TSTP Solution File: LCL879^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL879^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 14:11:47 EDT 2022
% Result : Theorem 77.86s 78.00s
% Output : Proof 77.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL879^1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 : Mon Jul 4 18:21:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 77.86/78.00 % SZS status Theorem
% 77.86/78.00 % Mode: mode484
% 77.86/78.00 % Inferences: 9664
% 77.86/78.00 % SZS output start Proof
% 77.86/78.00 thf(ty_eigen__2, type, eigen__2 : $i).
% 77.86/78.00 thf(ty_eigen__46, type, eigen__46 : $i).
% 77.86/78.00 thf(ty_eigen__44, type, eigen__44 : ($i>$o)).
% 77.86/78.00 thf(ty_eigen__1, type, eigen__1 : ($i>$i>$o)).
% 77.86/78.00 thf(ty_eigen__45, type, eigen__45 : $i).
% 77.86/78.00 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 77.86/78.00 thf(ty_eigen__4, type, eigen__4 : $i).
% 77.86/78.00 thf(ty_eigen__11, type, eigen__11 : $i).
% 77.86/78.00 thf(ty_eigen__3, type, eigen__3 : $i).
% 77.86/78.00 thf(ty_eigen__43, type, eigen__43 : $i).
% 77.86/78.00 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 77.86/78.00 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__2) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__11])])).
% 77.86/78.00 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP1])])).
% 77.86/78.00 thf(sP2,plain,sP2 <=> (![X1:$i]:(((eigen__0 @ eigen__2) @ X1) => ((eigen__0 @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 77.86/78.00 thf(sP3,plain,sP3 <=> (![X1:$i]:(((eigen__1 @ eigen__2) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => ((eigen__0 @ eigen__2) @ X2))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 77.86/78.00 thf(sP4,plain,sP4 <=> (sP2 => sP3),introduced(definition,[new_symbols(definition,[sP4])])).
% 77.86/78.00 thf(sP5,plain,sP5 <=> (((eigen__0 @ eigen__2) @ eigen__11) => ((eigen__0 @ eigen__2) @ eigen__11)),introduced(definition,[new_symbols(definition,[sP5])])).
% 77.86/78.00 thf(sP6,plain,sP6 <=> (((eigen__1 @ eigen__2) @ eigen__3) => (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ eigen__2) @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 77.86/78.00 thf(sP7,plain,sP7 <=> (![X1:$i]:(((eigen__0 @ eigen__3) @ X1) => ((eigen__0 @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 77.86/78.00 thf(sP8,plain,sP8 <=> (![X1:$i>$o]:((![X2:$i]:(((eigen__0 @ eigen__2) @ X2) => (X1 @ X2))) => (![X2:$i]:(((eigen__1 @ eigen__2) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 77.86/78.00 thf(sP9,plain,sP9 <=> (sP1 => ((eigen__0 @ eigen__2) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP9])])).
% 77.86/78.00 thf(sP10,plain,sP10 <=> ((eigen__1 @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP10])])).
% 77.86/78.00 thf(sP11,plain,sP11 <=> ((eigen__0 @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP11])])).
% 77.86/78.00 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((eigen__0 @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((eigen__1 @ X1) @ X3) => (![X4:$i]:(((eigen__0 @ X3) @ X4) => (X2 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 77.86/78.00 thf(sP13,plain,sP13 <=> ((eigen__0 @ eigen__2) @ eigen__11),introduced(definition,[new_symbols(definition,[sP13])])).
% 77.86/78.00 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 77.86/78.00 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 77.86/78.00 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 77.86/78.00 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 77.86/78.00 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 77.86/78.00 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 77.86/78.00 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 77.86/78.00 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 77.86/78.00 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 77.86/78.00 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 77.86/78.00 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 77.86/78.00 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 77.86/78.00 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 77.86/78.00 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 77.86/78.00 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 77.86/78.00 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 77.86/78.00 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 77.86/78.00 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 77.86/78.00 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 77.86/78.00 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 77.86/78.00 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 77.86/78.00 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 77.86/78.00 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 77.86/78.00 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 77.86/78.00 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 77.86/78.00 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))))))))).
% 77.86/78.00 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 77.86/78.00 thf(def_mvalid,definition,(mvalid = (!!))).
% 77.86/78.00 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 77.86/78.00 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 77.86/78.00 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 77.86/78.00 thf(conj,conjecture,(![X1:$i>$i>$o]:(![X2:$i>$i>$o]:((![X3:$i]:(![X4:$i>$o]:((~((~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 @ X5))))))) => (![X5:$i]:(((X2 @ X3) @ X5) => (![X6:$i]:(((X1 @ X5) @ X6) => (X4 @ X6)))))))) = (![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X2 @ X3) @ X4) => (~(((X1 @ X4) @ X5)))))) => ((X1 @ X3) @ X5))))))))).
% 77.86/78.00 thf(h1,negated_conjecture,(~((![X1:$i>$i>$o]:(![X2:$i>$i>$o]:((![X3:$i]:(![X4:$i>$o]:((![X5:$i]:(((X1 @ X3) @ X5) => (X4 @ X5))) => (![X5:$i]:(((X2 @ X3) @ X5) => (![X6:$i]:(((X1 @ X5) @ X6) => (X4 @ X6)))))))) = (![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X2 @ X3) @ X4) => (~(((X1 @ X4) @ X5)))))) => ((X1 @ X3) @ X5)))))))))),inference(assume_negation,[status(cth)],[conj])).
% 77.86/78.00 thf(h2,assumption,(~((![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((![X4:$i]:(((eigen__0 @ X2) @ X4) => (X3 @ X4))) => (![X4:$i]:(((X1 @ X2) @ X4) => (![X5:$i]:(((eigen__0 @ X4) @ X5) => (X3 @ X5)))))))) = (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((eigen__0 @ X3) @ X4)))))) => ((eigen__0 @ X2) @ X4))))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h3,assumption,(~((sP12 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__1 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3)))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h4,assumption,sP12,introduced(assumption,[])).
% 77.86/78.00 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__1 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))),introduced(assumption,[])).
% 77.86/78.00 thf(h6,assumption,(~(sP12)),introduced(assumption,[])).
% 77.86/78.00 thf(h7,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__1 @ X1) @ X2) => (~(((eigen__0 @ X2) @ X3)))))) => ((eigen__0 @ X1) @ X3))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h8,assumption,(~((![X1:$i]:(![X2:$i]:((~((((eigen__1 @ eigen__2) @ X1) => (~(((eigen__0 @ X1) @ X2)))))) => ((eigen__0 @ eigen__2) @ X2)))))),introduced(assumption,[])).
% 77.86/78.00 thf(h9,assumption,(~((![X1:$i]:((~((sP10 => (~(((eigen__0 @ eigen__3) @ X1)))))) => ((eigen__0 @ eigen__2) @ X1))))),introduced(assumption,[])).
% 77.86/78.00 thf(h10,assumption,(~(((~((sP10 => (~(sP1))))) => sP11))),introduced(assumption,[])).
% 77.86/78.00 thf(h11,assumption,(~((sP10 => (~(sP1))))),introduced(assumption,[])).
% 77.86/78.00 thf(h12,assumption,(~(sP11)),introduced(assumption,[])).
% 77.86/78.00 thf(h13,assumption,sP10,introduced(assumption,[])).
% 77.86/78.00 thf(h14,assumption,sP1,introduced(assumption,[])).
% 77.86/78.00 thf(1,plain,(sP5 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 77.86/78.00 thf(2,plain,(sP5 | sP13),inference(prop_rule,[status(thm)],[])).
% 77.86/78.00 thf(3,plain,((~(sP9) | ~(sP1)) | sP11),inference(prop_rule,[status(thm)],[])).
% 77.86/78.00 thf(4,plain,(~(sP7) | sP9),inference(all_rule,[status(thm)],[])).
% 77.86/78.00 thf(5,plain,((~(sP6) | ~(sP10)) | sP7),inference(prop_rule,[status(thm)],[])).
% 77.86/78.00 thf(6,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])).
% 77.86/78.00 thf(7,plain,(sP2 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])).
% 77.86/78.00 thf(8,plain,((~(sP4) | ~(sP2)) | sP3),inference(prop_rule,[status(thm)],[])).
% 77.86/78.00 thf(9,plain,(~(sP8) | sP4),inference(all_rule,[status(thm)],[])).
% 77.86/78.00 thf(10,plain,(~(sP12) | sP8),inference(all_rule,[status(thm)],[])).
% 77.86/78.00 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h4,h13,h14,h12])).
% 77.86/78.00 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,11,h13,h14])).
% 77.86/78.00 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,12,h11,h12])).
% 77.86/78.00 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h8,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h9,13,h10])).
% 77.86/78.00 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,14,h9])).
% 77.86/78.00 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h5,15,h8])).
% 77.86/78.00 thf(h15,assumption,(~((![X1:$i>$o]:((![X2:$i]:(((eigen__0 @ eigen__43) @ X2) => (X1 @ X2))) => (![X2:$i]:(((eigen__1 @ eigen__43) @ X2) => (![X3:$i]:(((eigen__0 @ X2) @ X3) => (X1 @ X3))))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h16,assumption,(~(((![X1:$i]:(((eigen__0 @ eigen__43) @ X1) => (eigen__44 @ X1))) => (![X1:$i]:(((eigen__1 @ eigen__43) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__44 @ X2)))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h17,assumption,(![X1:$i]:(((eigen__0 @ eigen__43) @ X1) => (eigen__44 @ X1))),introduced(assumption,[])).
% 77.86/78.00 thf(h18,assumption,(~((![X1:$i]:(((eigen__1 @ eigen__43) @ X1) => (![X2:$i]:(((eigen__0 @ X1) @ X2) => (eigen__44 @ X2))))))),introduced(assumption,[])).
% 77.86/78.00 thf(h19,assumption,(~((((eigen__1 @ eigen__43) @ eigen__45) => (![X1:$i]:(((eigen__0 @ eigen__45) @ X1) => (eigen__44 @ X1)))))),introduced(assumption,[])).
% 77.86/78.00 thf(h20,assumption,((eigen__1 @ eigen__43) @ eigen__45),introduced(assumption,[])).
% 77.86/78.00 thf(h21,assumption,(~((![X1:$i]:(((eigen__0 @ eigen__45) @ X1) => (eigen__44 @ X1))))),introduced(assumption,[])).
% 77.86/78.00 thf(h22,assumption,(~((((eigen__0 @ eigen__45) @ eigen__46) => (eigen__44 @ eigen__46)))),introduced(assumption,[])).
% 77.86/78.00 thf(h23,assumption,((eigen__0 @ eigen__45) @ eigen__46),introduced(assumption,[])).
% 77.86/78.00 thf(h24,assumption,(~((eigen__44 @ eigen__46))),introduced(assumption,[])).
% 77.86/78.00 thf(ax1004, axiom, (~(p1125)|p1130), file('<stdin>', ax1004)).
% 77.86/78.00 thf(ax981, axiom, (~(p1129)|p1153), file('<stdin>', ax981)).
% 77.86/78.00 thf(ax979, axiom, (~(p1130)|p1155), file('<stdin>', ax979)).
% 77.86/78.00 thf(ax1009, axiom, p1125, file('<stdin>', ax1009)).
% 77.86/78.00 thf(ax753, axiom, (~(p1153)|~(p1371)|p1126), file('<stdin>', ax753)).
% 77.86/78.00 thf(ax1005, axiom, p1129, file('<stdin>', ax1005)).
% 77.86/78.00 thf(ax1008, axiom, ~(p1126), file('<stdin>', ax1008)).
% 77.86/78.00 thf(ax727, axiom, (~(p1155)|p1396), file('<stdin>', ax727)).
% 77.86/78.00 thf(pax1128, axiom, (p1128=>f__1 @ f__43 @ f__45), file('<stdin>', pax1128)).
% 77.86/78.00 thf(pax1127, axiom, (p1127=>f__0 @ f__45 @ f__46), file('<stdin>', pax1127)).
% 77.86/78.00 thf(nax1371, axiom, (p1371<=f__0 @ f__43 @ f__46), file('<stdin>', nax1371)).
% 77.86/78.00 thf(pax1396, axiom, (p1396=>(~((f__1 @ f__43 @ f__45=>~(f__0 @ f__45 @ f__46)))=>f__0 @ f__43 @ f__46)), file('<stdin>', pax1396)).
% 77.86/78.00 thf(ax1006, axiom, p1128, file('<stdin>', ax1006)).
% 77.86/78.00 thf(ax1007, axiom, p1127, file('<stdin>', ax1007)).
% 77.86/78.00 thf(c_0_14, plain, (~p1125|p1130), inference(fof_simplification,[status(thm)],[ax1004])).
% 77.86/78.00 thf(c_0_15, plain, (~p1129|p1153), inference(fof_simplification,[status(thm)],[ax981])).
% 77.86/78.00 thf(c_0_16, plain, (~p1130|p1155), inference(fof_simplification,[status(thm)],[ax979])).
% 77.86/78.00 thf(c_0_17, plain, (p1130|~p1125), inference(split_conjunct,[status(thm)],[c_0_14])).
% 77.86/78.00 thf(c_0_18, plain, p1125, inference(split_conjunct,[status(thm)],[ax1009])).
% 77.86/78.00 thf(c_0_19, plain, (~p1153|~p1371|p1126), inference(fof_simplification,[status(thm)],[ax753])).
% 77.86/78.00 thf(c_0_20, plain, (p1153|~p1129), inference(split_conjunct,[status(thm)],[c_0_15])).
% 77.86/78.00 thf(c_0_21, plain, p1129, inference(split_conjunct,[status(thm)],[ax1005])).
% 77.86/78.00 thf(c_0_22, plain, ~p1126, inference(fof_simplification,[status(thm)],[ax1008])).
% 77.86/78.00 thf(c_0_23, plain, (~p1155|p1396), inference(fof_simplification,[status(thm)],[ax727])).
% 77.86/78.00 thf(c_0_24, plain, (p1155|~p1130), inference(split_conjunct,[status(thm)],[c_0_16])).
% 77.86/78.00 thf(c_0_25, plain, p1130, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 77.86/78.00 thf(c_0_26, plain, (~p1128|f__1 @ f__43 @ f__45), inference(fof_nnf,[status(thm)],[pax1128])).
% 77.86/78.00 thf(c_0_27, plain, (~p1127|f__0 @ f__45 @ f__46), inference(fof_nnf,[status(thm)],[pax1127])).
% 77.86/78.00 thf(c_0_28, plain, (~f__0 @ f__43 @ f__46|p1371), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1371])])).
% 77.86/78.00 thf(c_0_29, plain, (p1126|~p1153|~p1371), inference(split_conjunct,[status(thm)],[c_0_19])).
% 77.86/78.00 thf(c_0_30, plain, p1153, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 77.86/78.00 thf(c_0_31, plain, ~p1126, inference(split_conjunct,[status(thm)],[c_0_22])).
% 77.86/78.00 thf(c_0_32, plain, (~p1396|(~f__1 @ f__43 @ f__45|~f__0 @ f__45 @ f__46|f__0 @ f__43 @ f__46)), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1396])])).
% 77.86/78.00 thf(c_0_33, plain, (p1396|~p1155), inference(split_conjunct,[status(thm)],[c_0_23])).
% 77.86/78.00 thf(c_0_34, plain, p1155, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 77.86/78.00 thf(c_0_35, plain, (f__1 @ f__43 @ f__45|~p1128), inference(split_conjunct,[status(thm)],[c_0_26])).
% 77.86/78.00 thf(c_0_36, plain, p1128, inference(split_conjunct,[status(thm)],[ax1006])).
% 77.86/78.00 thf(c_0_37, plain, (f__0 @ f__45 @ f__46|~p1127), inference(split_conjunct,[status(thm)],[c_0_27])).
% 77.86/78.00 thf(c_0_38, plain, p1127, inference(split_conjunct,[status(thm)],[ax1007])).
% 77.86/78.00 thf(c_0_39, plain, (p1371|~f__0 @ f__43 @ f__46), inference(split_conjunct,[status(thm)],[c_0_28])).
% 77.86/78.00 thf(c_0_40, plain, ~p1371, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])]), c_0_31])).
% 77.86/78.00 thf(c_0_41, plain, (f__0 @ f__43 @ f__46|~p1396|~f__1 @ f__43 @ f__45|~f__0 @ f__45 @ f__46), inference(split_conjunct,[status(thm)],[c_0_32])).
% 77.86/78.00 thf(c_0_42, plain, p1396, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 77.86/78.00 thf(c_0_43, plain, f__1 @ f__43 @ f__45, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 77.86/78.00 thf(c_0_44, plain, f__0 @ f__45 @ f__46, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 77.86/78.00 thf(c_0_45, plain, ~f__0 @ f__43 @ f__46, inference(sr,[status(thm)],[c_0_39, c_0_40])).
% 77.86/78.00 thf(c_0_46, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44])]), c_0_45]), ['proof']).
% 77.86/78.00 thf(17,plain,$false,inference(eprover,[status(thm),assumptions([h23,h24,h22,h20,h21,h19,h17,h18,h16,h15,h6,h7,h3,h2,h1,h0])],[])).
% 77.86/78.00 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h20,h21,h19,h17,h18,h16,h15,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,17,h23,h24])).
% 77.86/78.00 thf(19,plain,$false,inference(tab_negall,[status(thm),assumptions([h20,h21,h19,h17,h18,h16,h15,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__46)],[h21,18,h22])).
% 77.86/78.00 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h16,h15,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,19,h20,h21])).
% 77.86/78.00 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h18,h16,h15,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__45)],[h18,20,h19])).
% 77.86/78.00 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h15,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,21,h17,h18])).
% 77.86/78.00 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h15,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__44)],[h15,22,h16])).
% 77.86/78.00 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__43)],[h6,23,h15])).
% 77.86/78.00 thf(25,plain,$false,inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,16,24,h4,h5,h6,h7])).
% 77.86/78.00 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,25,h3])).
% 77.86/78.00 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,26,h2])).
% 77.86/78.00 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0])).
% 77.86/78.00 thf(0,theorem,(![X1:$i>$i>$o]:(![X2:$i>$i>$o]:((![X3:$i]:(![X4:$i>$o]:((~((~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 @ X5))))))) => (![X5:$i]:(((X2 @ X3) @ X5) => (![X6:$i]:(((X1 @ X5) @ X6) => (X4 @ X6)))))))) = (![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X2 @ X3) @ X4) => (~(((X1 @ X4) @ X5)))))) => ((X1 @ X3) @ X5)))))))),inference(contra,[status(thm),contra(discharge,[h1])],[27,h1])).
% 77.86/78.00 % SZS output end Proof
%------------------------------------------------------------------------------