TSTP Solution File: SYO068^4.001 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO068^4.001 : 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 : n021.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 19:30:02 EDT 2022
% Result : Theorem 1.95s 2.18s
% Output : Proof 1.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO068^4.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 12:34:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.95/2.18 % SZS status Theorem
% 1.95/2.18 % Mode: mode506
% 1.95/2.18 % Inferences: 19456
% 1.95/2.18 % SZS output start Proof
% 1.95/2.18 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.95/2.18 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.95/2.18 thf(ty_irel, type, irel : ($i>$i>$o)).
% 1.95/2.18 thf(ty_p0, type, p0 : ($i>$o)).
% 1.95/2.18 thf(ty_p1, type, p1 : ($i>$o)).
% 1.95/2.18 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.95/2.18 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p1 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 1.95/2.18 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.95/2.18 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.95/2.18 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.95/2.18 thf(sP3,plain,sP3 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.95/2.18 thf(sP4,plain,sP4 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.95/2.18 thf(sP5,plain,sP5 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.95/2.18 thf(sP6,plain,sP6 <=> (((irel @ eigen__0) @ eigen__1) => (p1 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.95/2.18 thf(sP7,plain,sP7 <=> (p1 @ eigen__1),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.95/2.18 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.95/2.18 thf(sP9,plain,sP9 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.95/2.18 thf(sP10,plain,sP10 <=> (sP3 => sP5),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.95/2.18 thf(sP11,plain,sP11 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.95/2.18 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.95/2.18 thf(sP13,plain,sP13 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.95/2.18 thf(sP14,plain,sP14 <=> (sP3 => sP8),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.95/2.18 thf(sP15,plain,sP15 <=> ((!!) @ p1),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.95/2.18 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.95/2.18 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.95/2.18 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.95/2.18 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.95/2.18 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 1.95/2.18 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 1.95/2.18 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 1.95/2.18 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 1.95/2.18 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 1.95/2.18 thf(def_iand,definition,(iand = mand)).
% 1.95/2.18 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.95/2.18 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.95/2.18 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 1.95/2.18 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 1.95/2.18 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 1.95/2.18 thf(def_ivalid,definition,(ivalid = (!!))).
% 1.95/2.18 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.95/2.18 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.95/2.18 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.95/2.18 thf(con,conjecture,sP11).
% 1.95/2.18 thf(h1,negated_conjecture,(~(sP11)),inference(assume_negation,[status(cth)],[con])).
% 1.95/2.18 thf(1,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])).
% 1.95/2.18 thf(2,plain,(sP6 | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 1.95/2.18 thf(3,plain,(sP12 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 1.95/2.18 thf(4,plain,(~(sP9) | sP10),inference(all_rule,[status(thm)],[])).
% 1.95/2.18 thf(5,plain,((~(sP10) | ~(sP3)) | sP5),inference(prop_rule,[status(thm)],[])).
% 1.95/2.18 thf(6,plain,((~(sP2) | ~(sP12)) | sP13),inference(prop_rule,[status(thm)],[])).
% 1.95/2.18 thf(7,plain,(~(sP13) | sP14),inference(all_rule,[status(thm)],[])).
% 1.95/2.18 thf(8,plain,((~(sP14) | ~(sP3)) | sP8),inference(prop_rule,[status(thm)],[])).
% 1.95/2.18 thf(9,plain,((~(sP8) | ~(sP12)) | sP9),inference(prop_rule,[status(thm)],[])).
% 1.95/2.18 thf(10,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])).
% 1.95/2.18 thf(11,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])).
% 1.95/2.18 thf(12,plain,(sP11 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.95/2.18 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))).
% 1.95/2.18 thf(13,plain,sP4,inference(preprocess,[status(thm)],[axiom2]).
% 1.95/2.18 thf(axiom1,axiom,(ivalid @ (iatom @ p1))).
% 1.95/2.18 thf(14,plain,sP15,inference(preprocess,[status(thm)],[axiom1]).
% 1.95/2.18 thf(refl_axiom,axiom,sP1).
% 1.95/2.18 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,refl_axiom,h1])).
% 1.95/2.18 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0])).
% 1.95/2.18 thf(0,theorem,sP11,inference(contra,[status(thm),contra(discharge,[h1])],[15,h1])).
% 1.95/2.18 % SZS output end Proof
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