TSTP Solution File: SEU811^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU811^2 : 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 : n024.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 14:08:21 EDT 2022
% Result : Theorem 90.10s 89.84s
% Output : Proof 90.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU811^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 12:14:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 90.10/89.84 % SZS status Theorem
% 90.10/89.84 % Mode: mode484
% 90.10/89.84 % Inferences: 2630
% 90.10/89.84 % SZS output start Proof
% 90.10/89.84 thf(ty_eigen__1, type, eigen__1 : $i).
% 90.10/89.84 thf(ty_eigen__0, type, eigen__0 : $i).
% 90.10/89.84 thf(ty_omega, type, omega : $i).
% 90.10/89.84 thf(ty_in, type, in : ($i>$i>$o)).
% 90.10/89.84 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 90.10/89.84 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 90.10/89.84 thf(def_setadjoinE,definition,(setadjoinE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))).
% 90.10/89.84 thf(def_in__Cong,definition,(in__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))))).
% 90.10/89.84 thf(def_notinself2,definition,(notinself2 = (![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))))).
% 90.10/89.84 thf(def_omegaS,definition,(omegaS = (^[X1:$i]:((setadjoin @ X1) @ X1)))).
% 90.10/89.84 thf(peanoSinj,conjecture,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2))))))))))).
% 90.10/89.84 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2)))))))))))),inference(assume_negation,[status(cth)],[peanoSinj])).
% 90.10/89.84 thf(h1,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 90.10/89.84 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2))))))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h3,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2)))))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h5,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h6,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2))))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h7,assumption,(![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))),introduced(assumption,[])).
% 90.10/89.84 thf(h8,assumption,(~((![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2)))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h9,assumption,(~((((in @ eigen__0) @ omega) => (![X1:$i]:(((in @ X1) @ omega) => ((((setadjoin @ eigen__0) @ eigen__0) = ((setadjoin @ X1) @ X1)) => (eigen__0 = X1))))))),introduced(assumption,[])).
% 90.10/89.84 thf(h10,assumption,((in @ eigen__0) @ omega),introduced(assumption,[])).
% 90.10/89.84 thf(h11,assumption,(~((![X1:$i]:(((in @ X1) @ omega) => ((((setadjoin @ eigen__0) @ eigen__0) = ((setadjoin @ X1) @ X1)) => (eigen__0 = X1)))))),introduced(assumption,[])).
% 90.10/89.84 thf(h12,assumption,(~((((in @ eigen__1) @ omega) => ((((setadjoin @ eigen__0) @ eigen__0) = ((setadjoin @ eigen__1) @ eigen__1)) => (eigen__0 = eigen__1))))),introduced(assumption,[])).
% 90.10/89.84 thf(h13,assumption,((in @ eigen__1) @ omega),introduced(assumption,[])).
% 90.10/89.84 thf(h14,assumption,(~(((((setadjoin @ eigen__0) @ eigen__0) = ((setadjoin @ eigen__1) @ eigen__1)) => (eigen__0 = eigen__1)))),introduced(assumption,[])).
% 90.10/89.84 thf(h15,assumption,(((setadjoin @ eigen__0) @ eigen__0) = ((setadjoin @ eigen__1) @ eigen__1)),introduced(assumption,[])).
% 90.10/89.84 thf(h16,assumption,(~((eigen__0 = eigen__1))),introduced(assumption,[])).
% 90.10/89.84 thf(ax6715, axiom, (~(p5)|p22), file('<stdin>', ax6715)).
% 90.10/89.84 thf(ax6704, axiom, (~(p7)|p33), file('<stdin>', ax6704)).
% 90.10/89.84 thf(ax6705, axiom, (~(p7)|p32), file('<stdin>', ax6705)).
% 90.10/89.84 thf(ax6684, axiom, (~(p22)|p53), file('<stdin>', ax6684)).
% 90.10/89.84 thf(ax6734, axiom, p5, file('<stdin>', ax6734)).
% 90.10/89.84 thf(ax6629, axiom, (~(p33)|p108), file('<stdin>', ax6629)).
% 90.10/89.84 thf(ax6732, axiom, p7, file('<stdin>', ax6732)).
% 90.10/89.84 thf(ax6635, axiom, (~(p32)|p102), file('<stdin>', ax6635)).
% 90.10/89.84 thf(ax6699, axiom, (~(p8)|p38), file('<stdin>', ax6699)).
% 90.10/89.84 thf(ax6700, axiom, (~(p8)|p37), file('<stdin>', ax6700)).
% 90.10/89.84 thf(ax6723, axiom, (~(p10)|p16), file('<stdin>', ax6723)).
% 90.10/89.84 thf(pax4403, axiom, (p4403=>(((f__1)=(f__0)=>(f__0)=(f__1))=>((fin @ f__1 @ f__0=>(f__0)=(f__1))=>(f__0)=(f__1)))), file('<stdin>', pax4403)).
% 90.10/89.84 thf(ax6532, axiom, (~(p53)|~(p181)|~(p182)), file('<stdin>', ax6532)).
% 90.10/89.84 thf(nax1, axiom, (p1<=(f__0)=(f__1)), file('<stdin>', nax1)).
% 90.10/89.84 thf(ax6738, axiom, ~(p1), file('<stdin>', ax6738)).
% 90.10/89.84 thf(ax6349, axiom, (~(p108)|p316), file('<stdin>', ax6349)).
% 90.10/89.84 thf(ax6378, axiom, (~(p102)|p287), file('<stdin>', ax6378)).
% 90.10/89.84 thf(ax6604, axiom, (~(p38)|p133), file('<stdin>', ax6604)).
% 90.10/89.84 thf(ax6731, axiom, p8, file('<stdin>', ax6731)).
% 90.10/89.84 thf(ax6610, axiom, (~(p37)|p127), file('<stdin>', ax6610)).
% 90.10/89.84 thf(ax6722, axiom, (~(p16)|p17), file('<stdin>', ax6722)).
% 90.10/89.84 thf(ax6730, axiom, p10, file('<stdin>', ax6730)).
% 90.10/89.84 thf(nax182, axiom, (p182<=fin @ f__0 @ f__1), file('<stdin>', nax182)).
% 90.10/89.84 thf(nax181, axiom, (p181<=fin @ f__1 @ f__0), file('<stdin>', nax181)).
% 90.10/89.84 thf(pax4084, axiom, (p4084=>(((f__0)=(f__1)=>(f__0)=(f__1))=>((fin @ f__0 @ f__1=>(f__0)=(f__1))=>(f__0)=(f__1)))), file('<stdin>', pax4084)).
% 90.10/89.84 thf(ax4966, axiom, (~(p127)|p183|~(p179)|~(p15)), file('<stdin>', ax4966)).
% 90.10/89.84 thf(ax4820, axiom, (~(p133)|p176|~(p185)|~(p2)), file('<stdin>', ax4820)).
% 90.10/89.84 thf(ax5666, axiom, (~(p316)|~(p183)|p924), file('<stdin>', ax5666)).
% 90.10/89.84 thf(ax5695, axiom, (~(p287)|~(p176)|p875), file('<stdin>', ax5695)).
% 90.10/89.84 thf(ax6721, axiom, (~(p17)|~(p2)|p15), file('<stdin>', ax6721)).
% 90.10/89.84 thf(ax1833, axiom, (~(p924)|p4403), file('<stdin>', ax1833)).
% 90.10/89.84 thf(ax2152, axiom, (~(p875)|p4084), file('<stdin>', ax2152)).
% 90.10/89.84 thf(ax6521, axiom, p185, file('<stdin>', ax6521)).
% 90.10/89.84 thf(ax6536, axiom, p179, file('<stdin>', ax6536)).
% 90.10/89.84 thf(ax6737, axiom, p2, file('<stdin>', ax6737)).
% 90.10/89.84 thf(c_0_35, plain, (~p5|p22), inference(fof_simplification,[status(thm)],[ax6715])).
% 90.10/89.84 thf(c_0_36, plain, (~p7|p33), inference(fof_simplification,[status(thm)],[ax6704])).
% 90.10/89.84 thf(c_0_37, plain, (~p7|p32), inference(fof_simplification,[status(thm)],[ax6705])).
% 90.10/89.84 thf(c_0_38, plain, (~p22|p53), inference(fof_simplification,[status(thm)],[ax6684])).
% 90.10/89.84 thf(c_0_39, plain, (p22|~p5), inference(split_conjunct,[status(thm)],[c_0_35])).
% 90.10/89.84 thf(c_0_40, plain, p5, inference(split_conjunct,[status(thm)],[ax6734])).
% 90.10/89.84 thf(c_0_41, plain, (~p33|p108), inference(fof_simplification,[status(thm)],[ax6629])).
% 90.10/89.84 thf(c_0_42, plain, (p33|~p7), inference(split_conjunct,[status(thm)],[c_0_36])).
% 90.10/89.84 thf(c_0_43, plain, p7, inference(split_conjunct,[status(thm)],[ax6732])).
% 90.10/89.84 thf(c_0_44, plain, (~p32|p102), inference(fof_simplification,[status(thm)],[ax6635])).
% 90.10/89.84 thf(c_0_45, plain, (p32|~p7), inference(split_conjunct,[status(thm)],[c_0_37])).
% 90.10/89.84 thf(c_0_46, plain, (~p8|p38), inference(fof_simplification,[status(thm)],[ax6699])).
% 90.10/89.84 thf(c_0_47, plain, (~p8|p37), inference(fof_simplification,[status(thm)],[ax6700])).
% 90.10/89.84 thf(c_0_48, plain, (~p10|p16), inference(fof_simplification,[status(thm)],[ax6723])).
% 90.10/89.84 thf(c_0_49, plain, (((fin @ f__1 @ f__0|(f__0)=(f__1)|(f__1)=(f__0)|~p4403)&((f__0)!=(f__1)|(f__0)=(f__1)|(f__1)=(f__0)|~p4403))&((fin @ f__1 @ f__0|(f__0)=(f__1)|(f__0)!=(f__1)|~p4403)&((f__0)!=(f__1)|(f__0)=(f__1)|(f__0)!=(f__1)|~p4403))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4403])])).
% 90.10/89.84 thf(c_0_50, plain, (~p53|~p181|~p182), inference(fof_simplification,[status(thm)],[ax6532])).
% 90.10/89.84 thf(c_0_51, plain, (p53|~p22), inference(split_conjunct,[status(thm)],[c_0_38])).
% 90.10/89.84 thf(c_0_52, plain, p22, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 90.10/89.84 thf(c_0_53, plain, ((f__0)!=(f__1)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 90.10/89.84 thf(c_0_54, plain, ~p1, inference(fof_simplification,[status(thm)],[ax6738])).
% 90.10/89.84 thf(c_0_55, plain, (~p108|p316), inference(fof_simplification,[status(thm)],[ax6349])).
% 90.10/89.84 thf(c_0_56, plain, (p108|~p33), inference(split_conjunct,[status(thm)],[c_0_41])).
% 90.10/89.84 thf(c_0_57, plain, p33, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 90.10/89.84 thf(c_0_58, plain, (~p102|p287), inference(fof_simplification,[status(thm)],[ax6378])).
% 90.10/89.84 thf(c_0_59, plain, (p102|~p32), inference(split_conjunct,[status(thm)],[c_0_44])).
% 90.10/89.84 thf(c_0_60, plain, p32, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_43])])).
% 90.10/89.84 thf(c_0_61, plain, (~p38|p133), inference(fof_simplification,[status(thm)],[ax6604])).
% 90.10/89.84 thf(c_0_62, plain, (p38|~p8), inference(split_conjunct,[status(thm)],[c_0_46])).
% 90.10/89.84 thf(c_0_63, plain, p8, inference(split_conjunct,[status(thm)],[ax6731])).
% 90.10/89.84 thf(c_0_64, plain, (~p37|p127), inference(fof_simplification,[status(thm)],[ax6610])).
% 90.10/89.84 thf(c_0_65, plain, (p37|~p8), inference(split_conjunct,[status(thm)],[c_0_47])).
% 90.10/89.84 thf(c_0_66, plain, (~p16|p17), inference(fof_simplification,[status(thm)],[ax6722])).
% 90.10/89.84 thf(c_0_67, plain, (p16|~p10), inference(split_conjunct,[status(thm)],[c_0_48])).
% 90.10/89.84 thf(c_0_68, plain, p10, inference(split_conjunct,[status(thm)],[ax6730])).
% 90.10/89.84 thf(c_0_69, plain, (~fin @ f__0 @ f__1|p182), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax182])])).
% 90.10/89.84 thf(c_0_70, plain, (~fin @ f__1 @ f__0|p181), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax181])])).
% 90.10/89.84 thf(c_0_71, plain, ((fin @ f__0 @ f__1|(f__0)=(f__1)|~p4084)&((f__0)!=(f__1)|(f__0)=(f__1)|~p4084)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax4084])])])).
% 90.10/89.84 thf(c_0_72, plain, (fin @ f__1 @ f__0|(f__0)=(f__1)|(f__1)=(f__0)|~p4403), inference(split_conjunct,[status(thm)],[c_0_49])).
% 90.10/89.84 thf(c_0_73, plain, (~p127|p183|~p179|~p15), inference(fof_simplification,[status(thm)],[ax4966])).
% 90.10/89.84 thf(c_0_74, plain, (~p133|p176|~p185|~p2), inference(fof_simplification,[status(thm)],[ax4820])).
% 90.10/89.84 thf(c_0_75, plain, (~p316|~p183|p924), inference(fof_simplification,[status(thm)],[ax5666])).
% 90.10/89.84 thf(c_0_76, plain, (~p287|~p176|p875), inference(fof_simplification,[status(thm)],[ax5695])).
% 90.10/89.84 thf(c_0_77, plain, (~p17|~p2|p15), inference(fof_simplification,[status(thm)],[ax6721])).
% 90.10/89.84 thf(c_0_78, plain, (~p924|p4403), inference(fof_simplification,[status(thm)],[ax1833])).
% 90.10/89.84 thf(c_0_79, plain, (~p875|p4084), inference(fof_simplification,[status(thm)],[ax2152])).
% 90.10/89.84 thf(c_0_80, plain, (~p53|~p181|~p182), inference(split_conjunct,[status(thm)],[c_0_50])).
% 90.10/89.84 thf(c_0_81, plain, p53, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 90.10/89.84 thf(c_0_82, plain, (p1|(f__0)!=(f__1)), inference(split_conjunct,[status(thm)],[c_0_53])).
% 90.10/89.84 thf(c_0_83, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_54])).
% 90.10/89.84 thf(c_0_84, plain, (p316|~p108), inference(split_conjunct,[status(thm)],[c_0_55])).
% 90.10/89.84 thf(c_0_85, plain, p108, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 90.10/89.84 thf(c_0_86, plain, (p287|~p102), inference(split_conjunct,[status(thm)],[c_0_58])).
% 90.10/89.84 thf(c_0_87, plain, p102, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])).
% 90.10/89.84 thf(c_0_88, plain, (p133|~p38), inference(split_conjunct,[status(thm)],[c_0_61])).
% 90.10/89.84 thf(c_0_89, plain, p38, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 90.10/89.84 thf(c_0_90, plain, (p127|~p37), inference(split_conjunct,[status(thm)],[c_0_64])).
% 90.10/89.84 thf(c_0_91, plain, p37, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_63])])).
% 90.10/89.84 thf(c_0_92, plain, (p17|~p16), inference(split_conjunct,[status(thm)],[c_0_66])).
% 90.10/89.84 thf(c_0_93, plain, p16, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 90.10/89.84 thf(c_0_94, plain, (p182|~fin @ f__0 @ f__1), inference(split_conjunct,[status(thm)],[c_0_69])).
% 90.10/89.84 thf(c_0_95, plain, (p181|~fin @ f__1 @ f__0), inference(split_conjunct,[status(thm)],[c_0_70])).
% 90.10/89.84 thf(c_0_96, plain, (fin @ f__0 @ f__1|(f__0)=(f__1)|~p4084), inference(split_conjunct,[status(thm)],[c_0_71])).
% 90.10/89.84 thf(c_0_97, plain, ((f__0)=(f__1)|fin @ f__1 @ f__0|~p4403), inference(cn,[status(thm)],[c_0_72])).
% 90.10/89.84 thf(c_0_98, plain, (p183|~p127|~p179|~p15), inference(split_conjunct,[status(thm)],[c_0_73])).
% 90.10/89.84 thf(c_0_99, plain, (p176|~p133|~p185|~p2), inference(split_conjunct,[status(thm)],[c_0_74])).
% 90.10/89.84 thf(c_0_100, plain, (p924|~p316|~p183), inference(split_conjunct,[status(thm)],[c_0_75])).
% 90.10/89.84 thf(c_0_101, plain, (p875|~p287|~p176), inference(split_conjunct,[status(thm)],[c_0_76])).
% 90.10/89.84 thf(c_0_102, plain, (p15|~p17|~p2), inference(split_conjunct,[status(thm)],[c_0_77])).
% 90.10/89.84 thf(c_0_103, plain, (p4403|~p924), inference(split_conjunct,[status(thm)],[c_0_78])).
% 90.10/89.84 thf(c_0_104, plain, (p4084|~p875), inference(split_conjunct,[status(thm)],[c_0_79])).
% 90.10/89.84 thf(c_0_105, plain, (~p181|~p182), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 90.10/89.84 thf(c_0_106, plain, (f__0)!=(f__1), inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 90.10/89.84 thf(c_0_107, plain, p316, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])).
% 90.10/89.84 thf(c_0_108, plain, p287, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])])).
% 90.10/89.84 thf(c_0_109, plain, p133, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88, c_0_89])])).
% 90.10/89.84 thf(c_0_110, plain, p127, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])).
% 90.10/89.84 thf(c_0_111, plain, p17, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93])])).
% 90.10/89.84 thf(c_0_112, plain, p185, inference(split_conjunct,[status(thm)],[ax6521])).
% 90.10/89.84 thf(c_0_113, plain, p179, inference(split_conjunct,[status(thm)],[ax6536])).
% 90.10/89.84 thf(c_0_114, plain, p2, inference(split_conjunct,[status(thm)],[ax6737])).
% 90.10/89.84 thf(c_0_115, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_94, c_0_95, c_0_96, c_0_97, c_0_98, c_0_99, c_0_100, c_0_101, c_0_102, c_0_103, c_0_104, c_0_105, c_0_106, c_0_107, c_0_108, c_0_109, c_0_110, c_0_111, c_0_112, c_0_113, c_0_114]), ['proof']).
% 90.10/89.84 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[])).
% 90.10/89.84 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,1,h15,h16])).
% 90.10/89.84 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,2,h13,h14])).
% 90.10/89.84 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,3,h12])).
% 90.10/89.84 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11])).
% 90.10/89.84 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,5,h9])).
% 90.10/89.84 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8])).
% 90.10/89.84 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6])).
% 90.10/89.84 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,h3,h4])).
% 90.10/89.84 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2])).
% 90.10/89.84 thf(0,theorem,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))) => (![X1:$i]:(((in @ X1) @ omega) => (![X2:$i]:(((in @ X2) @ omega) => ((((setadjoin @ X1) @ X1) = ((setadjoin @ X2) @ X2)) => (X1 = X2)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])).
% 90.10/89.84 % SZS output end Proof
%------------------------------------------------------------------------------