%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 01:02:49 PM UTC 2026
% Result : Theorem 38.82s 39.46s
% Output : Proof 38.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 20:18:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 38.82/39.46 % SZS status Theorem
% 38.82/39.46 % Mode: mode484
% 38.82/39.46 % Inferences: 3447
% 38.82/39.46 % SZS output start Proof
% 38.82/39.46 thf(ty_eigen__2, type, eigen__2 : $i).
% 38.82/39.46 thf(ty_eigen__25, type, eigen__25 : $i).
% 38.82/39.46 thf(ty_eigen__1, type, eigen__1 : $i).
% 38.82/39.46 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 38.82/39.46 thf(ty_eigen__26, type, eigen__26 : ($i>$o)).
% 38.82/39.46 thf(ty_eigen__27, type, eigen__27 : $i).
% 38.82/39.46 thf(ty_eigen__3, type, eigen__3 : $i).
% 38.82/39.46 thf(ty_eigen__8, type, eigen__8 : $i).
% 38.82/39.46 thf(ty_eigen__28, type, eigen__28 : $i).
% 38.82/39.46 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 38.82/39.46 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__2) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__8])])).
% 38.82/39.46 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__1) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
% 38.82/39.46 thf(sP2,plain,sP2 <=> (![X1:$i>$o]:((~((![X2:$i]:(((eigen__0 @ eigen__1) @ X2) => (X1 @ X2))))) => (![X2:$i]:(((eigen__0 @ eigen__1) @ X2) => (~((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 38.82/39.46 thf(sP3,plain,sP3 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__2) @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 38.82/39.46 thf(sP4,plain,sP4 <=> (![X1:$i]:(((eigen__0 @ eigen__1) @ X1) => ((eigen__0 @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 38.82/39.46 thf(sP5,plain,sP5 <=> ((~(sP4)) => sP3),introduced(definition,[new_symbols(definition,[sP5])])).
% 38.82/39.46 thf(sP6,plain,sP6 <=> ((eigen__0 @ eigen__2) @ eigen__8),introduced(definition,[new_symbols(definition,[sP6])])).
% 38.82/39.46 thf(sP7,plain,sP7 <=> (sP1 => ((eigen__0 @ eigen__2) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP7])])).
% 38.82/39.46 thf(sP8,plain,sP8 <=> (((eigen__0 @ eigen__1) @ eigen__2) => (~((![X1:$i]:(((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 38.82/39.46 thf(sP9,plain,sP9 <=> ((eigen__0 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP9])])).
% 38.82/39.46 thf(sP10,plain,sP10 <=> ((eigen__0 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP10])])).
% 38.82/39.46 thf(sP11,plain,sP11 <=> (sP6 => sP6),introduced(definition,[new_symbols(definition,[sP11])])).
% 38.82/39.46 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((eigen__0 @ X1) @ X3) => (X2 @ X3))))) => (![X3:$i]:(((eigen__0 @ X1) @ X3) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => (X2 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 38.82/39.46 thf(sP13,plain,sP13 <=> (![X1:$i]:(((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
% 38.82/39.46 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 38.82/39.46 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 38.82/39.46 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 38.82/39.46 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 38.82/39.46 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 38.82/39.46 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 38.82/39.46 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 38.82/39.46 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 38.82/39.46 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 38.82/39.46 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 38.82/39.46 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 38.82/39.46 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 38.82/39.46 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 38.82/39.46 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 38.82/39.46 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 38.82/39.46 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 38.82/39.46 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 38.82/39.46 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 38.82/39.46 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 38.82/39.46 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 38.82/39.46 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 38.82/39.46 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 38.82/39.46 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 38.82/39.46 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 38.82/39.46 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 38.82/39.46 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 38.82/39.46 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 38.82/39.46 thf(def_mvalid,definition,(mvalid = (!!))).
% 38.82/39.46 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 38.82/39.46 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 38.82/39.46 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 38.82/39.46 thf(conj,conjecture,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 38.82/39.46 thf(h1,negated_conjecture,(~((![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))))),inference(assume_negation,[status(cth)],[conj])).
% 38.82/39.46 thf(h2,assumption,(~((sP12 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3)))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h3,assumption,sP12,introduced(assumption,[])).
% 38.82/39.46 thf(h4,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))),introduced(assumption,[])).
% 38.82/39.46 thf(h5,assumption,(~(sP12)),introduced(assumption,[])).
% 38.82/39.46 thf(h6,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h7,assumption,(~((![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__1) @ X1) => (~(((eigen__0 @ eigen__1) @ X2)))))) => ((eigen__0 @ X1) @ X2)))))),introduced(assumption,[])).
% 38.82/39.46 thf(h8,assumption,(~((![X1:$i]:((~((sP9 => (~(((eigen__0 @ eigen__1) @ X1)))))) => ((eigen__0 @ eigen__2) @ X1))))),introduced(assumption,[])).
% 38.82/39.46 thf(h9,assumption,(~(((~((sP9 => (~(sP1))))) => sP10))),introduced(assumption,[])).
% 38.82/39.46 thf(h10,assumption,(~((sP9 => (~(sP1))))),introduced(assumption,[])).
% 38.82/39.46 thf(h11,assumption,(~(sP10)),introduced(assumption,[])).
% 38.82/39.46 thf(h12,assumption,sP9,introduced(assumption,[])).
% 38.82/39.46 thf(h13,assumption,sP1,introduced(assumption,[])).
% 38.82/39.46 thf(1,plain,(sP11 | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 38.82/39.46 thf(2,plain,(sP11 | sP6),inference(prop_rule,[status(thm)],[])).
% 38.82/39.46 thf(3,plain,(sP13 | ~(sP11)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])).
% 38.82/39.46 thf(4,plain,((~(sP8) | ~(sP9)) | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 38.82/39.46 thf(5,plain,((~(sP7) | ~(sP1)) | sP10),inference(prop_rule,[status(thm)],[])).
% 38.82/39.46 thf(6,plain,(~(sP3) | sP8),inference(all_rule,[status(thm)],[])).
% 38.82/39.46 thf(7,plain,(~(sP4) | sP7),inference(all_rule,[status(thm)],[])).
% 38.82/39.46 thf(8,plain,((~(sP5) | sP4) | sP3),inference(prop_rule,[status(thm)],[])).
% 38.82/39.46 thf(9,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])).
% 38.82/39.46 thf(10,plain,(~(sP12) | sP2),inference(all_rule,[status(thm)],[])).
% 38.82/39.46 thf(11,plain,$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])).
% 38.82/39.46 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,11,h12,h13])).
% 38.82/39.46 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11])).
% 38.82/39.46 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,13,h9])).
% 38.82/39.46 thf(15,plain,$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])).
% 38.82/39.46 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h4,15,h7])).
% 38.82/39.46 thf(h14,assumption,(~((![X1:$i>$o]:((~((![X2:$i]:(((eigen__0 @ eigen__25) @ X2) => (X1 @ X2))))) => (![X2:$i]:(((eigen__0 @ eigen__25) @ X2) => (~((![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))))))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h15,assumption,(~(((~((![X1:$i]:(((eigen__0 @ eigen__25) @ X1) => (eigen__26 @ X1))))) => (![X1:$i]:(((eigen__0 @ eigen__25) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__26 @ X2)))))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h16,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__25) @ X1) => (eigen__26 @ X1))))),introduced(assumption,[])).
% 38.82/39.46 thf(h17,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__25) @ X1) => (~((![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__26 @ X2))))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h18,assumption,(~((((eigen__0 @ eigen__25) @ eigen__27) => (eigen__26 @ eigen__27)))),introduced(assumption,[])).
% 38.82/39.46 thf(h19,assumption,((eigen__0 @ eigen__25) @ eigen__27),introduced(assumption,[])).
% 38.82/39.46 thf(h20,assumption,(~((eigen__26 @ eigen__27))),introduced(assumption,[])).
% 38.82/39.46 thf(h21,assumption,(~((((eigen__0 @ eigen__25) @ eigen__28) => (~((![X1:$i]:(((eigen__0 @ eigen__28) @ X1) => (eigen__26 @ X1)))))))),introduced(assumption,[])).
% 38.82/39.46 thf(h22,assumption,((eigen__0 @ eigen__25) @ eigen__28),introduced(assumption,[])).
% 38.82/39.46 thf(h23,assumption,(![X1:$i]:(((eigen__0 @ eigen__28) @ X1) => (eigen__26 @ X1))),introduced(assumption,[])).
% 38.82/39.46 thf(ax1012, axiom, (~(p532)|p537), file('<stdin>', ax1012)).
% 38.82/39.46 thf(ax993, axiom, (~(p533)|p556), file('<stdin>', ax993)).
% 38.82/39.46 thf(ax991, axiom, (~(p537)|p558), file('<stdin>', ax991)).
% 38.82/39.46 thf(ax1017, axiom, p532, file('<stdin>', ax1017)).
% 38.82/39.46 thf(ax785, axiom, (~(p556)|~(p747)|p535), file('<stdin>', ax785)).
% 38.82/39.46 thf(ax1016, axiom, p533, file('<stdin>', ax1016)).
% 38.82/39.46 thf(ax1014, axiom, ~(p535), file('<stdin>', ax1014)).
% 38.82/39.46 thf(ax762, axiom, (~(p558)|p768), file('<stdin>', ax762)).
% 38.82/39.46 thf(pax534, axiom, (p534=>f__0 @ f__25 @ f__28), file('<stdin>', pax534)).
% 38.82/39.46 thf(pax536, axiom, (p536=>f__0 @ f__25 @ f__27), file('<stdin>', pax536)).
% 38.82/39.46 thf(nax747, axiom, (p747<=f__0 @ f__28 @ f__27), file('<stdin>', nax747)).
% 38.82/39.46 thf(pax768, axiom, (p768=>(~((f__0 @ f__25 @ f__28=>~(f__0 @ f__25 @ f__27)))=>f__0 @ f__28 @ f__27)), file('<stdin>', pax768)).
% 38.82/39.46 thf(ax1015, axiom, p534, file('<stdin>', ax1015)).
% 38.82/39.46 thf(ax1013, axiom, p536, file('<stdin>', ax1013)).
% 38.82/39.46 thf(c_0_14, plain, (~p532|p537), inference(fof_simplification,[status(thm)],[ax1012])).
% 38.82/39.46 thf(c_0_15, plain, (~p533|p556), inference(fof_simplification,[status(thm)],[ax993])).
% 38.82/39.46 thf(c_0_16, plain, (~p537|p558), inference(fof_simplification,[status(thm)],[ax991])).
% 38.82/39.46 thf(c_0_17, plain, (p537|~p532), inference(split_conjunct,[status(thm)],[c_0_14])).
% 38.82/39.46 thf(c_0_18, plain, p532, inference(split_conjunct,[status(thm)],[ax1017])).
% 38.82/39.46 thf(c_0_19, plain, (~p556|~p747|p535), inference(fof_simplification,[status(thm)],[ax785])).
% 38.82/39.46 thf(c_0_20, plain, (p556|~p533), inference(split_conjunct,[status(thm)],[c_0_15])).
% 38.82/39.46 thf(c_0_21, plain, p533, inference(split_conjunct,[status(thm)],[ax1016])).
% 38.82/39.46 thf(c_0_22, plain, ~p535, inference(fof_simplification,[status(thm)],[ax1014])).
% 38.82/39.46 thf(c_0_23, plain, (~p558|p768), inference(fof_simplification,[status(thm)],[ax762])).
% 38.82/39.46 thf(c_0_24, plain, (p558|~p537), inference(split_conjunct,[status(thm)],[c_0_16])).
% 38.82/39.46 thf(c_0_25, plain, p537, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 38.82/39.46 thf(c_0_26, plain, (~p534|f__0 @ f__25 @ f__28), inference(fof_nnf,[status(thm)],[pax534])).
% 38.82/39.46 thf(c_0_27, plain, (~p536|f__0 @ f__25 @ f__27), inference(fof_nnf,[status(thm)],[pax536])).
% 38.82/39.46 thf(c_0_28, plain, (~f__0 @ f__28 @ f__27|p747), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax747])])).
% 38.82/39.46 thf(c_0_29, plain, (p535|~p556|~p747), inference(split_conjunct,[status(thm)],[c_0_19])).
% 38.82/39.46 thf(c_0_30, plain, p556, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 38.82/39.46 thf(c_0_31, plain, ~p535, inference(split_conjunct,[status(thm)],[c_0_22])).
% 38.82/39.46 thf(c_0_32, plain, (~p768|(~f__0 @ f__25 @ f__28|~f__0 @ f__25 @ f__27|f__0 @ f__28 @ f__27)), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax768])])).
% 38.82/39.46 thf(c_0_33, plain, (p768|~p558), inference(split_conjunct,[status(thm)],[c_0_23])).
% 38.82/39.46 thf(c_0_34, plain, p558, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 38.82/39.46 thf(c_0_35, plain, (f__0 @ f__25 @ f__28|~p534), inference(split_conjunct,[status(thm)],[c_0_26])).
% 38.82/39.46 thf(c_0_36, plain, p534, inference(split_conjunct,[status(thm)],[ax1015])).
% 38.82/39.46 thf(c_0_37, plain, (f__0 @ f__25 @ f__27|~p536), inference(split_conjunct,[status(thm)],[c_0_27])).
% 38.82/39.46 thf(c_0_38, plain, p536, inference(split_conjunct,[status(thm)],[ax1013])).
% 38.82/39.46 thf(c_0_39, plain, (p747|~f__0 @ f__28 @ f__27), inference(split_conjunct,[status(thm)],[c_0_28])).
% 38.82/39.46 thf(c_0_40, plain, ~p747, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])]), c_0_31])).
% 38.82/39.46 thf(c_0_41, plain, (f__0 @ f__28 @ f__27|~p768|~f__0 @ f__25 @ f__28|~f__0 @ f__25 @ f__27), inference(split_conjunct,[status(thm)],[c_0_32])).
% 38.82/39.46 thf(c_0_42, plain, p768, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 38.82/39.46 thf(c_0_43, plain, f__0 @ f__25 @ f__28, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 38.82/39.46 thf(c_0_44, plain, f__0 @ f__25 @ f__27, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 38.82/39.46 thf(c_0_45, plain, ~f__0 @ f__28 @ f__27, inference(sr,[status(thm)],[c_0_39, c_0_40])).
% 38.82/39.46 thf(c_0_46, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44])]), c_0_45]), ['proof']).
% 38.82/39.46 thf(17,plain,$false,inference(eprover,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h17,h15,h14,h5,h6,h2,h1,h0])],[])).
% 38.82/39.46 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,17,h22,h23])).
% 38.82/39.46 thf(19,plain,$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__28)],[h17,18,h21])).
% 38.82/39.46 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,19,h19,h20])).
% 38.82/39.46 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__27)],[h16,20,h18])).
% 38.82/39.46 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,21,h16,h17])).
% 38.82/39.46 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__26)],[h14,22,h15])).
% 38.82/39.46 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__25)],[h5,23,h14])).
% 38.82/39.46 thf(25,plain,$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])).
% 38.82/39.46 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2])).
% 38.82/39.46 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0])).
% 38.82/39.46 thf(0,theorem,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (X3 @ X5)))))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))),inference(contra,[status(thm),contra(discharge,[h1])],[26,h1])).
% 38.82/39.46 % SZS output end Proof
%------------------------------------------------------------------------------