TSTP Solution File: GEG014^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GEG014^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 : Sat Jul 16 02:41:38 EDT 2022
% Result : Theorem 77.18s 77.13s
% Output : Proof 77.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEG014^1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 05:19:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 77.18/77.13 % SZS status Theorem
% 77.18/77.13 % Mode: mode484
% 77.18/77.13 % Inferences: 978
% 77.18/77.13 % SZS output start Proof
% 77.18/77.13 thf(ty_reg, type, reg : $tType).
% 77.18/77.13 thf(ty_a, type, a : ($i>$i>$o)).
% 77.18/77.13 thf(ty_paris, type, paris : reg).
% 77.18/77.13 thf(ty_eigen__1, type, eigen__1 : $i).
% 77.18/77.13 thf(ty_eigen__0, type, eigen__0 : $i).
% 77.18/77.13 thf(ty_france, type, france : reg).
% 77.18/77.13 thf(ty_c, type, c : (reg>reg>$o)).
% 77.18/77.13 thf(sP1,plain,sP1 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 77.18/77.13 thf(sP2,plain,sP2 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 77.18/77.13 thf(sP3,plain,sP3 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP3])])).
% 77.18/77.13 thf(sP4,plain,sP4 <=> (sP3 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 77.18/77.13 thf(sP5,plain,sP5 <=> ((~((((![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris))) => (~(sP3))) => sP2))) => sP2),introduced(definition,[new_symbols(definition,[sP5])])).
% 77.18/77.13 thf(sP6,plain,sP6 <=> (sP1 => (~(((~(sP4)) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 77.18/77.13 thf(sP7,plain,sP7 <=> ((~(sP4)) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 77.18/77.13 thf(sP8,plain,sP8 <=> (sP3 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP8])])).
% 77.18/77.13 thf(sP9,plain,sP9 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP9])])).
% 77.18/77.13 thf(sP10,plain,sP10 <=> (![X1:reg]:((~((((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => sP2))) => sP2)),introduced(definition,[new_symbols(definition,[sP10])])).
% 77.18/77.13 thf(sP11,plain,sP11 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP7)))),introduced(definition,[new_symbols(definition,[sP11])])).
% 77.18/77.13 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP7))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 77.18/77.13 thf(sP13,plain,sP13 <=> (![X1:reg]:(![X2:reg]:((~((((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1)))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 77.18/77.13 thf(sP14,plain,sP14 <=> (sP9 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP14])])).
% 77.18/77.13 thf(sP15,plain,sP15 <=> (sP14 => sP2),introduced(definition,[new_symbols(definition,[sP15])])).
% 77.18/77.13 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 77.18/77.13 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 77.18/77.13 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 77.18/77.13 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 77.18/77.13 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 77.18/77.13 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 77.18/77.13 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 77.18/77.13 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 77.18/77.13 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 77.18/77.13 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 77.18/77.13 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 77.18/77.13 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 77.18/77.13 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 77.18/77.13 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 77.18/77.13 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 77.18/77.13 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 77.18/77.13 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 77.18/77.13 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 77.18/77.13 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 77.18/77.13 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 77.18/77.13 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 77.18/77.13 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 77.18/77.13 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 77.18/77.13 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 77.18/77.13 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 77.18/77.13 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))))))))).
% 77.18/77.13 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 77.18/77.13 thf(def_mvalid,definition,(mvalid = (!!))).
% 77.18/77.13 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 77.18/77.13 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 77.18/77.13 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 77.18/77.13 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))).
% 77.18/77.13 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))).
% 77.18/77.13 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))).
% 77.18/77.13 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))).
% 77.18/77.13 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))).
% 77.18/77.13 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))).
% 77.18/77.13 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))).
% 77.18/77.13 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))).
% 77.18/77.13 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))).
% 77.18/77.13 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:(![X4:reg]:((~(((~((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ X4))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))))))))))).
% 77.18/77.13 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP13))))))),inference(assume_negation,[status(cth)],[con])).
% 77.18/77.13 thf(h1,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP13)))))),introduced(assumption,[])).
% 77.18/77.13 thf(h2,assumption,(~((sP1 => (~(sP13))))),introduced(assumption,[])).
% 77.18/77.13 thf(h3,assumption,sP1,introduced(assumption,[])).
% 77.18/77.13 thf(h4,assumption,sP13,introduced(assumption,[])).
% 77.18/77.13 thf(1,plain,((~(sP8) | ~(sP3)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(2,plain,(sP4 | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(3,plain,(sP4 | sP3),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(4,plain,(sP7 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(5,plain,(~(sP2) | sP8),inference(all_rule,[status(thm)],[])).
% 77.18/77.13 thf(6,plain,((~(sP6) | ~(sP1)) | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(7,plain,(sP14 | sP9),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(8,plain,((~(sP15) | ~(sP14)) | sP2),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(9,plain,((~(sP5) | sP15) | sP2),inference(prop_rule,[status(thm)],[])).
% 77.18/77.13 thf(10,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])).
% 77.18/77.13 thf(11,plain,(~(sP10) | sP5),inference(all_rule,[status(thm)],[])).
% 77.18/77.13 thf(12,plain,(~(sP12) | sP11),inference(all_rule,[status(thm)],[])).
% 77.18/77.13 thf(13,plain,(~(sP13) | sP10),inference(all_rule,[status(thm)],[])).
% 77.18/77.13 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))).
% 77.18/77.13 thf(14,plain,sP12,inference(preprocess,[status(thm)],[ax3]).
% 77.18/77.13 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h4])).
% 77.18/77.13 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4])).
% 77.18/77.13 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2])).
% 77.18/77.13 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1])).
% 77.18/77.13 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:(![X4:reg]:((~(((~((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ X4))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])).
% 77.18/77.13 % SZS output end Proof
%------------------------------------------------------------------------------