TSTP Solution File: PUZ150^18 by Satallax---3.5
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- Process Solution
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% File : Satallax---3.5
% Problem : PUZ150^18 : 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 : n018.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 18:26:07 EDT 2022
% Result : Theorem 2.07s 2.27s
% Output : Proof 2.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ150^18 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 20:42:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.07/2.27 % SZS status Theorem
% 2.07/2.27 % Mode: mode506
% 2.07/2.27 % Inferences: 39823
% 2.07/2.27 % SZS output start Proof
% 2.07/2.27 thf(ty_mindex, type, mindex : $tType).
% 2.07/2.27 thf(ty_mworld, type, mworld : $tType).
% 2.07/2.27 thf(ty_a0, type, a0 : (mworld>$o)).
% 2.07/2.27 thf(ty_eigen__2, type, eigen__2 : mworld).
% 2.07/2.27 thf(ty_eigen__1, type, eigen__1 : mworld).
% 2.07/2.27 thf(ty_eigen__0, type, eigen__0 : mworld).
% 2.07/2.27 thf(ty_mrel, type, mrel : (mindex>mworld>mworld>$o)).
% 2.07/2.27 thf(ty_'#b', type, '#b' : mindex).
% 2.07/2.27 thf(ty_mactual, type, mactual : mworld).
% 2.07/2.27 thf(ty_'#a', type, '#a' : mindex).
% 2.07/2.27 thf(ty_'#c', type, '#c' : mindex).
% 2.07/2.27 thf(h0, assumption, (![X1:mworld>$o]:(![X2:mworld]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 2.07/2.27 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:mworld]:(~(((((mrel @ '#a') @ eigen__0) @ X1) => (![X2:mworld]:((((mrel @ '#b') @ X1) @ X2) => (~((![X3:mworld]:((((mrel @ '#c') @ X2) @ X3) => (~((a0 @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 2.07/2.27 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:mworld]:(~(((((mrel @ '#b') @ mactual) @ X1) => (![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 2.07/2.27 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:mworld]:(~(((((mrel @ '#b') @ eigen__1) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (~((a0 @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 2.07/2.27 thf(sP1,plain,sP1 <=> (![X1:mworld]:((((mrel @ '#c') @ eigen__2) @ X1) => (~((a0 @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 2.07/2.27 thf(sP2,plain,sP2 <=> (![X1:mworld]:((!!) @ ((mrel @ '#c') @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 2.07/2.27 thf(sP3,plain,sP3 <=> ((!!) @ ((mrel @ '#c') @ eigen__2)),introduced(definition,[new_symbols(definition,[sP3])])).
% 2.07/2.27 thf(sP4,plain,sP4 <=> (![X1:mworld]:((((mrel @ '#b') @ eigen__1) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (~((a0 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 2.07/2.27 thf(sP5,plain,sP5 <=> ((((mrel @ '#c') @ eigen__2) @ mactual) => (~((a0 @ mactual)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 2.07/2.27 thf(sP6,plain,sP6 <=> (a0 @ mactual),introduced(definition,[new_symbols(definition,[sP6])])).
% 2.07/2.27 thf(sP7,plain,sP7 <=> (![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 2.07/2.27 thf(sP8,plain,sP8 <=> ((((mrel @ '#b') @ mactual) @ eigen__0) => (![X1:mworld]:((((mrel @ '#a') @ eigen__0) @ X1) => (![X2:mworld]:((((mrel @ '#b') @ X1) @ X2) => (~((![X3:mworld]:((((mrel @ '#c') @ X2) @ X3) => (~((a0 @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 2.07/2.27 thf(sP9,plain,sP9 <=> (((mrel @ '#c') @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP9])])).
% 2.07/2.27 thf(sP10,plain,sP10 <=> ((((mrel @ '#a') @ eigen__0) @ eigen__1) => sP4),introduced(definition,[new_symbols(definition,[sP10])])).
% 2.07/2.27 thf(sP11,plain,sP11 <=> (![X1:mworld]:((((mrel @ '#a') @ eigen__0) @ X1) => (![X2:mworld]:((((mrel @ '#b') @ X1) @ X2) => (~((![X3:mworld]:((((mrel @ '#c') @ X2) @ X3) => (~((a0 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 2.07/2.27 thf(sP12,plain,sP12 <=> ((((mrel @ '#b') @ eigen__1) @ eigen__2) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 2.07/2.27 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 2.07/2.27 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))).
% 2.07/2.27 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 2.07/2.27 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 2.07/2.27 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 2.07/2.27 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))).
% 2.07/2.27 thf(def_mbox,definition,(mbox = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(![X4:mworld]:((((mrel @ X1) @ X3) @ X4) => (X2 @ X4)))))))).
% 2.07/2.27 thf(def_mdia,definition,(mdia = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(~((![X4:mworld]:((((mrel @ X1) @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 2.07/2.27 thf(con,conjecture,(![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (~((~((![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (~((~((![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4)))))))))))))))))))))).
% 2.07/2.27 thf(h1,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[con])).
% 2.07/2.27 thf(1,plain,(~(sP3) | sP9),inference(all_rule,[status(thm)],[])).
% 2.07/2.27 thf(2,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])).
% 2.07/2.27 thf(3,plain,(~(sP1) | sP5),inference(all_rule,[status(thm)],[])).
% 2.07/2.27 thf(4,plain,((~(sP5) | ~(sP9)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 2.07/2.27 thf(5,plain,(sP12 | sP1),inference(prop_rule,[status(thm)],[])).
% 2.07/2.27 thf(6,plain,(sP4 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 2.07/2.27 thf(7,plain,(sP10 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 2.07/2.27 thf(8,plain,(sP11 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 2.07/2.27 thf(9,plain,(sP8 | ~(sP11)),inference(prop_rule,[status(thm)],[])).
% 2.07/2.27 thf(10,plain,(sP7 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 2.07/2.27 thf(axiom_a0,axiom,(mlocal @ a0)).
% 2.07/2.27 thf(11,plain,sP6,inference(preprocess,[status(thm)],[axiom_a0]).
% 2.07/2.27 thf('mrel_#c_universal',axiom,sP2).
% 2.07/2.27 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,'mrel_#c_universal',h1])).
% 2.07/2.27 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])).
% 2.07/2.27 thf(0,theorem,(![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (~((~((![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (~((~((![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])).
% 2.07/2.27 % SZS output end Proof
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