf(c_0_42, plain, ![X3:$i, X6:$i]:(~fc @ esk173_0 @ fcatalunya|~fa @ X3 @ X6), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_31])])).
% 109.29/109.36 thf(c_0_43, plain, ![X354:reg, X355:reg]:(~p9|(~fc @ X354 @ X355|fc @ X355 @ X354)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])])).
% 109.29/109.36 thf(c_0_44, plain, ![X1:reg, X3:$i, X6:$i]:(fc @ X1 @ fspain|~fc @ X1 @ fcatalunya|~fa @ X3 @ X6), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_31])])).
% 109.29/109.36 thf(c_0_45, plain, ![X1:reg]:(fc @ (esk200_1 @ X1) @ X1|fc @ esk173_0 @ X1), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 109.29/109.36 thf(c_0_46, plain, ~fc @ esk173_0 @ fcatalunya, inference(spm,[status(thm)],[c_0_42, c_0_37])).
% 109.29/109.36 thf(c_0_47, plain, (~p3|p13), inference(fof_simplification,[status(thm)],[ax88])).
% 109.29/109.36 thf(c_0_48, plain, (~p1|p34), inference(fof_simplification,[status(thm)],[ax68])).
% 109.29/109.36 thf(c_0_49, plain, ![X1:reg, X2:reg]:(fc @ X2 @ X1|~p9|~fc @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_43])).
% 109.29/109.36 thf(c_0_50, plain, p9, inference(split_conjunct,[status(thm)],[ax92])).
% 109.29/109.36 thf(c_0_51, plain, ![X3:$i, X6:$i]:(fc @ (esk200_1 @ fcatalunya) @ fspain|~fa @ X3 @ X6), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])).
% 109.29/109.36 thf(c_0_52, plain, (~p12|~p2|~p11), inference(fof_simplification,[status(thm)],[ax90])).
% 109.29/109.36 thf(c_0_53, plain, (~p13|p12), inference(fof_simplification,[status(thm)],[ax89])).
% 109.29/109.36 thf(c_0_54, plain, (p13|~p3), inference(split_conjunct,[status(thm)],[c_0_47])).
% 109.29/109.36 thf(c_0_55, plain, p3, inference(split_conjunct,[status(thm)],[ax98])).
% 109.29/109.36 thf(c_0_56, plain, ![X165:reg, X166:reg, X167:reg, X168:reg]:(((~fc @ X167 @ f__2|fc @ X167 @ fspain|(~fc @ X165 @ esk76_0|fc @ X165 @ f__2)|~p34)&(~fc @ X168 @ fspain|fc @ X168 @ f__2|(~fc @ X165 @ esk76_0|fc @ X165 @ f__2)|~p34))&((~fc @ X167 @ f__2|fc @ X167 @ fspain|(~fc @ X166 @ esk76_0|fc @ X166 @ fparis)|~p34)&(~fc @ X168 @ fspain|fc @ X168 @ f__2|(~fc @ X166 @ esk76_0|fc @ X166 @ fparis)|~p34))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax34])])])])])).
% 109.29/109.36 thf(c_0_57, plain, (p34|~p1), inference(split_conjunct,[status(thm)],[c_0_48])).
% 109.29/109.36 thf(c_0_58, plain, ![X1:reg, X4:reg, X2:reg]:(fc @ X1 @ X2|fc @ X4 @ fparis|~fc @ X1 @ fspain|~fc @ X4 @ (esk200_1 @ X2)|~p1), inference(split_conjunct,[status(thm)],[c_0_22])).
% 109.29/109.36 thf(c_0_59, plain, ![X2:reg, X1:reg]:(fc @ X1 @ X2|~fc @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 109.29/109.36 thf(c_0_60, plain, fc @ (esk200_1 @ fcatalunya) @ fspain, inference(spm,[status(thm)],[c_0_51, c_0_37])).
% 109.29/109.36 thf(c_0_61, plain, (~p12|~p2|~p11), inference(split_conjunct,[status(thm)],[c_0_52])).
% 109.29/109.36 thf(c_0_62, plain, (p12|~p13), inference(split_conjunct,[status(thm)],[c_0_53])).
% 109.29/109.36 thf(c_0_63, plain, p13, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 109.29/109.36 thf(c_0_64, plain, ![X1:reg, X2:reg]:(fc @ X1 @ f__2|fc @ X2 @ f__2|~fc @ X1 @ fspain|~fc @ X2 @ esk76_0|~p34), inference(split_conjunct,[status(thm)],[c_0_56])).
% 109.29/109.36 thf(c_0_65, plain, p34, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_27])])).
% 109.29/109.36 thf(c_0_66, plain, (~p84|fc @ fspain @ fparis), inference(fof_nnf,[status(thm)],[pax84])).
% 109.29/109.36 thf(c_0_67, plain, ![X1:reg, X4:reg, X2:reg]:(fc @ X1 @ fparis|fc @ X2 @ X4|~fc @ X1 @ (esk200_1 @ X4)|~fc @ X2 @ fspain), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_27])])).
% 109.29/109.36 thf(c_0_68, plain, fc @ fspain @ (esk200_1 @ fcatalunya), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 109.29/109.36 thf(c_0_69, plain, (p11|~p17), inference(fof_simplification,[status(thm)],[ax84])).
% 109.29/109.36 thf(c_0_70, plain, (~p11|~p12), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_33])])).
% 109.29/109.36 thf(c_0_71, plain, p12, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 109.29/109.36 thf(c_0_72, plain, ![X2:reg, X1:reg]:(fc @ X1 @ f__2|fc @ X2 @ f__2|~fc @ X2 @ esk76_0|~fc @ X1 @ fspain), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 109.29/109.36 thf(c_0_73, plain, (fc @ fspain @ fparis|~p84), inference(split_conjunct,[status(thm)],[c_0_66])).
% 109.29/109.36 thf(c_0_74, plain, (~fc @ fspain @ fparis|p84), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax84])])).
% 109.29/109.36 thf(c_0_75, plain, ![X1:reg]:(fc @ fspain @ fparis|fc @ X1 @ fcatalunya|~fc @ X1 @ fspain), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 109.29/109.36 thf(c_0_76, plain, (p17|~p20), inference(fof_simplification,[status(thm)],[ax81])).
% 109.29/109.36 thf(c_0_77, plain, (p11|~p17), inference(split_conjunct,[status(thm)],[c_0_69])).
% 109.29/109.36 thf(c_0_78, plain, ~p11, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70, c_0_71])])).
% 109.29/109.36 thf(c_0_79, plain, ![X1:reg]:(fc @ esk76_0 @ f__2|fc @ X1 @ f__2|~fc @ X1 @ fspain), inference(spm,[status(thm)],[c_0_72, c_0_35])).
% 109.29/109.36 thf(c_0_80, plain, (fc @ fparis @ fspain|~p84), inference(spm,[status(thm)],[c_0_59, c_0_73])).
% 109.29/109.36 thf(c_0_81, plain, (p84|~fc @ fspain @ fparis), inference(split_conjunct,[status(thm)],[c_0_74])).
% 109.29/109.36 thf(c_0_82, plain, fc @ fspain @ fparis, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_41]), c_0_46])).
% 109.29/109.36 thf(c_0_83, plain, (p20|~p25), inference(fof_simplification,[status(thm)],[ax76])).
% 109.29/109.36 thf(c_0_84, plain, (p17|~p20), inference(split_conjunct,[status(thm)],[c_0_76])).
% 109.29/109.36 thf(c_0_85, plain, ~p17, inference(sr,[status(thm)],[c_0_77, c_0_78])).
% 109.29/109.36 thf(c_0_86, plain, (fc @ fparis @ f__2|fc @ esk76_0 @ f__2|~p84), inference(spm,[status(thm)],[c_0_79, c_0_80])).
% 109.29/109.36 thf(c_0_87, plain, p84, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_82])])).
% 109.29/109.36 thf(c_0_88, plain, ((fc @ f__2 @ ffrance|p25)&(~fc @ f__2 @ fparis|p25)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax25])])])).
% 109.29/109.36 thf(c_0_89, plain, (p20|~p25), inference(split_conjunct,[status(thm)],[c_0_83])).
% 109.29/109.36 thf(c_0_90, plain, ~p20, inference(sr,[status(thm)],[c_0_84, c_0_85])).
% 109.29/109.36 thf(c_0_91, plain, ![X1:reg, X2:reg]:(fc @ X1 @ f__2|fc @ X2 @ fparis|~fc @ X1 @ fspain|~fc @ X2 @ esk76_0|~p34), inference(split_conjunct,[status(thm)],[c_0_56])).
% 109.29/109.36 thf(c_0_92, plain, (fc @ esk76_0 @ f__2|fc @ fparis @ f__2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])])).
% 109.29/109.36 thf(c_0_93, plain, (p25|~fc @ f__2 @ fparis), inference(split_conjunct,[status(thm)],[c_0_88])).
% 109.29/109.36 thf(c_0_94, plain, ~p25, inference(sr,[status(thm)],[c_0_89, c_0_90])).
% 109.29/109.36 thf(c_0_95, plain, ![X2:reg, X1:reg]:(fc @ X1 @ f__2|fc @ X2 @ fparis|~fc @ X2 @ esk76_0|~fc @ X1 @ fspain), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91, c_0_65])])).
% 109.29/109.36 thf(c_0_96, plain, (fc @ fparis @ f__2|fc @ f__2 @ esk76_0), inference(spm,[status(thm)],[c_0_59, c_0_92])).
% 109.29/109.36 thf(c_0_97, plain, ~fc @ f__2 @ fparis, inference(sr,[status(thm)],[c_0_93, c_0_94])).
% 109.29/109.36 thf(c_0_98, plain, ![X1:reg]:(fc @ fparis @ f__2|fc @ X1 @ f__2|~fc @ X1 @ fspain), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_97])).
% 109.29/109.36 thf(c_0_99, plain, fc @ fparis @ fspain, inference(spm,[status(thm)],[c_0_59, c_0_82])).
% 109.29/109.36 thf(c_0_100, plain, fc @ fparis @ f__2, inference(spm,[status(thm)],[c_0_98, c_0_99])).
% 109.29/109.36 thf(c_0_101, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_100]), c_0_97]), ['proof']).
% 109.29/109.36 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h3,h4,h2,h1,h0])],[])).
% 109.29/109.36 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,1,h3,h4])).
% 109.29/109.36 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,2,h2])).
% 109.29/109.36 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1])).
% 109.29/109.36 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]:(((c @ X4) @ X3) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[4,h0])).
% 109.29/109.36 % SZS output end Proof
%------------------------------------------------------------------------------