TSTP Solution File: LCL602^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL602^1 : 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 14:09:02 EDT 2022
% Result : Theorem 77.29s 77.48s
% Output : Proof 77.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL602^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13 % 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 : Tue Jul 5 00:23:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 77.29/77.48 % SZS status Theorem
% 77.29/77.48 % Mode: mode484
% 77.29/77.48 % Inferences: 2677
% 77.29/77.48 % SZS output start Proof
% 77.29/77.48 thf(ty_eigen__2, type, eigen__2 : $i).
% 77.29/77.48 thf(ty_eigen__25, type, eigen__25 : $i).
% 77.29/77.48 thf(ty_eigen__7, type, eigen__7 : $i).
% 77.29/77.48 thf(ty_eigen__24, type, eigen__24 : $i).
% 77.29/77.48 thf(ty_eigen__1, type, eigen__1 : $i).
% 77.29/77.48 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 77.29/77.48 thf(ty_eigen__21, type, eigen__21 : ($i>$o)).
% 77.29/77.48 thf(ty_eigen__4, type, eigen__4 : $i).
% 77.29/77.48 thf(ty_eigen__5, type, eigen__5 : $i).
% 77.29/77.48 thf(ty_eigen__3, type, eigen__3 : $i).
% 77.29/77.48 thf(ty_eigen__22, type, eigen__22 : $i).
% 77.29/77.48 thf(ty_eigen__23, type, eigen__23 : $i).
% 77.29/77.48 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 77.29/77.48 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__1) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 77.29/77.48 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ eigen__3) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__7])])).
% 77.29/77.48 thf(sP1,plain,sP1 <=> (![X1:$i]:((eigen__0 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 77.29/77.48 thf(sP2,plain,sP2 <=> (![X1:$i>$o]:(~(((![X2:$i]:((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (![X4:$i]:(((eigen__0 @ X3) @ X4) => (X1 @ X4))))))) => (~((![X2:$i]:((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 77.29/77.48 thf(sP3,plain,sP3 <=> (((eigen__0 @ eigen__4) @ eigen__5) => ((eigen__0 @ eigen__3) @ eigen__5)),introduced(definition,[new_symbols(definition,[sP3])])).
% 77.29/77.48 thf(sP4,plain,sP4 <=> ((![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__1) @ X1))) => ((eigen__0 @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP4])])).
% 77.29/77.48 thf(sP5,plain,sP5 <=> (((eigen__0 @ eigen__1) @ eigen__2) => ((eigen__0 @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP5])])).
% 77.29/77.48 thf(sP6,plain,sP6 <=> (![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__3) @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => ((eigen__0 @ eigen__3) @ X3))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 77.29/77.48 thf(sP7,plain,sP7 <=> (((eigen__0 @ eigen__3) @ eigen__7) => ((eigen__0 @ eigen__3) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP7])])).
% 77.29/77.48 thf(sP8,plain,sP8 <=> (![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__1) @ X2))) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 77.29/77.48 thf(sP9,plain,sP9 <=> (eigen__21 @ eigen__25),introduced(definition,[new_symbols(definition,[sP9])])).
% 77.29/77.48 thf(sP10,plain,sP10 <=> (![X1:$i]:(((eigen__0 @ eigen__4) @ X1) => ((eigen__0 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])).
% 77.29/77.48 thf(sP11,plain,sP11 <=> ((eigen__0 @ eigen__3) @ eigen__7),introduced(definition,[new_symbols(definition,[sP11])])).
% 77.29/77.48 thf(sP12,plain,sP12 <=> (sP6 => (~((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__3) @ X2))) => ((eigen__0 @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 77.29/77.48 thf(sP13,plain,sP13 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__3) @ X2))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 77.29/77.48 thf(sP14,plain,sP14 <=> ((eigen__0 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP14])])).
% 77.29/77.48 thf(sP15,plain,sP15 <=> (((eigen__0 @ eigen__3) @ eigen__4) => sP10),introduced(definition,[new_symbols(definition,[sP15])])).
% 77.29/77.48 thf(sP16,plain,sP16 <=> ((![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ eigen__3) @ X1))) => sP13),introduced(definition,[new_symbols(definition,[sP16])])).
% 77.29/77.48 thf(sP17,plain,sP17 <=> ((eigen__0 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP17])])).
% 77.29/77.48 thf(sP18,plain,sP18 <=> ((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__1) @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => ((eigen__0 @ eigen__1) @ X3))))))) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP18])])).
% 77.29/77.48 thf(sP19,plain,sP19 <=> ((eigen__0 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP19])])).
% 77.29/77.48 thf(sP20,plain,sP20 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP20])])).
% 77.29/77.48 thf(sP21,plain,sP21 <=> (((eigen__0 @ eigen__25) @ eigen__25) => sP9),introduced(definition,[new_symbols(definition,[sP21])])).
% 77.29/77.48 thf(sP22,plain,sP22 <=> ((eigen__0 @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP22])])).
% 77.29/77.48 thf(sP23,plain,sP23 <=> (![X1:$i]:(((eigen__0 @ eigen__25) @ X1) => (eigen__21 @ X1))),introduced(definition,[new_symbols(definition,[sP23])])).
% 77.29/77.48 thf(sP24,plain,sP24 <=> ((eigen__0 @ eigen__3) @ eigen__5),introduced(definition,[new_symbols(definition,[sP24])])).
% 77.29/77.48 thf(sP25,plain,sP25 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP25])])).
% 77.29/77.48 thf(sP26,plain,sP26 <=> ((eigen__0 @ eigen__25) @ eigen__25),introduced(definition,[new_symbols(definition,[sP26])])).
% 77.29/77.48 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 77.29/77.48 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 77.29/77.48 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 77.29/77.48 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 77.29/77.48 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 77.29/77.48 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 77.29/77.48 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
% 77.29/77.48 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 77.29/77.48 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 77.29/77.48 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
% 77.29/77.48 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
% 77.29/77.48 thf(def_mvalid,definition,(mvalid = (!!))).
% 77.29/77.48 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 77.29/77.48 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 77.29/77.48 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 77.29/77.48 thf(def_cartesian_product,definition,(cartesian_product = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X1 @ X3) => (~((X2 @ X4)))))))))))).
% 77.29/77.48 thf(def_pair_rel,definition,(pair_rel = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((~((X3 = X1))) => (X4 = X2)))))))).
% 77.29/77.48 thf(def_id_rel,definition,(id_rel = (^[X1:$i>$o]:(^[X2:$i]:(^[X3:$i]:(~(((X1 @ X2) => (~((X2 = X3))))))))))).
% 77.29/77.48 thf(def_sub_rel,definition,(sub_rel = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(![X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => ((X2 @ X3) @ X4)))))))).
% 77.29/77.48 thf(def_is_rel_on,definition,(is_rel_on = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i>$o]:(![X4:$i]:(![X5:$i]:(((X1 @ X4) @ X5) => (~(((X2 @ X4) => (~((X3 @ X5)))))))))))))).
% 77.29/77.48 thf(def_restrict_rel_domain,definition,(restrict_rel_domain = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X2 @ X3) => (~(((X1 @ X3) @ X4)))))))))))).
% 77.29/77.48 thf(def_rel_diagonal,definition,(rel_diagonal = (=))).
% 77.29/77.48 thf(def_rel_composition,definition,(rel_composition = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X2 @ X5) @ X4))))))))))))).
% 77.29/77.48 thf(def_reflexive,definition,(reflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 77.29/77.48 thf(def_irreflexive,definition,(irreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:(~(((X1 @ X2) @ X2))))))).
% 77.29/77.48 thf(def_symmetric,definition,(symmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 77.29/77.48 thf(def_transitive,definition,(transitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 77.29/77.48 thf(def_equiv_rel,definition,(equiv_rel = (^[X1:$i>$i>$o]:(~(((~(((reflexive @ X1) => (~((symmetric @ X1)))))) => (~((transitive @ X1))))))))).
% 77.29/77.48 thf(def_rel_codomain,definition,(rel_codomain = (^[X1:$i>$i>$o]:(^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))).
% 77.29/77.48 thf(def_rel_domain,definition,(rel_domain = (^[X1:$i>$i>$o]:(^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 77.29/77.48 thf(def_rel_inverse,definition,(rel_inverse = (^[X1:$i>$i>$o]:(^[X2:$i]:(^[X3:$i]:((X1 @ X3) @ X2)))))).
% 77.29/77.48 thf(def_equiv_classes,definition,(equiv_classes = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) = ((X1 @ X3) @ X4))))))))))))).
% 77.29/77.48 thf(def_restrict_rel_codomain,definition,(restrict_rel_codomain = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X2 @ X4) => (~(((X1 @ X3) @ X4)))))))))))).
% 77.29/77.48 thf(def_rel_field,definition,(rel_field = (^[X1:$i>$i>$o]:(^[X2:$i]:((~(((rel_domain @ X1) @ X2))) => ((rel_codomain @ X1) @ X2)))))).
% 77.29/77.48 thf(def_well_founded,definition,(well_founded = (^[X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (~((X2 @ X5))))))))))))))))).
% 77.29/77.48 thf(def_upwards_well_founded,definition,(upwards_well_founded = (^[X1:$i>$i>$o]:(![X2:$i>$o]:(![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X4) => (~((X2 @ X5))))))))))))))))).
% 77.29/77.48 thf(thm,conjecture,(![X1:$i>$i>$o]:((![X2:$i>$o]:(~(((![X3:$i]:((~((~((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))))))) => (![X4:$i]:(((X1 @ X3) @ X4) => (![X5:$i]:(((X1 @ X4) @ X5) => (X2 @ X5))))))) => (~((![X3:$i]:((~((~((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))))))) => (X2 @ X3))))))))) = (~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4))))))))))))).
% 77.29/77.48 thf(h1,negated_conjecture,(~((![X1:$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))))))) => (~((![X3:$i]:((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))) => (X2 @ X3))))))))) = (~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 77.29/77.48 thf(h2,assumption,(~((sP2 = (~((sP1 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))))))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h3,assumption,sP2,introduced(assumption,[])).
% 77.29/77.48 thf(h4,assumption,(~((sP1 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h5,assumption,(~(sP2)),introduced(assumption,[])).
% 77.29/77.48 thf(h6,assumption,(sP1 => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h7,assumption,(~(sP1)),introduced(assumption,[])).
% 77.29/77.48 thf(h8,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h9,assumption,(~(sP19)),introduced(assumption,[])).
% 77.29/77.48 thf(1,plain,(sP5 | ~(sP14)),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(2,plain,(sP5 | sP14),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(3,plain,((~(sP4) | ~(sP20)) | sP19),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(4,plain,(sP20 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 77.29/77.48 thf(5,plain,(~(sP8) | sP4),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(6,plain,(sP18 | sP8),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(7,plain,(~(sP2) | ~(sP18)),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h7,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,h3,h9])).
% 77.29/77.48 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,8,h9])).
% 77.29/77.48 thf(h10,assumption,(~((![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__3) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__3) @ X2)))))),introduced(assumption,[])).
% 77.29/77.48 thf(h11,assumption,(~((![X1:$i]:((~((sP17 => (~(((eigen__0 @ eigen__4) @ X1)))))) => ((eigen__0 @ eigen__3) @ X1))))),introduced(assumption,[])).
% 77.29/77.48 thf(h12,assumption,(~(((~((sP17 => (~(sP22))))) => sP24))),introduced(assumption,[])).
% 77.29/77.48 thf(h13,assumption,(~((sP17 => (~(sP22))))),introduced(assumption,[])).
% 77.29/77.48 thf(h14,assumption,(~(sP24)),introduced(assumption,[])).
% 77.29/77.48 thf(h15,assumption,sP17,introduced(assumption,[])).
% 77.29/77.48 thf(h16,assumption,sP22,introduced(assumption,[])).
% 77.29/77.48 thf(10,plain,(sP7 | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(11,plain,(sP7 | sP11),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(12,plain,((~(sP3) | ~(sP22)) | sP24),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(13,plain,(~(sP10) | sP3),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(14,plain,((~(sP15) | ~(sP17)) | sP10),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(15,plain,(~(sP13) | sP15),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(16,plain,(sP25 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])).
% 77.29/77.48 thf(17,plain,((~(sP16) | ~(sP25)) | sP13),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(18,plain,(~(sP6) | sP16),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(19,plain,(sP12 | sP6),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(20,plain,(~(sP2) | ~(sP12)),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(21,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h14,h12,h11,h10,h8,h3,h4,h2,h1,h0])],[10,11,12,13,14,15,16,17,18,19,20,h3,h15,h16,h14])).
% 77.29/77.48 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h11,h10,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,21,h15,h16])).
% 77.29/77.48 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h11,h10,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,22,h13,h14])).
% 77.29/77.48 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h10,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__5)],[h11,23,h12])).
% 77.29/77.48 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,24,h11])).
% 77.29/77.48 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h8,25,h10])).
% 77.29/77.48 thf(27,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h4,9,26,h7,h8])).
% 77.29/77.48 thf(h17,assumption,((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (eigen__21 @ X3))))))) => (~((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2))) => (eigen__21 @ X1)))))),introduced(assumption,[])).
% 77.29/77.48 thf(h18,assumption,(~((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (eigen__21 @ X3))))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h19,assumption,(~((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2))) => (eigen__21 @ X1))))),introduced(assumption,[])).
% 77.29/77.48 thf(h20,assumption,(~(((![X1:$i]:(((eigen__0 @ eigen__22) @ X1) => (eigen__21 @ X1))) => (![X1:$i]:(((eigen__0 @ eigen__22) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2)))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h21,assumption,(![X1:$i]:(((eigen__0 @ eigen__22) @ X1) => (eigen__21 @ X1))),introduced(assumption,[])).
% 77.29/77.48 thf(h22,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__22) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__21 @ X2))))))),introduced(assumption,[])).
% 77.29/77.48 thf(h23,assumption,(~((((eigen__0 @ eigen__22) @ eigen__23) => (![X1:$i]:(((eigen__0 @ eigen__23) @ X1) => (eigen__21 @ X1)))))),introduced(assumption,[])).
% 77.29/77.48 thf(h24,assumption,((eigen__0 @ eigen__22) @ eigen__23),introduced(assumption,[])).
% 77.29/77.48 thf(h25,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__23) @ X1) => (eigen__21 @ X1))))),introduced(assumption,[])).
% 77.29/77.48 thf(h26,assumption,(~((((eigen__0 @ eigen__23) @ eigen__24) => (eigen__21 @ eigen__24)))),introduced(assumption,[])).
% 77.29/77.48 thf(h27,assumption,((eigen__0 @ eigen__23) @ eigen__24),introduced(assumption,[])).
% 77.29/77.48 thf(h28,assumption,(~((eigen__21 @ eigen__24))),introduced(assumption,[])).
% 77.29/77.48 thf(h29,assumption,sP1,introduced(assumption,[])).
% 77.29/77.48 thf(h30,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(assumption,[])).
% 77.29/77.48 thf(ax1122, axiom, (~(p314)|p320), file('<stdin>', ax1122)).
% 77.29/77.48 thf(ax1097, axiom, (~(p320)|p340), file('<stdin>', ax1097)).
% 77.29/77.48 thf(ax1128, axiom, p314, file('<stdin>', ax1128)).
% 77.29/77.48 thf(ax1099, axiom, (~(p319)|p338), file('<stdin>', ax1099)).
% 77.29/77.48 thf(ax830, axiom, (~(p340)|p504), file('<stdin>', ax830)).
% 77.29/77.48 thf(ax846, axiom, (~(p338)|~(p488)|p316), file('<stdin>', ax846)).
% 77.29/77.48 thf(ax1123, axiom, p319, file('<stdin>', ax1123)).
% 77.29/77.48 thf(ax1126, axiom, ~(p316), file('<stdin>', ax1126)).
% 77.29/77.48 thf(ax276, axiom, (~(p504)|p1022|p488), file('<stdin>', ax276)).
% 77.29/77.48 thf(pax1022, axiom, (p1022=>(f__0 @ f__22 @ f__23=>~(f__0 @ f__23 @ f__24))), file('<stdin>', pax1022)).
% 77.29/77.48 thf(pax318, axiom, (p318=>f__0 @ f__22 @ f__23), file('<stdin>', pax318)).
% 77.29/77.48 thf(ax1124, axiom, p318, file('<stdin>', ax1124)).
% 77.29/77.48 thf(pax317, axiom, (p317=>f__0 @ f__23 @ f__24), file('<stdin>', pax317)).
% 77.29/77.48 thf(ax1125, axiom, p317, file('<stdin>', ax1125)).
% 77.29/77.48 thf(c_0_14, plain, (~p314|p320), inference(fof_simplification,[status(thm)],[ax1122])).
% 77.29/77.48 thf(c_0_15, plain, (~p320|p340), inference(fof_simplification,[status(thm)],[ax1097])).
% 77.29/77.48 thf(c_0_16, plain, (p320|~p314), inference(split_conjunct,[status(thm)],[c_0_14])).
% 77.29/77.48 thf(c_0_17, plain, p314, inference(split_conjunct,[status(thm)],[ax1128])).
% 77.29/77.48 thf(c_0_18, plain, (~p319|p338), inference(fof_simplification,[status(thm)],[ax1099])).
% 77.29/77.48 thf(c_0_19, plain, (~p340|p504), inference(fof_simplification,[status(thm)],[ax830])).
% 77.29/77.48 thf(c_0_20, plain, (p340|~p320), inference(split_conjunct,[status(thm)],[c_0_15])).
% 77.29/77.48 thf(c_0_21, plain, p320, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 77.29/77.48 thf(c_0_22, plain, (~p338|~p488|p316), inference(fof_simplification,[status(thm)],[ax846])).
% 77.29/77.48 thf(c_0_23, plain, (p338|~p319), inference(split_conjunct,[status(thm)],[c_0_18])).
% 77.29/77.48 thf(c_0_24, plain, p319, inference(split_conjunct,[status(thm)],[ax1123])).
% 77.29/77.48 thf(c_0_25, plain, ~p316, inference(fof_simplification,[status(thm)],[ax1126])).
% 77.29/77.48 thf(c_0_26, plain, (~p504|p1022|p488), inference(fof_simplification,[status(thm)],[ax276])).
% 77.29/77.48 thf(c_0_27, plain, (p504|~p340), inference(split_conjunct,[status(thm)],[c_0_19])).
% 77.29/77.48 thf(c_0_28, plain, p340, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 77.29/77.48 thf(c_0_29, plain, (p316|~p338|~p488), inference(split_conjunct,[status(thm)],[c_0_22])).
% 77.29/77.48 thf(c_0_30, plain, p338, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 77.29/77.48 thf(c_0_31, plain, ~p316, inference(split_conjunct,[status(thm)],[c_0_25])).
% 77.29/77.48 thf(c_0_32, plain, (~p1022|(~f__0 @ f__22 @ f__23|~f__0 @ f__23 @ f__24)), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1022])])).
% 77.29/77.48 thf(c_0_33, plain, (p1022|p488|~p504), inference(split_conjunct,[status(thm)],[c_0_26])).
% 77.29/77.48 thf(c_0_34, plain, p504, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 77.29/77.48 thf(c_0_35, plain, ~p488, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])]), c_0_31])).
% 77.29/77.48 thf(c_0_36, plain, (~p318|f__0 @ f__22 @ f__23), inference(fof_nnf,[status(thm)],[pax318])).
% 77.29/77.48 thf(c_0_37, plain, (~p1022|~f__0 @ f__22 @ f__23|~f__0 @ f__23 @ f__24), inference(split_conjunct,[status(thm)],[c_0_32])).
% 77.29/77.48 thf(c_0_38, plain, p1022, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])]), c_0_35])).
% 77.29/77.48 thf(c_0_39, plain, (f__0 @ f__22 @ f__23|~p318), inference(split_conjunct,[status(thm)],[c_0_36])).
% 77.29/77.48 thf(c_0_40, plain, p318, inference(split_conjunct,[status(thm)],[ax1124])).
% 77.29/77.48 thf(c_0_41, plain, (~p317|f__0 @ f__23 @ f__24), inference(fof_nnf,[status(thm)],[pax317])).
% 77.29/77.48 thf(c_0_42, plain, (~f__0 @ f__22 @ f__23|~f__0 @ f__23 @ f__24), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 77.29/77.48 thf(c_0_43, plain, f__0 @ f__22 @ f__23, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 77.29/77.48 thf(c_0_44, plain, (f__0 @ f__23 @ f__24|~p317), inference(split_conjunct,[status(thm)],[c_0_41])).
% 77.29/77.48 thf(c_0_45, plain, p317, inference(split_conjunct,[status(thm)],[ax1125])).
% 77.29/77.48 thf(c_0_46, plain, ~f__0 @ f__23 @ f__24, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 77.29/77.48 thf(c_0_47, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45])]), c_0_46]), ['proof']).
% 77.29/77.48 thf(28,plain,$false,inference(eprover,[status(thm),assumptions([h29,h30,h27,h28,h26,h24,h25,h23,h21,h22,h20,h18,h17,h5,h6,h2,h1,h0])],[])).
% 77.29/77.48 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h20,h18,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h6,28,h29,h30])).
% 77.29/77.48 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h20,h18,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,29,h27,h28])).
% 77.29/77.48 thf(31,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h17,h5,h6,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__24)],[h25,30,h26])).
% 77.29/77.48 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,31,h24,h25])).
% 77.29/77.48 thf(33,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h17,h5,h6,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__23)],[h22,32,h23])).
% 77.29/77.48 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h18,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,33,h21,h22])).
% 77.29/77.48 thf(35,plain,$false,inference(tab_negall,[status(thm),assumptions([h18,h17,h5,h6,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__22)],[h18,34,h20])).
% 77.29/77.48 thf(h31,assumption,(~((sP23 => sP9))),introduced(assumption,[])).
% 77.29/77.48 thf(h32,assumption,sP23,introduced(assumption,[])).
% 77.29/77.48 thf(h33,assumption,(~(sP9)),introduced(assumption,[])).
% 77.29/77.48 thf(36,plain,((~(sP21) | ~(sP26)) | sP9),inference(prop_rule,[status(thm)],[])).
% 77.29/77.48 thf(37,plain,(~(sP23) | sP21),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(38,plain,(~(sP1) | sP26),inference(all_rule,[status(thm)],[])).
% 77.29/77.48 thf(39,plain,$false,inference(prop_unsat,[status(thm),assumptions([h29,h30,h32,h33,h31,h19,h17,h5,h6,h2,h1,h0])],[36,37,38,h32,h33,h29])).
% 77.29/77.48 thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h32,h33,h31,h19,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h6,39,h29,h30])).
% 77.29/77.48 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h31,h19,h17,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,40,h32,h33])).
% 77.29/77.48 thf(42,plain,$false,inference(tab_negall,[status(thm),assumptions([h19,h17,h5,h6,h2,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__25)],[h19,41,h31])).
% 77.29/77.48 thf(43,plain,$false,inference(tab_imp,[status(thm),assumptions([h17,h5,h6,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h19])],[h17,35,42,h18,h19])).
% 77.29/77.48 thf(44,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__21)],[h5,43,h17])).
% 77.29/77.48 thf(45,plain,$false,inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,27,44,h3,h4,h5,h6])).
% 77.29/77.48 thf(46,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,45,h2])).
% 77.29/77.48 thf(47,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[46,h0])).
% 77.29/77.48 thf(0,theorem,(![X1:$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))))))) => (~((![X3:$i]:((~((~((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))))))) => (X2 @ X3))))))))) = (~(((![X2:$i]:((X1 @ X2) @ X2)) => (~((![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[46,h1])).
% 77.29/77.48 % SZS output end Proof
%------------------------------------------------------------------------------