%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU789^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : 300s
% DateTime : Thu Oct 9 02:50:00 PM UTC 2025
% Result : Theorem 116.12s 108.12s
% Output : Proof 116.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU789^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 20:52:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 116.12/108.12 % SZS status Theorem
% 116.12/108.12 % Mode: mode447
% 116.12/108.12 % Inferences: 28
% 116.12/108.12 % SZS output start Proof
% 116.12/108.12 thf(ty_subset, type, subset : ($i>$i>$o)).
% 116.12/108.12 thf(ty_breln1invset, type, breln1invset : ($i>$i>$i)).
% 116.12/108.12 thf(ty_eigen__1, type, eigen__1 : $i).
% 116.12/108.12 thf(ty_eigen__0, type, eigen__0 : $i).
% 116.12/108.12 thf(ty_breln1, type, breln1 : ($i>$i>$o)).
% 116.12/108.12 thf(ty_kpair, type, kpair : ($i>$i>$i)).
% 116.12/108.12 thf(ty_in, type, in : ($i>$i>$o)).
% 116.12/108.12 thf(def_setextsub,definition,(setextsub = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))))).
% 116.12/108.12 thf(def_subbreln1,definition,(subbreln1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))))).
% 116.12/108.12 thf(def_breln1invprop,definition,(breln1invprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))))).
% 116.12/108.12 thf(def_breln1invI,definition,(breln1invI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))))).
% 116.12/108.12 thf(def_breln1invE,definition,(breln1invE = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))))).
% 116.12/108.12 thf(woz2Ex,conjecture,((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))))))).
% 116.12/108.12 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2))))))))))))),inference(assume_negation,[status(cth)],[woz2Ex])).
% 116.12/108.12 thf(h1,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))),introduced(assumption,[])).
% 116.12/108.12 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h3,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2))))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))),introduced(assumption,[])).
% 116.12/108.12 thf(h6,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h7,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h8,assumption,(~(((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h9,assumption,(![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h10,assumption,(~((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h11,assumption,(~((![X1:$i]:(((breln1 @ eigen__0) @ X1) => (X1 = ((breln1invset @ eigen__0) @ ((breln1invset @ eigen__0) @ X1))))))),introduced(assumption,[])).
% 116.12/108.12 thf(h12,assumption,(~((((breln1 @ eigen__0) @ eigen__1) => (eigen__1 = ((breln1invset @ eigen__0) @ ((breln1invset @ eigen__0) @ eigen__1)))))),introduced(assumption,[])).
% 116.12/108.12 thf(h13,assumption,((breln1 @ eigen__0) @ eigen__1),introduced(assumption,[])).
% 116.12/108.12 thf(h14,assumption,(~((eigen__1 = ((breln1invset @ eigen__0) @ ((breln1invset @ eigen__0) @ eigen__1))))),introduced(assumption,[])).
% 116.12/108.12 thf(ax67, axiom, (~(p5)|p26), file('<stdin>', ax67)).
% 116.12/108.12 thf(ax62, axiom, (~(p6)|p31), file('<stdin>', ax62)).
% 116.12/108.12 thf(ax68, axiom, (~(p26)|p25), file('<stdin>', ax68)).
% 116.12/108.12 thf(ax89, axiom, p5, file('<stdin>', ax89)).
% 116.12/108.12 thf(ax10, axiom, (~(p31)|p88), file('<stdin>', ax10)).
% 116.12/108.12 thf(ax88, axiom, p6, file('<stdin>', ax88)).
% 116.12/108.12 thf(ax69, axiom, (~(p25)|~(p2)|p24), file('<stdin>', ax69)).
% 116.12/108.12 thf(ax25, axiom, (~(p26)|p73), file('<stdin>', ax25)).
% 116.12/108.12 thf(ax63, axiom, (~(p31)|p30), file('<stdin>', ax63)).
% 116.12/108.12 thf(ax11, axiom, (~(p88)|~(p72)|p87), file('<stdin>', ax11)).
% 116.12/108.12 thf(ax26, axiom, (~(p73)|~(p24)|p72), file('<stdin>', ax26)).
% 116.12/108.12 thf(ax92, axiom, p2, file('<stdin>', ax92)).
% 116.12/108.12 thf(ax53, axiom, (~(p7)|p42), file('<stdin>', ax53)).
% 116.12/108.12 thf(ax64, axiom, (~(p30)|~(p2)|p29), file('<stdin>', ax64)).
% 116.12/108.12 thf(ax54, axiom, (~(p42)|p41), file('<stdin>', ax54)).
% 116.12/108.12 thf(ax87, axiom, p7, file('<stdin>', ax87)).
% 116.12/108.12 thf(nax1, axiom, (p1<=(f__1)=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), file('<stdin>', nax1)).
% 116.12/108.12 thf(ax93, axiom, ~(p1), file('<stdin>', ax93)).
% 116.12/108.12 thf(ax20, axiom, (~(p29)|p78), file('<stdin>', ax20)).
% 116.12/108.12 thf(ax13, axiom, (~(p86)|~(p2)|p85), file('<stdin>', ax13)).
% 116.12/108.12 thf(ax12, axiom, (~(p87)|p86), file('<stdin>', ax12)).
% 116.12/108.12 thf(pax41, axiom, (p41=>(fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))=>(fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1=>(f__1)=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))))), file('<stdin>', pax41)).
% 116.12/108.12 thf(ax8, axiom, (~(p78)|~(p72)|p90), file('<stdin>', ax8)).
% 116.12/108.12 thf(nax40, axiom, (p40<=(fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1=>(f__1)=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)))), file('<stdin>', nax40)).
% 116.12/108.12 thf(ax56, axiom, (~(p40)|~(p38)|p1), file('<stdin>', ax56)).
% 116.12/108.12 thf(ax14, axiom, (~(p85)|~(p84)|p38), file('<stdin>', ax14)).
% 116.12/108.12 thf(pax39, axiom, (p39=>fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), file('<stdin>', pax39)).
% 116.12/108.12 thf(ax9, axiom, (~(p90)|~(p89)|p39), file('<stdin>', ax9)).
% 116.12/108.12 thf(pax3, axiom, (p3=>![X1:$i, X2:$i]:(fbreln1 @ X1 @ X2=>![X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X1=>(fin @ (fkpair @ X4 @ X3) @ (fbreln1invset @ X1 @ X2)=>fin @ (fkpair @ X3 @ X4) @ X2))))), file('<stdin>', pax3)).
% 116.12/108.12 thf(pax24, axiom, (p24=>fbreln1 @ f__0 @ (fbreln1invset @ f__0 @ f__1)), file('<stdin>', pax24)).
% 116.12/108.12 thf(ax91, axiom, p3, file('<stdin>', ax91)).
% 116.12/108.12 thf(nax84, axiom, (p84<=![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__0=>(fin @ (fkpair @ X1 @ X2) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))=>fin @ (fkpair @ X1 @ X2) @ f__1)))), file('<stdin>', nax84)).
% 116.12/108.12 thf(pax2, axiom, (p2=>fbreln1 @ f__0 @ f__1), file('<stdin>', pax2)).
% 116.12/108.12 thf(pax4, axiom, (p4=>![X1:$i, X2:$i]:(fbreln1 @ X1 @ X2=>![X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X1=>(fin @ (fkpair @ X3 @ X4) @ X2=>fin @ (fkpair @ X4 @ X3) @ (fbreln1invset @ X1 @ X2)))))), file('<stdin>', pax4)).
% 116.12/108.12 thf(nax89, axiom, (p89<=![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__0=>(fin @ (fkpair @ X1 @ X2) @ f__1=>fin @ (fkpair @ X1 @ X2) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)))))), file('<stdin>', nax89)).
% 116.12/108.12 thf(ax90, axiom, p4, file('<stdin>', ax90)).
% 116.12/108.12 thf(c_0_36, plain, (~p5|p26), inference(fof_simplification,[status(thm)],[ax67])).
% 116.12/108.12 thf(c_0_37, plain, (~p6|p31), inference(fof_simplification,[status(thm)],[ax62])).
% 116.12/108.12 thf(c_0_38, plain, (~p26|p25), inference(fof_simplification,[status(thm)],[ax68])).
% 116.12/108.12 thf(c_0_39, plain, (p26|~p5), inference(split_conjunct,[status(thm)],[c_0_36])).
% 116.12/108.12 thf(c_0_40, plain, p5, inference(split_conjunct,[status(thm)],[ax89])).
% 116.12/108.12 thf(c_0_41, plain, (~p31|p88), inference(fof_simplification,[status(thm)],[ax10])).
% 116.12/108.12 thf(c_0_42, plain, (p31|~p6), inference(split_conjunct,[status(thm)],[c_0_37])).
% 116.12/108.12 thf(c_0_43, plain, p6, inference(split_conjunct,[status(thm)],[ax88])).
% 116.12/108.12 thf(c_0_44, plain, (~p25|~p2|p24), inference(fof_simplification,[status(thm)],[ax69])).
% 116.12/108.12 thf(c_0_45, plain, (p25|~p26), inference(split_conjunct,[status(thm)],[c_0_38])).
% 116.12/108.12 thf(c_0_46, plain, p26, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 116.12/108.12 thf(c_0_47, plain, (~p26|p73), inference(fof_simplification,[status(thm)],[ax25])).
% 116.12/108.12 thf(c_0_48, plain, (~p31|p30), inference(fof_simplification,[status(thm)],[ax63])).
% 116.12/108.12 thf(c_0_49, plain, (~p88|~p72|p87), inference(fof_simplification,[status(thm)],[ax11])).
% 116.12/108.12 thf(c_0_50, plain, (p88|~p31), inference(split_conjunct,[status(thm)],[c_0_41])).
% 116.12/108.12 thf(c_0_51, plain, p31, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 116.12/108.12 thf(c_0_52, plain, (~p73|~p24|p72), inference(fof_simplification,[status(thm)],[ax26])).
% 116.12/108.12 thf(c_0_53, plain, (p24|~p25|~p2), inference(split_conjunct,[status(thm)],[c_0_44])).
% 116.12/108.12 thf(c_0_54, plain, p2, inference(split_conjunct,[status(thm)],[ax92])).
% 116.12/108.12 thf(c_0_55, plain, p25, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 116.12/108.12 thf(c_0_56, plain, (p73|~p26), inference(split_conjunct,[status(thm)],[c_0_47])).
% 116.12/108.12 thf(c_0_57, plain, (~p7|p42), inference(fof_simplification,[status(thm)],[ax53])).
% 116.12/108.12 thf(c_0_58, plain, (~p30|~p2|p29), inference(fof_simplification,[status(thm)],[ax64])).
% 116.12/108.12 thf(c_0_59, plain, (p30|~p31), inference(split_conjunct,[status(thm)],[c_0_48])).
% 116.12/108.12 thf(c_0_60, plain, (p87|~p88|~p72), inference(split_conjunct,[status(thm)],[c_0_49])).
% 116.12/108.12 thf(c_0_61, plain, p88, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
% 116.12/108.12 thf(c_0_62, plain, (p72|~p73|~p24), inference(split_conjunct,[status(thm)],[c_0_52])).
% 116.12/108.12 thf(c_0_63, plain, p24, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54]), c_0_55])])).
% 116.12/108.12 thf(c_0_64, plain, p73, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_46])])).
% 116.12/108.12 thf(c_0_65, plain, (~p42|p41), inference(fof_simplification,[status(thm)],[ax54])).
% 116.12/108.12 thf(c_0_66, plain, (p42|~p7), inference(split_conjunct,[status(thm)],[c_0_57])).
% 116.12/108.12 thf(c_0_67, plain, p7, inference(split_conjunct,[status(thm)],[ax87])).
% 116.12/108.12 thf(c_0_68, plain, ((f__1)!=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 116.12/108.12 thf(c_0_69, plain, ~p1, inference(fof_simplification,[status(thm)],[ax93])).
% 116.12/108.12 thf(c_0_70, plain, (~p29|p78), inference(fof_simplification,[status(thm)],[ax20])).
% 116.12/108.12 thf(c_0_71, plain, (p29|~p30|~p2), inference(split_conjunct,[status(thm)],[c_0_58])).
% 116.12/108.12 thf(c_0_72, plain, p30, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_51])])).
% 116.12/108.12 thf(c_0_73, plain, (~p86|~p2|p85), inference(fof_simplification,[status(thm)],[ax13])).
% 116.12/108.12 thf(c_0_74, plain, (~p87|p86), inference(fof_simplification,[status(thm)],[ax12])).
% 116.12/108.12 thf(c_0_75, plain, (p87|~p72), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 116.12/108.12 thf(c_0_76, plain, p72, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63]), c_0_64])])).
% 116.12/108.12 thf(c_0_77, plain, (~p41|(~fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|(~fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1|(f__1)=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))))), inference(fof_nnf,[status(thm)],[pax41])).
% 116.12/108.12 thf(c_0_78, plain, (p41|~p42), inference(split_conjunct,[status(thm)],[c_0_65])).
% 116.12/108.12 thf(c_0_79, plain, p42, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67])])).
% 116.12/108.12 thf(c_0_80, plain, (p1|(f__1)!=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), inference(split_conjunct,[status(thm)],[c_0_68])).
% 116.12/108.12 thf(c_0_81, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_69])).
% 116.12/108.12 thf(c_0_82, plain, (~p78|~p72|p90), inference(fof_simplification,[status(thm)],[ax8])).
% 116.12/108.12 thf(c_0_83, plain, (p78|~p29), inference(split_conjunct,[status(thm)],[c_0_70])).
% 116.12/108.12 thf(c_0_84, plain, p29, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_54]), c_0_72])])).
% 116.12/108.12 thf(c_0_85, plain, (p85|~p86|~p2), inference(split_conjunct,[status(thm)],[c_0_73])).
% 116.12/108.12 thf(c_0_86, plain, (p86|~p87), inference(split_conjunct,[status(thm)],[c_0_74])).
% 116.12/108.12 thf(c_0_87, plain, p87, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76])])).
% 116.12/108.12 thf(c_0_88, plain, ((f__1)=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|~p41|~fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|~fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1), inference(split_conjunct,[status(thm)],[c_0_77])).
% 116.12/108.12 thf(c_0_89, plain, p41, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_79])])).
% 116.12/108.12 thf(c_0_90, plain, (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))!=(f__1), inference(sr,[status(thm)],[c_0_80, c_0_81])).
% 116.12/108.12 thf(c_0_91, plain, ((fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1|p40)&((f__1)!=(fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|p40)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax40])])])).
% 116.12/108.12 thf(c_0_92, plain, (p90|~p78|~p72), inference(split_conjunct,[status(thm)],[c_0_82])).
% 116.12/108.12 thf(c_0_93, plain, p78, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])).
% 116.12/108.12 thf(c_0_94, plain, (~p40|~p38|p1), inference(fof_simplification,[status(thm)],[ax56])).
% 116.12/108.12 thf(c_0_95, plain, (~p85|~p84|p38), inference(fof_simplification,[status(thm)],[ax14])).
% 116.12/108.12 thf(c_0_96, plain, (p85|~p86), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_54])])).
% 116.12/108.12 thf(c_0_97, plain, p86, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])])).
% 116.12/108.12 thf(c_0_98, plain, (~fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|~fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88, c_0_89])]), c_0_90])).
% 116.12/108.12 thf(c_0_99, plain, (fsubset @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1)) @ f__1|p40), inference(split_conjunct,[status(thm)],[c_0_91])).
% 116.12/108.12 thf(c_0_100, plain, (~p39|fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), inference(fof_nnf,[status(thm)],[pax39])).
% 116.12/108.12 thf(c_0_101, plain, (~p90|~p89|p39), inference(fof_simplification,[status(thm)],[ax9])).
% 116.12/108.12 thf(c_0_102, plain, (p90|~p72), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93])])).
% 116.12/108.12 thf(c_0_103, plain, ![X274:$i, X275:$i, X276:$i, X277:$i]:(~p3|(~fbreln1 @ X274 @ X275|(~fin @ X276 @ X274|(~fin @ X277 @ X274|(~fin @ (fkpair @ X277 @ X276) @ (fbreln1invset @ X274 @ X275)|fin @ (fkpair @ X276 @ X277) @ X275))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])])).
% 116.12/108.12 thf(c_0_104, plain, (~p24|fbreln1 @ f__0 @ (fbreln1invset @ f__0 @ f__1)), inference(fof_nnf,[status(thm)],[pax24])).
% 116.12/108.12 thf(c_0_105, plain, (p1|~p40|~p38), inference(split_conjunct,[status(thm)],[c_0_94])).
% 116.12/108.12 thf(c_0_106, plain, (p38|~p85|~p84), inference(split_conjunct,[status(thm)],[c_0_95])).
% 116.12/108.12 thf(c_0_107, plain, p85, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])).
% 116.12/108.12 thf(c_0_108, plain, (p40|~fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), inference(spm,[status(thm)],[c_0_98, c_0_99])).
% 116.12/108.12 thf(c_0_109, plain, (fsubset @ f__1 @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|~p39), inference(split_conjunct,[status(thm)],[c_0_100])).
% 116.12/108.12 thf(c_0_110, plain, (p39|~p90|~p89), inference(split_conjunct,[status(thm)],[c_0_101])).
% 116.12/108.12 thf(c_0_111, plain, p90, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102, c_0_76])])).
% 116.12/108.12 thf(c_0_112, plain, ![X1:$i, X4:$i, X3:$i, X2:$i]:(fin @ (fkpair @ X3 @ X4) @ X2|~p3|~fbreln1 @ X1 @ X2|~fin @ X3 @ X1|~fin @ X4 @ X1|~fin @ (fkpair @ X4 @ X3) @ (fbreln1invset @ X1 @ X2)), inference(split_conjunct,[status(thm)],[c_0_103])).
% 116.12/108.12 thf(c_0_113, plain, p3, inference(split_conjunct,[status(thm)],[ax91])).
% 116.12/108.12 thf(c_0_114, plain, ((fin @ esk16_0 @ f__0|p84)&((fin @ esk17_0 @ f__0|p84)&((fin @ (fkpair @ esk16_0 @ esk17_0) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|p84)&(~fin @ (fkpair @ esk16_0 @ esk17_0) @ f__1|p84)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax84])])])])])).
% 116.12/108.12 thf(c_0_115, plain, (fbreln1 @ f__0 @ (fbreln1invset @ f__0 @ f__1)|~p24), inference(split_conjunct,[status(thm)],[c_0_104])).
% 116.12/108.12 thf(c_0_116, plain, (~p2|fbreln1 @ f__0 @ f__1), inference(fof_nnf,[status(thm)],[pax2])).
% 116.12/108.12 thf(c_0_117, plain, (~p38|~p40), inference(sr,[status(thm)],[c_0_105, c_0_81])).
% 116.12/108.12 thf(c_0_118, plain, (p38|~p84), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106, c_0_107])])).
% 116.12/108.12 thf(c_0_119, plain, (p40|~p39), inference(spm,[status(thm)],[c_0_108, c_0_109])).
% 116.12/108.12 thf(c_0_120, plain, (p39|~p89), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110, c_0_111])])).
% 116.12/108.12 thf(c_0_121, plain, ![X2:$i, X1:$i, X3:$i, X4:$i]:(fin @ (fkpair @ X1 @ X2) @ X3|~fin @ (fkpair @ X2 @ X1) @ (fbreln1invset @ X4 @ X3)|~fbreln1 @ X4 @ X3|~fin @ X2 @ X4|~fin @ X1 @ X4), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112, c_0_113])])).
% 116.12/108.12 thf(c_0_122, plain, (fin @ (fkpair @ esk16_0 @ esk17_0) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|p84), inference(split_conjunct,[status(thm)],[c_0_114])).
% 116.12/108.12 thf(c_0_123, plain, fbreln1 @ f__0 @ (fbreln1invset @ f__0 @ f__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115, c_0_63])])).
% 116.12/108.12 thf(c_0_124, plain, (fin @ esk17_0 @ f__0|p84), inference(split_conjunct,[status(thm)],[c_0_114])).
% 116.12/108.12 thf(c_0_125, plain, (fin @ esk16_0 @ f__0|p84), inference(split_conjunct,[status(thm)],[c_0_114])).
% 116.12/108.12 thf(c_0_126, plain, (fbreln1 @ f__0 @ f__1|~p2), inference(split_conjunct,[status(thm)],[c_0_116])).
% 116.12/108.12 thf(c_0_127, plain, (~p40|~p84), inference(spm,[status(thm)],[c_0_117, c_0_118])).
% 116.12/108.12 thf(c_0_128, plain, (p40|~p89), inference(spm,[status(thm)],[c_0_119, c_0_120])).
% 116.12/108.12 thf(c_0_129, plain, (fin @ (fkpair @ esk17_0 @ esk16_0) @ (fbreln1invset @ f__0 @ f__1)|p84), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122]), c_0_123])]), c_0_124]), c_0_125])).
% 116.12/108.12 thf(c_0_130, plain, fbreln1 @ f__0 @ f__1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126, c_0_54])])).
% 116.12/108.12 thf(c_0_131, plain, (p84|~fin @ (fkpair @ esk16_0 @ esk17_0) @ f__1), inference(split_conjunct,[status(thm)],[c_0_114])).
% 116.12/108.12 thf(c_0_132, plain, ![X266:$i, X267:$i, X268:$i, X269:$i]:(~p4|(~fbreln1 @ X266 @ X267|(~fin @ X268 @ X266|(~fin @ X269 @ X266|(~fin @ (fkpair @ X268 @ X269) @ X267|fin @ (fkpair @ X269 @ X268) @ (fbreln1invset @ X266 @ X267)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 116.12/108.12 thf(c_0_133, plain, ((fin @ esk4_0 @ f__0|p89)&((fin @ esk5_0 @ f__0|p89)&((fin @ (fkpair @ esk4_0 @ esk5_0) @ f__1|p89)&(~fin @ (fkpair @ esk4_0 @ esk5_0) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))|p89)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax89])])])])])).
% 116.12/108.12 thf(c_0_134, plain, (~p84|~p89), inference(spm,[status(thm)],[c_0_127, c_0_128])).
% 116.12/108.12 thf(c_0_135, plain, p84, inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_129]), c_0_130])]), c_0_125]), c_0_124]), c_0_131])).
% 116.12/108.12 thf(c_0_136, plain, ![X1:$i, X4:$i, X3:$i, X2:$i]:(fin @ (fkpair @ X4 @ X3) @ (fbreln1invset @ X1 @ X2)|~p4|~fbreln1 @ X1 @ X2|~fin @ X3 @ X1|~fin @ X4 @ X1|~fin @ (fkpair @ X3 @ X4) @ X2), inference(split_conjunct,[status(thm)],[c_0_132])).
% 116.12/108.12 thf(c_0_137, plain, p4, inference(split_conjunct,[status(thm)],[ax90])).
% 116.12/108.12 thf(c_0_138, plain, (fin @ esk4_0 @ f__0|p89), inference(split_conjunct,[status(thm)],[c_0_133])).
% 116.12/108.12 thf(c_0_139, plain, ~p89, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134, c_0_135])])).
% 116.12/108.12 thf(c_0_140, plain, (fin @ esk5_0 @ f__0|p89), inference(split_conjunct,[status(thm)],[c_0_133])).
% 116.12/108.12 thf(c_0_141, plain, (p89|~fin @ (fkpair @ esk4_0 @ esk5_0) @ (fbreln1invset @ f__0 @ (fbreln1invset @ f__0 @ f__1))), inference(split_conjunct,[status(thm)],[c_0_133])).
% 116.12/108.12 thf(c_0_142, plain, ![X1:$i, X2:$i, X4:$i, X3:$i]:(fin @ (fkpair @ X1 @ X2) @ (fbreln1invset @ X3 @ X4)|~fin @ (fkpair @ X2 @ X1) @ X4|~fbreln1 @ X3 @ X4|~fin @ X1 @ X3|~fin @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136, c_0_137])])).
% 116.12/108.12 thf(c_0_143, plain, fin @ esk4_0 @ f__0, inference(sr,[status(thm)],[c_0_138, c_0_139])).
% 116.12/108.12 thf(c_0_144, plain, fin @ esk5_0 @ f__0, inference(sr,[status(thm)],[c_0_140, c_0_139])).
% 116.12/108.12 thf(c_0_145, plain, (fin @ (fkpair @ esk4_0 @ esk5_0) @ f__1|p89), inference(split_conjunct,[status(thm)],[c_0_133])).
% 116.12/108.12 thf(c_0_146, plain, ~fin @ (fkpair @ esk5_0 @ esk4_0) @ (fbreln1invset @ f__0 @ f__1), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142]), c_0_123]), c_0_143]), c_0_144])]), c_0_139])).
% 116.12/108.12 thf(c_0_147, plain, fin @ (fkpair @ esk4_0 @ esk5_0) @ f__1, inference(sr,[status(thm)],[c_0_145, c_0_139])).
% 116.12/108.12 thf(c_0_148, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_142]), c_0_147]), c_0_130]), c_0_144]), c_0_143])]), ['proof']).
% 116.12/108.12 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[])).
% 116.12/108.12 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,1,h13,h14])).
% 116.12/108.12 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,2,h12])).
% 116.12/108.12 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h10,3,h11])).
% 116.12/108.12 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,4,h9,h10])).
% 116.12/108.12 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,5,h7,h8])).
% 116.12/108.12 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,6,h5,h6])).
% 116.12/108.12 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,7,h3,h4])).
% 116.12/108.12 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,8,h1,h2])).
% 116.12/108.12 thf(0,theorem,((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])).
% 116.12/108.12 % SZS output end Proof
%------------------------------------------------------------------------------