TSTP Solution File: LCL621^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL621^1 : TPTP v8.1.0. Released v3.6.0.
% 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 : Sun Jul 17 14:09:08 EDT 2022
% Result : Theorem 77.03s 77.16s
% Output : Proof 77.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL621^1 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.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 2 18:54:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 77.03/77.16 % SZS status Theorem
% 77.03/77.16 % Mode: mode484
% 77.03/77.16 % Inferences: 937
% 77.03/77.16 % SZS output start Proof
% 77.03/77.16 thf(ty_eigen__6, type, eigen__6 : $i).
% 77.03/77.16 thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
% 77.03/77.16 thf(ty_eigen__1, type, eigen__1 : ($i>$o)).
% 77.03/77.16 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 77.03/77.16 thf(ty_eigen__4, type, eigen__4 : $i).
% 77.03/77.16 thf(ty_eigen__3, type, eigen__3 : $i).
% 77.03/77.16 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 77.03/77.16 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__4) @ X1) => (~((eigen__1 @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 77.03/77.16 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP1])])).
% 77.03/77.16 thf(sP2,plain,sP2 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__2 @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 77.03/77.16 thf(sP3,plain,sP3 <=> (![X1:$i]:(((eigen__0 @ eigen__4) @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 77.03/77.16 thf(sP4,plain,sP4 <=> ((eigen__1 @ eigen__6) => (~((eigen__2 @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 77.03/77.16 thf(sP5,plain,sP5 <=> (((eigen__0 @ eigen__4) @ eigen__6) => (~((eigen__1 @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 77.03/77.16 thf(sP6,plain,sP6 <=> (![X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i]:((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))) => (![X4:$i]:(((X1 @ X3) @ X4) => (![X5:$i]:(((X1 @ X4) @ X5) => (X2 @ X5))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 77.03/77.16 thf(sP7,plain,sP7 <=> (((eigen__0 @ eigen__4) @ eigen__6) => sP4),introduced(definition,[new_symbols(definition,[sP7])])).
% 77.03/77.16 thf(sP8,plain,sP8 <=> ((eigen__0 @ eigen__4) @ eigen__6),introduced(definition,[new_symbols(definition,[sP8])])).
% 77.03/77.16 thf(sP9,plain,sP9 <=> (eigen__2 @ eigen__6),introduced(definition,[new_symbols(definition,[sP9])])).
% 77.03/77.16 thf(sP10,plain,sP10 <=> (sP8 => sP9),introduced(definition,[new_symbols(definition,[sP10])])).
% 77.03/77.16 thf(sP11,plain,sP11 <=> (sP1 => (~((![X1:$i]:(((eigen__0 @ eigen__4) @ X1) => (~((eigen__1 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 77.03/77.16 thf(sP12,plain,sP12 <=> (![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__2 @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (eigen__2 @ X3))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 77.03/77.16 thf(sP13,plain,sP13 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 77.03/77.16 thf(sP14,plain,sP14 <=> (![X1:$i]:(((eigen__0 @ eigen__4) @ X1) => ((eigen__1 @ X1) => (~((eigen__2 @ X1)))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 77.03/77.16 thf(sP15,plain,sP15 <=> (sP1 => sP3),introduced(definition,[new_symbols(definition,[sP15])])).
% 77.03/77.16 thf(sP16,plain,sP16 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (![X4:$i]:(((eigen__0 @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 77.03/77.16 thf(sP17,plain,sP17 <=> (eigen__1 @ eigen__6),introduced(definition,[new_symbols(definition,[sP17])])).
% 77.03/77.16 thf(sP18,plain,sP18 <=> (![X1:$i]:(((eigen__0 @ eigen__4) @ X1) => (~((eigen__1 @ X1))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 77.03/77.16 thf(sP19,plain,sP19 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => (~((eigen__1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 77.03/77.16 thf(sP20,plain,sP20 <=> (sP13 => sP2),introduced(definition,[new_symbols(definition,[sP20])])).
% 77.03/77.16 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 77.03/77.16 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 77.03/77.16 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 77.03/77.16 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 77.03/77.16 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 77.03/77.16 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 77.03/77.16 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
% 77.03/77.16 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 77.03/77.16 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 77.03/77.16 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
% 77.03/77.16 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
% 77.03/77.16 thf(def_mvalid,definition,(mvalid = (!!))).
% 77.03/77.16 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 77.03/77.16 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 77.03/77.16 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 77.03/77.16 thf(thm,conjecture,(![X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:((~((~((~(((![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => (~((X2 @ X6))))))))) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))))))) => (![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => (~((~(((X2 @ X6) => (~((X3 @ X6)))))))))))))))))))).
% 77.03/77.16 thf(h1,negated_conjecture,(~((![X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:((~(((![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => (~((X2 @ X6))))))))) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))) => (![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => ((X2 @ X6) => (~((X3 @ X6))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 77.03/77.16 thf(h2,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:((~(((![X4:$i]:(((eigen__0 @ X3) @ X4) => (~((![X5:$i]:(((eigen__0 @ X4) @ X5) => (~((X1 @ X5))))))))) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => (X2 @ X4)))))))) => (![X4:$i]:(((eigen__0 @ X3) @ X4) => (~((![X5:$i]:(((eigen__0 @ X4) @ X5) => ((X1 @ X5) => (~((X2 @ X5)))))))))))))))),introduced(assumption,[])).
% 77.03/77.16 thf(h3,assumption,(~((![X1:$i>$o]:(![X2:$i]:((~(((![X3:$i]:(((eigen__0 @ X2) @ X3) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => (~((eigen__1 @ X4))))))))) => (~((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3)))))))) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => ((eigen__1 @ X4) => (~((X1 @ X4))))))))))))))),introduced(assumption,[])).
% 77.03/77.16 thf(h4,assumption,(~((![X1:$i]:((~(((![X2:$i]:(((eigen__0 @ X1) @ X2) => (~((![X3:$i]:(((eigen__0 @ X2) @ X3) => (~((eigen__1 @ X3))))))))) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__2 @ X2)))))))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (~((![X3:$i]:(((eigen__0 @ X2) @ X3) => ((eigen__1 @ X3) => (~((eigen__2 @ X3)))))))))))))),introduced(assumption,[])).
% 77.03/77.16 thf(h5,assumption,(~(((~((sP19 => (~(sP13))))) => (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__1 @ X2) => (~((eigen__2 @ X2))))))))))))),introduced(assumption,[])).
% 77.03/77.16 thf(h6,assumption,(~((sP19 => (~(sP13))))),introduced(assumption,[])).
% 77.03/77.16 thf(h7,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__1 @ X2) => (~((eigen__2 @ X2)))))))))))),introduced(assumption,[])).
% 77.03/77.16 thf(h8,assumption,sP19,introduced(assumption,[])).
% 77.03/77.16 thf(h9,assumption,sP13,introduced(assumption,[])).
% 77.03/77.16 thf(h10,assumption,(~((sP1 => (~(sP14))))),introduced(assumption,[])).
% 77.03/77.16 thf(h11,assumption,sP1,introduced(assumption,[])).
% 77.03/77.16 thf(h12,assumption,sP14,introduced(assumption,[])).
% 77.03/77.16 thf(1,plain,((~(sP4) | ~(sP17)) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(2,plain,((~(sP7) | ~(sP8)) | sP4),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(3,plain,((~(sP10) | ~(sP8)) | sP9),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(4,plain,(~(sP14) | sP7),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(5,plain,(~(sP3) | sP10),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(6,plain,(sP5 | sP17),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(7,plain,(sP5 | sP8),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(8,plain,((~(sP15) | ~(sP1)) | sP3),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(9,plain,(~(sP2) | sP15),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(10,plain,((~(sP20) | ~(sP13)) | sP2),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(11,plain,(~(sP12) | sP20),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(12,plain,(sP18 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 77.03/77.16 thf(13,plain,(~(sP16) | sP12),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(14,plain,((~(sP11) | ~(sP1)) | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 77.03/77.16 thf(15,plain,(~(sP6) | sP16),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(16,plain,(~(sP19) | sP11),inference(all_rule,[status(thm)],[])).
% 77.03/77.16 thf(k4,axiom,(![X1:$i>$i>$o]:(![X2:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ X1) @ X2)) @ ((mbox @ X1) @ ((mbox @ X1) @ X2))))))).
% 77.03/77.16 thf(17,plain,sP6,inference(preprocess,[status(thm)],[k4]).
% 77.03/77.16 thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h8,h9,h11,h12])).
% 77.03/77.16 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12])).
% 77.03/77.16 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h7,19,h10])).
% 77.03/77.16 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,20,h8,h9])).
% 77.03/77.16 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7])).
% 77.03/77.16 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,22,h5])).
% 77.03/77.16 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,23,h4])).
% 77.03/77.16 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,24,h3])).
% 77.03/77.16 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2])).
% 77.03/77.16 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0])).
% 77.03/77.16 thf(0,theorem,(![X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:((~((~((~(((![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => (~((X2 @ X6))))))))) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))))))) => (![X5:$i]:(((X1 @ X4) @ X5) => (~((![X6:$i]:(((X1 @ X5) @ X6) => (~((~(((X2 @ X6) => (~((X3 @ X6))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[26,h1])).
% 77.03/77.16 % SZS output end Proof
%------------------------------------------------------------------------------