TSTP Solution File: SEU643^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU643^2 : 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 : 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 13:55:01 EDT 2022
% Result : Theorem 216.35s 215.65s
% Output : Proof 216.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU643^2 : 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 : n013.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 : Sun Jun 19 01:33:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 216.35/215.65 % SZS status Theorem
% 216.35/215.65 % Mode: mode447
% 216.35/215.65 % Inferences: 75
% 216.35/215.65 % SZS output start Proof
% 216.35/215.65 thf(ty_eigen__2, type, eigen__2 : $i).
% 216.35/215.65 thf(ty_setunion, type, setunion : ($i>$i)).
% 216.35/215.65 thf(ty_eigen__1, type, eigen__1 : $i).
% 216.35/215.65 thf(ty_eigen__0, type, eigen__0 : $i).
% 216.35/215.65 thf(ty_emptyset, type, emptyset : $i).
% 216.35/215.65 thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)).
% 216.35/215.65 thf(ty_in, type, in : ($i>$i>$o)).
% 216.35/215.65 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 216.35/215.65 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 216.35/215.65 thf(def_iskpair,definition,(iskpair = (^[X1:$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)))))))))))))).
% 216.35/215.65 thf(def_singleton,definition,(singleton = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset))))))))))).
% 216.35/215.65 thf(def_ex1,definition,(ex1 = (^[X1:$i]:(^[X2:$i>$o]:(singleton @ ((dsetconstr @ X1) @ X2)))))).
% 216.35/215.65 thf(def_ex1I,definition,(ex1I = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))))).
% 216.35/215.65 thf(def_setukpairinjL1,definition,(setukpairinjL1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))))).
% 216.35/215.65 thf(kfstsingleton,conjecture,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$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:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![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:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset)))))))))))))).
% 216.35/215.65 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![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]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$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]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset))))))))))))))),inference(assume_negation,[status(cth)],[kfstsingleton])).
% 216.35/215.65 thf(h1,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 216.35/215.65 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => (~((![X4:$i]:(((in @ X4) @ ((dsetconstr @ X1) @ X2)) => (~((((dsetconstr @ X1) @ X2) = ((setadjoin @ X4) @ emptyset)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![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:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset)))))))))))))),introduced(assumption,[])).
% 216.35/215.65 thf(h3,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,[])).
% 216.35/215.65 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$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]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset))))))))))))),introduced(assumption,[])).
% 216.35/215.65 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))),introduced(assumption,[])).
% 216.35/215.65 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:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset)))))))))))),introduced(assumption,[])).
% 216.35/215.65 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]:((in @ ((setadjoin @ X2) @ emptyset)) @ eigen__0)))) => (~((((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ eigen__0))) = ((setadjoin @ X1) @ emptyset))))))))))),introduced(assumption,[])).
% 216.35/215.65 thf(h8,assumption,(~((![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (![X2:$i]:(((in @ X2) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))))))),introduced(assumption,[])).
% 216.35/215.65 thf(h9,assumption,(![X1:$i]:(((in @ X1) @ ((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ eigen__0)))) => (~((((dsetconstr @ (setunion @ eigen__0)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ eigen__0))) = ((setadjoin @ X1) @ emptyset)))))),introduced(assumption,[])).
% 216.35/215.65 thf(h10,assumption,(~((((in @ eigen__1) @ (setunion @ eigen__0)) => (![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ X1) @ emptyset))) @ emptyset)))))))))),introduced(assumption,[])).
% 216.35/215.65 thf(h11,assumption,((in @ eigen__1) @ (setunion @ eigen__0)),introduced(assumption,[])).
% 216.35/215.65 thf(h12,assumption,(~((![X1:$i]:(((in @ X1) @ (setunion @ eigen__0)) => (~((eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ X1) @ emptyset))) @ emptyset))))))))),introduced(assumption,[])).
% 216.35/215.65 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,[])).
% 216.35/215.65 thf(h14,assumption,((in @ eigen__2) @ (setunion @ eigen__0)),introduced(assumption,[])).
% 216.35/215.65 thf(h15,assumption,(eigen__0 = ((setadjoin @ ((setadjoin @ eigen__1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ eigen__1) @ ((setadjoin @ eigen__2) @ emptyset))) @ emptyset))),introduced(assumption,[])).
% 216.35/215.65 thf(ax127, axiom, (~(p6)|p22), file('<stdin>', ax127)).
% 216.35/215.65 thf(ax128, axiom, (~(p22)|p21), file('<stdin>', ax128)).
% 216.35/215.65 thf(ax143, axiom, p6, file('<stdin>', ax143)).
% 216.35/215.65 thf(ax129, axiom, (~(p21)|p20), file('<stdin>', ax129)).
% 216.35/215.65 thf(ax130, axiom, (~(p20)|~(p4)|p19), file('<stdin>', ax130)).
% 216.35/215.65 thf(ax132, axiom, (~(p18)|~(p17)|~(p1)), file('<stdin>', ax132)).
% 216.35/215.65 thf(ax131, axiom, (~(p19)|~(p16)|p18), file('<stdin>', ax131)).
% 216.35/215.65 thf(ax145, axiom, p4, file('<stdin>', ax145)).
% 216.35/215.65 thf(pax7, axiom, (p7=>![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2)), file('<stdin>', pax7)).
% 216.35/215.65 thf(pax2, axiom, (p2=>(f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), file('<stdin>', pax2)).
% 216.35/215.65 thf(ax148, axiom, p1, file('<stdin>', ax148)).
% 216.35/215.65 thf(ax142, axiom, p7, file('<stdin>', ax142)).
% 216.35/215.65 thf(ax147, axiom, p2, file('<stdin>', ax147)).
% 216.35/215.65 thf(ax81, axiom, (p17|~(p69)), file('<stdin>', ax81)).
% 216.35/215.65 thf(nax16, axiom, (p16<=fin @ (fsetadjoin @ f__1 @ femptyset) @ f__0), file('<stdin>', nax16)).
% 216.35/215.65 thf(pax5, axiom, (p5=>![X1:$i, X2:$i, X3:$i]:(fin @ (fsetadjoin @ X3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))=>(X1)=(X3))), file('<stdin>', pax5)).
% 216.35/215.65 thf(nax69, axiom, (p69<=(fin @ f__3 @ (fsetunion @ f__0)=>(fin @ (fsetadjoin @ f__3 @ femptyset) @ f__0=>(f__3)=(f__1)))), file('<stdin>', nax69)).
% 216.35/215.65 thf(ax144, axiom, p5, file('<stdin>', ax144)).
% 216.35/215.65 thf(c_0_18, plain, (~p6|p22), inference(fof_simplification,[status(thm)],[ax127])).
% 216.35/215.65 thf(c_0_19, plain, (~p22|p21), inference(fof_simplification,[status(thm)],[ax128])).
% 216.35/215.65 thf(c_0_20, plain, (p22|~p6), inference(split_conjunct,[status(thm)],[c_0_18])).
% 216.35/215.65 thf(c_0_21, plain, p6, inference(split_conjunct,[status(thm)],[ax143])).
% 216.35/215.65 thf(c_0_22, plain, (~p21|p20), inference(fof_simplification,[status(thm)],[ax129])).
% 216.35/215.65 thf(c_0_23, plain, (p21|~p22), inference(split_conjunct,[status(thm)],[c_0_19])).
% 216.35/215.65 thf(c_0_24, plain, p22, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 216.35/215.65 thf(c_0_25, plain, (~p20|~p4|p19), inference(fof_simplification,[status(thm)],[ax130])).
% 216.35/215.65 thf(c_0_26, plain, (p20|~p21), inference(split_conjunct,[status(thm)],[c_0_22])).
% 216.35/215.65 thf(c_0_27, plain, p21, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 216.35/215.65 thf(c_0_28, plain, (~p18|~p17|~p1), inference(fof_simplification,[status(thm)],[ax132])).
% 216.35/215.65 thf(c_0_29, plain, (~p19|~p16|p18), inference(fof_simplification,[status(thm)],[ax131])).
% 216.35/215.65 thf(c_0_30, plain, (p19|~p20|~p4), inference(split_conjunct,[status(thm)],[c_0_25])).
% 216.35/215.65 thf(c_0_31, plain, p4, inference(split_conjunct,[status(thm)],[ax145])).
% 216.35/215.65 thf(c_0_32, plain, p20, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 216.35/215.65 thf(c_0_33, plain, ![X120:$i, X121:$i]:(~p7|fin @ X120 @ (fsetadjoin @ X120 @ X121)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])])).
% 216.35/215.65 thf(c_0_34, plain, (~p2|(f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))), inference(fof_nnf,[status(thm)],[pax2])).
% 216.35/215.65 thf(c_0_35, plain, (~p18|~p17|~p1), inference(split_conjunct,[status(thm)],[c_0_28])).
% 216.35/215.65 thf(c_0_36, plain, p1, inference(split_conjunct,[status(thm)],[ax148])).
% 216.35/215.65 thf(c_0_37, plain, (p18|~p19|~p16), inference(split_conjunct,[status(thm)],[c_0_29])).
% 216.35/215.65 thf(c_0_38, plain, p19, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_32])])).
% 216.35/215.65 thf(c_0_39, plain, ![X1:$i, X2:$i]:(fin @ X1 @ (fsetadjoin @ X1 @ X2)|~p7), inference(split_conjunct,[status(thm)],[c_0_33])).
% 216.35/215.65 thf(c_0_40, plain, p7, inference(split_conjunct,[status(thm)],[ax142])).
% 216.35/215.65 thf(c_0_41, plain, ((f__0)=(fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))|~p2), inference(split_conjunct,[status(thm)],[c_0_34])).
% 216.35/215.65 thf(c_0_42, plain, p2, inference(split_conjunct,[status(thm)],[ax147])).
% 216.35/215.65 thf(c_0_43, plain, (~p17|~p18), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 216.35/215.65 thf(c_0_44, plain, (p18|~p16), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 216.35/215.65 thf(c_0_45, plain, (p17|~p69), inference(fof_simplification,[status(thm)],[ax81])).
% 216.35/215.65 thf(c_0_46, plain, (~fin @ (fsetadjoin @ f__1 @ femptyset) @ f__0|p16), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax16])])).
% 216.35/215.65 thf(c_0_47, plain, ![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 216.35/215.65 thf(c_0_48, plain, (fsetadjoin @ (fsetadjoin @ f__1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__1 @ (fsetadjoin @ f__2 @ femptyset)) @ femptyset))=(f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 216.35/215.65 thf(c_0_49, plain, ![X124:$i, X125:$i, X126:$i]:(~p5|(~fin @ (fsetadjoin @ X126 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X124 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X124 @ (fsetadjoin @ X125 @ femptyset)) @ femptyset))|(X124)=(X126))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])])).
% 216.35/215.65 thf(c_0_50, plain, (~p17|~p16), inference(spm,[status(thm)],[c_0_43, c_0_44])).
% 216.35/215.65 thf(c_0_51, plain, (p17|~p69), inference(split_conjunct,[status(thm)],[c_0_45])).
% 216.35/215.65 thf(c_0_52, plain, (p16|~fin @ (fsetadjoin @ f__1 @ femptyset) @ f__0), inference(split_conjunct,[status(thm)],[c_0_46])).
% 216.35/215.65 thf(c_0_53, plain, fin @ (fsetadjoin @ f__1 @ femptyset) @ f__0, inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 216.35/215.65 thf(c_0_54, plain, ((fin @ f__3 @ (fsetunion @ f__0)|p69)&((fin @ (fsetadjoin @ f__3 @ femptyset) @ f__0|p69)&((f__3)!=(f__1)|p69))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax69])])])).
% 216.35/215.65 thf(c_0_55, plain, ![X1:$i, X2:$i, X3:$i]:((X2)=(X1)|~p5|~fin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset)) @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_49])).
% 216.35/215.65 thf(c_0_56, plain, p5, inference(split_conjunct,[status(thm)],[ax144])).
% 216.35/215.65 thf(c_0_57, plain, (~p16|~p69), inference(spm,[status(thm)],[c_0_50, c_0_51])).
% 216.35/215.65 thf(c_0_58, plain, p16, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 216.35/215.65 thf(c_0_59, plain, (p69|(f__3)!=(f__1)), inference(split_conjunct,[status(thm)],[c_0_54])).
% 216.35/215.65 thf(c_0_60, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(X2)|~fin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset)) @ femptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56])])).
% 216.35/215.65 thf(c_0_61, plain, (fin @ (fsetadjoin @ f__3 @ femptyset) @ f__0|p69), inference(split_conjunct,[status(thm)],[c_0_54])).
% 216.35/215.65 thf(c_0_62, plain, ~p69, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 216.35/215.65 thf(c_0_63, plain, ((f__3)!=(f__1)|~p16), inference(spm,[status(thm)],[c_0_57, c_0_59])).
% 216.35/215.65 thf(c_0_64, plain, ![X1:$i]:((X1)=(f__1)|~fin @ (fsetadjoin @ X1 @ femptyset) @ f__0), inference(spm,[status(thm)],[c_0_60, c_0_48])).
% 216.35/215.65 thf(c_0_65, plain, fin @ (fsetadjoin @ f__3 @ femptyset) @ f__0, inference(sr,[status(thm)],[c_0_61, c_0_62])).
% 216.35/215.65 thf(c_0_66, plain, (f__3)!=(f__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_58])])).
% 216.35/215.65 thf(c_0_67, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66]), ['proof']).
% 216.35/215.65 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[])).
% 216.35/215.65 thf(2,plain,$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])).
% 216.35/215.65 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,2,h13])).
% 216.35/215.65 thf(4,plain,$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])).
% 216.35/215.65 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h8,4,h10])).
% 216.35/215.65 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,5,h8,h9])).
% 216.35/215.65 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,6,h7])).
% 216.35/215.65 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6])).
% 216.35/215.65 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,h3,h4])).
% 216.35/215.65 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2])).
% 216.35/215.65 thf(0,theorem,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![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]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$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]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1)))) => (~((((dsetconstr @ (setunion @ X1)) @ (^[X3:$i]:((in @ ((setadjoin @ X3) @ emptyset)) @ X1))) = ((setadjoin @ X2) @ emptyset))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])).
% 216.35/215.65 % SZS output end Proof
%------------------------------------------------------------------------------