TSTP Solution File: PLA053^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PLA053^5 : 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 : n032.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 : Mon Jul 18 17:31:54 EDT 2022
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : PLA053^5 : TPTP v8.1.0. Released v8.1.0.
% 0.02/0.08 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Tue May 31 22:38:59 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % Mode: mode213
% 0.11/0.38 % Inferences: 2036
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 thf(ty_mworld, type, mworld : $tType).
% 0.11/0.38 thf(ty_h, type, h : ($i>mworld>$o)).
% 0.11/0.38 thf(ty_eigen__14, type, eigen__14 : $i).
% 0.11/0.38 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.11/0.38 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.11/0.38 thf(ty_eigen__0, type, eigen__0 : mworld).
% 0.11/0.38 thf(ty_mrel, type, mrel : (mworld>mworld>$o)).
% 0.11/0.38 thf(ty_mactual, type, mactual : mworld).
% 0.11/0.38 thf(ty_bomb, type, bomb : ($i>mworld>$o)).
% 0.11/0.38 thf(ty_defused, type, defused : ($i>mworld>$o)).
% 0.11/0.38 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.11/0.38 thf(eigendef_eigen__14, definition, eigen__14 = (eps__0 @ (^[X1:$i]:(~((~((![X2:mworld]:(((mrel @ mactual) @ X2) => ((~((((bomb @ eigen__1) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__1) @ X2)))))))))), introduced(definition,[new_symbols(definition,[eigen__14])])).
% 0.11/0.38 thf(sP1,plain,sP1 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.11/0.38 thf(sP2,plain,sP2 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.11/0.38 thf(sP3,plain,sP3 <=> ((~((((bomb @ eigen__1) @ eigen__0) => (~(((h @ eigen__14) @ eigen__0)))))) => ((defused @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.11/0.38 thf(sP4,plain,sP4 <=> (sP1 => sP3),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.11/0.38 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((![X2:mworld]:(((mrel @ mactual) @ X2) => ((~((((bomb @ eigen__1) @ X2) => (~(((h @ X1) @ X2)))))) => ((defused @ eigen__1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.11/0.38 thf(sP6,plain,sP6 <=> (![X1:$i]:(~((![X2:$i]:(~((![X3:mworld]:(((mrel @ mactual) @ X3) => ((~((((bomb @ X1) @ X3) => (~(((h @ X2) @ X3)))))) => ((defused @ X1) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.11/0.38 thf(sP7,plain,sP7 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => ((~((((bomb @ eigen__1) @ X1) => (~(((h @ eigen__14) @ X1)))))) => ((defused @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.11/0.38 thf(sP8,plain,sP8 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(~((![X3:$i]:(~((![X4:mworld]:(((mrel @ X1) @ X4) => ((~((((bomb @ X2) @ X4) => (~(((h @ X3) @ X4)))))) => ((defused @ X2) @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.11/0.38 thf(sP9,plain,sP9 <=> (![X1:$i]:(~(((~((((bomb @ eigen__1) @ eigen__0) => (~(((h @ X1) @ eigen__0)))))) => ((defused @ eigen__1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.11/0.38 thf(sP10,plain,sP10 <=> ((mrel @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.11/0.38 thf(sP11,plain,sP11 <=> (sP10 => sP6),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.11/0.38 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 0.11/0.38 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 0.11/0.38 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 0.11/0.38 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.11/0.38 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 0.11/0.38 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 0.11/0.38 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 0.11/0.38 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))).
% 0.11/0.38 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))).
% 0.11/0.38 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))).
% 0.11/0.38 thf(con,conjecture,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(~((![X3:$i]:(~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1))))))))))).
% 0.11/0.38 thf(h1,negated_conjecture,(~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(~((![X3:$i]:(~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1)))))))))))),inference(assume_negation,[status(cth)],[con])).
% 0.11/0.38 thf(h2,assumption,(~((sP1 => (![X1:$i]:(~((![X2:$i]:(~(((~((((bomb @ X1) @ eigen__0) => (~(((h @ X2) @ eigen__0)))))) => ((defused @ X1) @ eigen__0))))))))))),introduced(assumption,[])).
% 0.11/0.38 thf(h3,assumption,sP1,introduced(assumption,[])).
% 0.11/0.38 thf(h4,assumption,(~((![X1:$i]:(~((![X2:$i]:(~(((~((((bomb @ X1) @ eigen__0) => (~(((h @ X2) @ eigen__0)))))) => ((defused @ X1) @ eigen__0)))))))))),introduced(assumption,[])).
% 0.11/0.38 thf(h5,assumption,sP9,introduced(assumption,[])).
% 0.11/0.38 thf(h6,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:((~((((bomb @ X2) @ X1) => (~(((h @ eigen__2) @ X1)))))) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((bomb @ X2) @ X3))))))),introduced(assumption,[])).
% 0.11/0.38 thf(1,plain,(~(sP9) | ~(sP3)),inference(all_rule,[status(thm)],[])).
% 0.11/0.38 thf(2,plain,(~(sP7) | sP4),inference(all_rule,[status(thm)],[])).
% 0.11/0.38 thf(3,plain,((~(sP4) | ~(sP1)) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.11/0.38 thf(4,plain,(sP5 | sP7),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14])).
% 0.11/0.38 thf(5,plain,(~(sP6) | ~(sP5)),inference(all_rule,[status(thm)],[])).
% 0.11/0.38 thf(6,plain,((~(sP11) | ~(sP10)) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.11/0.38 thf(7,plain,(~(sP8) | sP11),inference(all_rule,[status(thm)],[])).
% 0.11/0.38 thf(8,plain,(~(sP2) | sP10),inference(all_rule,[status(thm)],[])).
% 0.11/0.38 thf(mrel_reflexive,axiom,sP2).
% 0.11/0.38 thf(ax3,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mexists_di @ (^[X2:$i]:(mbox @ ((mimplies @ ((mand @ (bomb @ X1)) @ (h @ X2))) @ (defused @ X1)))))))))).
% 0.11/0.38 thf(9,plain,sP8,inference(preprocess,[status(thm)],[ax3]).
% 0.11/0.38 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,mrel_reflexive,9,h3,h5])).
% 0.11/0.38 thf(ax2,axiom,(mlocal @ (mexists_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:((mimplies @ ((mand @ (bomb @ X2)) @ (h @ X1))) @ (mbox @ (bomb @ X2)))))))))).
% 0.11/0.38 thf(11,plain,(~((![X1:$i]:(~((![X2:mworld]:(((mrel @ mactual) @ X2) => (![X3:$i]:((~((((bomb @ X3) @ X2) => (~(((h @ X1) @ X2)))))) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((bomb @ X3) @ X4)))))))))))),inference(preprocess,[status(thm)],[ax2]).
% 0.11/0.38 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[11,10,h6])).
% 0.11/0.38 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,12,h5])).
% 0.11/0.38 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,13,h3,h4])).
% 0.11/0.38 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,14,h2])).
% 0.11/0.38 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0])).
% 0.11/0.38 thf(0,theorem,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(~((![X3:$i]:(~(((~((((bomb @ X2) @ X1) => (~(((h @ X3) @ X1)))))) => ((defused @ X2) @ X1)))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[15,h1])).
% 0.11/0.38 % SZS output end Proof
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