TSTP Solution File: SYO064^4.001 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO064^4.001 : 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 : n013.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 19:29:58 EDT 2022
% Result : Theorem 1.37s 1.59s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO064^4.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n013.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 : Sat Jul 9 04:07:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.37/1.59 % SZS status Theorem
% 1.37/1.59 % Mode: mode213
% 1.37/1.59 % Inferences: 35894
% 1.37/1.59 % SZS output start Proof
% 1.37/1.59 thf(ty_a, type, a : ($i>$o)).
% 1.37/1.59 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.37/1.59 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.37/1.59 thf(ty_b, type, b : ($i>$o)).
% 1.37/1.59 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.37/1.59 thf(ty_irel, type, irel : ($i>$i>$o)).
% 1.37/1.59 thf(ty_c, type, c : ($i>$o)).
% 1.37/1.59 thf(sP1,plain,sP1 <=> ((irel @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.37/1.59 thf(sP2,plain,sP2 <=> (((irel @ eigen__0) @ eigen__1) => (a @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.37/1.59 thf(sP3,plain,sP3 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a @ X2)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.37/1.59 thf(sP4,plain,sP4 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.37/1.59 thf(sP5,plain,sP5 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.37/1.59 thf(sP6,plain,sP6 <=> ((!!) @ c),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.37/1.59 thf(sP7,plain,sP7 <=> (sP5 => ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.37/1.59 thf(sP8,plain,sP8 <=> ((~(sP3)) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.37/1.59 thf(sP9,plain,sP9 <=> (a @ eigen__1),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.37/1.59 thf(sP10,plain,sP10 <=> (b @ eigen__2),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.37/1.59 thf(sP11,plain,sP11 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.37/1.59 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.37/1.59 thf(sP13,plain,sP13 <=> ((~(sP12)) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.37/1.59 thf(sP14,plain,sP14 <=> (sP1 => sP10),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.37/1.59 thf(sP15,plain,sP15 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.37/1.59 thf(sP16,plain,sP16 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.37/1.59 thf(sP17,plain,sP17 <=> (c @ eigen__2),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.37/1.59 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.37/1.59 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.37/1.59 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.37/1.59 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.37/1.59 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 1.37/1.59 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 1.37/1.59 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 1.37/1.59 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 1.37/1.59 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 1.37/1.59 thf(def_iand,definition,(iand = mand)).
% 1.37/1.59 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.37/1.59 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.37/1.59 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 1.37/1.59 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 1.37/1.59 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 1.37/1.59 thf(def_ivalid,definition,(ivalid = (!!))).
% 1.37/1.59 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.37/1.59 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.37/1.59 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.37/1.59 thf(con,conjecture,(![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((c @ X2))))))))))).
% 1.37/1.59 thf(h0,negated_conjecture,(~((![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((c @ X2)))))))))))),inference(assume_negation,[status(cth)],[con])).
% 1.37/1.59 thf(h1,assumption,(~(((~(sP15)) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((b @ X1) => (~((c @ X1))))))))))),introduced(assumption,[])).
% 1.37/1.59 thf(h2,assumption,(~(sP15)),introduced(assumption,[])).
% 1.37/1.59 thf(h3,assumption,(~((![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((b @ X1) => (~((c @ X1)))))))))),introduced(assumption,[])).
% 1.37/1.59 thf(h4,assumption,(~(sP2)),introduced(assumption,[])).
% 1.37/1.59 thf(h5,assumption,sP16,introduced(assumption,[])).
% 1.37/1.59 thf(h6,assumption,(~(sP9)),introduced(assumption,[])).
% 1.37/1.59 thf(h7,assumption,(~((sP1 => (~((sP10 => (~(sP17)))))))),introduced(assumption,[])).
% 1.37/1.59 thf(h8,assumption,sP1,introduced(assumption,[])).
% 1.37/1.59 thf(h9,assumption,(sP10 => (~(sP17))),introduced(assumption,[])).
% 1.37/1.59 thf(h10,assumption,(~(sP10)),introduced(assumption,[])).
% 1.37/1.59 thf(h11,assumption,(~(sP17)),introduced(assumption,[])).
% 1.37/1.59 thf(1,plain,(~(sP11) | sP5),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(2,plain,(~(sP3) | sP7),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(3,plain,((~(sP7) | ~(sP5)) | sP13),inference(prop_rule,[status(thm)],[])).
% 1.37/1.59 thf(4,plain,((~(sP13) | sP12) | sP15),inference(prop_rule,[status(thm)],[])).
% 1.37/1.59 thf(5,plain,(~(sP15) | sP2),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(6,plain,((~(sP2) | ~(sP16)) | sP9),inference(prop_rule,[status(thm)],[])).
% 1.37/1.59 thf(7,plain,(~(sP12) | sP14),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(8,plain,((~(sP14) | ~(sP1)) | sP10),inference(prop_rule,[status(thm)],[])).
% 1.37/1.59 thf(9,plain,(~(sP4) | sP8),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(10,plain,((~(sP8) | sP3) | sP12),inference(prop_rule,[status(thm)],[])).
% 1.37/1.59 thf(refl_axiom,axiom,sP11).
% 1.37/1.59 thf(axiom2,axiom,(ivalid @ ((ior @ ((ior @ (iatom @ b)) @ (iatom @ a))) @ (iatom @ b)))).
% 1.37/1.59 thf(11,plain,sP4,inference(preprocess,[status(thm)],[axiom2]).
% 1.37/1.59 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,refl_axiom,11,h5,h6,h8,h10])).
% 1.37/1.59 thf(13,plain,(~(sP6) | sP17),inference(all_rule,[status(thm)],[])).
% 1.37/1.59 thf(axiom1,axiom,(ivalid @ (iatom @ c))).
% 1.37/1.59 thf(14,plain,sP6,inference(preprocess,[status(thm)],[axiom1]).
% 1.37/1.59 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[13,14,h11])).
% 1.37/1.59 thf(16,plain,$false,inference(tab_imp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h9,12,15,h10,h11])).
% 1.37/1.59 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,16,h8,h9])).
% 1.37/1.59 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,17,h7])).
% 1.37/1.59 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,18,h5,h6])).
% 1.37/1.59 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,19,h4])).
% 1.37/1.59 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3])).
% 1.37/1.59 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1])).
% 1.37/1.59 thf(0,theorem,(![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((c @ X2)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[22,h0])).
% 1.37/1.59 % SZS output end Proof
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