TSTP Solution File: SET063^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET063^4 : 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 : n016.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 04:50:33 EDT 2022
% Result : Theorem 2.22s 2.54s
% Output : Proof 2.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET063^4 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.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 : Mon Jul 11 05:14:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.22/2.54 % SZS status Theorem
% 2.22/2.54 % Mode: mode506
% 2.22/2.54 % Inferences: 11053
% 2.22/2.54 % SZS output start Proof
% 2.22/2.54 thf(ty_mworld, type, mworld : $tType).
% 2.22/2.54 thf(ty_subset, type, subset : ($i>$i>mworld>$o)).
% 2.22/2.54 thf(ty_eigen__1, type, eigen__1 : $i).
% 2.22/2.54 thf(ty_eigen__0, type, eigen__0 : $i).
% 2.22/2.54 thf(ty_member, type, member : ($i>$i>mworld>$o)).
% 2.22/2.54 thf(ty_eigen__3, type, eigen__3 : $i).
% 2.22/2.54 thf(ty_equal_set, type, equal_set : ($i>$i>mworld>$o)).
% 2.22/2.54 thf(ty_mactual, type, mactual : mworld).
% 2.22/2.54 thf(ty_empty_set, type, empty_set : $i).
% 2.22/2.54 thf(ty_intersection, type, intersection : ($i>$i>$i)).
% 2.22/2.54 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 2.22/2.54 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~(((((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => (((member @ X1) @ empty_set) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 2.22/2.54 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((((member @ X1) @ empty_set) @ mactual) => (((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual)))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 2.22/2.54 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((equal_set @ ((intersection @ X1) @ empty_set)) @ empty_set) @ mactual))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 2.22/2.54 thf(sP1,plain,sP1 <=> (![X1:$i]:((((equal_set @ ((intersection @ eigen__0) @ empty_set)) @ X1) @ mactual) = (~(((((subset @ ((intersection @ eigen__0) @ empty_set)) @ X1) @ mactual) => (~((((subset @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual)))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 2.22/2.54 thf(sP2,plain,sP2 <=> (((((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual) = (![X1:$i]:((((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => (((member @ X1) @ empty_set) @ mactual)))) => ((![X1:$i]:((((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => (((member @ X1) @ empty_set) @ mactual))) = (((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual))),introduced(definition,[new_symbols(definition,[sP2])])).
% 2.22/2.54 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((((member @ X1) @ ((intersection @ X2) @ X3)) @ mactual) = (~(((((member @ X1) @ X2) @ mactual) => (~((((member @ X1) @ X3) @ mactual)))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 2.22/2.54 thf(sP4,plain,sP4 <=> (![X1:$i]:((((member @ X1) @ empty_set) @ mactual) => (((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual))),introduced(definition,[new_symbols(definition,[sP4])])).
% 2.22/2.54 thf(sP5,plain,sP5 <=> ((((subset @ empty_set) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) = sP4),introduced(definition,[new_symbols(definition,[sP5])])).
% 2.22/2.54 thf(sP6,plain,sP6 <=> (![X1:$o]:(((((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual) = X1) => (X1 = (((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 2.22/2.54 thf(sP7,plain,sP7 <=> (![X1:$i]:(![X2:$i]:((((member @ eigen__3) @ ((intersection @ X1) @ X2)) @ mactual) = (~(((((member @ eigen__3) @ X1) @ mactual) => (~((((member @ eigen__3) @ X2) @ mactual))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 2.22/2.54 thf(sP8,plain,sP8 <=> ((((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual) => (~((((subset @ empty_set) @ ((intersection @ eigen__0) @ empty_set)) @ mactual)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 2.22/2.54 thf(sP9,plain,sP9 <=> ((((equal_set @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual) = (~(sP8))),introduced(definition,[new_symbols(definition,[sP9])])).
% 2.22/2.54 thf(sP10,plain,sP10 <=> (![X1:$i]:((((subset @ empty_set) @ X1) @ mactual) = (![X2:$i]:((((member @ X2) @ empty_set) @ mactual) => (((member @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 2.22/2.54 thf(sP11,plain,sP11 <=> ((((member @ eigen__3) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) = (~(((((member @ eigen__3) @ eigen__0) @ mactual) => (~((((member @ eigen__3) @ empty_set) @ mactual))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 2.22/2.54 thf(sP12,plain,sP12 <=> (![X1:$i]:((((member @ X1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => (((member @ X1) @ empty_set) @ mactual))),introduced(definition,[new_symbols(definition,[sP12])])).
% 2.22/2.54 thf(sP13,plain,sP13 <=> ((((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual) = sP12),introduced(definition,[new_symbols(definition,[sP13])])).
% 2.22/2.54 thf(sP14,plain,sP14 <=> (sP12 = (((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual)),introduced(definition,[new_symbols(definition,[sP14])])).
% 2.22/2.54 thf(sP15,plain,sP15 <=> (![X1:$i]:((((member @ eigen__3) @ ((intersection @ eigen__0) @ X1)) @ mactual) = (~(((((member @ eigen__3) @ eigen__0) @ mactual) => (~((((member @ eigen__3) @ X1) @ mactual)))))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 2.22/2.54 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i]:((((equal_set @ X1) @ X2) @ mactual) = (~(((((subset @ X1) @ X2) @ mactual) => (~((((subset @ X2) @ X1) @ mactual))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 2.22/2.54 thf(sP17,plain,sP17 <=> (((subset @ empty_set) @ ((intersection @ eigen__0) @ empty_set)) @ mactual),introduced(definition,[new_symbols(definition,[sP17])])).
% 2.22/2.54 thf(sP18,plain,sP18 <=> ((((member @ eigen__1) @ empty_set) @ mactual) => (((member @ eigen__1) @ ((intersection @ eigen__0) @ empty_set)) @ mactual)),introduced(definition,[new_symbols(definition,[sP18])])).
% 2.22/2.54 thf(sP19,plain,sP19 <=> (((equal_set @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP19])])).
% 2.22/2.54 thf(sP20,plain,sP20 <=> (((member @ eigen__3) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP20])])).
% 2.22/2.54 thf(sP21,plain,sP21 <=> (![X1:$i]:(((equal_set @ ((intersection @ X1) @ empty_set)) @ empty_set) @ mactual)),introduced(definition,[new_symbols(definition,[sP21])])).
% 2.22/2.54 thf(sP22,plain,sP22 <=> (((member @ eigen__1) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP22])])).
% 2.22/2.54 thf(sP23,plain,sP23 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 2.22/2.54 thf(sP24,plain,sP24 <=> (![X1:$i]:((((subset @ ((intersection @ eigen__0) @ empty_set)) @ X1) @ mactual) = (![X2:$i]:((((member @ X2) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => (((member @ X2) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 2.22/2.54 thf(sP25,plain,sP25 <=> ((((member @ eigen__3) @ ((intersection @ eigen__0) @ empty_set)) @ mactual) => sP20),introduced(definition,[new_symbols(definition,[sP25])])).
% 2.22/2.54 thf(sP26,plain,sP26 <=> (![X1:$i]:(~((((member @ X1) @ empty_set) @ mactual)))),introduced(definition,[new_symbols(definition,[sP26])])).
% 2.22/2.54 thf(sP27,plain,sP27 <=> (((member @ eigen__3) @ ((intersection @ eigen__0) @ empty_set)) @ mactual),introduced(definition,[new_symbols(definition,[sP27])])).
% 2.22/2.54 thf(sP28,plain,sP28 <=> (![X1:$i]:(![X2:$i]:((((subset @ X1) @ X2) @ mactual) = (![X3:$i]:((((member @ X3) @ X1) @ mactual) => (((member @ X3) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP28])])).
% 2.22/2.54 thf(sP29,plain,sP29 <=> (((subset @ ((intersection @ eigen__0) @ empty_set)) @ empty_set) @ mactual),introduced(definition,[new_symbols(definition,[sP29])])).
% 2.22/2.54 thf(sP30,plain,sP30 <=> ((((member @ eigen__3) @ eigen__0) @ mactual) => (~(sP20))),introduced(definition,[new_symbols(definition,[sP30])])).
% 2.22/2.54 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 2.22/2.54 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 2.22/2.54 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 2.22/2.54 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 2.22/2.54 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 2.22/2.54 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 2.22/2.54 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 2.22/2.54 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))).
% 2.22/2.54 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))).
% 2.22/2.54 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))).
% 2.22/2.54 thf(thI17,conjecture,sP21).
% 2.22/2.54 thf(h1,negated_conjecture,(~(sP21)),inference(assume_negation,[status(cth)],[thI17])).
% 2.22/2.54 thf(1,plain,(sP30 | sP20),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(2,plain,((~(sP11) | ~(sP27)) | ~(sP30)),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(3,plain,(~(sP26) | ~(sP20)),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(4,plain,(sP25 | sP27),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(5,plain,(~(sP3) | sP7),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(6,plain,(~(sP7) | sP15),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(7,plain,(~(sP15) | sP11),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(8,plain,(sP12 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 2.22/2.54 thf(9,plain,(~(sP26) | ~(sP22)),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(10,plain,(sP18 | sP22),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(11,plain,((~(sP14) | ~(sP12)) | sP29),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(12,plain,(sP4 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 2.22/2.54 thf(13,plain,((~(sP5) | sP17) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(14,plain,((~(sP2) | ~(sP13)) | sP14),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(15,plain,(~(sP6) | sP2),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(16,plain,(~(sP28) | sP10),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(17,plain,(~(sP10) | sP5),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(18,plain,(~(sP28) | sP24),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(19,plain,(~(sP24) | sP13),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(20,plain,(~(sP23) | sP6),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(21,plain,((~(sP8) | ~(sP29)) | ~(sP17)),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(22,plain,((~(sP9) | sP19) | sP8),inference(prop_rule,[status(thm)],[])).
% 2.22/2.54 thf(23,plain,sP23,inference(eq_sym,[status(thm)],[])).
% 2.22/2.54 thf(24,plain,(~(sP16) | sP1),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(25,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])).
% 2.22/2.54 thf(26,plain,(sP21 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 2.22/2.54 thf(empty_set_0,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mnot @ ((member @ X1) @ empty_set)))))).
% 2.22/2.54 thf(27,plain,sP26,inference(preprocess,[status(thm)],[empty_set_0]).
% 2.22/2.54 thf(intersection_0,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:(mforall_di @ (^[X3:$i]:((mequiv @ ((member @ X1) @ ((intersection @ X2) @ X3))) @ ((mand @ ((member @ X1) @ X2)) @ ((member @ X1) @ X3))))))))))).
% 2.22/2.54 thf(28,plain,sP3,inference(preprocess,[status(thm)],[intersection_0]).
% 2.22/2.54 thf(equal_set_0,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((equal_set @ X1) @ X2)) @ ((mand @ ((subset @ X1) @ X2)) @ ((subset @ X2) @ X1))))))))).
% 2.22/2.54 thf(29,plain,sP16,inference(preprocess,[status(thm)],[equal_set_0]).
% 2.22/2.54 thf(subset_0,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((subset @ X1) @ X2)) @ (mforall_di @ (^[X3:$i]:((mimplies @ ((member @ X3) @ X1)) @ ((member @ X3) @ X2))))))))))).
% 2.22/2.54 thf(30,plain,sP28,inference(preprocess,[status(thm)],[subset_0]).
% 2.22/2.54 thf(31,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,h1])).
% 2.22/2.54 thf(32,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[31,h0])).
% 2.22/2.54 thf(0,theorem,sP21,inference(contra,[status(thm),contra(discharge,[h1])],[31,h1])).
% 2.22/2.54 % SZS output end Proof
%------------------------------------------------------------------------------