TSTP Solution File: SYO435^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO435^1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : Thu Jul 21 19:32:03 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO435^1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Jul 9 07:04:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 27
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 thf(ty_p, type, p : ($i>$o)).
% 0.13/0.37 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.13/0.37 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.13/0.37 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.13/0.37 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.13/0.37 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.13/0.37 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.13/0.37 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((p @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 0.13/0.37 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__1) @ X1) => (~((p @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 0.13/0.37 thf(sP1,plain,sP1 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.13/0.37 thf(sP2,plain,sP2 <=> ((rel_s4 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.13/0.37 thf(sP3,plain,sP3 <=> ((rel_s4 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.13/0.37 thf(sP4,plain,sP4 <=> (((rel_s4 @ eigen__1) @ eigen__2) => (~((p @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.13/0.37 thf(sP5,plain,sP5 <=> (sP1 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.13/0.37 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__1) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.13/0.37 thf(sP7,plain,sP7 <=> ((rel_s4 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.13/0.37 thf(sP8,plain,sP8 <=> ((~(sP5)) => sP7),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.13/0.37 thf(sP9,plain,sP9 <=> (sP2 => (~((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (~((p @ X1)))))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.13/0.37 thf(sP10,plain,sP10 <=> ((~((((rel_s4 @ eigen__1) @ eigen__2) => (~(sP2))))) => sP3),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.13/0.37 thf(sP11,plain,sP11 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.13/0.37 thf(sP12,plain,sP12 <=> (sP1 => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((p @ X1)))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.13/0.37 thf(sP13,plain,sP13 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.13/0.37 thf(sP14,plain,sP14 <=> (sP11 => (~((![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((p @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.13/0.37 thf(sP15,plain,sP15 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((p @ X2))))))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.13/0.37 thf(sP16,plain,sP16 <=> (sP7 => (~(sP13))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.13/0.37 thf(sP17,plain,sP17 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((p @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.13/0.37 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__0) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.13/0.37 thf(sP19,plain,sP19 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.13/0.37 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((p @ X2))))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.13/0.37 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.13/0.37 thf(sP22,plain,sP22 <=> (![X1:$i]:((~((sP1 => (~(((rel_s4 @ eigen__1) @ X1)))))) => ((rel_s4 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.13/0.37 thf(sP23,plain,sP23 <=> (![X1:$i]:((~((sP11 => (~(((rel_s4 @ eigen__2) @ X1)))))) => ((rel_s4 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.13/0.37 thf(sP24,plain,sP24 <=> (sP11 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.13/0.37 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.13/0.37 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.13/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.13/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.13/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.13/0.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.13/0.37 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.13/0.37 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.13/0.37 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.13/0.37 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.13/0.37 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.13/0.37 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.13/0.37 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.13/0.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.13/0.37 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.13/0.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.13/0.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.13/0.37 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.13/0.37 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.13/0.37 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.13/0.37 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.13/0.37 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.13/0.37 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 0.13/0.37 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.13/0.37 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.13/0.37 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))))))))).
% 0.13/0.37 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.13/0.37 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.13/0.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.13/0.37 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.13/0.37 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.13/0.37 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.13/0.37 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.13/0.37 thf(prove,conjecture,(![X1:$i]:((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((p @ X3))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (~((p @ X5)))))))))))))))))))).
% 0.13/0.37 thf(h1,negated_conjecture,(~((![X1:$i]:((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((p @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (~((p @ X5))))))))))))))))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.13/0.37 thf(h2,assumption,(~((sP15 => (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((p @ X4)))))))))))))))))))),introduced(assumption,[])).
% 0.13/0.37 thf(h3,assumption,sP15,introduced(assumption,[])).
% 0.13/0.37 thf(h4,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((p @ X4))))))))))))))))))),introduced(assumption,[])).
% 0.13/0.37 thf(h5,assumption,(~((sP1 => (~(sP17))))),introduced(assumption,[])).
% 0.13/0.37 thf(h6,assumption,sP1,introduced(assumption,[])).
% 0.13/0.37 thf(h7,assumption,sP17,introduced(assumption,[])).
% 0.13/0.37 thf(1,plain,(~(sP21) | sP6),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(2,plain,(~(sP6) | sP23),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(3,plain,(~(sP23) | sP10),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(4,plain,((~(sP10) | sP24) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(5,plain,((~(sP24) | ~(sP11)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(6,plain,(~(sP18) | sP22),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(7,plain,(~(sP22) | sP8),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(8,plain,((~(sP8) | sP5) | sP7),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(9,plain,((~(sP5) | ~(sP1)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(10,plain,(~(sP21) | sP18),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(11,plain,(~(sP15) | sP16),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(12,plain,((~(sP16) | ~(sP7)) | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(13,plain,(sP9 | sP13),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(14,plain,(sP9 | sP2),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(15,plain,(sP20 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 0.13/0.37 thf(16,plain,(~(sP17) | sP14),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(17,plain,((~(sP14) | ~(sP11)) | ~(sP20)),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(18,plain,(sP4 | sP11),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(19,plain,(sP19 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 0.13/0.37 thf(20,plain,(~(sP15) | sP12),inference(all_rule,[status(thm)],[])).
% 0.13/0.37 thf(21,plain,((~(sP12) | ~(sP1)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 0.13/0.37 thf(a2,axiom,(mtransitive @ rel_s4)).
% 0.13/0.37 thf(22,plain,sP21,inference(preprocess,[status(thm)],[a2]).
% 0.13/0.37 thf(23,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,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,h3,h6,h7])).
% 0.13/0.37 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,23,h6,h7])).
% 0.13/0.37 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,24,h5])).
% 0.13/0.37 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,25,h3,h4])).
% 0.13/0.37 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,26,h2])).
% 0.13/0.37 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0])).
% 0.13/0.37 thf(0,theorem,(![X1:$i]:((~((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((p @ X3))))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (~((p @ X5))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[27,h1])).
% 0.13/0.37 % SZS output end Proof
%------------------------------------------------------------------------------