TSTP Solution File: PLA032^7 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PLA032^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 17:31:52 EDT 2022
% Result : Theorem 0.97s 1.24s
% Output : Proof 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PLA032^7 : TPTP v8.1.0. Released v5.5.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.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 : Tue May 31 22:53:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.24 % SZS status Theorem
% 0.97/1.24 % Mode: mode213
% 0.97/1.24 % Inferences: 3378
% 0.97/1.24 % SZS output start Proof
% 0.97/1.24 thf(ty_mu, type, mu : $tType).
% 0.97/1.24 thf(ty_h, type, h : (mu>$i>$o)).
% 0.97/1.24 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.97/1.24 thf(ty_eigen__2, type, eigen__2 : mu).
% 0.97/1.24 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.97/1.24 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.97/1.24 thf(ty_eigen__3, type, eigen__3 : mu).
% 0.97/1.24 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 0.97/1.24 thf(ty_bomb, type, bomb : (mu>$i>$o)).
% 0.97/1.24 thf(ty_defused, type, defused : (mu>$i>$o)).
% 0.97/1.24 thf(h0, assumption, (![X1:mu>$o]:(![X2:mu]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.97/1.24 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:mu]:(~((((exists_in_world @ X1) @ eigen__1) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((~((((bomb @ eigen__2) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__2) @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 0.97/1.24 thf(sP1,plain,sP1 <=> ((exists_in_world @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.97/1.24 thf(sP2,plain,sP2 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~((![X2:$i]:(((rel_s4 @ eigen__1) @ X2) => ((~((((bomb @ eigen__2) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__2) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.97/1.24 thf(sP3,plain,sP3 <=> (((exists_in_world @ eigen__3) @ eigen__1) => (~(((~((((bomb @ eigen__2) @ eigen__1) => (~(((h @ eigen__3) @ eigen__1)))))) => ((defused @ eigen__2) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.97/1.24 thf(sP4,plain,sP4 <=> (((exists_in_world @ eigen__3) @ eigen__1) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((~((((bomb @ eigen__2) @ X1) => (~(((h @ eigen__3) @ X1)))))) => ((defused @ eigen__2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.97/1.24 thf(sP5,plain,sP5 <=> ((~((((bomb @ eigen__2) @ eigen__1) => (~(((h @ eigen__3) @ eigen__1)))))) => ((defused @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.97/1.24 thf(sP6,plain,sP6 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~((![X2:mu]:(((exists_in_world @ X2) @ eigen__1) => (~((![X3:$i]:(((rel_s4 @ eigen__1) @ X3) => ((~((((bomb @ X1) @ X3) => (~(((h @ X2) @ X3)))))) => ((defused @ X1) @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.97/1.24 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:mu]:(((exists_in_world @ X3) @ X1) => (~((![X4:$i]:(((rel_s4 @ X1) @ X4) => ((~((((bomb @ X2) @ X4) => (~(((h @ X3) @ X4)))))) => ((defused @ X2) @ X4)))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.97/1.24 thf(sP8,plain,sP8 <=> (((rel_s4 @ eigen__1) @ eigen__1) => sP5),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.97/1.24 thf(sP9,plain,sP9 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.97/1.24 thf(sP10,plain,sP10 <=> (sP1 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.97/1.24 thf(sP11,plain,sP11 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((~((((bomb @ eigen__2) @ X1) => (~(((h @ eigen__3) @ X1)))))) => ((defused @ eigen__2) @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.97/1.24 thf(sP12,plain,sP12 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.97/1.24 thf(sP13,plain,sP13 <=> ((exists_in_world @ eigen__3) @ eigen__1),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.97/1.24 thf(sP14,plain,sP14 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~(((~((((bomb @ eigen__2) @ eigen__1) => (~(((h @ X1) @ eigen__1)))))) => ((defused @ eigen__2) @ eigen__1)))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.97/1.24 thf(sP15,plain,sP15 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.97/1.24 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:mu]:(((exists_in_world @ X4) @ X2) => (~((![X5:$i]:(((rel_s4 @ X2) @ X5) => ((~((((bomb @ X3) @ X5) => (~(((h @ X4) @ X5)))))) => ((defused @ X3) @ X5))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.97/1.24 thf(sP17,plain,sP17 <=> (sP12 => sP6),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.97/1.24 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.97/1.24 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.97/1.24 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.97/1.24 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.97/1.24 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.97/1.24 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.97/1.24 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.97/1.24 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.97/1.24 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.97/1.24 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.97/1.24 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.97/1.24 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.97/1.24 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.97/1.24 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 0.97/1.24 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.97/1.24 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.97/1.24 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.97/1.24 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.97/1.24 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.97/1.24 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.97/1.24 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.97/1.24 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)))))))).
% 0.97/1.24 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.97/1.24 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.97/1.24 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.97/1.24 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.97/1.24 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.97/1.24 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.97/1.24 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.97/1.24 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.97/1.24 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.97/1.24 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.97/1.24 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:mu]:(((exists_in_world @ X4) @ X2) => (~(((~((~((~(((~((~(((bomb @ X3) @ X2))))) => (~(((h @ X4) @ X2)))))))))) => ((defused @ X3) @ X2)))))))))))))).
% 0.97/1.24 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:mu]:(((exists_in_world @ X4) @ X2) => (~(((~((((bomb @ X3) @ X2) => (~(((h @ X4) @ X2)))))) => ((defused @ X3) @ X2))))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 0.97/1.24 thf(h2,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:mu]:(((exists_in_world @ X3) @ X1) => (~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1)))))))))))))),introduced(assumption,[])).
% 0.97/1.24 thf(h3,assumption,(~((sP12 => (![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~((![X2:mu]:(((exists_in_world @ X2) @ eigen__1) => (~(((~((((bomb @ X1) @ eigen__1) => (~(((h @ X2) @ eigen__1)))))) => ((defused @ X1) @ eigen__1))))))))))))),introduced(assumption,[])).
% 0.97/1.24 thf(h4,assumption,sP12,introduced(assumption,[])).
% 0.97/1.24 thf(h5,assumption,(~((![X1:mu]:(((exists_in_world @ X1) @ eigen__1) => (~((![X2:mu]:(((exists_in_world @ X2) @ eigen__1) => (~(((~((((bomb @ X1) @ eigen__1) => (~(((h @ X2) @ eigen__1)))))) => ((defused @ X1) @ eigen__1)))))))))))),introduced(assumption,[])).
% 0.97/1.24 thf(h6,assumption,(~((sP1 => (~(sP14))))),introduced(assumption,[])).
% 0.97/1.24 thf(h7,assumption,sP1,introduced(assumption,[])).
% 0.97/1.24 thf(h8,assumption,sP14,introduced(assumption,[])).
% 0.97/1.24 thf(1,plain,(~(sP9) | sP15),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(2,plain,(~(sP11) | sP8),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(3,plain,((~(sP8) | ~(sP15)) | sP5),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(4,plain,(~(sP14) | sP3),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(5,plain,((~(sP3) | ~(sP13)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(6,plain,(sP4 | sP11),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(7,plain,(sP4 | sP13),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(8,plain,(sP2 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 0.97/1.24 thf(9,plain,(~(sP6) | sP10),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(10,plain,((~(sP10) | ~(sP1)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(11,plain,(~(sP16) | sP7),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(12,plain,(~(sP7) | sP17),inference(all_rule,[status(thm)],[])).
% 0.97/1.24 thf(13,plain,((~(sP17) | ~(sP12)) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.97/1.24 thf(a1,axiom,(mreflexive @ rel_s4)).
% 0.97/1.24 thf(14,plain,sP9,inference(preprocess,[status(thm)],[a1]).
% 0.97/1.24 thf(ax3,axiom,(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X1:mu]:(mexists_ind @ (^[X2:mu]:(mbox_s4 @ ((mimplies @ ((mand @ (bomb @ X1)) @ (h @ X2))) @ (defused @ X1)))))))))).
% 0.97/1.24 thf(15,plain,sP16,inference(preprocess,[status(thm)],[ax3]).
% 0.97/1.24 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4,h7,h8])).
% 0.97/1.24 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,16,h7,h8])).
% 0.97/1.24 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,17,h6])).
% 0.97/1.24 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,18,h4,h5])).
% 0.97/1.24 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,19,h3])).
% 0.97/1.24 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,20,h2])).
% 0.97/1.24 thf(22,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0])).
% 0.97/1.24 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((![X4:mu]:(((exists_in_world @ X4) @ X2) => (~(((~((~((~(((~((~(((bomb @ X3) @ X2))))) => (~(((h @ X4) @ X2)))))))))) => ((defused @ X3) @ X2))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[21,h1])).
% 0.97/1.24 % SZS output end Proof
%------------------------------------------------------------------------------