0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : satallax -E eprover -P picomus -M modes -p tstp -t %d %s
0.02/0.24	% Computer   : n133.star.cs.uiowa.edu
0.02/0.24	% Model      : x86_64 x86_64
0.02/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.24	% Memory     : 32218.625MB
0.02/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.24	% CPULimit   : 300
0.02/0.24	% DateTime   : Sun Jul 15 13:40:25 CDT 2018
0.02/0.24	% CPUTime    : 
0.02/0.26	% SZS status Theorem
0.02/0.26	% Mode: mode213
0.02/0.26	% Inferences: 20
0.02/0.26	% SZS output start Proof
0.02/0.26	thf(ty_$i, type, $i : $tType).
0.02/0.26	thf(ty_eps, type, eps : (($i>$o)>$i)).
0.02/0.26	thf(ty_eigen__1, type, eigen__1 : $i).
0.02/0.26	thf(ty_eigen__0, type, eigen__0 : $o).
0.02/0.26	thf(sP1,plain,(sP1 <=> ((eigen__0 => (~((eigen__1 = eigen__1)))) => (~(((~(eigen__0)) => (~((eigen__1 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP1])]))).
0.02/0.26	thf(sP2,plain,(sP2 <=> eigen__0,introduced(definition,[new_symbols(definition,[sP2])]))).
0.02/0.26	thf(sP3,plain,(sP3 <=> ((sP2 => (~(((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__1))))))))) = eigen__1)))) => (~(((~(sP2)) => (~(((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__1))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP3])]))).
0.02/0.26	thf(sP4,plain,(sP4 <=> (sP2 => (~((eigen__1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP4])]))).
0.02/0.26	thf(sP5,plain,(sP5 <=> ((~(sP2)) => (~(((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__1))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP5])]))).
0.02/0.26	thf(sP6,plain,(sP6 <=> ((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__1))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP6])]))).
0.02/0.26	thf(sP7,plain,(sP7 <=> (![X1:$i]:(~(((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__1)))))))))),introduced(definition,[new_symbols(definition,[sP7])]))).
0.02/0.26	thf(sP8,plain,(sP8 <=> ((~(sP2)) => (~((eigen__1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP8])]))).
0.02/0.26	thf(sP9,plain,(sP9 <=> (sP2 => (~(sP6))),introduced(definition,[new_symbols(definition,[sP9])]))).
0.02/0.26	thf(sP10,plain,(sP10 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP10])]))).
0.02/0.26	thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3)))))))))))))).
0.02/0.26	thf(conj,conjecture,(![X1:$o]:(![X2:$i]:((((if @ X1) @ X2) @ X2) = X2)))).
0.02/0.26	thf(h0,negated_conjecture,(~((![X1:$o]:(![X2:$i]:((eps @ (^[X3:$i]:((X1 => (~((X3 = X2)))) => (~(((~(X1)) => (~((X3 = X2))))))))) = X2))))),inference(assume_negation,[status(cth)],[conj])).
0.02/0.26	thf(h1,assumption,(~((![X1:$i]:((eps @ (^[X2:$i]:((sP2 => (~((X2 = X1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = X1)))),introduced(assumption,[])).
0.02/0.26	thf(h2,assumption,(~(sP6)),introduced(assumption,[])).
0.02/0.26	thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
0.02/0.26	thf(1,plain,(sP3 | sP7),inference(choice_rule,[status(thm)],[choiceax])).
0.02/0.26	thf(2,plain,(~(sP7) | ~(sP1)),inference(all_rule,[status(thm)],[])).
0.02/0.26	thf(3,plain,(sP1 | sP4),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(4,plain,(sP1 | sP8),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(5,plain,((~(sP4) | ~(sP2)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(6,plain,((~(sP8) | sP2) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(7,plain,sP10,inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(8,plain,((~(sP3) | ~(sP9)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(9,plain,(sP9 | sP6),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(10,plain,(sP5 | sP6),inference(prop_rule,[status(thm)],[])).
0.02/0.26	thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[h2,1,2,3,4,5,6,7,8,9,10])).
0.02/0.26	thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2])).
0.02/0.26	thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1])).
0.02/0.26	% SZS output end Proof
0.02/0.26	EOF