TSTP Solution File: SYO068^4.020 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO068^4.020 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 : Thu Jul 21 19:30:03 EDT 2022
% Result : Theorem 35.16s 35.52s
% Output : Proof 35.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO068^4.020 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 19:38:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 35.16/35.52 % SZS status Theorem
% 35.16/35.52 % Mode: mode466
% 35.16/35.52 % Inferences: 45036
% 35.16/35.52 % SZS output start Proof
% 35.16/35.52 thf(ty_p6, type, p6 : ($i>$o)).
% 35.16/35.52 thf(ty_p12, type, p12 : ($i>$o)).
% 35.16/35.52 thf(ty_p13, type, p13 : ($i>$o)).
% 35.16/35.52 thf(ty_p14, type, p14 : ($i>$o)).
% 35.16/35.52 thf(ty_eigen__0, type, eigen__0 : $i).
% 35.16/35.52 thf(ty_p3, type, p3 : ($i>$o)).
% 35.16/35.52 thf(ty_eigen__21, type, eigen__21 : $i).
% 35.16/35.52 thf(ty_p10, type, p10 : ($i>$o)).
% 35.16/35.52 thf(ty_p16, type, p16 : ($i>$o)).
% 35.16/35.52 thf(ty_p4, type, p4 : ($i>$o)).
% 35.16/35.52 thf(ty_p2, type, p2 : ($i>$o)).
% 35.16/35.52 thf(ty_irel, type, irel : ($i>$i>$o)).
% 35.16/35.52 thf(ty_p8, type, p8 : ($i>$o)).
% 35.16/35.52 thf(ty_p17, type, p17 : ($i>$o)).
% 35.16/35.52 thf(ty_p15, type, p15 : ($i>$o)).
% 35.16/35.52 thf(ty_p11, type, p11 : ($i>$o)).
% 35.16/35.52 thf(ty_p20, type, p20 : ($i>$o)).
% 35.16/35.52 thf(ty_p7, type, p7 : ($i>$o)).
% 35.16/35.52 thf(ty_p18, type, p18 : ($i>$o)).
% 35.16/35.52 thf(ty_p19, type, p19 : ($i>$o)).
% 35.16/35.52 thf(ty_p0, type, p0 : ($i>$o)).
% 35.16/35.52 thf(ty_p5, type, p5 : ($i>$o)).
% 35.16/35.52 thf(ty_p9, type, p9 : ($i>$o)).
% 35.16/35.52 thf(ty_p1, type, p1 : ($i>$o)).
% 35.16/35.52 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 35.16/35.52 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 35.16/35.52 thf(eigendef_eigen__21, definition, eigen__21 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p20 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__21])])).
% 35.16/35.52 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 35.16/35.52 thf(sP2,plain,sP2 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p16 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p15 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 35.16/35.52 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 35.16/35.52 thf(sP4,plain,sP4 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 35.16/35.52 thf(sP5,plain,sP5 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 35.16/35.52 thf(sP6,plain,sP6 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 35.16/35.52 thf(sP7,plain,sP7 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2)))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 35.16/35.52 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 35.16/35.52 thf(sP9,plain,sP9 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => sP6)),introduced(definition,[new_symbols(definition,[sP9])])).
% 35.16/35.52 thf(sP10,plain,sP10 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2))))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 35.16/35.52 thf(sP11,plain,sP11 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 35.16/35.52 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p18 @ X1))),introduced(definition,[new_symbols(definition,[sP12])])).
% 35.16/35.52 thf(sP13,plain,sP13 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 35.16/35.52 thf(sP14,plain,sP14 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))),introduced(definition,[new_symbols(definition,[sP14])])).
% 35.16/35.52 thf(sP15,plain,sP15 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))) => sP13),introduced(definition,[new_symbols(definition,[sP15])])).
% 35.16/35.52 thf(sP16,plain,sP16 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))))))),introduced(definition,[new_symbols(definition,[sP16])])).
% 35.16/35.52 thf(sP17,plain,sP17 <=> (((irel @ eigen__0) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP17])])).
% 35.16/35.52 thf(sP18,plain,sP18 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p20 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 35.16/35.52 thf(sP19,plain,sP19 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))),introduced(definition,[new_symbols(definition,[sP19])])).
% 35.16/35.52 thf(sP20,plain,sP20 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1)))),introduced(definition,[new_symbols(definition,[sP20])])).
% 35.16/35.52 thf(sP21,plain,sP21 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))) => sP12)),introduced(definition,[new_symbols(definition,[sP21])])).
% 35.16/35.52 thf(sP22,plain,sP22 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1)))),introduced(definition,[new_symbols(definition,[sP22])])).
% 35.16/35.52 thf(sP23,plain,sP23 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))))),introduced(definition,[new_symbols(definition,[sP23])])).
% 35.16/35.52 thf(sP24,plain,sP24 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))),introduced(definition,[new_symbols(definition,[sP24])])).
% 35.16/35.52 thf(sP25,plain,sP25 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))))))),introduced(definition,[new_symbols(definition,[sP25])])).
% 35.16/35.52 thf(sP26,plain,sP26 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1)))),introduced(definition,[new_symbols(definition,[sP26])])).
% 35.16/35.52 thf(sP27,plain,sP27 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP27])])).
% 35.16/35.52 thf(sP28,plain,sP28 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2)))))),introduced(definition,[new_symbols(definition,[sP28])])).
% 35.16/35.52 thf(sP29,plain,sP29 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))))),introduced(definition,[new_symbols(definition,[sP29])])).
% 35.16/35.52 thf(sP30,plain,sP30 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))))))),introduced(definition,[new_symbols(definition,[sP30])])).
% 35.16/35.52 thf(sP31,plain,sP31 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1)))),introduced(definition,[new_symbols(definition,[sP31])])).
% 35.16/35.52 thf(sP32,plain,sP32 <=> (p20 @ eigen__21),introduced(definition,[new_symbols(definition,[sP32])])).
% 35.16/35.52 thf(sP33,plain,sP33 <=> (((irel @ eigen__0) @ eigen__0) => sP20),introduced(definition,[new_symbols(definition,[sP33])])).
% 35.16/35.52 thf(sP34,plain,sP34 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2)))))),introduced(definition,[new_symbols(definition,[sP34])])).
% 35.16/35.52 thf(sP35,plain,sP35 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2)))))),introduced(definition,[new_symbols(definition,[sP35])])).
% 35.16/35.52 thf(sP36,plain,sP36 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))),introduced(definition,[new_symbols(definition,[sP36])])).
% 35.16/35.52 thf(sP37,plain,sP37 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p18 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p17 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP37])])).
% 35.16/35.52 thf(sP38,plain,sP38 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))) => sP28),introduced(definition,[new_symbols(definition,[sP38])])).
% 35.16/35.52 thf(sP39,plain,sP39 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))),introduced(definition,[new_symbols(definition,[sP39])])).
% 35.16/35.52 thf(sP40,plain,sP40 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1)))),introduced(definition,[new_symbols(definition,[sP40])])).
% 35.16/35.52 thf(sP41,plain,sP41 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))),introduced(definition,[new_symbols(definition,[sP41])])).
% 35.16/35.52 thf(sP42,plain,sP42 <=> (sP12 => sP7),introduced(definition,[new_symbols(definition,[sP42])])).
% 35.16/35.52 thf(sP43,plain,sP43 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))) => sP36),introduced(definition,[new_symbols(definition,[sP43])])).
% 35.16/35.52 thf(sP44,plain,sP44 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2)))))),introduced(definition,[new_symbols(definition,[sP44])])).
% 35.16/35.52 thf(sP45,plain,sP45 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2)))))),introduced(definition,[new_symbols(definition,[sP45])])).
% 35.16/35.52 thf(sP46,plain,sP46 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => sP14),introduced(definition,[new_symbols(definition,[sP46])])).
% 35.16/35.52 thf(sP47,plain,sP47 <=> (((irel @ eigen__0) @ eigen__0) => (sP12 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))))),introduced(definition,[new_symbols(definition,[sP47])])).
% 35.16/35.52 thf(sP48,plain,sP48 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))),introduced(definition,[new_symbols(definition,[sP48])])).
% 35.16/35.52 thf(sP49,plain,sP49 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p20 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))))))),introduced(definition,[new_symbols(definition,[sP49])])).
% 35.16/35.52 thf(sP50,plain,sP50 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2)))))),introduced(definition,[new_symbols(definition,[sP50])])).
% 35.16/35.52 thf(sP51,plain,sP51 <=> (((irel @ eigen__0) @ eigen__0) => (p0 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP51])])).
% 35.16/35.52 thf(sP52,plain,sP52 <=> (((irel @ eigen__0) @ eigen__0) => sP22),introduced(definition,[new_symbols(definition,[sP52])])).
% 35.16/35.52 thf(sP53,plain,sP53 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP53])])).
% 35.16/35.52 thf(sP54,plain,sP54 <=> (sP39 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1)))),introduced(definition,[new_symbols(definition,[sP54])])).
% 35.16/35.52 thf(sP55,plain,sP55 <=> (((irel @ eigen__0) @ eigen__0) => sP46),introduced(definition,[new_symbols(definition,[sP55])])).
% 35.16/35.52 thf(sP56,plain,sP56 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP56])])).
% 35.16/35.52 thf(sP57,plain,sP57 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP57])])).
% 35.16/35.52 thf(sP58,plain,sP58 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))) => sP41),introduced(definition,[new_symbols(definition,[sP58])])).
% 35.16/35.52 thf(sP59,plain,sP59 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p20 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1)))),introduced(definition,[new_symbols(definition,[sP59])])).
% 35.16/35.52 thf(sP60,plain,sP60 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p14 @ X1))),introduced(definition,[new_symbols(definition,[sP60])])).
% 35.16/35.52 thf(sP61,plain,sP61 <=> (((irel @ eigen__0) @ eigen__0) => (sP24 => sP19)),introduced(definition,[new_symbols(definition,[sP61])])).
% 35.16/35.52 thf(sP62,plain,sP62 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => sP56),introduced(definition,[new_symbols(definition,[sP62])])).
% 35.16/35.52 thf(sP63,plain,sP63 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))),introduced(definition,[new_symbols(definition,[sP63])])).
% 35.16/35.52 thf(sP64,plain,sP64 <=> (((irel @ eigen__0) @ eigen__0) => (sP19 => sP60)),introduced(definition,[new_symbols(definition,[sP64])])).
% 35.16/35.52 thf(sP65,plain,sP65 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p13 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p12 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP65])])).
% 35.16/35.52 thf(sP66,plain,sP66 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))))))),introduced(definition,[new_symbols(definition,[sP66])])).
% 35.16/35.52 thf(sP67,plain,sP67 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP67])])).
% 35.16/35.52 thf(sP68,plain,sP68 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p15 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p14 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP68])])).
% 35.16/35.52 thf(sP69,plain,sP69 <=> (sP14 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP69])])).
% 35.16/35.52 thf(sP70,plain,sP70 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))))),introduced(definition,[new_symbols(definition,[sP70])])).
% 35.16/35.52 thf(sP71,plain,sP71 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))),introduced(definition,[new_symbols(definition,[sP71])])).
% 35.16/35.52 thf(sP72,plain,sP72 <=> (((irel @ eigen__0) @ eigen__0) => sP31),introduced(definition,[new_symbols(definition,[sP72])])).
% 35.16/35.52 thf(sP73,plain,sP73 <=> (((irel @ eigen__0) @ eigen__0) => sP54),introduced(definition,[new_symbols(definition,[sP73])])).
% 35.16/35.52 thf(sP74,plain,sP74 <=> (sP60 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1)))),introduced(definition,[new_symbols(definition,[sP74])])).
% 35.16/35.52 thf(sP75,plain,sP75 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))),introduced(definition,[new_symbols(definition,[sP75])])).
% 35.16/35.52 thf(sP76,plain,sP76 <=> (((irel @ eigen__0) @ eigen__0) => (sP14 => sP63)),introduced(definition,[new_symbols(definition,[sP76])])).
% 35.16/35.52 thf(sP77,plain,sP77 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p9 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p8 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP77])])).
% 35.16/35.52 thf(sP78,plain,sP78 <=> (sP19 => sP60),introduced(definition,[new_symbols(definition,[sP78])])).
% 35.16/35.52 thf(sP79,plain,sP79 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP79])])).
% 35.16/35.52 thf(sP80,plain,sP80 <=> (sP39 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP80])])).
% 35.16/35.52 thf(sP81,plain,sP81 <=> (sP14 => sP63),introduced(definition,[new_symbols(definition,[sP81])])).
% 35.16/35.52 thf(sP82,plain,sP82 <=> (((irel @ eigen__0) @ eigen__0) => sP26),introduced(definition,[new_symbols(definition,[sP82])])).
% 35.16/35.52 thf(sP83,plain,sP83 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p7 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP83])])).
% 35.16/35.52 thf(sP84,plain,sP84 <=> (sP60 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))))))),introduced(definition,[new_symbols(definition,[sP84])])).
% 35.16/35.52 thf(sP85,plain,sP85 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP85])])).
% 35.16/35.52 thf(sP86,plain,sP86 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))),introduced(definition,[new_symbols(definition,[sP86])])).
% 35.16/35.52 thf(sP87,plain,sP87 <=> (sP36 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))))))),introduced(definition,[new_symbols(definition,[sP87])])).
% 35.16/35.52 thf(sP88,plain,sP88 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p20 @ X1))),introduced(definition,[new_symbols(definition,[sP88])])).
% 35.16/35.52 thf(sP89,plain,sP89 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p17 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p16 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP89])])).
% 35.16/35.52 thf(sP90,plain,sP90 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p12 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p11 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP90])])).
% 35.16/35.52 thf(sP91,plain,sP91 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p20 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p19 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP91])])).
% 35.16/35.52 thf(sP92,plain,sP92 <=> (sP71 => sP12),introduced(definition,[new_symbols(definition,[sP92])])).
% 35.16/35.52 thf(sP93,plain,sP93 <=> (sP71 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2))))))),introduced(definition,[new_symbols(definition,[sP93])])).
% 35.16/35.52 thf(sP94,plain,sP94 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))),introduced(definition,[new_symbols(definition,[sP94])])).
% 35.16/35.52 thf(sP95,plain,sP95 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p19 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p18 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP95])])).
% 35.16/35.52 thf(sP96,plain,sP96 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))),introduced(definition,[new_symbols(definition,[sP96])])).
% 35.16/35.52 thf(sP97,plain,sP97 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP97])])).
% 35.16/35.52 thf(sP98,plain,sP98 <=> (sP94 => sP44),introduced(definition,[new_symbols(definition,[sP98])])).
% 35.16/35.52 thf(sP99,plain,sP99 <=> (sP41 => sP96),introduced(definition,[new_symbols(definition,[sP99])])).
% 35.16/35.52 thf(sP100,plain,sP100 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))),introduced(definition,[new_symbols(definition,[sP100])])).
% 35.16/35.52 thf(sP101,plain,sP101 <=> (((irel @ eigen__0) @ eigen__0) => sP40),introduced(definition,[new_symbols(definition,[sP101])])).
% 35.16/35.52 thf(sP102,plain,sP102 <=> (sP12 => sP86),introduced(definition,[new_symbols(definition,[sP102])])).
% 35.16/35.52 thf(sP103,plain,sP103 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2)))))),introduced(definition,[new_symbols(definition,[sP103])])).
% 35.16/35.52 thf(sP104,plain,sP104 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))) => sP45),introduced(definition,[new_symbols(definition,[sP104])])).
% 35.16/35.52 thf(sP105,plain,sP105 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP105])])).
% 35.16/35.52 thf(sP106,plain,sP106 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p8 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p7 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP106])])).
% 35.16/35.52 thf(sP107,plain,sP107 <=> (sP24 => sP19),introduced(definition,[new_symbols(definition,[sP107])])).
% 35.16/35.52 thf(sP108,plain,sP108 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2)))))),introduced(definition,[new_symbols(definition,[sP108])])).
% 35.16/35.52 thf(sP109,plain,sP109 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP109])])).
% 35.16/35.52 thf(sP110,plain,sP110 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p11 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p10 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP110])])).
% 35.16/35.52 thf(sP111,plain,sP111 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))),introduced(definition,[new_symbols(definition,[sP111])])).
% 35.16/35.52 thf(sP112,plain,sP112 <=> (((irel @ eigen__0) @ eigen__21) => sP32),introduced(definition,[new_symbols(definition,[sP112])])).
% 35.16/35.52 thf(sP113,plain,sP113 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p10 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p9 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP113])])).
% 35.16/35.52 thf(sP114,plain,sP114 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2)))))),introduced(definition,[new_symbols(definition,[sP114])])).
% 35.16/35.52 thf(sP115,plain,sP115 <=> (sP109 => sP74),introduced(definition,[new_symbols(definition,[sP115])])).
% 35.16/35.52 thf(sP116,plain,sP116 <=> (sP109 => sP99),introduced(definition,[new_symbols(definition,[sP116])])).
% 35.16/35.52 thf(sP117,plain,sP117 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2)))))),introduced(definition,[new_symbols(definition,[sP117])])).
% 35.16/35.52 thf(sP118,plain,sP118 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2)))))),introduced(definition,[new_symbols(definition,[sP118])])).
% 35.16/35.52 thf(sP119,plain,sP119 <=> ((!!) @ p20),introduced(definition,[new_symbols(definition,[sP119])])).
% 35.16/35.52 thf(sP120,plain,sP120 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP120])])).
% 35.16/35.52 thf(sP121,plain,sP121 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2)))))),introduced(definition,[new_symbols(definition,[sP121])])).
% 35.16/35.52 thf(sP122,plain,sP122 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP122])])).
% 35.16/35.52 thf(sP123,plain,sP123 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))) => sP100),introduced(definition,[new_symbols(definition,[sP123])])).
% 35.16/35.52 thf(sP124,plain,sP124 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))),introduced(definition,[new_symbols(definition,[sP124])])).
% 35.16/35.52 thf(sP125,plain,sP125 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p14 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p13 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP125])])).
% 35.16/35.52 thf(sP126,plain,sP126 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP126])])).
% 35.16/35.52 thf(sP127,plain,sP127 <=> (sP24 => sP50),introduced(definition,[new_symbols(definition,[sP127])])).
% 35.16/35.52 thf(sP128,plain,sP128 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2)))))),introduced(definition,[new_symbols(definition,[sP128])])).
% 35.16/35.52 thf(sP129,plain,sP129 <=> (sP57 => sP6),introduced(definition,[new_symbols(definition,[sP129])])).
% 35.16/35.52 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 35.16/35.52 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 35.16/35.52 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 35.16/35.52 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 35.16/35.52 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 35.16/35.52 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 35.16/35.52 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 35.16/35.52 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 35.16/35.52 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 35.16/35.52 thf(def_iand,definition,(iand = mand)).
% 35.16/35.52 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 35.16/35.52 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 35.16/35.52 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 35.16/35.52 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 35.16/35.52 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 35.16/35.52 thf(def_ivalid,definition,(ivalid = (!!))).
% 35.16/35.52 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 35.16/35.52 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 35.16/35.52 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 35.16/35.52 thf(con,conjecture,sP97).
% 35.16/35.52 thf(h1,negated_conjecture,(~(sP97)),inference(assume_negation,[status(cth)],[con])).
% 35.16/35.52 thf(1,plain,(~(sP119) | sP32),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(2,plain,(sP112 | ~(sP32)),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(3,plain,(sP88 | ~(sP112)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__21])).
% 35.16/35.52 thf(4,plain,((~(sP18) | ~(sP109)) | sP59),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(5,plain,((~(sP21) | ~(sP109)) | sP92),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(6,plain,((~(sP47) | ~(sP109)) | sP102),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(7,plain,((~(sP33) | ~(sP109)) | sP20),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(8,plain,((~(sP61) | ~(sP109)) | sP107),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(9,plain,((~(sP64) | ~(sP109)) | sP78),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(10,plain,((~(sP115) | ~(sP109)) | sP74),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(11,plain,((~(sP17) | ~(sP109)) | sP3),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(12,plain,((~(sP29) | ~(sP109)) | sP58),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(13,plain,((~(sP116) | ~(sP109)) | sP99),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(14,plain,((~(sP101) | ~(sP109)) | sP40),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(15,plain,((~(sP23) | ~(sP109)) | sP43),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(16,plain,((~(sP82) | ~(sP109)) | sP26),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(17,plain,((~(sP52) | ~(sP109)) | sP22),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(18,plain,((~(sP70) | ~(sP109)) | sP123),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(19,plain,((~(sP55) | ~(sP109)) | sP46),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(20,plain,((~(sP76) | ~(sP109)) | sP81),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(21,plain,((~(sP72) | ~(sP109)) | sP31),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(22,plain,((~(sP73) | ~(sP109)) | sP54),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(23,plain,((~(sP9) | ~(sP109)) | sP129),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(24,plain,((~(sP51) | ~(sP109)) | sP120),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(25,plain,(~(sP6) | sP51),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(26,plain,((~(sP129) | ~(sP57)) | sP6),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(27,plain,((~(sP54) | ~(sP39)) | sP57),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(28,plain,((~(sP31) | ~(sP63)) | sP39),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(29,plain,((~(sP81) | ~(sP14)) | sP63),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(30,plain,((~(sP46) | ~(sP100)) | sP14),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(31,plain,((~(sP123) | ~(sP124)) | sP100),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(32,plain,((~(sP22) | ~(sP75)) | sP124),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(33,plain,((~(sP26) | ~(sP36)) | sP75),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(34,plain,((~(sP43) | ~(sP48)) | sP36),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(35,plain,((~(sP40) | ~(sP96)) | sP48),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(36,plain,((~(sP99) | ~(sP41)) | sP96),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(37,plain,((~(sP58) | ~(sP111)) | sP41),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(38,plain,((~(sP3) | ~(sP94)) | sP111),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(39,plain,((~(sP74) | ~(sP60)) | sP94),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(40,plain,((~(sP78) | ~(sP19)) | sP60),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(41,plain,((~(sP107) | ~(sP24)) | sP19),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(42,plain,((~(sP20) | ~(sP86)) | sP24),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(43,plain,((~(sP102) | ~(sP12)) | sP86),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(44,plain,((~(sP92) | ~(sP71)) | sP12),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(45,plain,((~(sP59) | ~(sP88)) | sP71),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(46,plain,(~(sP67) | sP9),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(47,plain,((~(sP10) | ~(sP57)) | sP67),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(48,plain,(~(sP126) | sP73),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(49,plain,((~(sP80) | ~(sP39)) | sP126),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(50,plain,(~(sP56) | sP72),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(51,plain,((~(sP62) | ~(sP63)) | sP56),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(52,plain,(~(sP122) | sP76),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(53,plain,((~(sP69) | ~(sP14)) | sP122),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(54,plain,(~(sP85) | sP55),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(55,plain,((~(sP66) | ~(sP100)) | sP85),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(56,plain,(~(sP121) | sP70),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(57,plain,((~(sP8) | ~(sP124)) | sP121),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(58,plain,(~(sP35) | sP52),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(59,plain,((~(sP25) | ~(sP75)) | sP35),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(60,plain,(~(sP128) | sP82),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(61,plain,((~(sP87) | ~(sP36)) | sP128),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(62,plain,(~(sP13) | sP23),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(63,plain,((~(sP15) | ~(sP48)) | sP13),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(64,plain,(~(sP34) | sP101),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(65,plain,((~(sP16) | ~(sP96)) | sP34),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(66,plain,(~(sP28) | sP116),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(67,plain,((~(sP38) | ~(sP41)) | sP28),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(68,plain,(~(sP45) | sP29),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(69,plain,((~(sP104) | ~(sP111)) | sP45),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(70,plain,(~(sP44) | sP17),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(71,plain,((~(sP98) | ~(sP94)) | sP44),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(72,plain,(~(sP108) | sP115),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(73,plain,((~(sP84) | ~(sP60)) | sP108),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(74,plain,(~(sP114) | sP64),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(75,plain,((~(sP4) | ~(sP19)) | sP114),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(76,plain,(~(sP50) | sP61),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(77,plain,((~(sP127) | ~(sP24)) | sP50),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(78,plain,(~(sP118) | sP33),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(79,plain,((~(sP30) | ~(sP86)) | sP118),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(80,plain,(~(sP7) | sP47),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(81,plain,((~(sP42) | ~(sP12)) | sP7),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(82,plain,(~(sP117) | sP21),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(83,plain,((~(sP93) | ~(sP71)) | sP117),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(84,plain,(~(sP103) | sP18),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(85,plain,((~(sP49) | ~(sP88)) | sP103),inference(prop_rule,[status(thm)],[])).
% 35.16/35.52 thf(86,plain,(~(sP91) | sP49),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(87,plain,(~(sP95) | sP93),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(88,plain,(~(sP37) | sP42),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(89,plain,(~(sP89) | sP30),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(90,plain,(~(sP2) | sP127),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(91,plain,(~(sP68) | sP4),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(92,plain,(~(sP125) | sP84),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(93,plain,(~(sP65) | sP98),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(94,plain,(~(sP90) | sP104),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(95,plain,(~(sP110) | sP38),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(96,plain,(~(sP113) | sP16),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(97,plain,(~(sP77) | sP15),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(98,plain,(~(sP106) | sP87),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(99,plain,(~(sP83) | sP25),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(100,plain,(~(sP11) | sP8),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(101,plain,(~(sP79) | sP66),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(102,plain,(~(sP105) | sP69),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(103,plain,(~(sP5) | sP62),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(104,plain,(~(sP53) | sP80),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(105,plain,(~(sP27) | sP10),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(106,plain,(~(sP1) | sP109),inference(all_rule,[status(thm)],[])).
% 35.16/35.52 thf(107,plain,(sP97 | ~(sP120)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 35.16/35.52 thf(axiom21,axiom,(ivalid @ ((iimplies @ (iatom @ p20)) @ ((iimplies @ (iatom @ p20)) @ (iatom @ p19))))).
% 35.16/35.52 thf(108,plain,sP91,inference(preprocess,[status(thm)],[axiom21]).
% 35.16/35.52 thf(axiom20,axiom,(ivalid @ ((iimplies @ (iatom @ p19)) @ ((iimplies @ (iatom @ p19)) @ (iatom @ p18))))).
% 35.16/35.52 thf(109,plain,sP95,inference(preprocess,[status(thm)],[axiom20]).
% 35.16/35.52 thf(axiom19,axiom,(ivalid @ ((iimplies @ (iatom @ p18)) @ ((iimplies @ (iatom @ p18)) @ (iatom @ p17))))).
% 35.16/35.52 thf(110,plain,sP37,inference(preprocess,[status(thm)],[axiom19]).
% 35.16/35.52 thf(axiom18,axiom,(ivalid @ ((iimplies @ (iatom @ p17)) @ ((iimplies @ (iatom @ p17)) @ (iatom @ p16))))).
% 35.16/35.52 thf(111,plain,sP89,inference(preprocess,[status(thm)],[axiom18]).
% 35.16/35.52 thf(axiom17,axiom,(ivalid @ ((iimplies @ (iatom @ p16)) @ ((iimplies @ (iatom @ p16)) @ (iatom @ p15))))).
% 35.16/35.52 thf(112,plain,sP2,inference(preprocess,[status(thm)],[axiom17]).
% 35.16/35.52 thf(axiom16,axiom,(ivalid @ ((iimplies @ (iatom @ p15)) @ ((iimplies @ (iatom @ p15)) @ (iatom @ p14))))).
% 35.16/35.52 thf(113,plain,sP68,inference(preprocess,[status(thm)],[axiom16]).
% 35.16/35.52 thf(axiom15,axiom,(ivalid @ ((iimplies @ (iatom @ p14)) @ ((iimplies @ (iatom @ p14)) @ (iatom @ p13))))).
% 35.16/35.52 thf(114,plain,sP125,inference(preprocess,[status(thm)],[axiom15]).
% 35.16/35.52 thf(axiom14,axiom,(ivalid @ ((iimplies @ (iatom @ p13)) @ ((iimplies @ (iatom @ p13)) @ (iatom @ p12))))).
% 35.16/35.52 thf(115,plain,sP65,inference(preprocess,[status(thm)],[axiom14]).
% 35.16/35.52 thf(axiom13,axiom,(ivalid @ ((iimplies @ (iatom @ p12)) @ ((iimplies @ (iatom @ p12)) @ (iatom @ p11))))).
% 35.16/35.52 thf(116,plain,sP90,inference(preprocess,[status(thm)],[axiom13]).
% 35.16/35.52 thf(axiom12,axiom,(ivalid @ ((iimplies @ (iatom @ p11)) @ ((iimplies @ (iatom @ p11)) @ (iatom @ p10))))).
% 35.16/35.52 thf(117,plain,sP110,inference(preprocess,[status(thm)],[axiom12]).
% 35.16/35.52 thf(axiom11,axiom,(ivalid @ ((iimplies @ (iatom @ p10)) @ ((iimplies @ (iatom @ p10)) @ (iatom @ p9))))).
% 35.16/35.52 thf(118,plain,sP113,inference(preprocess,[status(thm)],[axiom11]).
% 35.16/35.52 thf(axiom10,axiom,(ivalid @ ((iimplies @ (iatom @ p9)) @ ((iimplies @ (iatom @ p9)) @ (iatom @ p8))))).
% 35.16/35.52 thf(119,plain,sP77,inference(preprocess,[status(thm)],[axiom10]).
% 35.16/35.52 thf(axiom9,axiom,(ivalid @ ((iimplies @ (iatom @ p8)) @ ((iimplies @ (iatom @ p8)) @ (iatom @ p7))))).
% 35.16/35.52 thf(120,plain,sP106,inference(preprocess,[status(thm)],[axiom9]).
% 35.16/35.52 thf(axiom8,axiom,(ivalid @ ((iimplies @ (iatom @ p7)) @ ((iimplies @ (iatom @ p7)) @ (iatom @ p6))))).
% 35.16/35.52 thf(121,plain,sP83,inference(preprocess,[status(thm)],[axiom8]).
% 35.16/35.52 thf(axiom7,axiom,(ivalid @ ((iimplies @ (iatom @ p6)) @ ((iimplies @ (iatom @ p6)) @ (iatom @ p5))))).
% 35.16/35.52 thf(122,plain,sP11,inference(preprocess,[status(thm)],[axiom7]).
% 35.16/35.52 thf(axiom6,axiom,(ivalid @ ((iimplies @ (iatom @ p5)) @ ((iimplies @ (iatom @ p5)) @ (iatom @ p4))))).
% 35.16/35.52 thf(123,plain,sP79,inference(preprocess,[status(thm)],[axiom6]).
% 35.16/35.52 thf(axiom5,axiom,(ivalid @ ((iimplies @ (iatom @ p4)) @ ((iimplies @ (iatom @ p4)) @ (iatom @ p3))))).
% 35.16/35.52 thf(124,plain,sP105,inference(preprocess,[status(thm)],[axiom5]).
% 35.16/35.52 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ p3)) @ ((iimplies @ (iatom @ p3)) @ (iatom @ p2))))).
% 35.16/35.52 thf(125,plain,sP5,inference(preprocess,[status(thm)],[axiom4]).
% 35.16/35.52 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ p2)) @ ((iimplies @ (iatom @ p2)) @ (iatom @ p1))))).
% 35.16/35.52 thf(126,plain,sP53,inference(preprocess,[status(thm)],[axiom3]).
% 35.16/35.52 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))).
% 35.16/35.52 thf(127,plain,sP27,inference(preprocess,[status(thm)],[axiom2]).
% 35.16/35.52 thf(axiom1,axiom,(ivalid @ (iatom @ p20))).
% 35.16/35.52 thf(128,plain,sP119,inference(preprocess,[status(thm)],[axiom1]).
% 35.16/35.52 thf(refl_axiom,axiom,sP1).
% 35.16/35.52 thf(129,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,refl_axiom,h1])).
% 35.16/35.52 thf(130,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[129,h0])).
% 35.16/35.52 thf(0,theorem,sP97,inference(contra,[status(thm),contra(discharge,[h1])],[129,h1])).
% 35.16/35.52 % SZS output end Proof
%------------------------------------------------------------------------------