TSTP Solution File: SYO432^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO432^1 : 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 : n006.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 19:32:02 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO432^1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.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 : Fri Jul 8 17:00:36 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % Mode: mode213
% 0.19/0.36 % Inferences: 21
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 thf(ty_p, type, p : ($i>$o)).
% 0.19/0.36 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.19/0.36 thf(ty_q, type, q : ($i>$o)).
% 0.19/0.36 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.19/0.36 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.19/0.36 thf(ty_rel_b, type, rel_b : ($i>$i>$o)).
% 0.19/0.36 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.19/0.36 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel_b @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => ((p @ X2) => (q @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 0.19/0.36 thf(sP1,plain,sP1 <=> ((rel_b @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.36 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel_b @ eigen__1) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => ((p @ X2) => (q @ X2)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.36 thf(sP3,plain,sP3 <=> (sP1 => (p @ eigen__1)),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.36 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:(((rel_b @ X1) @ X2) => ((rel_b @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.19/0.36 thf(sP5,plain,sP5 <=> (![X1:$i]:(((rel_b @ eigen__2) @ X1) => ((p @ X1) => (q @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.19/0.36 thf(sP6,plain,sP6 <=> (p @ eigen__1),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.19/0.36 thf(sP7,plain,sP7 <=> (((rel_b @ eigen__1) @ eigen__2) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.19/0.36 thf(sP8,plain,sP8 <=> (((rel_b @ eigen__2) @ eigen__1) => (sP6 => (q @ eigen__1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.19/0.36 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_b @ eigen__1) @ X1) => ((rel_b @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.19/0.36 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_b @ eigen__0) @ X1) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => ((p @ X3) => (q @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.19/0.36 thf(sP11,plain,sP11 <=> (q @ eigen__1),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.19/0.36 thf(sP12,plain,sP12 <=> (sP1 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.19/0.36 thf(sP13,plain,sP13 <=> ((rel_b @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.19/0.36 thf(sP14,plain,sP14 <=> (sP6 => sP11),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.19/0.36 thf(sP15,plain,sP15 <=> ((rel_b @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.19/0.36 thf(sP16,plain,sP16 <=> (![X1:$i]:(((rel_b @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.19/0.36 thf(sP17,plain,sP17 <=> (sP13 => sP15),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.19/0.36 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.19/0.36 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.19/0.36 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.19/0.36 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.19/0.36 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.19/0.36 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.19/0.36 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.19/0.36 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.19/0.36 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.19/0.36 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.19/0.36 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.19/0.36 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.36 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.36 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.19/0.36 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.19/0.36 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.19/0.36 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.19/0.36 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.19/0.36 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.19/0.36 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.19/0.36 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.19/0.36 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.19/0.36 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 0.19/0.36 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.19/0.36 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.19/0.36 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))))))))).
% 0.19/0.36 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.19/0.36 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.19/0.36 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.19/0.36 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.19/0.36 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.19/0.36 thf(def_mbox_b,definition,(mbox_b = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_b @ X2) @ X3) => (X1 @ X3))))))).
% 0.19/0.36 thf(def_mdia_b,definition,(mdia_b = (^[X1:$i>$o]:(mnot @ (mbox_b @ (mnot @ X1)))))).
% 0.19/0.36 thf(prove,conjecture,(![X1:$i]:((~((~((~(((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => ((~((~((p @ X4))))) => (q @ X4))))))))))))))))))))) => (![X2:$i]:(((rel_b @ X1) @ X2) => (q @ X2)))))).
% 0.19/0.36 thf(h1,negated_conjecture,(~((![X1:$i]:((~(((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => ((p @ X4) => (q @ X4))))))))))))))))) => (![X2:$i]:(((rel_b @ X1) @ X2) => (q @ X2))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.19/0.36 thf(h2,assumption,(~(((~((sP16 => (~(sP10))))) => (![X1:$i]:(((rel_b @ eigen__0) @ X1) => (q @ X1)))))),introduced(assumption,[])).
% 0.19/0.36 thf(h3,assumption,(~((sP16 => (~(sP10))))),introduced(assumption,[])).
% 0.19/0.36 thf(h4,assumption,(~((![X1:$i]:(((rel_b @ eigen__0) @ X1) => (q @ X1))))),introduced(assumption,[])).
% 0.19/0.36 thf(h5,assumption,sP16,introduced(assumption,[])).
% 0.19/0.36 thf(h6,assumption,sP10,introduced(assumption,[])).
% 0.19/0.36 thf(h7,assumption,(~((sP1 => sP11))),introduced(assumption,[])).
% 0.19/0.36 thf(h8,assumption,sP1,introduced(assumption,[])).
% 0.19/0.36 thf(h9,assumption,(~(sP11)),introduced(assumption,[])).
% 0.19/0.36 thf(1,plain,(~(sP9) | sP17),inference(all_rule,[status(thm)],[])).
% 0.19/0.36 thf(2,plain,((~(sP17) | ~(sP13)) | sP15),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(3,plain,(~(sP4) | sP9),inference(all_rule,[status(thm)],[])).
% 0.19/0.36 thf(4,plain,(~(sP5) | sP8),inference(all_rule,[status(thm)],[])).
% 0.19/0.36 thf(5,plain,((~(sP8) | ~(sP15)) | sP14),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(6,plain,((~(sP14) | ~(sP6)) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(7,plain,(sP7 | sP5),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(8,plain,(sP7 | sP13),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(9,plain,(sP2 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 0.19/0.36 thf(10,plain,(~(sP16) | sP3),inference(all_rule,[status(thm)],[])).
% 0.19/0.36 thf(11,plain,((~(sP3) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(12,plain,(~(sP10) | sP12),inference(all_rule,[status(thm)],[])).
% 0.19/0.36 thf(13,plain,((~(sP12) | ~(sP1)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.36 thf(a2,axiom,(msymmetric @ rel_b)).
% 0.19/0.36 thf(14,plain,sP4,inference(preprocess,[status(thm)],[a2]).
% 0.19/0.36 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h5,h6,h8,h9])).
% 0.19/0.36 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,15,h8,h9])).
% 0.19/0.36 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h4,16,h7])).
% 0.19/0.36 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,17,h5,h6])).
% 0.19/0.36 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4])).
% 0.19/0.36 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,19,h2])).
% 0.19/0.36 thf(21,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0])).
% 0.19/0.36 thf(0,theorem,(![X1:$i]:((~((~((~(((~((~((![X2:$i]:(((rel_b @ X1) @ X2) => (p @ X2))))))) => (~((![X2:$i]:(((rel_b @ X1) @ X2) => (~((![X3:$i]:(((rel_b @ X2) @ X3) => (~((![X4:$i]:(((rel_b @ X3) @ X4) => ((~((~((p @ X4))))) => (q @ X4))))))))))))))))))))) => (![X2:$i]:(((rel_b @ X1) @ X2) => (q @ X2))))),inference(contra,[status(thm),contra(discharge,[h1])],[20,h1])).
% 0.19/0.36 % SZS output end Proof
%------------------------------------------------------------------------------