0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : satallax -s schedule_3_1 -E eprover -P picomus -M modes -p tstp -t %d %s
0.02/0.22	% Computer   : n131.star.cs.uiowa.edu
0.02/0.22	% Model      : x86_64 x86_64
0.02/0.22	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.22	% Memory     : 32218.625MB
0.02/0.22	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.22	% CPULimit   : 300
0.02/0.22	% DateTime   : Sun Jul 15 13:33:55 CDT 2018
0.02/0.22	% CPUTime    : 
4.89/5.09	% SZS status Theorem
4.89/5.09	% Mode: mode495
4.89/5.09	% Inferences: 8
4.89/5.09	% SZS output start Proof
4.89/5.09	thf(ty_$i, type, $i : $tType).
4.89/5.09	thf(ty_eigen__1, type, eigen__1 : $i).
4.89/5.09	thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
4.89/5.09	thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
4.89/5.09	thf(eigendef_eigen__1, definition, (eigen__1 = (eps__0 @ (^[X1:$i]:(~(((![X2:$i]:((X1 = X2) => (eigen__0 @ X2))) => (eigen__0 @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__1]))).
4.89/5.09	thf(h1, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
4.89/5.09	thf(eigendef_eigen__0, definition, (eigen__0 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i]:((![X3:$i]:((X2 = X3) => (X1 @ X3))) => (X1 @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__0]))).
4.89/5.09	thf(sP1,plain,(sP1 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP1])]))).
4.89/5.09	thf(sP2,plain,(sP2 <=> ((![X1:$i]:((eigen__1 = X1) => (eigen__0 @ X1))) => (eigen__0 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])]))).
4.89/5.09	thf(sP3,plain,(sP3 <=> (eigen__0 @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])]))).
4.89/5.09	thf(sP4,plain,(sP4 <=> (sP1 => sP3),introduced(definition,[new_symbols(definition,[sP4])]))).
4.89/5.09	thf(sP5,plain,(sP5 <=> (![X1:$i]:((![X2:$i]:((X1 = X2) => (eigen__0 @ X2))) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP5])]))).
4.89/5.09	thf(sP6,plain,(sP6 <=> (![X1:$i>$i>$o]:(~((![X2:$i>$o]:(![X3:$i]:((![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4))) => (X2 @ X3))))))),introduced(definition,[new_symbols(definition,[sP6])]))).
4.89/5.09	thf(sP7,plain,(sP7 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:((X2 = X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP7])]))).
4.89/5.09	thf(sP8,plain,(sP8 <=> (![X1:$i]:((eigen__1 = X1) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP8])]))).
4.89/5.09	thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
4.89/5.09	thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
4.89/5.09	thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
4.89/5.09	thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
4.89/5.09	thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
4.89/5.09	thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
4.89/5.09	thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
4.89/5.09	thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
4.89/5.09	thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
4.89/5.09	thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
4.89/5.09	thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
4.89/5.09	thf(def_mvalid,definition,(mvalid = (!!))).
4.89/5.09	thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
4.89/5.09	thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
4.89/5.09	thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
4.89/5.09	thf(thm,conjecture,(~((![X1:$i>$i>$o]:(~((![X2:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ X1) @ X2)) @ X2))))))))).
4.89/5.09	thf(h2,negated_conjecture,sP6,inference(assume_negation,[status(cth)],[thm])).
4.89/5.09	thf(1,plain,(~(sP6) | ~(sP7)),inference(all_rule,[status(thm)],[])).
4.89/5.09	thf(2,plain,(sP7 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])).
4.89/5.09	thf(3,plain,(sP5 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
4.89/5.09	thf(4,plain,(sP2 | sP8),inference(prop_rule,[status(thm)],[])).
4.89/5.09	thf(5,plain,(sP2 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
4.89/5.09	thf(6,plain,((~(sP4) | ~(sP1)) | sP3),inference(prop_rule,[status(thm)],[])).
4.89/5.09	thf(7,plain,(~(sP8) | sP4),inference(all_rule,[status(thm)],[])).
4.89/5.09	thf(8,plain,sP1,inference(prop_rule,[status(thm)],[])).
4.89/5.09	thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[h2,1,2,3,4,5,6,7,8])).
4.89/5.09	thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[9,h1])).
4.89/5.09	thf(11,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[10,h0])).
4.89/5.09	thf(0,theorem,(~((![X1:$i>$i>$o]:(~((![X2:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ X1) @ X2)) @ X2)))))))),inference(contra,[status(thm),contra(discharge,[h2])],[9,h2])).
4.89/5.09	% SZS output end Proof
4.89/5.10	EOF