TSTP Solution File: SEU512^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU512^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Tue Jul 19 13:52:39 EDT 2022
% Result : Theorem 6.18s 6.38s
% Output : Proof 6.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU512^1 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 10:39:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 6.18/6.38 % SZS status Theorem
% 6.18/6.38 % Mode: mode506
% 6.18/6.38 % Inferences: 23817
% 6.18/6.38 % SZS output start Proof
% 6.18/6.38 thf(def_exu,definition,(exu = (^[X1:$i>$o]:(~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))).
% 6.18/6.38 thf(def_setextAx,definition,(setextAx = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))))).
% 6.18/6.38 thf(def_emptysetAx,definition,(emptysetAx = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 6.18/6.38 thf(def_setadjoinAx,definition,(setadjoinAx = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 6.18/6.38 thf(def_powersetAx,definition,(powersetAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 6.18/6.38 thf(def_setunionAx,definition,(setunionAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))))).
% 6.18/6.38 thf(def_omega0Ax,definition,(omega0Ax = ((in @ emptyset) @ omega))).
% 6.18/6.38 thf(def_omegaSAx,definition,(omegaSAx = (![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))))).
% 6.18/6.38 thf(def_omegaIndAx,definition,(omegaIndAx = (![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))))).
% 6.18/6.38 thf(def_replAx,definition,(replAx = (![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (exu @ (X1 @ X3)))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))))).
% 6.18/6.38 thf(def_foundationAx,definition,(foundationAx = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))))).
% 6.18/6.38 thf(def_wellorderingAx,definition,(wellorderingAx = (![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))))).
% 6.18/6.38 thf(def_descrp,definition,(descrp = (![X1:$i>$o]:((exu @ X1) => (X1 @ (descr @ X1)))))).
% 6.18/6.38 thf(def_dsetconstrI,definition,(dsetconstrI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))))).
% 6.18/6.38 thf(def_dsetconstrEL,definition,(dsetconstrEL = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 6.18/6.38 thf(def_dsetconstrER,definition,(dsetconstrER = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))))).
% 6.18/6.38 thf(def_exuE1,definition,(exuE1 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))))).
% 6.18/6.38 thf(def_prop2set,definition,(prop2set = (^[X1:$o]:((dsetconstr @ (powerset @ emptyset)) @ (^[X2:$i]:X1))))).
% 6.18/6.38 thf(def_prop2setE,definition,(prop2setE = (![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))))).
% 6.18/6.38 thf(def_emptysetE,definition,(emptysetE = (![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))))).
% 6.18/6.38 thf(def_emptysetimpfalse,definition,(emptysetimpfalse = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 6.18/6.38 thf(def_notinemptyset,definition,(notinemptyset = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 6.18/6.38 thf(def_exuE3e,definition,(exuE3e = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((X1 @ X2)))))))))).
% 6.18/6.38 thf(def_setext,definition,(setext = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))))).
% 6.18/6.38 thf(def_emptyI,definition,(emptyI = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 6.18/6.38 thf(def_noeltsimpempty,definition,(noeltsimpempty = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 6.18/6.38 thf(def_setbeta,definition,(setbeta = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))))).
% 6.18/6.38 thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(~((X1 = emptyset)))))).
% 6.18/6.38 thf(def_nonemptyE1,definition,(nonemptyE1 = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 6.18/6.38 thf(def_nonemptyI,definition,(nonemptyI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (nonempty @ ((dsetconstr @ X1) @ X2))))))))).
% 6.18/6.38 thf(def_nonemptyI1,definition,(nonemptyI1 = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (nonempty @ X1))))).
% 6.18/6.38 thf(setadjoinIL,conjecture,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))) => ((![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))) => ((![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (~((![X4:$i]:(((X1 @ X3) @ X4) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 = X5))))))))))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$o]:(![X2:$i]:(((in @ X2) @ ((dsetconstr @ (powerset @ emptyset)) @ (^[X3:$i]:X1))) => X1))) => ((![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2))))))))))))))))))))))))))))))))).
% 6.18/6.39 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))) => ((![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))) => ((![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (~((![X4:$i]:(((X1 @ X3) @ X4) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 = X5))))))))))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$o]:(![X2:$i]:(((in @ X2) @ ((dsetconstr @ (powerset @ emptyset)) @ (^[X3:$i]:X1))) => X1))) => ((![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[setadjoinIL])).
% 6.18/6.39 thf(ax7238, axiom, (p1|~(p3)), file('<stdin>', ax7238)).
% 6.18/6.39 thf(ax7240, axiom, ~(p1), file('<stdin>', ax7240)).
% 6.18/6.39 thf(ax7236, axiom, (p3|~(p5)), file('<stdin>', ax7236)).
% 6.18/6.39 thf(ax7234, axiom, (p5|~(p7)), file('<stdin>', ax7234)).
% 6.18/6.39 thf(ax7232, axiom, (p7|~(p9)), file('<stdin>', ax7232)).
% 6.18/6.39 thf(ax7230, axiom, (p9|~(p11)), file('<stdin>', ax7230)).
% 6.18/6.39 thf(ax7228, axiom, (p11|~(p13)), file('<stdin>', ax7228)).
% 6.18/6.39 thf(ax7226, axiom, (p13|~(p15)), file('<stdin>', ax7226)).
% 6.18/6.39 thf(ax7224, axiom, (p15|~(p17)), file('<stdin>', ax7224)).
% 6.18/6.39 thf(ax7222, axiom, (p17|~(p19)), file('<stdin>', ax7222)).
% 6.18/6.39 thf(ax7220, axiom, (p19|~(p21)), file('<stdin>', ax7220)).
% 6.18/6.39 thf(ax7218, axiom, (p21|~(p23)), file('<stdin>', ax7218)).
% 6.18/6.39 thf(ax7216, axiom, (p23|~(p25)), file('<stdin>', ax7216)).
% 6.18/6.39 thf(ax7214, axiom, (p25|~(p27)), file('<stdin>', ax7214)).
% 6.18/6.39 thf(ax7212, axiom, (p27|~(p29)), file('<stdin>', ax7212)).
% 6.18/6.39 thf(ax7210, axiom, (p29|~(p31)), file('<stdin>', ax7210)).
% 6.18/6.39 thf(ax7208, axiom, (p31|~(p33)), file('<stdin>', ax7208)).
% 6.18/6.39 thf(ax7206, axiom, (p33|~(p35)), file('<stdin>', ax7206)).
% 6.18/6.39 thf(ax7204, axiom, (p35|~(p37)), file('<stdin>', ax7204)).
% 6.18/6.39 thf(ax7202, axiom, (p37|~(p38)), file('<stdin>', ax7202)).
% 6.18/6.39 thf(ax7200, axiom, (p38|~(p39)), file('<stdin>', ax7200)).
% 6.18/6.39 thf(ax7198, axiom, (p39|~(p41)), file('<stdin>', ax7198)).
% 6.18/6.39 thf(ax7196, axiom, (p41|~(p43)), file('<stdin>', ax7196)).
% 6.18/6.39 thf(ax7194, axiom, (p43|~(p45)), file('<stdin>', ax7194)).
% 6.18/6.39 thf(ax4762, axiom, (~(p6)|p1943), file('<stdin>', ax4762)).
% 6.18/6.39 thf(ax7235, axiom, (p5|p6), file('<stdin>', ax7235)).
% 6.18/6.39 thf(ax7192, axiom, (p45|~(p46)), file('<stdin>', ax7192)).
% 6.18/6.39 thf(ax4749, axiom, (~(p1943)|p1956), file('<stdin>', ax4749)).
% 6.18/6.39 thf(ax7190, axiom, (p46|~(p48)), file('<stdin>', ax7190)).
% 6.18/6.39 thf(nax1950, axiom, (p1950<=(~((f__0)=(f__0))=>fin @ f__0 @ f__1)), file('<stdin>', nax1950)).
% 6.18/6.39 thf(ax4750, axiom, (~(p1956)|p1951), file('<stdin>', ax4750)).
% 6.18/6.39 thf(ax7188, axiom, (p48|~(p50)), file('<stdin>', ax7188)).
% 6.18/6.39 thf(ax4755, axiom, (~(p1941)|p1955), file('<stdin>', ax4755)).
% 6.18/6.39 thf(ax4751, axiom, (~(p1952)|~(p1951)|~(p1950)), file('<stdin>', ax4751)).
% 6.18/6.39 thf(ax7186, axiom, (p50|~(p52)), file('<stdin>', ax7186)).
% 6.18/6.39 thf(ax4754, axiom, (~(p1955)|p1954), file('<stdin>', ax4754)).
% 6.18/6.39 thf(ax4770, axiom, p1941, file('<stdin>', ax4770)).
% 6.18/6.39 thf(ax4753, axiom, (~(p1954)|p56|p1953), file('<stdin>', ax4753)).
% 6.18/6.39 thf(ax7182, axiom, (p55|~(p56)), file('<stdin>', ax7182)).
% 6.18/6.39 thf(ax7183, axiom, (p54|~(p55)), file('<stdin>', ax7183)).
% 6.18/6.39 thf(ax4752, axiom, (~(p1953)|p1952), file('<stdin>', ax4752)).
% 6.18/6.39 thf(ax7184, axiom, (p52|~(p54)), file('<stdin>', ax7184)).
% 6.18/6.39 thf(c_0_42, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax7238])).
% 6.18/6.39 thf(c_0_43, plain, ~p1, inference(fof_simplification,[status(thm)],[ax7240])).
% 6.18/6.39 thf(c_0_44, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax7236])).
% 6.18/6.39 thf(c_0_45, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_42])).
% 6.18/6.39 thf(c_0_46, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_43])).
% 6.18/6.39 thf(c_0_47, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax7234])).
% 6.18/6.39 thf(c_0_48, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_44])).
% 6.18/6.39 thf(c_0_49, plain, ~p3, inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 6.18/6.39 thf(c_0_50, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax7232])).
% 6.18/6.39 thf(c_0_51, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_47])).
% 6.18/6.39 thf(c_0_52, plain, ~p5, inference(sr,[status(thm)],[c_0_48, c_0_49])).
% 6.18/6.39 thf(c_0_53, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax7230])).
% 6.18/6.39 thf(c_0_54, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_50])).
% 6.18/6.39 thf(c_0_55, plain, ~p7, inference(sr,[status(thm)],[c_0_51, c_0_52])).
% 6.18/6.39 thf(c_0_56, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax7228])).
% 6.18/6.39 thf(c_0_57, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_53])).
% 6.18/6.39 thf(c_0_58, plain, ~p9, inference(sr,[status(thm)],[c_0_54, c_0_55])).
% 6.18/6.39 thf(c_0_59, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax7226])).
% 6.18/6.39 thf(c_0_60, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_56])).
% 6.18/6.39 thf(c_0_61, plain, ~p11, inference(sr,[status(thm)],[c_0_57, c_0_58])).
% 6.18/6.39 thf(c_0_62, plain, (p15|~p17), inference(fof_simplification,[status(thm)],[ax7224])).
% 6.18/6.39 thf(c_0_63, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_59])).
% 6.18/6.39 thf(c_0_64, plain, ~p13, inference(sr,[status(thm)],[c_0_60, c_0_61])).
% 6.18/6.39 thf(c_0_65, plain, (p17|~p19), inference(fof_simplification,[status(thm)],[ax7222])).
% 6.18/6.39 thf(c_0_66, plain, (p15|~p17), inference(split_conjunct,[status(thm)],[c_0_62])).
% 6.18/6.39 thf(c_0_67, plain, ~p15, inference(sr,[status(thm)],[c_0_63, c_0_64])).
% 6.18/6.39 thf(c_0_68, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax7220])).
% 6.18/6.39 thf(c_0_69, plain, (p17|~p19), inference(split_conjunct,[status(thm)],[c_0_65])).
% 6.18/6.39 thf(c_0_70, plain, ~p17, inference(sr,[status(thm)],[c_0_66, c_0_67])).
% 6.18/6.39 thf(c_0_71, plain, (p21|~p23), inference(fof_simplification,[status(thm)],[ax7218])).
% 6.18/6.39 thf(c_0_72, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_68])).
% 6.18/6.39 thf(c_0_73, plain, ~p19, inference(sr,[status(thm)],[c_0_69, c_0_70])).
% 6.18/6.39 thf(c_0_74, plain, (p23|~p25), inference(fof_simplification,[status(thm)],[ax7216])).
% 6.18/6.39 thf(c_0_75, plain, (p21|~p23), inference(split_conjunct,[status(thm)],[c_0_71])).
% 6.18/6.39 thf(c_0_76, plain, ~p21, inference(sr,[status(thm)],[c_0_72, c_0_73])).
% 6.18/6.39 thf(c_0_77, plain, (p25|~p27), inference(fof_simplification,[status(thm)],[ax7214])).
% 6.18/6.39 thf(c_0_78, plain, (p23|~p25), inference(split_conjunct,[status(thm)],[c_0_74])).
% 6.18/6.39 thf(c_0_79, plain, ~p23, inference(sr,[status(thm)],[c_0_75, c_0_76])).
% 6.18/6.39 thf(c_0_80, plain, (p27|~p29), inference(fof_simplification,[status(thm)],[ax7212])).
% 6.18/6.39 thf(c_0_81, plain, (p25|~p27), inference(split_conjunct,[status(thm)],[c_0_77])).
% 6.18/6.39 thf(c_0_82, plain, ~p25, inference(sr,[status(thm)],[c_0_78, c_0_79])).
% 6.18/6.39 thf(c_0_83, plain, (p29|~p31), inference(fof_simplification,[status(thm)],[ax7210])).
% 6.18/6.39 thf(c_0_84, plain, (p27|~p29), inference(split_conjunct,[status(thm)],[c_0_80])).
% 6.18/6.39 thf(c_0_85, plain, ~p27, inference(sr,[status(thm)],[c_0_81, c_0_82])).
% 6.18/6.39 thf(c_0_86, plain, (p31|~p33), inference(fof_simplification,[status(thm)],[ax7208])).
% 6.18/6.39 thf(c_0_87, plain, (p29|~p31), inference(split_conjunct,[status(thm)],[c_0_83])).
% 6.18/6.39 thf(c_0_88, plain, ~p29, inference(sr,[status(thm)],[c_0_84, c_0_85])).
% 6.18/6.39 thf(c_0_89, plain, (p33|~p35), inference(fof_simplification,[status(thm)],[ax7206])).
% 6.18/6.39 thf(c_0_90, plain, (p31|~p33), inference(split_conjunct,[status(thm)],[c_0_86])).
% 6.18/6.39 thf(c_0_91, plain, ~p31, inference(sr,[status(thm)],[c_0_87, c_0_88])).
% 6.18/6.39 thf(c_0_92, plain, (p35|~p37), inference(fof_simplification,[status(thm)],[ax7204])).
% 6.18/6.39 thf(c_0_93, plain, (p33|~p35), inference(split_conjunct,[status(thm)],[c_0_89])).
% 6.18/6.39 thf(c_0_94, plain, ~p33, inference(sr,[status(thm)],[c_0_90, c_0_91])).
% 6.18/6.39 thf(c_0_95, plain, (p37|~p38), inference(fof_simplification,[status(thm)],[ax7202])).
% 6.18/6.39 thf(c_0_96, plain, (p35|~p37), inference(split_conjunct,[status(thm)],[c_0_92])).
% 6.18/6.39 thf(c_0_97, plain, ~p35, inference(sr,[status(thm)],[c_0_93, c_0_94])).
% 6.18/6.39 thf(c_0_98, plain, (p38|~p39), inference(fof_simplification,[status(thm)],[ax7200])).
% 6.18/6.39 thf(c_0_99, plain, (p37|~p38), inference(split_conjunct,[status(thm)],[c_0_95])).
% 6.18/6.39 thf(c_0_100, plain, ~p37, inference(sr,[status(thm)],[c_0_96, c_0_97])).
% 6.18/6.39 thf(c_0_101, plain, (p39|~p41), inference(fof_simplification,[status(thm)],[ax7198])).
% 6.18/6.39 thf(c_0_102, plain, (p38|~p39), inference(split_conjunct,[status(thm)],[c_0_98])).
% 6.18/6.39 thf(c_0_103, plain, ~p38, inference(sr,[status(thm)],[c_0_99, c_0_100])).
% 6.18/6.39 thf(c_0_104, plain, (p41|~p43), inference(fof_simplification,[status(thm)],[ax7196])).
% 6.18/6.39 thf(c_0_105, plain, (p39|~p41), inference(split_conjunct,[status(thm)],[c_0_101])).
% 6.18/6.39 thf(c_0_106, plain, ~p39, inference(sr,[status(thm)],[c_0_102, c_0_103])).
% 6.18/6.39 thf(c_0_107, plain, (p43|~p45), inference(fof_simplification,[status(thm)],[ax7194])).
% 6.18/6.39 thf(c_0_108, plain, (p41|~p43), inference(split_conjunct,[status(thm)],[c_0_104])).
% 6.18/6.39 thf(c_0_109, plain, ~p41, inference(sr,[status(thm)],[c_0_105, c_0_106])).
% 6.18/6.39 thf(c_0_110, plain, (~p6|p1943), inference(fof_simplification,[status(thm)],[ax4762])).
% 6.18/6.39 thf(c_0_111, plain, (p5|p6), inference(split_conjunct,[status(thm)],[ax7235])).
% 6.18/6.39 thf(c_0_112, plain, (p45|~p46), inference(fof_simplification,[status(thm)],[ax7192])).
% 6.18/6.39 thf(c_0_113, plain, (p43|~p45), inference(split_conjunct,[status(thm)],[c_0_107])).
% 6.18/6.39 thf(c_0_114, plain, ~p43, inference(sr,[status(thm)],[c_0_108, c_0_109])).
% 6.18/6.39 thf(c_0_115, plain, (~p1943|p1956), inference(fof_simplification,[status(thm)],[ax4749])).
% 6.18/6.39 thf(c_0_116, plain, (p1943|~p6), inference(split_conjunct,[status(thm)],[c_0_110])).
% 6.18/6.39 thf(c_0_117, plain, p6, inference(sr,[status(thm)],[c_0_111, c_0_52])).
% 6.18/6.39 thf(c_0_118, plain, (p46|~p48), inference(fof_simplification,[status(thm)],[ax7190])).
% 6.18/6.39 thf(c_0_119, plain, (p45|~p46), inference(split_conjunct,[status(thm)],[c_0_112])).
% 6.18/6.39 thf(c_0_120, plain, ~p45, inference(sr,[status(thm)],[c_0_113, c_0_114])).
% 6.18/6.39 thf(c_0_121, plain, (((f__0)!=(f__0)|p1950)&(~fin @ f__0 @ f__1|p1950)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1950])])])).
% 6.18/6.39 thf(c_0_122, plain, (~p1956|p1951), inference(fof_simplification,[status(thm)],[ax4750])).
% 6.18/6.39 thf(c_0_123, plain, (p1956|~p1943), inference(split_conjunct,[status(thm)],[c_0_115])).
% 6.18/6.39 thf(c_0_124, plain, p1943, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116, c_0_117])])).
% 6.18/6.39 thf(c_0_125, plain, (p48|~p50), inference(fof_simplification,[status(thm)],[ax7188])).
% 6.18/6.39 thf(c_0_126, plain, (p46|~p48), inference(split_conjunct,[status(thm)],[c_0_118])).
% 6.18/6.39 thf(c_0_127, plain, ~p46, inference(sr,[status(thm)],[c_0_119, c_0_120])).
% 6.18/6.39 thf(c_0_128, plain, (~p1941|p1955), inference(fof_simplification,[status(thm)],[ax4755])).
% 6.18/6.39 thf(c_0_129, plain, (~p1952|~p1951|~p1950), inference(fof_simplification,[status(thm)],[ax4751])).
% 6.18/6.39 thf(c_0_130, plain, (p1950|(f__0)!=(f__0)), inference(split_conjunct,[status(thm)],[c_0_121])).
% 6.18/6.39 thf(c_0_131, plain, (p1951|~p1956), inference(split_conjunct,[status(thm)],[c_0_122])).
% 6.18/6.39 thf(c_0_132, plain, p1956, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_124])])).
% 6.18/6.39 thf(c_0_133, plain, (p50|~p52), inference(fof_simplification,[status(thm)],[ax7186])).
% 6.18/6.39 thf(c_0_134, plain, (p48|~p50), inference(split_conjunct,[status(thm)],[c_0_125])).
% 6.18/6.39 thf(c_0_135, plain, ~p48, inference(sr,[status(thm)],[c_0_126, c_0_127])).
% 6.18/6.39 thf(c_0_136, plain, (~p1955|p1954), inference(fof_simplification,[status(thm)],[ax4754])).
% 6.18/6.39 thf(c_0_137, plain, (p1955|~p1941), inference(split_conjunct,[status(thm)],[c_0_128])).
% 6.18/6.39 thf(c_0_138, plain, p1941, inference(split_conjunct,[status(thm)],[ax4770])).
% 6.18/6.39 thf(c_0_139, plain, (~p1954|p56|p1953), inference(fof_simplification,[status(thm)],[ax4753])).
% 6.18/6.39 thf(c_0_140, plain, (p55|~p56), inference(fof_simplification,[status(thm)],[ax7182])).
% 6.18/6.39 thf(c_0_141, plain, (p54|~p55), inference(fof_simplification,[status(thm)],[ax7183])).
% 6.18/6.39 thf(c_0_142, plain, (~p1953|p1952), inference(fof_simplification,[status(thm)],[ax4752])).
% 6.18/6.39 thf(c_0_143, plain, (p52|~p54), inference(fof_simplification,[status(thm)],[ax7184])).
% 6.18/6.39 thf(c_0_144, plain, (~p1952|~p1951|~p1950), inference(split_conjunct,[status(thm)],[c_0_129])).
% 6.18/6.39 thf(c_0_145, plain, p1950, inference(cn,[status(thm)],[c_0_130])).
% 6.18/6.39 thf(c_0_146, plain, p1951, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131, c_0_132])])).
% 6.18/6.39 thf(c_0_147, plain, (p50|~p52), inference(split_conjunct,[status(thm)],[c_0_133])).
% 6.18/6.39 thf(c_0_148, plain, ~p50, inference(sr,[status(thm)],[c_0_134, c_0_135])).
% 6.18/6.39 thf(c_0_149, plain, (p1954|~p1955), inference(split_conjunct,[status(thm)],[c_0_136])).
% 6.18/6.39 thf(c_0_150, plain, p1955, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137, c_0_138])])).
% 6.18/6.39 thf(c_0_151, plain, (p56|p1953|~p1954), inference(split_conjunct,[status(thm)],[c_0_139])).
% 6.18/6.39 thf(c_0_152, plain, (p55|~p56), inference(split_conjunct,[status(thm)],[c_0_140])).
% 6.18/6.39 thf(c_0_153, plain, (p54|~p55), inference(split_conjunct,[status(thm)],[c_0_141])).
% 6.18/6.39 thf(c_0_154, plain, (p1952|~p1953), inference(split_conjunct,[status(thm)],[c_0_142])).
% 6.18/6.39 thf(c_0_155, plain, (p52|~p54), inference(split_conjunct,[status(thm)],[c_0_143])).
% 6.18/6.39 thf(c_0_156, plain, ~p1952, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144, c_0_145]), c_0_146])])).
% 6.18/6.39 thf(c_0_157, plain, ~p52, inference(sr,[status(thm)],[c_0_147, c_0_148])).
% 6.18/6.39 thf(c_0_158, plain, p1954, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149, c_0_150])])).
% 6.18/6.39 thf(c_0_159, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_151, c_0_152, c_0_153, c_0_154, c_0_155, c_0_156, c_0_157, c_0_158]), ['proof']).
% 6.18/6.39 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 6.18/6.39 thf(0,theorem,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))) => ((![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))) => ((![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (~((![X4:$i]:(((X1 @ X3) @ X4) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 = X5))))))))))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$o]:(![X2:$i]:(((in @ X2) @ ((dsetconstr @ (powerset @ emptyset)) @ (^[X3:$i]:X1))) => X1))) => ((![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 6.18/6.39 % SZS output end Proof
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