TSTP Solution File: SEU691^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU691^2 : 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 : n010.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 13:56:53 EDT 2022
% Result : Theorem 215.80s 215.63s
% Output : Proof 215.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU691^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.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 : Mon Jun 20 14:05:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 66.82/66.50 slave returned with unknown status
% 215.80/215.63 % SZS status Theorem
% 215.80/215.63 % Mode: mode447
% 215.80/215.63 % Inferences: 107
% 215.80/215.63 % SZS output start Proof
% 215.80/215.63 thf(ty_subset, type, subset : ($i>$i>$o)).
% 215.80/215.63 thf(ty_eigen__2, type, eigen__2 : $i).
% 215.80/215.63 thf(ty_eigen__1, type, eigen__1 : $i).
% 215.80/215.63 thf(ty_eigen__0, type, eigen__0 : $i).
% 215.80/215.63 thf(ty_cartprod, type, cartprod : ($i>$i>$i)).
% 215.80/215.63 thf(ty_emptyset, type, emptyset : $i).
% 215.80/215.63 thf(ty_kpair, type, kpair : ($i>$i>$i)).
% 215.80/215.63 thf(ty_eigen__3, type, eigen__3 : $i).
% 215.80/215.63 thf(ty_ap, type, ap : ($i>$i>$i>$i>$i)).
% 215.80/215.63 thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)).
% 215.80/215.63 thf(ty_in, type, in : ($i>$i>$o)).
% 215.80/215.63 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 215.80/215.63 thf(def_singleton,definition,(singleton = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset))))))))))).
% 215.80/215.63 thf(def_ex1,definition,(ex1 = (^[X1:$i]:(^[X2:$i>$o]:(singleton @ ((dsetconstr @ X1) @ X2)))))).
% 215.80/215.63 thf(def_breln,definition,(breln = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((subset @ X3) @ ((cartprod @ X1) @ X2))))))).
% 215.80/215.63 thf(def_func,definition,(func = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:(~(((((breln @ X1) @ X2) @ X3) => (~((![X4:$i]:(((in @ X4) @ X1) => ((ex1 @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))))))))))))).
% 215.80/215.63 thf(def_funcGraphProp1,definition,(funcGraphProp1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))))).
% 215.80/215.63 thf(def_funcGraphProp2,definition,(funcGraphProp2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))))).
% 215.80/215.63 thf(def_eqbreln,definition,(eqbreln = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))))).
% 215.80/215.63 thf(funcext,conjecture,((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))))).
% 215.80/215.63 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4))))))))))))),inference(assume_negation,[status(cth)],[funcext])).
% 215.80/215.63 thf(h1,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h3,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4))))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h6,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h7,assumption,(~((![X1:$i]:(![X2:$i]:((~((((subset @ X2) @ ((cartprod @ eigen__0) @ X1)) => (~((![X3:$i]:(((in @ X3) @ eigen__0) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((in @ ((kpair @ X3) @ X5)) @ X2)))) => (~((((dsetconstr @ X1) @ (^[X5:$i]:((in @ ((kpair @ X3) @ X5)) @ X2))) = ((setadjoin @ X4) @ emptyset))))))))))))))) => (![X3:$i]:((~((((subset @ X3) @ ((cartprod @ eigen__0) @ X1)) => (~((![X4:$i]:(((in @ X4) @ eigen__0) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X1) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X1) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => ((![X4:$i]:(((in @ X4) @ eigen__0) => (((((ap @ eigen__0) @ X1) @ X2) @ X4) = ((((ap @ eigen__0) @ X1) @ X3) @ X4)))) => (X2 = X3))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h8,assumption,(~((![X1:$i]:((~((((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X2:$i]:(((in @ X2) @ eigen__0) => (~((![X3:$i]:(((in @ X3) @ ((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1)))) => (~((((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1))) = ((setadjoin @ X3) @ emptyset))))))))))))))) => (![X2:$i]:((~((((subset @ X2) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X3:$i]:(((in @ X3) @ eigen__0) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ eigen__1) @ (^[X5:$i]:((in @ ((kpair @ X3) @ X5)) @ X2)))) => (~((((dsetconstr @ eigen__1) @ (^[X5:$i]:((in @ ((kpair @ X3) @ X5)) @ X2))) = ((setadjoin @ X4) @ emptyset))))))))))))))) => ((![X3:$i]:(((in @ X3) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ X1) @ X3) = ((((ap @ eigen__0) @ eigen__1) @ X2) @ X3)))) => (X1 = X2)))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h9,assumption,(~(((~((((subset @ eigen__2) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2))) = ((setadjoin @ X2) @ emptyset))))))))))))))) => (![X1:$i]:((~((((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X2:$i]:(((in @ X2) @ eigen__0) => (~((![X3:$i]:(((in @ X3) @ ((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1)))) => (~((((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1))) = ((setadjoin @ X3) @ emptyset))))))))))))))) => ((![X2:$i]:(((in @ X2) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ eigen__2) @ X2) = ((((ap @ eigen__0) @ eigen__1) @ X1) @ X2)))) => (eigen__2 = X1))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h10,assumption,(~((((subset @ eigen__2) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2))) = ((setadjoin @ X2) @ emptyset))))))))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h11,assumption,(~((![X1:$i]:((~((((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X2:$i]:(((in @ X2) @ eigen__0) => (~((![X3:$i]:(((in @ X3) @ ((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1)))) => (~((((dsetconstr @ eigen__1) @ (^[X4:$i]:((in @ ((kpair @ X2) @ X4)) @ X1))) = ((setadjoin @ X3) @ emptyset))))))))))))))) => ((![X2:$i]:(((in @ X2) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ eigen__2) @ X2) = ((((ap @ eigen__0) @ eigen__1) @ X1) @ X2)))) => (eigen__2 = X1)))))),introduced(assumption,[])).
% 215.80/215.63 thf(h12,assumption,((subset @ eigen__2) @ ((cartprod @ eigen__0) @ eigen__1)),introduced(assumption,[])).
% 215.80/215.63 thf(h13,assumption,(![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__2))) = ((setadjoin @ X2) @ emptyset)))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h14,assumption,(~(((~((((subset @ eigen__3) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3))) = ((setadjoin @ X2) @ emptyset))))))))))))))) => ((![X1:$i]:(((in @ X1) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ eigen__2) @ X1) = ((((ap @ eigen__0) @ eigen__1) @ eigen__3) @ X1)))) => (eigen__2 = eigen__3))))),introduced(assumption,[])).
% 215.80/215.63 thf(h15,assumption,(~((((subset @ eigen__3) @ ((cartprod @ eigen__0) @ eigen__1)) => (~((![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3))) = ((setadjoin @ X2) @ emptyset))))))))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h16,assumption,(~(((![X1:$i]:(((in @ X1) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ eigen__2) @ X1) = ((((ap @ eigen__0) @ eigen__1) @ eigen__3) @ X1)))) => (eigen__2 = eigen__3)))),introduced(assumption,[])).
% 215.80/215.63 thf(h17,assumption,((subset @ eigen__3) @ ((cartprod @ eigen__0) @ eigen__1)),introduced(assumption,[])).
% 215.80/215.63 thf(h18,assumption,(![X1:$i]:(((in @ X1) @ eigen__0) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3)))) => (~((((dsetconstr @ eigen__1) @ (^[X3:$i]:((in @ ((kpair @ X1) @ X3)) @ eigen__3))) = ((setadjoin @ X2) @ emptyset)))))))))),introduced(assumption,[])).
% 215.80/215.63 thf(h19,assumption,(![X1:$i]:(((in @ X1) @ eigen__0) => (((((ap @ eigen__0) @ eigen__1) @ eigen__2) @ X1) = ((((ap @ eigen__0) @ eigen__1) @ eigen__3) @ X1)))),introduced(assumption,[])).
% 215.80/215.63 thf(h20,assumption,(~((eigen__2 = eigen__3))),introduced(assumption,[])).
% 215.80/215.63 thf(ax83, axiom, (~(p56)|~(p6)|~(p5)), file('<stdin>', ax83)).
% 215.80/215.63 thf(ax82, axiom, (~(p57)|p56|p55), file('<stdin>', ax82)).
% 215.80/215.63 thf(ax132, axiom, p5, file('<stdin>', ax132)).
% 215.80/215.63 thf(ax131, axiom, p6, file('<stdin>', ax131)).
% 215.80/215.63 thf(ax79, axiom, (~(p8)|p59), file('<stdin>', ax79)).
% 215.80/215.63 thf(ax111, axiom, (~(p7)|p25), file('<stdin>', ax111)).
% 215.80/215.63 thf(ax69, axiom, (~(p9)|p69), file('<stdin>', ax69)).
% 215.80/215.63 thf(ax81, axiom, (~(p58)|p57), file('<stdin>', ax81)).
% 215.80/215.63 thf(ax80, axiom, (~(p59)|p58), file('<stdin>', ax80)).
% 215.80/215.63 thf(ax129, axiom, p8, file('<stdin>', ax129)).
% 215.80/215.63 thf(ax112, axiom, (~(p25)|p24), file('<stdin>', ax112)).
% 215.80/215.63 thf(ax130, axiom, p7, file('<stdin>', ax130)).
% 215.80/215.63 thf(ax78, axiom, (~(p61)|~(p4)|~(p3)), file('<stdin>', ax78)).
% 215.80/215.63 thf(ax70, axiom, (~(p69)|p68), file('<stdin>', ax70)).
% 215.80/215.63 thf(ax128, axiom, p9, file('<stdin>', ax128)).
% 215.80/215.63 thf(nax1, axiom, (p1<=(f__2)=(f__3)), file('<stdin>', nax1)).
% 215.80/215.63 thf(ax136, axiom, ~(p1), file('<stdin>', ax136)).
% 215.80/215.63 thf(ax110, axiom, (~(p27)|~(p4)|p26), file('<stdin>', ax110)).
% 215.80/215.63 thf(ax109, axiom, (~(p24)|p27), file('<stdin>', ax109)).
% 215.80/215.63 thf(ax72, axiom, (~(p67)|p56|p66), file('<stdin>', ax72)).
% 215.80/215.63 thf(ax68, axiom, (~(p71)|p61|p70), file('<stdin>', ax68)).
% 215.80/215.63 thf(ax134, axiom, p3, file('<stdin>', ax134)).
% 215.80/215.63 thf(ax133, axiom, p4, file('<stdin>', ax133)).
% 215.80/215.63 thf(ax67, axiom, (~(p68)|p71), file('<stdin>', ax67)).
% 215.80/215.63 thf(pax55, axiom, (p55=>![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__1=>(fin @ (fkpair @ X1 @ X2) @ f__2=>(fap @ f__0 @ f__1 @ f__2 @ X1)=(X2))))), file('<stdin>', pax55)).
% 215.80/215.63 thf(pax35, axiom, (p35=>(![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__1=>(fin @ (fkpair @ X1 @ X2) @ f__2=>fin @ (fkpair @ X1 @ X2) @ f__3)))=>(f__3)=(f__2))), file('<stdin>', pax35)).
% 215.80/215.63 thf(ax71, axiom, (~(p68)|p67), file('<stdin>', ax71)).
% 215.80/215.63 thf(pax2, axiom, (p2=>![X1:$i]:(fin @ X1 @ f__0=>(fap @ f__0 @ f__1 @ f__2 @ X1)=(fap @ f__0 @ f__1 @ f__3 @ X1))), file('<stdin>', pax2)).
% 215.80/215.63 thf(ax102, axiom, (~(p37)|~(p6)|p36), file('<stdin>', ax102)).
% 215.80/215.63 thf(ax101, axiom, (~(p26)|p37), file('<stdin>', ax101)).
% 215.80/215.63 thf(pax70, axiom, (p70=>![X1:$i]:(fin @ X1 @ f__0=>fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__3 @ X1)) @ f__3)), file('<stdin>', pax70)).
% 215.80/215.63 thf(ax135, axiom, p2, file('<stdin>', ax135)).
% 215.80/215.63 thf(pax66, axiom, (p66=>![X1:$i]:(fin @ X1 @ f__0=>fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__2 @ X1)) @ f__2)), file('<stdin>', pax66)).
% 215.80/215.63 thf(ax103, axiom, (~(p36)|~(p33)|p35), file('<stdin>', ax103)).
% 215.80/215.63 thf(ax77, axiom, (~(p62)|p61|p60), file('<stdin>', ax77)).
% 215.80/215.63 thf(ax76, axiom, (~(p58)|p62), file('<stdin>', ax76)).
% 215.80/215.63 thf(nax136, axiom, (p136<=fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2), file('<stdin>', nax136)).
% 215.80/215.63 thf(nax80, axiom, (p80<=(fin @ f__5 @ f__0=>![X1:$i]:(fin @ X1 @ f__1=>(fin @ (fkpair @ f__5 @ X1) @ f__3=>fin @ (fkpair @ f__5 @ X1) @ f__2)))), file('<stdin>', nax80)).
% 215.80/215.63 thf(ax58, axiom, (p33|~(p80)), file('<stdin>', ax58)).
% 215.80/215.63 thf(pax60, axiom, (p60=>![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__1=>(fin @ (fkpair @ X1 @ X2) @ f__3=>(fap @ f__0 @ f__1 @ f__3 @ X1)=(X2))))), file('<stdin>', pax60)).
% 215.80/215.63 thf(pax136, axiom, (p136=>fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2), file('<stdin>', pax136)).
% 215.80/215.63 thf(c_0_41, plain, (~p56|~p6|~p5), inference(fof_simplification,[status(thm)],[ax83])).
% 215.80/215.63 thf(c_0_42, plain, (~p57|p56|p55), inference(fof_simplification,[status(thm)],[ax82])).
% 215.80/215.63 thf(c_0_43, plain, (~p56|~p6|~p5), inference(split_conjunct,[status(thm)],[c_0_41])).
% 215.80/215.63 thf(c_0_44, plain, p5, inference(split_conjunct,[status(thm)],[ax132])).
% 215.80/215.63 thf(c_0_45, plain, p6, inference(split_conjunct,[status(thm)],[ax131])).
% 215.80/215.63 thf(c_0_46, plain, (~p8|p59), inference(fof_simplification,[status(thm)],[ax79])).
% 215.80/215.63 thf(c_0_47, plain, (~p7|p25), inference(fof_simplification,[status(thm)],[ax111])).
% 215.80/215.63 thf(c_0_48, plain, (~p9|p69), inference(fof_simplification,[status(thm)],[ax69])).
% 215.80/215.63 thf(c_0_49, plain, (p56|p55|~p57), inference(split_conjunct,[status(thm)],[c_0_42])).
% 215.80/215.63 thf(c_0_50, plain, ~p56, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44]), c_0_45])])).
% 215.80/215.63 thf(c_0_51, plain, (~p58|p57), inference(fof_simplification,[status(thm)],[ax81])).
% 215.80/215.63 thf(c_0_52, plain, (~p59|p58), inference(fof_simplification,[status(thm)],[ax80])).
% 215.80/215.63 thf(c_0_53, plain, (p59|~p8), inference(split_conjunct,[status(thm)],[c_0_46])).
% 215.80/215.63 thf(c_0_54, plain, p8, inference(split_conjunct,[status(thm)],[ax129])).
% 215.80/215.63 thf(c_0_55, plain, (~p25|p24), inference(fof_simplification,[status(thm)],[ax112])).
% 215.80/215.63 thf(c_0_56, plain, (p25|~p7), inference(split_conjunct,[status(thm)],[c_0_47])).
% 215.80/215.63 thf(c_0_57, plain, p7, inference(split_conjunct,[status(thm)],[ax130])).
% 215.80/215.63 thf(c_0_58, plain, (~p61|~p4|~p3), inference(fof_simplification,[status(thm)],[ax78])).
% 215.80/215.63 thf(c_0_59, plain, (~p69|p68), inference(fof_simplification,[status(thm)],[ax70])).
% 215.80/215.63 thf(c_0_60, plain, (p69|~p9), inference(split_conjunct,[status(thm)],[c_0_48])).
% 215.80/215.63 thf(c_0_61, plain, p9, inference(split_conjunct,[status(thm)],[ax128])).
% 215.80/215.63 thf(c_0_62, plain, (p55|~p57), inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 215.80/215.63 thf(c_0_63, plain, (p57|~p58), inference(split_conjunct,[status(thm)],[c_0_51])).
% 215.80/215.63 thf(c_0_64, plain, (p58|~p59), inference(split_conjunct,[status(thm)],[c_0_52])).
% 215.80/215.63 thf(c_0_65, plain, p59, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 215.80/215.63 thf(c_0_66, plain, ((f__2)!=(f__3)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 215.80/215.63 thf(c_0_67, plain, ~p1, inference(fof_simplification,[status(thm)],[ax136])).
% 215.80/215.63 thf(c_0_68, plain, (~p27|~p4|p26), inference(fof_simplification,[status(thm)],[ax110])).
% 215.80/215.63 thf(c_0_69, plain, (~p24|p27), inference(fof_simplification,[status(thm)],[ax109])).
% 215.80/215.63 thf(c_0_70, plain, (p24|~p25), inference(split_conjunct,[status(thm)],[c_0_55])).
% 215.80/215.63 thf(c_0_71, plain, p25, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 215.80/215.63 thf(c_0_72, plain, (~p67|p56|p66), inference(fof_simplification,[status(thm)],[ax72])).
% 215.80/215.63 thf(c_0_73, plain, (~p71|p61|p70), inference(fof_simplification,[status(thm)],[ax68])).
% 215.80/215.63 thf(c_0_74, plain, (~p61|~p4|~p3), inference(split_conjunct,[status(thm)],[c_0_58])).
% 215.80/215.63 thf(c_0_75, plain, p3, inference(split_conjunct,[status(thm)],[ax134])).
% 215.80/215.63 thf(c_0_76, plain, p4, inference(split_conjunct,[status(thm)],[ax133])).
% 215.80/215.63 thf(c_0_77, plain, (~p68|p71), inference(fof_simplification,[status(thm)],[ax67])).
% 215.80/215.63 thf(c_0_78, plain, (p68|~p69), inference(split_conjunct,[status(thm)],[c_0_59])).
% 215.80/215.63 thf(c_0_79, plain, p69, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 215.80/215.63 thf(c_0_80, plain, ![X111:$i, X112:$i]:(~p55|(~fin @ X111 @ f__0|(~fin @ X112 @ f__1|(~fin @ (fkpair @ X111 @ X112) @ f__2|(fap @ f__0 @ f__1 @ f__2 @ X111)=(X112))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax55])])])).
% 215.80/215.63 thf(c_0_81, plain, (p55|~p58), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 215.80/215.63 thf(c_0_82, plain, p58, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 215.80/215.63 thf(c_0_83, plain, ((fin @ esk94_0 @ f__0|(f__3)=(f__2)|~p35)&((fin @ esk95_0 @ f__1|(f__3)=(f__2)|~p35)&((fin @ (fkpair @ esk94_0 @ esk95_0) @ f__2|(f__3)=(f__2)|~p35)&(~fin @ (fkpair @ esk94_0 @ esk95_0) @ f__3|(f__3)=(f__2)|~p35)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax35])])])])).
% 215.80/215.63 thf(c_0_84, plain, (p1|(f__2)!=(f__3)), inference(split_conjunct,[status(thm)],[c_0_66])).
% 215.80/215.63 thf(c_0_85, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_67])).
% 215.80/215.63 thf(c_0_86, plain, (p26|~p27|~p4), inference(split_conjunct,[status(thm)],[c_0_68])).
% 215.80/215.63 thf(c_0_87, plain, (p27|~p24), inference(split_conjunct,[status(thm)],[c_0_69])).
% 215.80/215.63 thf(c_0_88, plain, p24, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70, c_0_71])])).
% 215.80/215.63 thf(c_0_89, plain, (p56|p66|~p67), inference(split_conjunct,[status(thm)],[c_0_72])).
% 215.80/215.63 thf(c_0_90, plain, (~p68|p67), inference(fof_simplification,[status(thm)],[ax71])).
% 215.80/215.63 thf(c_0_91, plain, (p61|p70|~p71), inference(split_conjunct,[status(thm)],[c_0_73])).
% 215.80/215.63 thf(c_0_92, plain, ~p61, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75]), c_0_76])])).
% 215.80/215.63 thf(c_0_93, plain, (p71|~p68), inference(split_conjunct,[status(thm)],[c_0_77])).
% 215.80/215.63 thf(c_0_94, plain, p68, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_79])])).
% 215.80/215.63 thf(c_0_95, plain, ![X295:$i]:(~p2|(~fin @ X295 @ f__0|(fap @ f__0 @ f__1 @ f__2 @ X295)=(fap @ f__0 @ f__1 @ f__3 @ X295))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 215.80/215.63 thf(c_0_96, plain, ![X1:$i, X2:$i]:((fap @ f__0 @ f__1 @ f__2 @ X1)=(X2)|~p55|~fin @ X1 @ f__0|~fin @ X2 @ f__1|~fin @ (fkpair @ X1 @ X2) @ f__2), inference(split_conjunct,[status(thm)],[c_0_80])).
% 215.80/215.63 thf(c_0_97, plain, p55, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_82])])).
% 215.80/215.63 thf(c_0_98, plain, (fin @ (fkpair @ esk94_0 @ esk95_0) @ f__2|(f__3)=(f__2)|~p35), inference(split_conjunct,[status(thm)],[c_0_83])).
% 215.80/215.63 thf(c_0_99, plain, (f__2)!=(f__3), inference(sr,[status(thm)],[c_0_84, c_0_85])).
% 215.80/215.63 thf(c_0_100, plain, (fin @ esk94_0 @ f__0|(f__3)=(f__2)|~p35), inference(split_conjunct,[status(thm)],[c_0_83])).
% 215.80/215.63 thf(c_0_101, plain, (fin @ esk95_0 @ f__1|(f__3)=(f__2)|~p35), inference(split_conjunct,[status(thm)],[c_0_83])).
% 215.80/215.63 thf(c_0_102, plain, (~p37|~p6|p36), inference(fof_simplification,[status(thm)],[ax102])).
% 215.80/215.63 thf(c_0_103, plain, (~p26|p37), inference(fof_simplification,[status(thm)],[ax101])).
% 215.80/215.63 thf(c_0_104, plain, (p26|~p27), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_76])])).
% 215.80/215.63 thf(c_0_105, plain, p27, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88])])).
% 215.80/215.63 thf(c_0_106, plain, (p66|~p67), inference(sr,[status(thm)],[c_0_89, c_0_50])).
% 215.80/215.63 thf(c_0_107, plain, (p67|~p68), inference(split_conjunct,[status(thm)],[c_0_90])).
% 215.80/215.63 thf(c_0_108, plain, ![X103:$i]:(~p70|(~fin @ X103 @ f__0|fin @ (fkpair @ X103 @ (fap @ f__0 @ f__1 @ f__3 @ X103)) @ f__3)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax70])])])).
% 215.80/215.63 thf(c_0_109, plain, (p70|~p71), inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 215.80/215.63 thf(c_0_110, plain, p71, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93, c_0_94])])).
% 215.80/215.63 thf(c_0_111, plain, ![X1:$i]:((fap @ f__0 @ f__1 @ f__2 @ X1)=(fap @ f__0 @ f__1 @ f__3 @ X1)|~p2|~fin @ X1 @ f__0), inference(split_conjunct,[status(thm)],[c_0_95])).
% 215.80/215.63 thf(c_0_112, plain, p2, inference(split_conjunct,[status(thm)],[ax135])).
% 215.80/215.63 thf(c_0_113, plain, ![X2:$i, X1:$i]:((fap @ f__0 @ f__1 @ f__2 @ X1)=(X2)|~fin @ (fkpair @ X1 @ X2) @ f__2|~fin @ X2 @ f__1|~fin @ X1 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])).
% 215.80/215.63 thf(c_0_114, plain, (fin @ (fkpair @ esk94_0 @ esk95_0) @ f__2|~p35), inference(sr,[status(thm)],[c_0_98, c_0_99])).
% 215.80/215.63 thf(c_0_115, plain, (fin @ esk94_0 @ f__0|~p35), inference(sr,[status(thm)],[c_0_100, c_0_99])).
% 215.80/215.63 thf(c_0_116, plain, (fin @ esk95_0 @ f__1|~p35), inference(sr,[status(thm)],[c_0_101, c_0_99])).
% 215.80/215.63 thf(c_0_117, plain, (p36|~p37|~p6), inference(split_conjunct,[status(thm)],[c_0_102])).
% 215.80/215.63 thf(c_0_118, plain, (p37|~p26), inference(split_conjunct,[status(thm)],[c_0_103])).
% 215.80/215.63 thf(c_0_119, plain, p26, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105])])).
% 215.80/215.63 thf(c_0_120, plain, ![X105:$i]:(~p66|(~fin @ X105 @ f__0|fin @ (fkpair @ X105 @ (fap @ f__0 @ f__1 @ f__2 @ X105)) @ f__2)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax66])])])).
% 215.80/215.63 thf(c_0_121, plain, (p66|~p68), inference(spm,[status(thm)],[c_0_106, c_0_107])).
% 215.80/215.63 thf(c_0_122, plain, ![X1:$i]:(fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__3 @ X1)) @ f__3|~p70|~fin @ X1 @ f__0), inference(split_conjunct,[status(thm)],[c_0_108])).
% 215.80/215.63 thf(c_0_123, plain, p70, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110])])).
% 215.80/215.63 thf(c_0_124, plain, ![X1:$i]:((fap @ f__0 @ f__1 @ f__2 @ X1)=(fap @ f__0 @ f__1 @ f__3 @ X1)|~fin @ X1 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111, c_0_112])])).
% 215.80/215.63 thf(c_0_125, plain, ((fap @ f__0 @ f__1 @ f__2 @ esk94_0)=(esk95_0)|~p35), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_115]), c_0_116])).
% 215.80/215.63 thf(c_0_126, plain, ((f__3)=(f__2)|~fin @ (fkpair @ esk94_0 @ esk95_0) @ f__3|~p35), inference(split_conjunct,[status(thm)],[c_0_83])).
% 215.80/215.63 thf(c_0_127, plain, (~p36|~p33|p35), inference(fof_simplification,[status(thm)],[ax103])).
% 215.80/215.63 thf(c_0_128, plain, (p36|~p37), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117, c_0_45])])).
% 215.80/215.63 thf(c_0_129, plain, p37, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_119])])).
% 215.80/215.63 thf(c_0_130, plain, (~p62|p61|p60), inference(fof_simplification,[status(thm)],[ax77])).
% 215.80/215.63 thf(c_0_131, plain, (~p58|p62), inference(fof_simplification,[status(thm)],[ax76])).
% 215.80/215.63 thf(c_0_132, plain, (~fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2|p136), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax136])])).
% 215.80/215.63 thf(c_0_133, plain, ![X1:$i]:(fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__2 @ X1)) @ f__2|~p66|~fin @ X1 @ f__0), inference(split_conjunct,[status(thm)],[c_0_120])).
% 215.80/215.63 thf(c_0_134, plain, p66, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121, c_0_94])])).
% 215.80/215.63 thf(c_0_135, plain, ![X1:$i]:(fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__3 @ X1)) @ f__3|~fin @ X1 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122, c_0_123])])).
% 215.80/215.63 thf(c_0_136, plain, ((fap @ f__0 @ f__1 @ f__3 @ esk94_0)=(esk95_0)|~p35), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_125]), c_0_115])).
% 215.80/215.63 thf(c_0_137, plain, (~fin @ (fkpair @ esk94_0 @ esk95_0) @ f__3|~p35), inference(sr,[status(thm)],[c_0_126, c_0_99])).
% 215.80/215.63 thf(c_0_138, plain, (p35|~p36|~p33), inference(split_conjunct,[status(thm)],[c_0_127])).
% 215.80/215.63 thf(c_0_139, plain, p36, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128, c_0_129])])).
% 215.80/215.63 thf(c_0_140, plain, (p61|p60|~p62), inference(split_conjunct,[status(thm)],[c_0_130])).
% 215.80/215.63 thf(c_0_141, plain, (p62|~p58), inference(split_conjunct,[status(thm)],[c_0_131])).
% 215.80/215.63 thf(c_0_142, plain, (p136|~fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2), inference(split_conjunct,[status(thm)],[c_0_132])).
% 215.80/215.63 thf(c_0_143, plain, ![X1:$i]:(fin @ (fkpair @ X1 @ (fap @ f__0 @ f__1 @ f__2 @ X1)) @ f__2|~fin @ X1 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133, c_0_134])])).
% 215.80/215.63 thf(c_0_144, plain, ((fin @ f__5 @ f__0|p80)&((fin @ esk32_0 @ f__1|p80)&((fin @ (fkpair @ f__5 @ esk32_0) @ f__3|p80)&(~fin @ (fkpair @ f__5 @ esk32_0) @ f__2|p80)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax80])])])])])).
% 215.80/215.63 thf(c_0_145, plain, ~p35, inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136]), c_0_115]), c_0_137])).
% 215.80/215.63 thf(c_0_146, plain, (p35|~p33), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_139])])).
% 215.80/215.63 thf(c_0_147, plain, (p33|~p80), inference(fof_simplification,[status(thm)],[ax58])).
% 215.80/215.63 thf(c_0_148, plain, ![X107:$i, X108:$i]:(~p60|(~fin @ X107 @ f__0|(~fin @ X108 @ f__1|(~fin @ (fkpair @ X107 @ X108) @ f__3|(fap @ f__0 @ f__1 @ f__3 @ X107)=(X108))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax60])])])).
% 215.80/215.63 thf(c_0_149, plain, (p60|~p62), inference(sr,[status(thm)],[c_0_140, c_0_92])).
% 215.80/215.63 thf(c_0_150, plain, p62, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141, c_0_82])])).
% 215.80/215.63 thf(c_0_151, plain, (p136|~fin @ f__5 @ f__0), inference(spm,[status(thm)],[c_0_142, c_0_143])).
% 215.80/215.63 thf(c_0_152, plain, (fin @ f__5 @ f__0|p80), inference(split_conjunct,[status(thm)],[c_0_144])).
% 215.80/215.63 thf(c_0_153, plain, ~p33, inference(spm,[status(thm)],[c_0_145, c_0_146])).
% 215.80/215.63 thf(c_0_154, plain, (p33|~p80), inference(split_conjunct,[status(thm)],[c_0_147])).
% 215.80/215.63 thf(c_0_155, plain, ![X1:$i, X2:$i]:((fap @ f__0 @ f__1 @ f__3 @ X1)=(X2)|~p60|~fin @ X1 @ f__0|~fin @ X2 @ f__1|~fin @ (fkpair @ X1 @ X2) @ f__3), inference(split_conjunct,[status(thm)],[c_0_148])).
% 215.80/215.63 thf(c_0_156, plain, p60, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149, c_0_150])])).
% 215.80/215.63 thf(c_0_157, plain, (~p136|fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2), inference(fof_nnf,[status(thm)],[pax136])).
% 215.80/215.63 thf(c_0_158, plain, (p80|p136), inference(spm,[status(thm)],[c_0_151, c_0_152])).
% 215.80/215.63 thf(c_0_159, plain, ~p80, inference(spm,[status(thm)],[c_0_153, c_0_154])).
% 215.80/215.63 thf(c_0_160, plain, ![X2:$i, X1:$i]:((fap @ f__0 @ f__1 @ f__3 @ X1)=(X2)|~fin @ (fkpair @ X1 @ X2) @ f__3|~fin @ X2 @ f__1|~fin @ X1 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155, c_0_156])])).
% 215.80/215.63 thf(c_0_161, plain, (fin @ (fkpair @ f__5 @ esk32_0) @ f__3|p80), inference(split_conjunct,[status(thm)],[c_0_144])).
% 215.80/215.63 thf(c_0_162, plain, (fin @ esk32_0 @ f__1|p80), inference(split_conjunct,[status(thm)],[c_0_144])).
% 215.80/215.63 thf(c_0_163, plain, (fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2|~p136), inference(split_conjunct,[status(thm)],[c_0_157])).
% 215.80/215.63 thf(c_0_164, plain, p136, inference(sr,[status(thm)],[c_0_158, c_0_159])).
% 215.80/215.63 thf(c_0_165, plain, ((fap @ f__0 @ f__1 @ f__3 @ f__5)=(esk32_0)|p80), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_161]), c_0_152]), c_0_162])).
% 215.80/215.63 thf(c_0_166, plain, fin @ (fkpair @ f__5 @ (fap @ f__0 @ f__1 @ f__2 @ f__5)) @ f__2, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163, c_0_164])])).
% 215.80/215.63 thf(c_0_167, plain, (fap @ f__0 @ f__1 @ f__3 @ f__5)=(esk32_0), inference(sr,[status(thm)],[c_0_165, c_0_159])).
% 215.80/215.63 thf(c_0_168, plain, fin @ f__5 @ f__0, inference(sr,[status(thm)],[c_0_152, c_0_159])).
% 215.80/215.63 thf(c_0_169, plain, (p80|~fin @ (fkpair @ f__5 @ esk32_0) @ f__2), inference(split_conjunct,[status(thm)],[c_0_144])).
% 215.80/215.63 thf(c_0_170, plain, fin @ (fkpair @ f__5 @ esk32_0) @ f__2, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166, c_0_124]), c_0_167]), c_0_168])])).
% 215.80/215.63 thf(c_0_171, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169, c_0_170])]), c_0_159]), ['proof']).
% 215.80/215.63 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[])).
% 215.80/215.63 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h16,1,h19,h20])).
% 215.80/215.63 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,2,h17,h18])).
% 215.80/215.63 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,3,h15,h16])).
% 215.80/215.63 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h11,4,h14])).
% 215.80/215.63 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,5,h12,h13])).
% 215.80/215.63 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,6,h10,h11])).
% 215.80/215.63 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,7,h9])).
% 215.80/215.63 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,8,h8])).
% 215.80/215.63 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,9,h7])).
% 215.80/215.63 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,10,h5,h6])).
% 215.80/215.63 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4])).
% 215.80/215.63 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,12,h1,h2])).
% 215.80/215.63 thf(0,theorem,((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((subset @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ ((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3)))) => (~((((dsetconstr @ X2) @ (^[X6:$i]:((in @ ((kpair @ X4) @ X6)) @ X3))) = ((setadjoin @ X5) @ emptyset))))))))))))))) => (![X4:$i]:((~((((subset @ X4) @ ((cartprod @ X1) @ X2)) => (~((![X5:$i]:(((in @ X5) @ X1) => (~((![X6:$i]:(((in @ X6) @ ((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4)))) => (~((((dsetconstr @ X2) @ (^[X7:$i]:((in @ ((kpair @ X5) @ X7)) @ X4))) = ((setadjoin @ X6) @ emptyset))))))))))))))) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])).
% 215.80/215.63 % SZS output end Proof
%------------------------------------------------------------------------------