TSTP Solution File: SEU655^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU655^2 : 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 : n032.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 13:55:27 EDT 2022
% Result : Theorem 202.02s 200.16s
% Output : Proof 202.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU655^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 20 05:09:03 EDT 2022
% 0.16/0.31 % CPUTime :
% 202.02/200.16 % SZS status Theorem
% 202.02/200.16 % Mode: mode478
% 202.02/200.16 % Inferences: 529
% 202.02/200.16 % SZS output start Proof
% 202.02/200.16 thf(ty_kfst, type, kfst : ($i>$i)).
% 202.02/200.16 thf(ty_eigen__2, type, eigen__2 : $i).
% 202.02/200.16 thf(ty_setunion, type, setunion : ($i>$i)).
% 202.02/200.16 thf(ty_eigen__1, type, eigen__1 : $i).
% 202.02/200.16 thf(ty_eigen__0, type, eigen__0 : $i).
% 202.02/200.16 thf(ty_emptyset, type, emptyset : $i).
% 202.02/200.16 thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)).
% 202.02/200.16 thf(ty_in, type, in : ($i>$i>$o)).
% 202.02/200.16 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 202.02/200.16 thf(def_iskpair,definition,(iskpair = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))))))))))).
% 202.02/200.16 thf(def_kpair,definition,(kpair = (^[X1:$i]:(^[X2:$i]:((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))).
% 202.02/200.16 thf(def_singleton,definition,(singleton = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset))))))))))).
% 202.02/200.16 thf(def_ex1,definition,(ex1 = (^[X1:$i]:(^[X2:$i>$o]:(singleton @ ((dsetconstr @ X1) @ X2)))))).
% 202.02/200.16 thf(def_ex1I,definition,(ex1I = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))))).
% 202.02/200.16 thf(def_kfstpairEq,definition,(kfstpairEq = (![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))))).
% 202.02/200.16 thf(def_setukpairinjR,definition,(setukpairinjR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))))).
% 202.02/200.16 thf(ksndsingleton,conjecture,((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ X2)) => (~((((dsetconstr @ X1) @ X2) = ((setadjoin @ X4) @ emptyset)))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset)))))))))))))).
% 202.02/200.16 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ X2)) => (~((((dsetconstr @ X1) @ X2) = ((setadjoin @ X4) @ emptyset)))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset))))))))))))))),inference(assume_negation,[status(cth)],[ksndsingleton])).
% 202.02/200.16 thf(h1,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ X2)) => (~((((dsetconstr @ X1) @ X2) = ((setadjoin @ X4) @ emptyset)))))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset)))))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h3,assumption,(![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))),introduced(assumption,[])).
% 202.02/200.16 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset))))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))),introduced(assumption,[])).
% 202.02/200.16 thf(h6,assumption,(~((![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset)))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h7,assumption,(~(((~((![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (![X2:$i]:(((in @ X2) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))))))) => (~((![X1:$i]:(((in @ X1) @ ((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:(eigen__0 = ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:(eigen__0 = ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) = ((setadjoin @ X1) @ emptyset))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h8,assumption,(~((![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (![X2:$i]:(((in @ X2) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h9,assumption,(![X1:$i]:(((in @ X1) @ ((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:(eigen__0 = ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:(eigen__0 = ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ eigen__0)) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) = ((setadjoin @ X1) @ emptyset)))))),introduced(assumption,[])).
% 202.02/200.16 thf(h10,assumption,(~((((in @ eigen__1) @ (setunion @ eigen__0)) => (![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ X1) @ emptyset))) @ emptyset)))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h11,assumption,((in @ eigen__1) @ (setunion @ eigen__0)),introduced(assumption,[])).
% 202.02/200.16 thf(h12,assumption,(~((![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ X1) @ emptyset))) @ emptyset))))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h13,assumption,(~((((in @ eigen__2) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ eigen__2) @ emptyset))) @ emptyset)))))))),introduced(assumption,[])).
% 202.02/200.16 thf(h14,assumption,((in @ eigen__2) @ (setunion @ eigen__0)),introduced(assumption,[])).
% 202.02/200.16 thf(h15,assumption,(eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ eigen__2) @ emptyset))) @ emptyset))),introduced(assumption,[])).
% 202.02/200.16 thf(ax6378, axiom, (~(p7)|p62), file('<stdin>', ax6378)).
% 202.02/200.16 thf(ax6396, axiom, (~(p6)|p44), file('<stdin>', ax6396)).
% 202.02/200.16 thf(ax3430, axiom, (~(p22)|p2969), file('<stdin>', ax3430)).
% 202.02/200.16 thf(ax5936, axiom, (~(p62)|p517), file('<stdin>', ax5936)).
% 202.02/200.16 thf(ax6434, axiom, p7, file('<stdin>', ax6434)).
% 202.02/200.16 thf(ax6137, axiom, (~(p44)|p316), file('<stdin>', ax6137)).
% 202.02/200.16 thf(ax6435, axiom, p6, file('<stdin>', ax6435)).
% 202.02/200.16 thf(ax3429, axiom, (~(p2969)|p2970), file('<stdin>', ax3429)).
% 202.02/200.16 thf(ax6420, axiom, p22, file('<stdin>', ax6420)).
% 202.02/200.16 thf(ax89, axiom, (~(p517)|p6403), file('<stdin>', ax89)).
% 202.02/200.16 thf(pax2, axiom, (p2=>(f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), file('<stdin>', pax2)).
% 202.02/200.16 thf(ax3428, axiom, (~(p2970)|~(p316)|p2968), file('<stdin>', ax3428)).
% 202.02/200.16 thf(ax90, axiom, (~(p6403)|~(p3)|p6402), file('<stdin>', ax90)).
% 202.02/200.16 thf(pax2968, axiom, (p2968=>(f__1)=(fkfst @ (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset)))), file('<stdin>', pax2968)).
% 202.02/200.16 thf(ax6439, axiom, p2, file('<stdin>', ax6439)).
% 202.02/200.16 thf(ax91, axiom, (~(p6402)|~(p6400)|p6401), file('<stdin>', ax91)).
% 202.02/200.16 thf(ax6438, axiom, p3, file('<stdin>', ax6438)).
% 202.02/200.16 thf(nax6400, axiom, (p6400<=(f__0)=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), file('<stdin>', nax6400)).
% 202.02/200.16 thf(ax6409, axiom, (~(p5)|p31), file('<stdin>', ax6409)).
% 202.02/200.16 thf(ax92, axiom, (~(p6401)|~(p6399)|~(p1)), file('<stdin>', ax92)).
% 202.02/200.16 thf(ax6306, axiom, (~(p31)|p147), file('<stdin>', ax6306)).
% 202.02/200.16 thf(ax6436, axiom, p5, file('<stdin>', ax6436)).
% 202.02/200.16 thf(ax6440, axiom, p1, file('<stdin>', ax6440)).
% 202.02/200.16 thf(pax147, axiom, (p147=>![X1:$i, X2:$i]:((fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))=(fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))=>(f__2)=(X2))), file('<stdin>', pax147)).
% 202.02/200.16 thf(nax6399, axiom, (p6399<=![X1:$i]:(fin @ X1 @ (fsetunion @ f__0)=>((f__0)=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ X1 @ femptyset)) @ femptyset))=>(X1)=(f__2)))), file('<stdin>', nax6399)).
% 202.02/200.16 thf(c_0_25, plain, (~p7|p62), inference(fof_simplification,[status(thm)],[ax6378])).
% 202.02/200.16 thf(c_0_26, plain, (~p6|p44), inference(fof_simplification,[status(thm)],[ax6396])).
% 202.02/200.16 thf(c_0_27, plain, (~p22|p2969), inference(fof_simplification,[status(thm)],[ax3430])).
% 202.02/200.16 thf(c_0_28, plain, (~p62|p517), inference(fof_simplification,[status(thm)],[ax5936])).
% 202.02/200.16 thf(c_0_29, plain, (p62|~p7), inference(split_conjunct,[status(thm)],[c_0_25])).
% 202.02/200.16 thf(c_0_30, plain, p7, inference(split_conjunct,[status(thm)],[ax6434])).
% 202.02/200.16 thf(c_0_31, plain, (~p44|p316), inference(fof_simplification,[status(thm)],[ax6137])).
% 202.02/200.16 thf(c_0_32, plain, (p44|~p6), inference(split_conjunct,[status(thm)],[c_0_26])).
% 202.02/200.16 thf(c_0_33, plain, p6, inference(split_conjunct,[status(thm)],[ax6435])).
% 202.02/200.16 thf(c_0_34, plain, (~p2969|p2970), inference(fof_simplification,[status(thm)],[ax3429])).
% 202.02/200.16 thf(c_0_35, plain, (p2969|~p22), inference(split_conjunct,[status(thm)],[c_0_27])).
% 202.02/200.16 thf(c_0_36, plain, p22, inference(split_conjunct,[status(thm)],[ax6420])).
% 202.02/200.16 thf(c_0_37, plain, (~p517|p6403), inference(fof_simplification,[status(thm)],[ax89])).
% 202.02/200.16 thf(c_0_38, plain, (p517|~p62), inference(split_conjunct,[status(thm)],[c_0_28])).
% 202.02/200.16 thf(c_0_39, plain, p62, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 202.02/200.16 thf(c_0_40, plain, (~p2|(f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), inference(fof_nnf,[status(thm)],[pax2])).
% 202.02/200.16 thf(c_0_41, plain, (~p2970|~p316|p2968), inference(fof_simplification,[status(thm)],[ax3428])).
% 202.02/200.16 thf(c_0_42, plain, (p316|~p44), inference(split_conjunct,[status(thm)],[c_0_31])).
% 202.02/200.16 thf(c_0_43, plain, p44, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 202.02/200.16 thf(c_0_44, plain, (p2970|~p2969), inference(split_conjunct,[status(thm)],[c_0_34])).
% 202.02/200.16 thf(c_0_45, plain, p2969, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 202.02/200.16 thf(c_0_46, plain, (~p6403|~p3|p6402), inference(fof_simplification,[status(thm)],[ax90])).
% 202.02/200.16 thf(c_0_47, plain, (p6403|~p517), inference(split_conjunct,[status(thm)],[c_0_37])).
% 202.02/200.16 thf(c_0_48, plain, p517, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 202.02/200.16 thf(c_0_49, plain, (~p2968|(f__1)=(fkfst @ (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset)))), inference(fof_nnf,[status(thm)],[pax2968])).
% 202.02/200.16 thf(c_0_50, plain, ((f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))|~p2), inference(split_conjunct,[status(thm)],[c_0_40])).
% 202.02/200.16 thf(c_0_51, plain, p2, inference(split_conjunct,[status(thm)],[ax6439])).
% 202.02/200.16 thf(c_0_52, plain, (p2968|~p2970|~p316), inference(split_conjunct,[status(thm)],[c_0_41])).
% 202.02/200.16 thf(c_0_53, plain, p316, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 202.02/200.16 thf(c_0_54, plain, p2970, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45])])).
% 202.02/200.16 thf(c_0_55, plain, (~p6402|~p6400|p6401), inference(fof_simplification,[status(thm)],[ax91])).
% 202.02/200.16 thf(c_0_56, plain, (p6402|~p6403|~p3), inference(split_conjunct,[status(thm)],[c_0_46])).
% 202.02/200.16 thf(c_0_57, plain, p3, inference(split_conjunct,[status(thm)],[ax6438])).
% 202.02/200.16 thf(c_0_58, plain, p6403, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 202.02/200.16 thf(c_0_59, plain, ((f__0)!=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))|p6400), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6400])])).
% 202.02/200.16 thf(c_0_60, plain, ((f__1)=(fkfst @ (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset)))|~p2968), inference(split_conjunct,[status(thm)],[c_0_49])).
% 202.02/200.16 thf(c_0_61, plain, (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))=(f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
% 202.02/200.16 thf(c_0_62, plain, p2968, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53]), c_0_54])])).
% 202.02/200.16 thf(c_0_63, plain, (~p5|p31), inference(fof_simplification,[status(thm)],[ax6409])).
% 202.02/200.16 thf(c_0_64, plain, (~p6401|~p6399|~p1), inference(fof_simplification,[status(thm)],[ax92])).
% 202.02/200.16 thf(c_0_65, plain, (p6401|~p6402|~p6400), inference(split_conjunct,[status(thm)],[c_0_55])).
% 202.02/200.16 thf(c_0_66, plain, p6402, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57]), c_0_58])])).
% 202.02/200.16 thf(c_0_67, plain, (p6400|(f__0)!=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_59])).
% 202.02/200.16 thf(c_0_68, plain, (fkfst @ f__0)=(f__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61]), c_0_62])])).
% 202.02/200.16 thf(c_0_69, plain, (~p31|p147), inference(fof_simplification,[status(thm)],[ax6306])).
% 202.02/200.16 thf(c_0_70, plain, (p31|~p5), inference(split_conjunct,[status(thm)],[c_0_63])).
% 202.02/200.16 thf(c_0_71, plain, p5, inference(split_conjunct,[status(thm)],[ax6436])).
% 202.02/200.16 thf(c_0_72, plain, (~p6401|~p6399|~p1), inference(split_conjunct,[status(thm)],[c_0_64])).
% 202.02/200.16 thf(c_0_73, plain, p1, inference(split_conjunct,[status(thm)],[ax6440])).
% 202.02/200.16 thf(c_0_74, plain, (p6401|~p6400), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 202.02/200.16 thf(c_0_75, plain, p6400, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68]), c_0_68]), c_0_61])])).
% 202.02/200.16 thf(c_0_76, plain, ![X5503:$i, X5504:$i]:(~p147|((fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))!=(fsetadjoin @ (fsetadjoin @ X5503 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X5503 @ (fsetadjoin @ X5504 @ femptyset)) @ femptyset))|(f__2)=(X5504))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax147])])])).
% 202.02/200.16 thf(c_0_77, plain, (p147|~p31), inference(split_conjunct,[status(thm)],[c_0_69])).
% 202.02/200.16 thf(c_0_78, plain, p31, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70, c_0_71])])).
% 202.02/200.16 thf(c_0_79, plain, ((fin @ esk28_0 @ (fsetunion @ f__0)|p6399)&(((f__0)=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ esk28_0 @ femptyset)) @ femptyset))|p6399)&((esk28_0)!=(f__2)|p6399))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6399])])])])])).
% 202.02/200.16 thf(c_0_80, plain, (~p6399|~p6401), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73])])).
% 202.02/200.16 thf(c_0_81, plain, p6401, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])).
% 202.02/200.16 thf(c_0_82, plain, ![X1:$i, X2:$i]:((f__2)=(X2)|~p147|(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))!=(fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 202.02/200.16 thf(c_0_83, plain, p147, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77, c_0_78])])).
% 202.02/200.16 thf(c_0_84, plain, ((f__0)=(fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ femptyset) @ (fsetadjoin @ (fsetadjoin @ (fkfst @ f__0) @ (fsetadjoin @ esk28_0 @ femptyset)) @ femptyset))|p6399), inference(split_conjunct,[status(thm)],[c_0_79])).
% 202.02/200.16 thf(c_0_85, plain, ~p6399, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 202.02/200.16 thf(c_0_86, plain, (p6399|(esk28_0)!=(f__2)), inference(split_conjunct,[status(thm)],[c_0_79])).
% 202.02/200.16 thf(c_0_87, plain, ![X2:$i, X1:$i]:((f__2)=(X1)|(fsetadjoin @ (fsetadjoin @ X2 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ (fsetadjoin @ X1 @ femptyset)) @ femptyset))!=(f__0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82, c_0_61]), c_0_83])])).
% 202.02/200.16 thf(c_0_88, plain, (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ esk28_0 @ femptyset)) @ femptyset))=(f__0), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_68]), c_0_68]), c_0_85])).
% 202.02/200.16 thf(c_0_89, plain, (esk28_0)!=(f__2), inference(sr,[status(thm)],[c_0_86, c_0_85])).
% 202.02/200.16 thf(c_0_90, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89]), ['proof']).
% 202.02/200.16 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[])).
% 202.02/200.16 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,1,h14,h15])).
% 202.02/200.16 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,2,h13])).
% 202.02/200.16 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,3,h11,h12])).
% 202.02/200.16 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h8,4,h10])).
% 202.02/200.16 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,5,h8,h9])).
% 202.02/200.16 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,6,h7])).
% 202.02/200.16 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6])).
% 202.02/200.16 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,h3,h4])).
% 202.02/200.16 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2])).
% 202.02/200.16 thf(0,theorem,((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ X2)) => (~((((dsetconstr @ X1) @ X2) = ((setadjoin @ X4) @ emptyset)))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$i]:(((in @ X3) @ (setunion @ X1)) => (~((X1 = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))))))))) => (~((![X2:$i]:(((in @ X2) @ ((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)))))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:(X1 = ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ emptyset)) @ ((setadjoin @ ((setadjoin @ (kfst @ X1)) @ ((setadjoin @ X3) @ emptyset))) @ emptyset))))) = ((setadjoin @ X2) @ emptyset))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])).
% 202.02/200.16 % SZS output end Proof
%------------------------------------------------------------------------------