%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:02:06 PM UTC 2026
% Result : Theorem 38.85s 39.96s
% Output : Proof 38.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 04:55:06 UTC 2026
% 0.08/0.34 % CPUTime :
% 38.85/39.96 % SZS status Theorem
% 38.85/39.96 % Mode: mode484
% 38.85/39.96 % Inferences: 3118
% 38.85/39.96 % SZS output start Proof
% 38.85/39.96 thf(ty_eigen__2, type, eigen__2 : $i).
% 38.85/39.96 thf(ty_eigen__1, type, eigen__1 : $i).
% 38.85/39.96 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 38.85/39.96 thf(ty_eigen__21, type, eigen__21 : $i).
% 38.85/39.96 thf(ty_eigen__19, type, eigen__19 : $i).
% 38.85/39.96 thf(ty_eigen__3, type, eigen__3 : $i).
% 38.85/39.96 thf(ty_eigen__8, type, eigen__8 : $i).
% 38.85/39.96 thf(ty_eigen__20, type, eigen__20 : $i).
% 38.85/39.96 thf(ty_eigen__18, type, eigen__18 : ($i>$o)).
% 38.85/39.96 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 38.85/39.96 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__1) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 38.85/39.96 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
% 38.85/39.96 thf(sP2,plain,sP2 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 38.85/39.96 thf(sP3,plain,sP3 <=> (![X1:$i]:(((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 38.85/39.96 thf(sP4,plain,sP4 <=> (((eigen__0 @ eigen__1) @ eigen__8) => ((eigen__0 @ eigen__1) @ eigen__8)),introduced(definition,[new_symbols(definition,[sP4])])).
% 38.85/39.96 thf(sP5,plain,sP5 <=> (![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__1) @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => ((eigen__0 @ eigen__1) @ X3))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 38.85/39.96 thf(sP6,plain,sP6 <=> (((eigen__0 @ eigen__1) @ eigen__2) => sP3),introduced(definition,[new_symbols(definition,[sP6])])).
% 38.85/39.96 thf(sP7,plain,sP7 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__1) @ X2))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 38.85/39.96 thf(sP8,plain,sP8 <=> ((eigen__0 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP8])])).
% 38.85/39.96 thf(sP9,plain,sP9 <=> ((eigen__0 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP9])])).
% 38.85/39.96 thf(sP10,plain,sP10 <=> ((eigen__0 @ eigen__1) @ eigen__8),introduced(definition,[new_symbols(definition,[sP10])])).
% 38.85/39.96 thf(sP11,plain,sP11 <=> (sP1 => sP9),introduced(definition,[new_symbols(definition,[sP11])])).
% 38.85/39.96 thf(sP12,plain,sP12 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (![X4:$i]:(((eigen__0 @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 38.85/39.96 thf(sP13,plain,sP13 <=> (sP2 => sP7),introduced(definition,[new_symbols(definition,[sP13])])).
% 38.85/39.96 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 38.85/39.96 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 38.85/39.96 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 38.85/39.96 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 38.85/39.96 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 38.85/39.96 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 38.85/39.96 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
% 38.85/39.96 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 38.85/39.96 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 38.85/39.96 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
% 38.85/39.96 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
% 38.85/39.96 thf(def_mvalid,definition,(mvalid = (!!))).
% 38.85/39.96 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 38.85/39.96 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 38.85/39.96 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 38.85/39.96 thf(def_cartesian_product,definition,(cartesian_product = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X1 @ X3) => (~((X2 @ X4)))))))))))).
% 38.85/39.96 thf(def_pair_rel,definition,(pair_rel = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:((~((X3 = X1))) => (X4 = X2)))))))).
% 38.85/39.96 thf(def_id_rel,definition,(id_rel = (^[X1:$i>$o]:(^[X2:$i]:(^[X3:$i]:(~(((X1 @ X2) => (~((X2 = X3))))))))))).
% 38.85/39.96 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)))))))).
% 38.85/39.96 thf(def_is_rel_on,definition,(is_rel_on = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i>$o]:(![X4:$i]:(![X5:$i]:(((X1 @ X4) @ X5) => (~(((X2 @ X4) => (~((X3 @ X5)))))))))))))).
% 38.85/39.96 thf(def_restrict_rel_domain,definition,(restrict_rel_domain = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X2 @ X3) => (~(((X1 @ X3) @ X4)))))))))))).
% 38.85/39.96 thf(def_rel_diagonal,definition,(rel_diagonal = (=))).
% 38.85/39.96 thf(def_rel_composition,definition,(rel_composition = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(^[X3:$i]:(^[X4:$i]:(~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X2 @ X5) @ X4))))))))))))).
% 38.85/39.96 thf(def_reflexive,definition,(reflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 38.85/39.96 thf(def_irreflexive,definition,(irreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:(~(((X1 @ X2) @ X2))))))).
% 38.85/39.96 thf(def_symmetric,definition,(symmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 38.85/39.96 thf(def_transitive,definition,(transitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 38.85/39.96 thf(def_equiv_rel,definition,(equiv_rel = (^[X1:$i>$i>$o]:(~(((~(((reflexive @ X1) => (~((symmetric @ X1)))))) => (~((transitive @ X1))))))))).
% 38.85/39.96 thf(def_rel_codomain,definition,(rel_codomain = (^[X1:$i>$i>$o]:(^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))).
% 38.85/39.96 thf(def_rel_domain,definition,(rel_domain = (^[X1:$i>$i>$o]:(^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 38.85/39.96 thf(def_rel_inverse,definition,(rel_inverse = (^[X1:$i>$i>$o]:(^[X2:$i]:(^[X3:$i]:((X1 @ X3) @ X2)))))).
% 38.85/39.96 thf(def_equiv_classes,definition,(equiv_classes = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) = ((X1 @ X3) @ X4))))))))))))).
% 38.85/39.96 thf(def_restrict_rel_codomain,definition,(restrict_rel_codomain = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(^[X4:$i]:(~(((X2 @ X4) => (~(((X1 @ X3) @ X4)))))))))))).
% 38.85/39.96 thf(def_rel_field,definition,(rel_field = (^[X1:$i>$i>$o]:(^[X2:$i]:((~(((rel_domain @ X1) @ X2))) => ((rel_codomain @ X1) @ X2)))))).
% 38.85/39.96 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))))))))))))))))).
% 38.85/39.96 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))))))))))))))))).
% 38.85/39.96 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:$i]:(((X1 @ X4) @ X5) => (X2 @ X5)))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 38.85/39.96 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:$i]:(((X1 @ X4) @ X5) => (X2 @ X5)))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
% 38.85/39.96 thf(h2,assumption,(~((sP12 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))),introduced(assumption,[])).
% 38.85/39.96 thf(h3,assumption,sP12,introduced(assumption,[])).
% 38.85/39.96 thf(h4,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(assumption,[])).
% 38.85/39.96 thf(h5,assumption,(~(sP12)),introduced(assumption,[])).
% 38.85/39.96 thf(h6,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))))),introduced(assumption,[])).
% 38.85/39.96 thf(h7,assumption,(~((![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__1) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__1) @ X2)))))),introduced(assumption,[])).
% 38.85/39.96 thf(h8,assumption,(~((![X1:$i]:((~((sP8 => (~(((eigen__0 @ eigen__2) @ X1)))))) => ((eigen__0 @ eigen__1) @ X1))))),introduced(assumption,[])).
% 38.85/39.96 thf(h9,assumption,(~(((~((sP8 => (~(sP1))))) => sP9))),introduced(assumption,[])).
% 38.85/39.96 thf(h10,assumption,(~((sP8 => (~(sP1))))),introduced(assumption,[])).
% 38.85/39.96 thf(h11,assumption,(~(sP9)),introduced(assumption,[])).
% 38.85/39.96 thf(h12,assumption,sP8,introduced(assumption,[])).
% 38.85/39.96 thf(h13,assumption,sP1,introduced(assumption,[])).
% 38.85/39.96 thf(1,plain,(sP4 | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 38.85/39.96 thf(2,plain,(sP4 | sP10),inference(prop_rule,[status(thm)],[])).
% 38.85/39.96 thf(3,plain,((~(sP11) | ~(sP1)) | sP9),inference(prop_rule,[status(thm)],[])).
% 38.85/39.96 thf(4,plain,(~(sP3) | sP11),inference(all_rule,[status(thm)],[])).
% 38.85/39.96 thf(5,plain,((~(sP6) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])).
% 38.85/39.96 thf(6,plain,(~(sP7) | sP6),inference(all_rule,[status(thm)],[])).
% 38.85/39.96 thf(7,plain,(sP2 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 38.85/39.96 thf(8,plain,((~(sP13) | ~(sP2)) | sP7),inference(prop_rule,[status(thm)],[])).
% 38.85/39.96 thf(9,plain,(~(sP5) | sP13),inference(all_rule,[status(thm)],[])).
% 38.85/39.96 thf(10,plain,(~(sP12) | sP5),inference(all_rule,[status(thm)],[])).
% 38.85/39.96 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h7,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h3,h12,h13,h11])).
% 38.85/39.96 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,11,h12,h13])).
% 38.85/39.96 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11])).
% 38.85/39.96 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,13,h9])).
% 38.85/39.97 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,14,h8])).
% 38.85/39.97 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h4,15,h7])).
% 38.85/39.97 thf(h14,assumption,(~((![X1:$i]:((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__18 @ X2))) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (eigen__18 @ X3))))))))),introduced(assumption,[])).
% 38.85/39.97 thf(h15,assumption,(~(((![X1:$i]:(((eigen__0 @ eigen__19) @ X1) => (eigen__18 @ X1))) => (![X1:$i]:(((eigen__0 @ eigen__19) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__18 @ X2)))))))),introduced(assumption,[])).
% 38.85/39.97 thf(h16,assumption,(![X1:$i]:(((eigen__0 @ eigen__19) @ X1) => (eigen__18 @ X1))),introduced(assumption,[])).
% 38.85/39.97 thf(h17,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__19) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__18 @ X2))))))),introduced(assumption,[])).
% 38.85/39.97 thf(h18,assumption,(~((((eigen__0 @ eigen__19) @ eigen__20) => (![X1:$i]:(((eigen__0 @ eigen__20) @ X1) => (eigen__18 @ X1)))))),introduced(assumption,[])).
% 38.85/39.97 thf(h19,assumption,((eigen__0 @ eigen__19) @ eigen__20),introduced(assumption,[])).
% 38.85/39.97 thf(h20,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__20) @ X1) => (eigen__18 @ X1))))),introduced(assumption,[])).
% 38.85/39.97 thf(h21,assumption,(~((((eigen__0 @ eigen__20) @ eigen__21) => (eigen__18 @ eigen__21)))),introduced(assumption,[])).
% 38.85/39.97 thf(h22,assumption,((eigen__0 @ eigen__20) @ eigen__21),introduced(assumption,[])).
% 38.85/39.97 thf(h23,assumption,(~((eigen__18 @ eigen__21))),introduced(assumption,[])).
% 38.85/39.97 thf(ax997, axiom, (~(p405)|p417), file('<stdin>', ax997)).
% 38.85/39.97 thf(ax999, axiom, (~(p401)|p415), file('<stdin>', ax999)).
% 38.85/39.97 thf(ax887, axiom, (~(p417)|~(p527)|p402), file('<stdin>', ax887)).
% 38.85/39.97 thf(ax1009, axiom, p405, file('<stdin>', ax1009)).
% 38.85/39.97 thf(ax1012, axiom, ~(p402), file('<stdin>', ax1012)).
% 38.85/39.97 thf(ax898, axiom, (~(p415)|p516), file('<stdin>', ax898)).
% 38.85/39.97 thf(ax1013, axiom, p401, file('<stdin>', ax1013)).
% 38.85/39.97 thf(pax404, axiom, (p404=>f__0 @ f__19 @ f__20), file('<stdin>', pax404)).
% 38.85/39.97 thf(nax527, axiom, (p527<=f__0 @ f__19 @ f__21), file('<stdin>', nax527)).
% 38.85/39.97 thf(pax516, axiom, (p516=>![X1:$i]:(~((f__0 @ f__19 @ f__20=>~(f__0 @ f__20 @ X1)))=>f__0 @ f__19 @ X1)), file('<stdin>', pax516)).
% 38.85/39.97 thf(ax1010, axiom, p404, file('<stdin>', ax1010)).
% 38.85/39.97 thf(pax403, axiom, (p403=>f__0 @ f__20 @ f__21), file('<stdin>', pax403)).
% 38.85/39.97 thf(ax1011, axiom, p403, file('<stdin>', ax1011)).
% 38.85/39.97 thf(c_0_13, plain, (~p405|p417), inference(fof_simplification,[status(thm)],[ax997])).
% 38.85/39.97 thf(c_0_14, plain, (~p401|p415), inference(fof_simplification,[status(thm)],[ax999])).
% 38.85/39.97 thf(c_0_15, plain, (~p417|~p527|p402), inference(fof_simplification,[status(thm)],[ax887])).
% 38.85/39.97 thf(c_0_16, plain, (p417|~p405), inference(split_conjunct,[status(thm)],[c_0_13])).
% 38.85/39.97 thf(c_0_17, plain, p405, inference(split_conjunct,[status(thm)],[ax1009])).
% 38.85/39.97 thf(c_0_18, plain, ~p402, inference(fof_simplification,[status(thm)],[ax1012])).
% 38.85/39.97 thf(c_0_19, plain, (~p415|p516), inference(fof_simplification,[status(thm)],[ax898])).
% 38.85/39.97 thf(c_0_20, plain, (p415|~p401), inference(split_conjunct,[status(thm)],[c_0_14])).
% 38.85/39.97 thf(c_0_21, plain, p401, inference(split_conjunct,[status(thm)],[ax1013])).
% 38.85/39.97 thf(c_0_22, plain, (~p404|f__0 @ f__19 @ f__20), inference(fof_nnf,[status(thm)],[pax404])).
% 38.85/39.97 thf(c_0_23, plain, (~f__0 @ f__19 @ f__21|p527), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax527])])).
% 38.85/39.97 thf(c_0_24, plain, (p402|~p417|~p527), inference(split_conjunct,[status(thm)],[c_0_15])).
% 38.85/39.97 thf(c_0_25, plain, p417, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 38.85/39.97 thf(c_0_26, plain, ~p402, inference(split_conjunct,[status(thm)],[c_0_18])).
% 38.85/39.97 thf(c_0_27, plain, ![X28:$i]:(~p516|(~f__0 @ f__19 @ f__20|~f__0 @ f__20 @ X28|f__0 @ f__19 @ X28)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax516])])])])).
% 38.85/39.97 thf(c_0_28, plain, (p516|~p415), inference(split_conjunct,[status(thm)],[c_0_19])).
% 38.85/39.97 thf(c_0_29, plain, p415, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 38.85/39.97 thf(c_0_30, plain, (f__0 @ f__19 @ f__20|~p404), inference(split_conjunct,[status(thm)],[c_0_22])).
% 38.85/39.97 thf(c_0_31, plain, p404, inference(split_conjunct,[status(thm)],[ax1010])).
% 38.85/39.97 thf(c_0_32, plain, (~p403|f__0 @ f__20 @ f__21), inference(fof_nnf,[status(thm)],[pax403])).
% 38.85/39.97 thf(c_0_33, plain, (p527|~f__0 @ f__19 @ f__21), inference(split_conjunct,[status(thm)],[c_0_23])).
% 38.85/39.97 thf(c_0_34, plain, ~p527, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])]), c_0_26])).
% 38.85/39.97 thf(c_0_35, plain, ![X1:$i]:(f__0 @ f__19 @ X1|~p516|~f__0 @ f__19 @ f__20|~f__0 @ f__20 @ X1), inference(split_conjunct,[status(thm)],[c_0_27])).
% 38.85/39.97 thf(c_0_36, plain, p516, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 38.85/39.97 thf(c_0_37, plain, f__0 @ f__19 @ f__20, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 38.85/39.97 thf(c_0_38, plain, (f__0 @ f__20 @ f__21|~p403), inference(split_conjunct,[status(thm)],[c_0_32])).
% 38.85/39.97 thf(c_0_39, plain, p403, inference(split_conjunct,[status(thm)],[ax1011])).
% 38.85/39.97 thf(c_0_40, plain, ~f__0 @ f__19 @ f__21, inference(sr,[status(thm)],[c_0_33, c_0_34])).
% 38.85/39.97 thf(c_0_41, plain, ![X1:$i]:(f__0 @ f__19 @ X1|~f__0 @ f__20 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36]), c_0_37])])).
% 38.85/39.97 thf(c_0_42, plain, f__0 @ f__20 @ f__21, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 38.85/39.97 thf(c_0_43, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42])]), ['proof']).
% 38.85/39.97 thf(17,plain,$false,inference(eprover,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h17,h15,h14,h5,h6,h2,h1,h0])],[])).
% 38.85/39.97 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,17,h22,h23])).
% 38.85/39.97 thf(19,plain,$false,inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__21)],[h20,18,h21])).
% 38.85/39.97 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,19,h19,h20])).
% 38.85/39.97 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__20)],[h17,20,h18])).
% 38.85/39.97 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,21,h16,h17])).
% 38.85/39.97 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__19)],[h14,22,h15])).
% 38.85/39.97 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__18)],[h5,23,h14])).
% 38.85/39.97 thf(25,plain,$false,inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,16,24,h3,h4,h5,h6])).
% 38.85/39.97 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2])).
% 38.85/39.97 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0])).
% 38.85/39.97 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:$i]:(((X1 @ X4) @ X5) => (X2 @ X5)))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4))))))),inference(contra,[status(thm),contra(discharge,[h1])],[26,h1])).
% 38.85/39.97 % SZS output end Proof
%------------------------------------------------------------------------------