TSTP Solution File: SET926^11 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET926^11 : 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 : n015.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 04:56:41 EDT 2022
% Result : Theorem 1.97s 2.18s
% Output : Proof 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET926^11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n015.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 : Sun Jul 10 06:16:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.18 % SZS status Theorem
% 1.97/2.18 % Mode: mode506
% 1.97/2.18 % Inferences: 8226
% 1.97/2.18 % SZS output start Proof
% 1.97/2.18 thf(ty_mworld, type, mworld : $tType).
% 1.97/2.18 thf(ty_singleton, type, singleton : ($i>$i)).
% 1.97/2.18 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)).
% 1.97/2.18 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.97/2.18 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.97/2.18 thf(ty_mactual, type, mactual : mworld).
% 1.97/2.18 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)).
% 1.97/2.18 thf(ty_empty_set, type, empty_set : $i).
% 1.97/2.18 thf(ty_set_difference, type, set_difference : ($i>$i>$i)).
% 1.97/2.18 thf(ty_in, type, in : ($i>$i>mworld>$o)).
% 1.97/2.18 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.97/2.18 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 1.97/2.18 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.97/2.18 thf(sP1,plain,sP1 <=> (((eiw_di @ eigen__0) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.97/2.18 thf(sP2,plain,sP2 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X3 = X1) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.97/2.18 thf(sP3,plain,sP3 <=> ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ (singleton @ eigen__0)) @ mactual) = (~((((in @ eigen__0) @ eigen__1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.97/2.18 thf(sP4,plain,sP4 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual) = (((in @ eigen__0) @ X1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.97/2.18 thf(sP5,plain,sP5 <=> (sP3 => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ (singleton @ eigen__0)) @ mactual)),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.97/2.18 thf(sP6,plain,sP6 <=> (((eiw_di @ eigen__0) @ mactual) => sP4),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.97/2.18 thf(sP7,plain,sP7 <=> (((eiw_di @ eigen__1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ empty_set) @ mactual) = (((in @ eigen__0) @ eigen__1) @ mactual))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.97/2.18 thf(sP8,plain,sP8 <=> (((eiw_di @ eigen__0) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual) = (~((((in @ eigen__0) @ X1) @ mactual))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.97/2.18 thf(sP9,plain,sP9 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.97/2.18 thf(sP10,plain,sP10 <=> (((in @ eigen__0) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.97/2.18 thf(sP11,plain,sP11 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ X1)) @ (singleton @ eigen__0)) @ mactual) = (~((((in @ eigen__0) @ X1) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.97/2.18 thf(sP12,plain,sP12 <=> (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ (singleton @ eigen__0)) @ mactual),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.97/2.18 thf(sP13,plain,sP13 <=> (![X1:$o]:((X1 = (~(sP10))) => X1)),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.97/2.18 thf(sP14,plain,sP14 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual) = (((in @ X1) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.97/2.18 thf(sP15,plain,sP15 <=> (((qmltpeq @ ((set_difference @ (singleton @ eigen__0)) @ eigen__1)) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.97/2.18 thf(sP16,plain,sP16 <=> (sP15 = sP10),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.97/2.18 thf(sP17,plain,sP17 <=> ((eiw_di @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.97/2.18 thf(sP18,plain,sP18 <=> ((eiw_di @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.97/2.18 thf(sP19,plain,sP19 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual) = (~((((in @ X1) @ X2) @ mactual)))))))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.97/2.18 thf(sP20,plain,sP20 <=> (sP18 => ((~(sP15)) => sP12)),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.97/2.18 thf(sP21,plain,sP21 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set) @ mactual))) => (((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.97/2.18 thf(sP22,plain,sP22 <=> (![X1:$o>$o]:((X1 @ (~(sP10))) => (![X2:$o]:((X2 = (~(sP10))) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.97/2.18 thf(sP23,plain,sP23 <=> ((~(sP10)) => sP13),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.97/2.18 thf(sP24,plain,sP24 <=> ((~(sP15)) => sP12),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.97/2.18 thf(sP25,plain,sP25 <=> (sP18 => sP3),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.97/2.18 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 1.97/2.18 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 1.97/2.18 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.97/2.18 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.97/2.18 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 1.97/2.18 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 1.97/2.18 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 1.97/2.18 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))).
% 1.97/2.18 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 1.97/2.18 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))).
% 1.97/2.18 thf(t69_zfmisc_1,conjecture,sP21).
% 1.97/2.18 thf(h1,negated_conjecture,(~(sP21)),inference(assume_negation,[status(cth)],[t69_zfmisc_1])).
% 1.97/2.18 thf(1,plain,((~(sP5) | ~(sP3)) | sP12),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(2,plain,(~(sP13) | sP5),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(3,plain,((~(sP23) | sP10) | sP13),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(4,plain,(~(sP22) | sP23),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(5,plain,(~(sP2) | sP22),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(6,plain,(~(sP19) | sP8),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(7,plain,((~(sP8) | ~(sP17)) | sP11),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(8,plain,(~(sP11) | sP25),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(9,plain,((~(sP25) | ~(sP18)) | sP3),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(10,plain,((~(sP16) | sP15) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(11,plain,sP2,inference(eq_ind_sym,[status(thm)],[])).
% 1.97/2.18 thf(12,plain,(~(sP14) | sP6),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(13,plain,((~(sP6) | ~(sP17)) | sP4),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(14,plain,(~(sP4) | sP7),inference(all_rule,[status(thm)],[])).
% 1.97/2.18 thf(15,plain,((~(sP7) | ~(sP18)) | sP16),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(16,plain,(sP24 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(17,plain,(sP24 | ~(sP15)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(18,plain,(sP20 | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(19,plain,(sP20 | sP18),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(20,plain,(sP9 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 1.97/2.18 thf(21,plain,(sP1 | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(22,plain,(sP1 | sP17),inference(prop_rule,[status(thm)],[])).
% 1.97/2.18 thf(23,plain,(sP21 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.97/2.18 thf(l36_zfmisc_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set)) @ ((in @ X1) @ X2)))))))).
% 1.97/2.18 thf(24,plain,sP14,inference(preprocess,[status(thm)],[l36_zfmisc_1]).
% 1.97/2.18 thf(l34_zfmisc_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1))) @ (mnot @ ((in @ X1) @ X2))))))))).
% 1.97/2.18 thf(25,plain,sP19,inference(preprocess,[status(thm)],[l34_zfmisc_1]).
% 1.97/2.18 thf(26,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h1])).
% 1.97/2.18 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0])).
% 1.97/2.18 thf(0,theorem,sP21,inference(contra,[status(thm),contra(discharge,[h1])],[26,h1])).
% 1.97/2.18 % SZS output end Proof
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