TSTP Solution File: SET047^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET047^1 : TPTP v8.1.0. Released v8.1.0.
% 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 : Tue Jul 19 04:50:20 EDT 2022
% Result : Theorem 2.00s 2.22s
% Output : Proof 2.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET047^1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 21:16:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.00/2.22 % SZS status Theorem
% 2.00/2.22 % Mode: mode506
% 2.00/2.22 % Inferences: 10194
% 2.00/2.22 % SZS output start Proof
% 2.00/2.22 thf(ty_mworld, type, mworld : $tType).
% 2.00/2.22 thf(ty_element, type, element : ($i>$i>mworld>$o)).
% 2.00/2.22 thf(ty_eigen__2, type, eigen__2 : $i).
% 2.00/2.22 thf(ty_eigen__1, type, eigen__1 : $i).
% 2.00/2.22 thf(ty_set_equal, type, set_equal : ($i>$i>mworld>$o)).
% 2.00/2.22 thf(ty_eigen__0, type, eigen__0 : $i).
% 2.00/2.22 thf(ty_eigen__3, type, eigen__3 : $i).
% 2.00/2.22 thf(ty_mactual, type, mactual : mworld).
% 2.00/2.22 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 2.00/2.22 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~(((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 2.00/2.22 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((((set_equal @ eigen__0) @ X1) @ mactual) = (((set_equal @ X1) @ eigen__0) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 2.00/2.22 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (((set_equal @ X2) @ X1) @ mactual))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 2.00/2.22 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~(((((element @ X1) @ eigen__0) @ mactual) = (((element @ X1) @ eigen__1) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 2.00/2.22 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (![X3:$i]:((((element @ X3) @ X1) @ mactual) = (((element @ X3) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 2.00/2.22 thf(sP2,plain,sP2 <=> (![X1:$i]:((((element @ X1) @ eigen__0) @ mactual) = (((element @ X1) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP2])])).
% 2.00/2.22 thf(sP3,plain,sP3 <=> (![X1:$i]:((((set_equal @ eigen__0) @ X1) @ mactual) = (![X2:$i]:((((element @ X2) @ eigen__0) @ mactual) = (((element @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 2.00/2.22 thf(sP4,plain,sP4 <=> ((~(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))) => (![X1:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X1) => (~((X1 = (((set_equal @ eigen__1) @ eigen__0) @ mactual))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 2.00/2.22 thf(sP5,plain,sP5 <=> (((((set_equal @ eigen__0) @ eigen__1) @ mactual) = sP2) => (~((sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 2.00/2.22 thf(sP6,plain,sP6 <=> (![X1:$i]:((((set_equal @ eigen__1) @ X1) @ mactual) = (![X2:$i]:((((element @ X2) @ eigen__1) @ mactual) = (((element @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 2.00/2.22 thf(sP7,plain,sP7 <=> ((((set_equal @ eigen__1) @ eigen__0) @ mactual) = (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 2.00/2.22 thf(sP8,plain,sP8 <=> (sP2 = (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 2.00/2.22 thf(sP9,plain,sP9 <=> (sP7 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP9])])).
% 2.00/2.22 thf(sP10,plain,sP10 <=> (![X1:$o]:(((((element @ eigen__3) @ eigen__0) @ mactual) = X1) => (X1 = (((element @ eigen__3) @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP10])])).
% 2.00/2.22 thf(sP11,plain,sP11 <=> (![X1:$o>$o]:((X1 @ (((set_equal @ eigen__0) @ eigen__1) @ mactual)) => (![X2:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 2.00/2.22 thf(sP12,plain,sP12 <=> (![X1:$o]:(((((set_equal @ eigen__0) @ eigen__1) @ mactual) = X1) => (~((X1 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 2.00/2.22 thf(sP13,plain,sP13 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X1 = X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 2.00/2.22 thf(sP14,plain,sP14 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP14])])).
% 2.00/2.22 thf(sP15,plain,sP15 <=> (((((element @ eigen__3) @ eigen__0) @ mactual) = (((element @ eigen__3) @ eigen__1) @ mactual)) => ((((element @ eigen__3) @ eigen__1) @ mactual) = (((element @ eigen__3) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP15])])).
% 2.00/2.22 thf(sP16,plain,sP16 <=> ((~((sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)))) => (![X1:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X1) => (~((sP2 = X1)))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 2.00/2.22 thf(sP17,plain,sP17 <=> (((((element @ eigen__2) @ eigen__1) @ mactual) = (((element @ eigen__2) @ eigen__0) @ mactual)) => ((((element @ eigen__2) @ eigen__0) @ mactual) = (((element @ eigen__2) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP17])])).
% 2.00/2.22 thf(sP18,plain,sP18 <=> ((((element @ eigen__3) @ eigen__0) @ mactual) = (((element @ eigen__3) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP18])])).
% 2.00/2.22 thf(sP19,plain,sP19 <=> (![X1:$o>$o]:((X1 @ (((set_equal @ eigen__1) @ eigen__0) @ mactual)) => (![X2:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 2.00/2.22 thf(sP20,plain,sP20 <=> (sP2 = (((set_equal @ eigen__1) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP20])])).
% 2.00/2.22 thf(sP21,plain,sP21 <=> (![X1:$i]:((((element @ X1) @ eigen__1) @ mactual) = (((element @ X1) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP21])])).
% 2.00/2.22 thf(sP22,plain,sP22 <=> (![X1:$i]:((((set_equal @ eigen__0) @ X1) @ mactual) = (((set_equal @ X1) @ eigen__0) @ mactual))),introduced(definition,[new_symbols(definition,[sP22])])).
% 2.00/2.22 thf(sP23,plain,sP23 <=> ((((element @ eigen__3) @ eigen__1) @ mactual) = (((element @ eigen__3) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP23])])).
% 2.00/2.22 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:((((set_equal @ X1) @ X2) @ mactual) = (((set_equal @ X2) @ X1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP24])])).
% 2.00/2.22 thf(sP25,plain,sP25 <=> (![X1:$o]:(((((set_equal @ eigen__1) @ eigen__0) @ mactual) = X1) => (~((sP2 = X1))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 2.00/2.22 thf(sP26,plain,sP26 <=> ((((element @ eigen__2) @ eigen__0) @ mactual) = (((element @ eigen__2) @ eigen__1) @ mactual)),introduced(definition,[new_symbols(definition,[sP26])])).
% 2.00/2.22 thf(sP27,plain,sP27 <=> ((((element @ eigen__2) @ eigen__1) @ mactual) = (((element @ eigen__2) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP27])])).
% 2.00/2.22 thf(sP28,plain,sP28 <=> (![X1:$o]:(((((element @ eigen__2) @ eigen__1) @ mactual) = X1) => (X1 = (((element @ eigen__2) @ eigen__1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP28])])).
% 2.00/2.22 thf(sP29,plain,sP29 <=> ((((set_equal @ eigen__0) @ eigen__1) @ mactual) = sP2),introduced(definition,[new_symbols(definition,[sP29])])).
% 2.00/2.22 thf(sP30,plain,sP30 <=> ((((set_equal @ eigen__0) @ eigen__1) @ mactual) = (((set_equal @ eigen__1) @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP30])])).
% 2.00/2.22 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 2.00/2.22 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 2.00/2.22 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 2.00/2.22 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 2.00/2.22 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 2.00/2.22 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 2.00/2.22 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 2.00/2.22 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))).
% 2.00/2.22 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))).
% 2.00/2.22 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))).
% 2.00/2.22 thf(pel43,conjecture,sP24).
% 2.00/2.22 thf(h1,negated_conjecture,(~(sP24)),inference(assume_negation,[status(cth)],[pel43])).
% 2.00/2.22 thf(1,plain,((~(sP15) | ~(sP18)) | sP23),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(2,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(3,plain,(~(sP14) | sP10),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(4,plain,(~(sP2) | sP18),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(5,plain,(sP21 | ~(sP23)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 2.00/2.22 thf(6,plain,((~(sP17) | ~(sP27)) | sP26),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(7,plain,(~(sP28) | sP17),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(8,plain,(~(sP14) | sP28),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(9,plain,(~(sP21) | sP27),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(10,plain,((~(sP9) | ~(sP7)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(11,plain,(~(sP25) | sP9),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(12,plain,((~(sP16) | sP20) | sP25),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(13,plain,(~(sP19) | sP16),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(14,plain,((sP8 | ~(sP2)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(15,plain,((sP8 | sP2) | sP21),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(16,plain,(sP2 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 2.00/2.22 thf(17,plain,((~(sP5) | ~(sP29)) | ~(sP20)),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(18,plain,(~(sP12) | sP5),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(19,plain,((~(sP4) | sP30) | sP12),inference(prop_rule,[status(thm)],[])).
% 2.00/2.22 thf(20,plain,(~(sP11) | sP4),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(21,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(22,plain,(~(sP3) | sP29),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(23,plain,(~(sP13) | sP11),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(24,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(25,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(26,plain,(~(sP13) | sP19),inference(all_rule,[status(thm)],[])).
% 2.00/2.22 thf(27,plain,sP13,inference(eq_ind,[status(thm)],[])).
% 2.00/2.22 thf(28,plain,sP14,inference(eq_sym,[status(thm)],[])).
% 2.00/2.22 thf(29,plain,(sP22 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 2.00/2.22 thf(30,plain,(sP24 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 2.00/2.22 thf(pel43_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((set_equal @ X1) @ X2)) @ (mforall_di @ (^[X3:$i]:((mequiv @ ((element @ X3) @ X1)) @ ((element @ X3) @ X2))))))))))).
% 2.00/2.22 thf(31,plain,sP1,inference(preprocess,[status(thm)],[pel43_1]).
% 2.00/2.22 thf(32,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h1])).
% 2.00/2.22 thf(33,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[32,h0])).
% 2.00/2.22 thf(0,theorem,sP24,inference(contra,[status(thm),contra(discharge,[h1])],[32,h1])).
% 2.00/2.22 % SZS output end Proof
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