TSTP Solution File: SET574^20 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET574^20 : 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 : n012.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 04:53:59 EDT 2022
% Result : Theorem 1.99s 2.24s
% Output : Proof 1.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET574^20 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n012.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 : Sun Jul 10 15:48:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.99/2.24 % SZS status Theorem
% 1.99/2.24 % Mode: mode506
% 1.99/2.24 % Inferences: 19442
% 1.99/2.24 % SZS output start Proof
% 1.99/2.24 thf(ty_mworld, type, mworld : $tType).
% 1.99/2.24 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)).
% 1.99/2.24 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.99/2.24 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.99/2.24 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.99/2.24 thf(ty_member, type, member : ($i>$i>mworld>$o)).
% 1.99/2.24 thf(ty_mactual, type, mactual : mworld).
% 1.99/2.24 thf(ty_intersect, type, intersect : ($i>$i>mworld>$o)).
% 1.99/2.24 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.99/2.24 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~(((((member @ eigen__0) @ X1) @ mactual) => (~((((member @ eigen__0) @ X2) @ mactual)))))) => (((intersect @ X1) @ X2) @ mactual))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 1.99/2.24 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => (![X3:$i]:(((eiw_di @ X3) @ mactual) => ((~(((((member @ X1) @ X2) @ mactual) => (~((((member @ X1) @ X3) @ mactual)))))) => (((intersect @ X2) @ X3) @ mactual))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.99/2.24 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ mactual) => ((~(((((member @ eigen__0) @ eigen__1) @ mactual) => (~((((member @ eigen__0) @ X1) @ mactual)))))) => (((intersect @ eigen__1) @ X1) @ mactual))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 1.99/2.24 thf(sP1,plain,sP1 <=> (((eiw_di @ eigen__1) @ mactual) => ((((intersect @ eigen__2) @ eigen__1) @ mactual) => (((intersect @ eigen__1) @ eigen__2) @ mactual))),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.99/2.24 thf(sP2,plain,sP2 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((member @ X1) @ eigen__2) @ mactual) => (~((((member @ X1) @ eigen__1) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.99/2.24 thf(sP3,plain,sP3 <=> (((eiw_di @ eigen__0) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~(((((member @ eigen__0) @ X1) @ mactual) => (~((((member @ eigen__0) @ X2) @ mactual)))))) => (((intersect @ X1) @ X2) @ mactual))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.99/2.24 thf(sP4,plain,sP4 <=> (((eiw_di @ eigen__1) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~(((((member @ eigen__0) @ eigen__1) @ mactual) => (~((((member @ eigen__0) @ X1) @ mactual)))))) => (((intersect @ eigen__1) @ X1) @ mactual))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.99/2.24 thf(sP5,plain,sP5 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((intersect @ eigen__2) @ X1) @ mactual) = (~((![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((member @ X2) @ eigen__2) @ mactual) => (~((((member @ X2) @ X1) @ mactual))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.99/2.24 thf(sP6,plain,sP6 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((intersect @ X1) @ X2) @ mactual) = (~((![X3:$i]:(((eiw_di @ X3) @ mactual) => ((((member @ X3) @ X1) @ mactual) => (~((((member @ X3) @ X2) @ mactual))))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.99/2.24 thf(sP7,plain,sP7 <=> (((eiw_di @ eigen__2) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((intersect @ eigen__2) @ X1) @ mactual) => (((intersect @ X1) @ eigen__2) @ mactual))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.99/2.24 thf(sP8,plain,sP8 <=> ((((member @ eigen__0) @ eigen__2) @ mactual) => (~((((member @ eigen__0) @ eigen__1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.99/2.24 thf(sP9,plain,sP9 <=> (((eiw_di @ eigen__2) @ mactual) => sP5),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.99/2.24 thf(sP10,plain,sP10 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((((intersect @ X1) @ X2) @ mactual) => (((intersect @ X2) @ X1) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 1.99/2.24 thf(sP11,plain,sP11 <=> (((intersect @ eigen__1) @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP11])])).
% 1.99/2.24 thf(sP12,plain,sP12 <=> ((((intersect @ eigen__2) @ eigen__1) @ mactual) => sP11),introduced(definition,[new_symbols(definition,[sP12])])).
% 1.99/2.24 thf(sP13,plain,sP13 <=> (((eiw_di @ eigen__2) @ mactual) => ((~(((((member @ eigen__0) @ eigen__1) @ mactual) => (~((((member @ eigen__0) @ eigen__2) @ mactual)))))) => sP11)),introduced(definition,[new_symbols(definition,[sP13])])).
% 1.99/2.24 thf(sP14,plain,sP14 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => ((~(((((member @ eigen__0) @ X1) @ mactual) => (~((((member @ eigen__0) @ X2) @ mactual)))))) => (((intersect @ X1) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP14])])).
% 1.99/2.24 thf(sP15,plain,sP15 <=> ((eiw_di @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP15])])).
% 1.99/2.24 thf(sP16,plain,sP16 <=> (((member @ eigen__0) @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP16])])).
% 1.99/2.24 thf(sP17,plain,sP17 <=> (sP15 => ((((intersect @ eigen__2) @ eigen__1) @ mactual) = (~(sP2)))),introduced(definition,[new_symbols(definition,[sP17])])).
% 1.99/2.24 thf(sP18,plain,sP18 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((((intersect @ eigen__2) @ X1) @ mactual) => (((intersect @ X1) @ eigen__2) @ mactual)))),introduced(definition,[new_symbols(definition,[sP18])])).
% 1.99/2.24 thf(sP19,plain,sP19 <=> ((((member @ eigen__0) @ eigen__1) @ mactual) => (~(sP16))),introduced(definition,[new_symbols(definition,[sP19])])).
% 1.99/2.24 thf(sP20,plain,sP20 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:$i]:(((eiw_di @ X2) @ mactual) => (![X3:$i]:(((eiw_di @ X3) @ mactual) => ((~(((((member @ X1) @ X2) @ mactual) => (~((((member @ X1) @ X3) @ mactual)))))) => (((intersect @ X2) @ X3) @ mactual)))))))),introduced(definition,[new_symbols(definition,[sP20])])).
% 1.99/2.24 thf(sP21,plain,sP21 <=> (((eiw_di @ eigen__0) @ mactual) => sP8),introduced(definition,[new_symbols(definition,[sP21])])).
% 1.99/2.24 thf(sP22,plain,sP22 <=> ((eiw_di @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP22])])).
% 1.99/2.24 thf(sP23,plain,sP23 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => ((~(((((member @ eigen__0) @ eigen__1) @ mactual) => (~((((member @ eigen__0) @ X1) @ mactual)))))) => (((intersect @ eigen__1) @ X1) @ mactual)))),introduced(definition,[new_symbols(definition,[sP23])])).
% 1.99/2.24 thf(sP24,plain,sP24 <=> (((member @ eigen__0) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP24])])).
% 1.99/2.24 thf(sP25,plain,sP25 <=> ((~(sP19)) => sP11),introduced(definition,[new_symbols(definition,[sP25])])).
% 1.99/2.24 thf(sP26,plain,sP26 <=> ((eiw_di @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP26])])).
% 1.99/2.24 thf(sP27,plain,sP27 <=> ((((intersect @ eigen__2) @ eigen__1) @ mactual) = (~(sP2))),introduced(definition,[new_symbols(definition,[sP27])])).
% 1.99/2.24 thf(sP28,plain,sP28 <=> (((intersect @ eigen__2) @ eigen__1) @ mactual),introduced(definition,[new_symbols(definition,[sP28])])).
% 1.99/2.24 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 1.99/2.24 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 1.99/2.24 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.99/2.24 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.99/2.24 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 1.99/2.24 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 1.99/2.24 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 1.99/2.24 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))).
% 1.99/2.24 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 1.99/2.24 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))).
% 1.99/2.24 thf(prove_th13,conjecture,sP20).
% 1.99/2.24 thf(h1,negated_conjecture,(~(sP20)),inference(assume_negation,[status(cth)],[prove_th13])).
% 1.99/2.24 thf(1,plain,(~(sP2) | sP21),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(2,plain,((~(sP21) | ~(sP22)) | sP8),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(3,plain,((~(sP8) | ~(sP16)) | ~(sP24)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(4,plain,(sP19 | sP16),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(5,plain,(sP19 | sP24),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(6,plain,((~(sP27) | sP28) | sP2),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(7,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(8,plain,((~(sP9) | ~(sP26)) | sP5),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(9,plain,(~(sP5) | sP17),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(10,plain,((~(sP17) | ~(sP15)) | sP27),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(11,plain,(~(sP10) | sP7),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(12,plain,((~(sP7) | ~(sP26)) | sP18),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(13,plain,(~(sP18) | sP1),inference(all_rule,[status(thm)],[])).
% 1.99/2.24 thf(14,plain,((~(sP1) | ~(sP15)) | sP12),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(15,plain,((~(sP12) | ~(sP28)) | sP11),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(16,plain,(sP25 | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(17,plain,(sP25 | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(18,plain,(sP13 | ~(sP25)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(19,plain,(sP13 | sP26),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(20,plain,(sP23 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 1.99/2.24 thf(21,plain,(sP4 | ~(sP23)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(22,plain,(sP4 | sP15),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(23,plain,(sP14 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 1.99/2.24 thf(24,plain,(sP3 | ~(sP14)),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(25,plain,(sP3 | sP22),inference(prop_rule,[status(thm)],[])).
% 1.99/2.24 thf(26,plain,(sP20 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.99/2.24 thf(symmetry_of_intersect,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mimplies @ ((intersect @ X1) @ X2)) @ ((intersect @ X2) @ X1)))))))).
% 1.99/2.24 thf(27,plain,sP10,inference(preprocess,[status(thm)],[symmetry_of_intersect]).
% 1.99/2.24 thf(intersect_defn,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((intersect @ X1) @ X2)) @ (mexists_di @ (^[X3:$i]:((mand @ ((member @ X3) @ X1)) @ ((member @ X3) @ X2))))))))))).
% 1.99/2.24 thf(28,plain,sP6,inference(preprocess,[status(thm)],[intersect_defn]).
% 1.99/2.24 thf(29,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h1])).
% 1.99/2.24 thf(30,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0])).
% 1.99/2.24 thf(0,theorem,sP20,inference(contra,[status(thm),contra(discharge,[h1])],[29,h1])).
% 1.99/2.24 % SZS output end Proof
%------------------------------------------------------------------------------