0.00/0.04 % 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 0.03/0.23 % Computer : n135.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sun Jul 15 13:08:55 CDT 2018 0.03/0.23 % CPUTime : 0.03/0.25 % SZS status Theorem 0.03/0.25 % Mode: mode213 0.03/0.25 % Inferences: 7 0.03/0.25 % SZS output start Proof 0.03/0.25 thf(ty_$i, type, $i : $tType). 0.03/0.25 thf(ty_eigen__2, type, eigen__2 : $i). 0.03/0.25 thf(ty_eps, type, eps : (($i>$o)>$i)). 0.03/0.25 thf(ty_eigen__1, type, eigen__1 : $i). 0.03/0.25 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$i>$o)). 0.03/0.25 thf(ty_eigen__3, type, eigen__3 : $i). 0.03/0.25 thf(sP1,plain,(sP1 <=> (((eigen__0 @ eigen__1) @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])]))). 0.03/0.25 thf(sP2,plain,(sP2 <=> (![X1:$i]:(~((((eigen__0 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((eigen__0 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((eigen__0 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((eigen__0 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])]))). 0.03/0.25 thf(sP3,plain,(sP3 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP3])]))). 0.03/0.25 thf(sP4,plain,(sP4 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ eigen__1) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP4])]))). 0.03/0.25 thf(sP5,plain,(sP5 <=> (((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))) @ (eps @ ((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP5])]))). 0.03/0.25 thf(sP6,plain,(sP6 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP6])]))). 0.03/0.25 thf(sP7,plain,(sP7 <=> (![X1:$i]:(~((((eigen__0 @ eigen__1) @ eigen__2) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])]))). 0.03/0.25 thf(def_epsa,definition,(epsa = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))))). 0.03/0.25 thf(def_epsb,definition,(epsb = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (epsa @ X1)) @ X2) @ X3))))))))))). 0.03/0.25 thf(def_epsc,definition,(epsc = (^[X1:$i>$i>$i>$o]:(eps @ ((X1 @ (epsa @ X1)) @ (epsb @ X1)))))). 0.03/0.25 thf(conj,conjecture,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (epsa @ X1)) @ (epsb @ X1)) @ (epsc @ X1))))). 0.03/0.25 thf(h0,negated_conjecture,(~((![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[conj])). 0.03/0.25 thf(h1,assumption,(~(((~(sP6)) => sP5))),introduced(assumption,[])). 0.03/0.25 thf(h2,assumption,(~(sP6)),introduced(assumption,[])). 0.03/0.25 thf(h3,assumption,(~(sP5)),introduced(assumption,[])). 0.03/0.25 thf(h4,assumption,(~(sP4)),introduced(assumption,[])). 0.03/0.25 thf(h5,assumption,(~(sP7)),introduced(assumption,[])). 0.03/0.25 thf(h6,assumption,sP1,introduced(assumption,[])). 0.03/0.25 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). 0.03/0.25 thf(1,plain,(~(sP3) | sP6),inference(choice_rule,[status(thm)],[choiceax])). 0.03/0.25 thf(2,plain,(~(sP2) | sP3),inference(choice_rule,[status(thm)],[choiceax])). 0.03/0.25 thf(3,plain,(sP5 | sP2),inference(choice_rule,[status(thm)],[choiceax])). 0.03/0.25 thf(4,plain,(~(sP7) | ~(sP1)),inference(all_rule,[status(thm)],[])). 0.03/0.25 thf(5,plain,(~(sP4) | sP7),inference(all_rule,[status(thm)],[])). 0.03/0.25 thf(6,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])). 0.03/0.25 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0])],[h3,h6,1,2,3,4,5,6])). 0.03/0.25 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,7,h6])). 0.03/0.25 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,8,h5])). 0.03/0.25 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,9,h4])). 0.03/0.25 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,10,h2,h3])). 0.03/0.25 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1])). 0.03/0.25 thf(0,theorem,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (epsa @ X1)) @ (epsb @ X1)) @ (epsc @ X1)))),inference(contra,[status(thm),contra(discharge,[h0])],[12,h0])). 0.03/0.25 % SZS output end Proof 0.03/0.25 EOF