TSTP Solution File: PHI003^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PHI003^2 : 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 : n028.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 1.97s 2.17s
% Output : Proof 1.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PHI003^2 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 02:05:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.17 % SZS status Theorem
% 1.97/2.17 % Mode: mode506
% 1.97/2.17 % Inferences: 14
% 1.97/2.17 % SZS output start Proof
% 1.97/2.17 thf(ty_mu, type, mu : $tType).
% 1.97/2.17 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.97/2.17 thf(ty_positive, type, positive : ((mu>$i>$o)>$i>$o)).
% 1.97/2.17 thf(ty_rel, type, rel : ($i>$i>$o)).
% 1.97/2.17 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.97/2.17 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((![X2:$i]:(((rel @ X1) @ X2) => (![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.97/2.17 thf(sP1,plain,sP1 <=> ((!!) @ (positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.97/2.17 thf(sP2,plain,sP2 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.97/2.17 thf(sP3,plain,sP3 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__0) => (~((![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:(~(((X1 @ X3) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.97/2.17 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((positive @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (![X4:mu]:(~(((X2 @ X4) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.97/2.17 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.97/2.17 thf(sP6,plain,sP6 <=> (sP2 => (~((![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.97/2.17 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.97/2.17 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 1.97/2.17 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 1.97/2.17 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 1.97/2.17 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.97/2.17 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.97/2.17 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.97/2.17 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))).
% 1.97/2.17 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))).
% 1.97/2.17 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 1.97/2.17 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
% 1.97/2.17 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 1.97/2.17 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))).
% 1.97/2.17 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 1.97/2.17 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))).
% 1.97/2.17 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))).
% 1.97/2.17 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))).
% 1.97/2.17 thf(def_mbox_generic,definition,(mbox_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 1.97/2.17 thf(def_mdia_generic,definition,(mdia_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 1.97/2.17 thf(def_mbox,definition,(mbox = (mbox_generic @ rel))).
% 1.97/2.17 thf(def_mdia,definition,(mdia = (mdia_generic @ rel))).
% 1.97/2.17 thf(def_mvalid,definition,(mvalid = (!!))).
% 1.97/2.17 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.97/2.17 thf(def_god,definition,(god = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (positive @ X2)) @ (X2 @ X1))))))).
% 1.97/2.17 thf(corC,conjecture,(![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (~((~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2)))))))))))))))).
% 1.97/2.17 thf(h1,negated_conjecture,(~(sP5)),inference(assume_negation,[status(cth)],[corC])).
% 1.97/2.17 thf(1,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])).
% 1.97/2.17 thf(2,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
% 1.97/2.17 thf(3,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])).
% 1.97/2.17 thf(4,plain,((~(sP6) | ~(sP2)) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.17 thf(5,plain,(sP5 | sP7),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.97/2.17 thf(thmT1,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:((mimplies @ (positive @ X1)) @ (mdia @ (mexists_ind @ X1))))))).
% 1.97/2.17 thf(6,plain,sP4,inference(preprocess,[status(thm)],[thmT1]).
% 1.97/2.17 thf(axA3,axiom,(mvalid @ (positive @ god))).
% 1.97/2.17 thf(7,plain,sP1,inference(preprocess,[status(thm)],[axA3]).
% 1.97/2.17 thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h1])).
% 1.97/2.17 thf(9,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0])).
% 1.97/2.17 thf(0,theorem,(![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (~((~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[8,h1])).
% 1.97/2.17 % SZS output end Proof
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