TSTP Solution File: PHI004^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PHI004^1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : Mon Jul 18 16:48:35 EDT 2022
% Result : Theorem 77.12s 77.23s
% Output : Proof 77.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PHI004^1 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 01:49:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 77.12/77.23 % SZS status Theorem
% 77.12/77.23 % Mode: mode484
% 77.12/77.23 % Inferences: 1354
% 77.12/77.23 % SZS output start Proof
% 77.12/77.23 thf(ty_mu, type, mu : $tType).
% 77.12/77.23 thf(ty_eigen__6, type, eigen__6 : mu).
% 77.12/77.23 thf(ty_eigen__2, type, eigen__2 : (mu>$i>$o)).
% 77.12/77.23 thf(ty_eigen__1, type, eigen__1 : mu).
% 77.12/77.23 thf(ty_eigen__0, type, eigen__0 : $i).
% 77.12/77.23 thf(ty_eigen__4, type, eigen__4 : (mu>$i>$o)).
% 77.12/77.23 thf(ty_positive, type, positive : ((mu>$i>$o)>$i>$o)).
% 77.12/77.23 thf(ty_eigen__5, type, eigen__5 : $i).
% 77.12/77.23 thf(ty_rel, type, rel : ($i>$i>$o)).
% 77.12/77.23 thf(sP1,plain,sP1 <=> ((positive @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 77.12/77.23 thf(sP2,plain,sP2 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__5) => ((X1 @ eigen__6) @ eigen__5))),introduced(definition,[new_symbols(definition,[sP2])])).
% 77.12/77.23 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => ((positive @ eigen__4) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 77.12/77.23 thf(sP4,plain,sP4 <=> (sP1 => ((eigen__2 @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP4])])).
% 77.12/77.23 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((positive @ X2) @ X1) => (![X3:$i]:(((rel @ X1) @ X3) => ((positive @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 77.12/77.23 thf(sP6,plain,sP6 <=> (((positive @ (^[X1:mu]:(^[X2:$i]:(~(((eigen__4 @ X1) @ X2)))))) @ eigen__0) = (~(((positive @ eigen__4) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 77.12/77.23 thf(sP7,plain,sP7 <=> ((eigen__4 @ eigen__6) @ eigen__5),introduced(definition,[new_symbols(definition,[sP7])])).
% 77.12/77.23 thf(sP8,plain,sP8 <=> (((positive @ eigen__4) @ eigen__5) => sP7),introduced(definition,[new_symbols(definition,[sP8])])).
% 77.12/77.23 thf(sP9,plain,sP9 <=> (((positive @ eigen__4) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP9])])).
% 77.12/77.23 thf(sP10,plain,sP10 <=> ((positive @ eigen__4) @ eigen__0),introduced(definition,[new_symbols(definition,[sP10])])).
% 77.12/77.23 thf(sP11,plain,sP11 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__0) => (![X2:$i]:(((rel @ eigen__0) @ X2) => ((positive @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 77.12/77.23 thf(sP12,plain,sP12 <=> (((positive @ (^[X1:mu]:(^[X2:$i]:(~(((eigen__4 @ X1) @ X2)))))) @ eigen__0) => (~(((eigen__4 @ eigen__1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP12])])).
% 77.12/77.23 thf(sP13,plain,sP13 <=> ((positive @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP13])])).
% 77.12/77.23 thf(sP14,plain,sP14 <=> (![X1:mu>$i>$o]:(((positive @ (^[X2:mu]:(^[X3:$i]:(~(((X1 @ X2) @ X3)))))) @ eigen__0) = (~(((positive @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 77.12/77.23 thf(sP15,plain,sP15 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__0) => ((X1 @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP15])])).
% 77.12/77.23 thf(sP16,plain,sP16 <=> ((eigen__2 @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP16])])).
% 77.12/77.23 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((positive @ (^[X3:mu]:(^[X4:$i]:(~(((X2 @ X3) @ X4)))))) @ X1) = (~(((positive @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP17])])).
% 77.12/77.23 thf(sP18,plain,sP18 <=> ((eigen__4 @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP18])])).
% 77.12/77.23 thf(sP19,plain,sP19 <=> (((rel @ eigen__0) @ eigen__5) => sP13),introduced(definition,[new_symbols(definition,[sP19])])).
% 77.12/77.23 thf(sP20,plain,sP20 <=> ((rel @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP20])])).
% 77.12/77.23 thf(sP21,plain,sP21 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(~(((eigen__4 @ X1) @ X2)))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP21])])).
% 77.12/77.23 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 77.12/77.23 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 77.12/77.23 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 77.12/77.23 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 77.12/77.23 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 77.12/77.23 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 77.12/77.23 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))).
% 77.12/77.23 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))).
% 77.12/77.23 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 77.12/77.23 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
% 77.12/77.23 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 77.12/77.23 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))).
% 77.12/77.23 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 77.12/77.23 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))).
% 77.12/77.23 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))).
% 77.12/77.23 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))).
% 77.12/77.23 thf(def_mbox_generic,definition,(mbox_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 77.12/77.23 thf(def_mdia_generic,definition,(mdia_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 77.12/77.23 thf(def_mbox,definition,(mbox = (mbox_generic @ rel))).
% 77.12/77.23 thf(def_mdia,definition,(mdia = (mdia_generic @ rel))).
% 77.12/77.23 thf(def_mvalid,definition,(mvalid = (!!))).
% 77.12/77.23 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 77.12/77.23 thf(def_god,definition,(god = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (positive @ X2)) @ (X2 @ X1))))))).
% 77.12/77.23 thf(def_essence,definition,(essence = (^[X1:mu>$i>$o]:(^[X2:mu]:((mand @ (X1 @ X2)) @ (mforall_indset @ (^[X3:mu>$i>$o]:((mimplies @ (X3 @ X2)) @ (mbox @ (mforall_ind @ (^[X4:mu]:((mimplies @ (X1 @ X4)) @ (X3 @ X4))))))))))))).
% 77.12/77.23 thf(def_necessary_existence,definition,(necessary_existence = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ ((essence @ X2) @ X1)) @ (mbox @ (mexists_ind @ X2)))))))).
% 77.12/77.23 thf(thmT2,conjecture,(![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~(((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:(((X3 @ X2) @ X1) => (![X4:$i]:(((rel @ X1) @ X4) => (![X5:mu]:((![X6:mu>$i>$o]:(((positive @ X6) @ X4) => ((X6 @ X5) @ X4))) => ((X3 @ X5) @ X4)))))))))))))))).
% 77.12/77.23 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~(((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:(((X3 @ X2) @ X1) => (![X4:$i]:(((rel @ X1) @ X4) => (![X5:mu]:((![X6:mu>$i>$o]:(((positive @ X6) @ X4) => ((X6 @ X5) @ X4))) => ((X3 @ X5) @ X4))))))))))))))))),inference(assume_negation,[status(cth)],[thmT2])).
% 77.12/77.23 thf(h1,assumption,(~((![X1:mu]:((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__0) => ((X2 @ X1) @ eigen__0))) => (~(((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__0) => ((X2 @ X1) @ eigen__0))) => (~((![X2:mu>$i>$o]:(((X2 @ X1) @ eigen__0) => (![X3:$i]:(((rel @ eigen__0) @ X3) => (![X4:mu]:((![X5:mu>$i>$o]:(((positive @ X5) @ X3) => ((X5 @ X4) @ X3))) => ((X2 @ X4) @ X3)))))))))))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h2,assumption,(~((sP15 => (~((sP15 => (~((![X1:mu>$i>$o]:(((X1 @ eigen__1) @ eigen__0) => (![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))) => ((X1 @ X3) @ X2))))))))))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h3,assumption,sP15,introduced(assumption,[])).
% 77.12/77.23 thf(h4,assumption,(sP15 => (~((![X1:mu>$i>$o]:(((X1 @ eigen__1) @ eigen__0) => (![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))) => ((X1 @ X3) @ X2)))))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h5,assumption,(~(sP15)),introduced(assumption,[])).
% 77.12/77.23 thf(h6,assumption,(~((![X1:mu>$i>$o]:(((X1 @ eigen__1) @ eigen__0) => (![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))) => ((X1 @ X3) @ X2))))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h7,assumption,(~(sP4)),introduced(assumption,[])).
% 77.12/77.23 thf(h8,assumption,sP1,introduced(assumption,[])).
% 77.12/77.23 thf(h9,assumption,(~(sP16)),introduced(assumption,[])).
% 77.12/77.23 thf(1,plain,((~(sP4) | ~(sP1)) | sP16),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(2,plain,(~(sP15) | sP4),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(3,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h3,h4,h2,h1,h0])],[1,2,h3,h8,h9])).
% 77.12/77.23 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,3,h8,h9])).
% 77.12/77.23 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h5,4,h7])).
% 77.12/77.23 thf(h10,assumption,(~((sP18 => (![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => ((eigen__4 @ X2) @ X1)))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h11,assumption,sP18,introduced(assumption,[])).
% 77.12/77.23 thf(h12,assumption,(~((![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => ((eigen__4 @ X2) @ X1))))))),introduced(assumption,[])).
% 77.12/77.23 thf(h13,assumption,(~((sP20 => (![X1:mu]:((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__5) => ((X2 @ X1) @ eigen__5))) => ((eigen__4 @ X1) @ eigen__5)))))),introduced(assumption,[])).
% 77.12/77.23 thf(h14,assumption,sP20,introduced(assumption,[])).
% 77.12/77.23 thf(h15,assumption,(~((![X1:mu]:((![X2:mu>$i>$o]:(((positive @ X2) @ eigen__5) => ((X2 @ X1) @ eigen__5))) => ((eigen__4 @ X1) @ eigen__5))))),introduced(assumption,[])).
% 77.12/77.23 thf(h16,assumption,(~((sP2 => sP7))),introduced(assumption,[])).
% 77.12/77.23 thf(h17,assumption,sP2,introduced(assumption,[])).
% 77.12/77.23 thf(h18,assumption,(~(sP7)),introduced(assumption,[])).
% 77.12/77.23 thf(6,plain,((~(sP19) | ~(sP20)) | sP13),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(7,plain,((~(sP12) | ~(sP21)) | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(8,plain,(~(sP3) | sP19),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(9,plain,((~(sP6) | sP21) | sP10),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(10,plain,(~(sP15) | sP12),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(11,plain,((~(sP9) | ~(sP10)) | sP3),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(12,plain,(~(sP14) | sP6),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(13,plain,(~(sP11) | sP9),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(14,plain,((~(sP8) | ~(sP13)) | sP7),inference(prop_rule,[status(thm)],[])).
% 77.12/77.23 thf(15,plain,(~(sP17) | sP14),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(16,plain,(~(sP5) | sP11),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(17,plain,(~(sP2) | sP8),inference(all_rule,[status(thm)],[])).
% 77.12/77.23 thf(axA1,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:((mequiv @ (positive @ (^[X2:mu]:(mnot @ (X1 @ X2))))) @ (mnot @ (positive @ X1))))))).
% 77.12/77.23 thf(18,plain,sP17,inference(preprocess,[status(thm)],[axA1]).
% 77.12/77.23 thf(axA4,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:((mimplies @ (positive @ X1)) @ (mbox @ (positive @ X1))))))).
% 77.12/77.23 thf(19,plain,sP5,inference(preprocess,[status(thm)],[axA4]).
% 77.12/77.23 thf(20,plain,$false,inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0])],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,h3,h11,h14,h17,h18])).
% 77.12/77.23 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,20,h17,h18])).
% 77.12/77.23 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h15,21,h16])).
% 77.12/77.23 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,22,h14,h15])).
% 77.12/77.23 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__5)],[h12,23,h13])).
% 77.12/77.23 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,24,h11,h12])).
% 77.12/77.23 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h6,25,h10])).
% 77.12/77.23 thf(27,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,5,26,h5,h6])).
% 77.12/77.23 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,27,h3,h4])).
% 77.12/77.23 thf(29,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,28,h2])).
% 77.12/77.23 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,29,h1])).
% 77.12/77.23 thf(0,theorem,(![X1:$i]:(![X2:mu]:((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~(((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))) => (~((![X3:mu>$i>$o]:(((X3 @ X2) @ X1) => (![X4:$i]:(((rel @ X1) @ X4) => (![X5:mu]:((![X6:mu>$i>$o]:(((positive @ X6) @ X4) => ((X6 @ X5) @ X4))) => ((X3 @ X5) @ X4))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[30,h0])).
% 77.12/77.23 % SZS output end Proof
%------------------------------------------------------------------------------