TSTP Solution File: SWC044+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n027.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 : Tue Sep 20 11:18:15 EDT 2022
% Result : Theorem 44.71s 8.59s
% Output : Proof 44.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n027.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 : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:11:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.36 Conjecture not found
% 0.13/0.36 Start search
% 0.13/0.37 nb_step : 1 - limit : 207
% 0.13/0.37 Launch Gotab with destructive = true
% 44.61/8.52 % SZS output start Proof for theBenchmark.p
% 44.71/8.59 [0] ALPHA_AND : ((! [U6_6] : ((ssItem(U6_6) => ! [V7_7] : ((ssItem(V7_7) => (neq(U6_6, V7_7) <=> ~=(U6_6, V7_7)))))) & ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9))))) & ! [U10_10] : ((ssList(U10_10) => ! [V11_11] : ((ssItem(V11_11) => (memberP(U10_10, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), U10_10)))))))))) & ! [U14_14] : ((ssList(U14_14) => (singletonP(U14_14) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), U14_14)))))) & ! [U16_16] : ((ssList(U16_16) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(U16_16, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), U16_16)))))))) & ! [U19_19] : ((ssList(U19_19) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(U19_19, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), U19_19)))))))) & ! [U22_22] : ((ssList(U22_22) => ! [V23_23] : ((ssList(V23_23) => (segmentP(U22_22, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), U22_22)))))))))) & ! [U26_26] : ((ssList(U26_26) => (cyclefreeP(U26_26) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), U26_26) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))) & ! [U32_32] : ((ssList(U32_32) => (totalorderP(U32_32) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), U32_32) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))) & ! [U38_38] : ((ssList(U38_38) => (strictorderP(U38_38) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), U38_38) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))) & ! [U44_44] : ((ssList(U44_44) => (totalorderedP(U44_44) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), U44_44) => leq(V45_45, W46_46))))))))))))))) & ! [U50_50] : ((ssList(U50_50) => (strictorderedP(U50_50) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), U50_50) => lt(V51_51, W52_52))))))))))))))) & ! [U56_56] : ((ssList(U56_56) => (duplicatefreeP(U56_56) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), U56_56) => ~=(V57_57, W58_58))))))))))))))) & ! [U62_62] : ((ssList(U62_62) => (equalelemsP(U62_62) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), U62_62) => =(V63_63, W64_64))))))))))))) & ! [U67_67] : ((ssList(U67_67) => ! [V68_68] : ((ssList(V68_68) => (neq(U67_67, V68_68) <=> ~=(U67_67, V68_68)))))) & ! [U69_69] : ((ssList(U69_69) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, U69_69)))))) & ssList(nil) & ! [U71_71] : ((ssList(U71_71) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, U71_71), U71_71))))) & ! [U73_73] : ((ssList(U73_73) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, U73_73), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, U73_73))))))))))) & ! [U77_77] : ((ssList(U77_77) => (=(nil, U77_77) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), U77_77)))))))) & ! [U80_80] : ((ssList(U80_80) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, U80_80)))))) & ! [U82_82] : ((ssList(U82_82) => (~=(nil, U82_82) => ssItem(hd(U82_82))))) & ! [U83_83] : ((ssList(U83_83) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, U83_83)), V84_84))))) & ! [U85_85] : ((ssList(U85_85) => (~=(nil, U85_85) => ssList(tl(U85_85))))) & ! [U86_86] : ((ssList(U86_86) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, U86_86)), U86_86))))) & ! [U88_88] : ((ssList(U88_88) => ! [V89_89] : ((ssList(V89_89) => ssList(app(U88_88, V89_89)))))) & ! [U90_90] : ((ssList(U90_90) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, U90_90)), app(cons(W92_92, V91_91), U90_90)))))))) & ! [U93_93] : ((ssList(U93_93) => =(app(nil, U93_93), U93_93))) & ! [U94_94] : ((ssItem(U94_94) => ! [V95_95] : ((ssItem(V95_95) => ((leq(U94_94, V95_95) & leq(V95_95, U94_94)) => =(U94_94, V95_95)))))) & ! [U96_96] : ((ssItem(U96_96) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(U96_96, V97_97) & leq(V97_97, W98_98)) => leq(U96_96, W98_98)))))))) & ! [U99_99] : ((ssItem(U99_99) => leq(U99_99, U99_99))) & ! [U100_100] : ((ssItem(U100_100) => ! [V101_101] : ((ssItem(V101_101) => (geq(U100_100, V101_101) <=> leq(V101_101, U100_100)))))) & ! [U102_102] : ((ssItem(U102_102) => ! [V103_103] : ((ssItem(V103_103) => (lt(U102_102, V103_103) => ~lt(V103_103, U102_102)))))) & ! [U104_104] : ((ssItem(U104_104) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(U104_104, V105_105) & lt(V105_105, W106_106)) => lt(U104_104, W106_106)))))))) & ! [U107_107] : ((ssItem(U107_107) => ! [V108_108] : ((ssItem(V108_108) => (gt(U107_107, V108_108) <=> lt(V108_108, U107_107)))))) & ! [U109_109] : ((ssItem(U109_109) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), U109_109) <=> (memberP(V110_110, U109_109) | memberP(W111_111, U109_109))))))))) & ! [U112_112] : ((ssItem(U112_112) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), U112_112) <=> (=(U112_112, V113_113) | memberP(W114_114, U112_112))))))))) & ! [U115_115] : ((ssItem(U115_115) => ~memberP(nil, U115_115))) & ~singletonP(nil) & ! [U116_116] : ((ssList(U116_116) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(U116_116, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(U116_116, W118_118)))))))) & ! [U119_119] : ((ssList(U119_119) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(U119_119, V120_120) & frontsegP(V120_120, U119_119)) => =(U119_119, V120_120)))))) & ! [U121_121] : ((ssList(U121_121) => frontsegP(U121_121, U121_121))) & ! [U122_122] : ((ssList(U122_122) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(U122_122, V123_123) => frontsegP(app(U122_122, W124_124), V123_123)))))))) & ! [U125_125] : ((ssItem(U125_125) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(U125_125, W127_127), cons(V126_126, X128_128)) <=> (=(U125_125, V126_126) & frontsegP(W127_127, X128_128))))))))))) & ! [U129_129] : ((ssList(U129_129) => frontsegP(U129_129, nil))) & ! [U130_130] : ((ssList(U130_130) => (frontsegP(nil, U130_130) <=> =(nil, U130_130)))) & ! [U131_131] : ((ssList(U131_131) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(U131_131, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(U131_131, W133_133)))))))) & ! [U134_134] : ((ssList(U134_134) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(U134_134, V135_135) & rearsegP(V135_135, U134_134)) => =(U134_134, V135_135)))))) & ! [U136_136] : ((ssList(U136_136) => rearsegP(U136_136, U136_136))) & ! [U137_137] : ((ssList(U137_137) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(U137_137, V138_138) => rearsegP(app(W139_139, U137_137), V138_138)))))))) & ! [U140_140] : ((ssList(U140_140) => rearsegP(U140_140, nil))) & ! [U141_141] : ((ssList(U141_141) => (rearsegP(nil, U141_141) <=> =(nil, U141_141)))) & ! [U142_142] : ((ssList(U142_142) => ! [V143_143] : ((ssList(V143_143) => ! [W144_144] : ((ssList(W144_144) => ((segmentP(U142_142, V143_143) & segmentP(V143_143, W144_144)) => segmentP(U142_142, W144_144)))))))) & ! [U145_145] : ((ssList(U145_145) => ! [V146_146] : ((ssList(V146_146) => ((segmentP(U145_145, V146_146) & segmentP(V146_146, U145_145)) => =(U145_145, V146_146)))))) & ! [U147_147] : ((ssList(U147_147) => segmentP(U147_147, U147_147))) & ! [U148_148] : ((ssList(U148_148) => ! [V149_149] : ((ssList(V149_149) => ! [W150_150] : ((ssList(W150_150) => ! [X151_151] : ((ssList(X151_151) => (segmentP(U148_148, V149_149) => segmentP(app(app(W150_150, U148_148), X151_151), V149_149)))))))))) & ! [U152_152] : ((ssList(U152_152) => segmentP(U152_152, nil))) & ! [U153_153] : ((ssList(U153_153) => (segmentP(nil, U153_153) <=> =(nil, U153_153)))) & ! [U154_154] : ((ssItem(U154_154) => cyclefreeP(cons(U154_154, nil)))) & cyclefreeP(nil) & ! [U155_155] : ((ssItem(U155_155) => totalorderP(cons(U155_155, nil)))) & totalorderP(nil) & ! [U156_156] : ((ssItem(U156_156) => strictorderP(cons(U156_156, nil)))) & strictorderP(nil) & ! [U157_157] : ((ssItem(U157_157) => totalorderedP(cons(U157_157, nil)))) & totalorderedP(nil) & ! [U158_158] : ((ssItem(U158_158) => ! [V159_159] : ((ssList(V159_159) => (totalorderedP(cons(U158_158, V159_159)) <=> (=(nil, V159_159) | ((~=(nil, V159_159) & totalorderedP(V159_159)) & leq(U158_158, hd(V159_159))))))))) & ! [U160_160] : ((ssItem(U160_160) => strictorderedP(cons(U160_160, nil)))) & strictorderedP(nil) & ! [U161_161] : ((ssItem(U161_161) => ! [V162_162] : ((ssList(V162_162) => (strictorderedP(cons(U161_161, V162_162)) <=> (=(nil, V162_162) | ((~=(nil, V162_162) & strictorderedP(V162_162)) & lt(U161_161, hd(V162_162))))))))) & ! [U163_163] : ((ssItem(U163_163) => duplicatefreeP(cons(U163_163, nil)))) & duplicatefreeP(nil) & ! [U164_164] : ((ssItem(U164_164) => equalelemsP(cons(U164_164, nil)))) & equalelemsP(nil) & ! [U165_165] : ((ssList(U165_165) => (~=(nil, U165_165) => ? [V166_166] : ((ssItem(V166_166) & =(hd(U165_165), V166_166)))))) & ! [U167_167] : ((ssList(U167_167) => (~=(nil, U167_167) => ? [V168_168] : ((ssList(V168_168) & =(tl(U167_167), V168_168)))))) & ! [U169_169] : ((ssList(U169_169) => ! [V170_170] : ((ssList(V170_170) => ((((~=(nil, V170_170) & ~=(nil, U169_169)) & =(hd(V170_170), hd(U169_169))) & =(tl(V170_170), tl(U169_169))) => =(V170_170, U169_169)))))) & ! [U171_171] : ((ssList(U171_171) => (~=(nil, U171_171) => =(cons(hd(U171_171), tl(U171_171)), U171_171)))) & ! [U172_172] : ((ssList(U172_172) => ! [V173_173] : ((ssList(V173_173) => ! [W174_174] : ((ssList(W174_174) => (=(app(W174_174, V173_173), app(U172_172, V173_173)) => =(W174_174, U172_172)))))))) & ! [U175_175] : ((ssList(U175_175) => ! [V176_176] : ((ssList(V176_176) => ! [W177_177] : ((ssList(W177_177) => (=(app(V176_176, W177_177), app(V176_176, U175_175)) => =(W177_177, U175_175)))))))) & ! [U178_178] : ((ssList(U178_178) => ! [V179_179] : ((ssItem(V179_179) => =(cons(V179_179, U178_178), app(cons(V179_179, nil), U178_178)))))) & ! [U180_180] : ((ssList(U180_180) => ! [V181_181] : ((ssList(V181_181) => ! [W182_182] : ((ssList(W182_182) => =(app(app(U180_180, V181_181), W182_182), app(U180_180, app(V181_181, W182_182))))))))) & ! [U183_183] : ((ssList(U183_183) => ! [V184_184] : ((ssList(V184_184) => (=(nil, app(U183_183, V184_184)) <=> (=(nil, V184_184) & =(nil, U183_183))))))) & ! [U185_185] : ((ssList(U185_185) => =(app(U185_185, nil), U185_185))) & ! [U186_186] : ((ssList(U186_186) => ! [V187_187] : ((ssList(V187_187) => (~=(nil, U186_186) => =(hd(app(U186_186, V187_187)), hd(U186_186))))))) & ! [U188_188] : ((ssList(U188_188) => ! [V189_189] : ((ssList(V189_189) => (~=(nil, U188_188) => =(tl(app(U188_188, V189_189)), app(tl(U188_188), V189_189))))))) & ! [U190_190] : ((ssItem(U190_190) => ! [V191_191] : ((ssItem(V191_191) => ((geq(U190_190, V191_191) & geq(V191_191, U190_190)) => =(U190_190, V191_191)))))) & ! [U192_192] : ((ssItem(U192_192) => ! [V193_193] : ((ssItem(V193_193) => ! [W194_194] : ((ssItem(W194_194) => ((geq(U192_192, V193_193) & geq(V193_193, W194_194)) => geq(U192_192, W194_194)))))))) & ! [U195_195] : ((ssItem(U195_195) => geq(U195_195, U195_195))) & ! [U196_196] : ((ssItem(U196_196) => ~lt(U196_196, U196_196))) & ! [U197_197] : ((ssItem(U197_197) => ! [V198_198] : ((ssItem(V198_198) => ! [W199_199] : ((ssItem(W199_199) => ((leq(U197_197, V198_198) & lt(V198_198, W199_199)) => lt(U197_197, W199_199)))))))) & ! [U200_200] : ((ssItem(U200_200) => ! [V201_201] : ((ssItem(V201_201) => (leq(U200_200, V201_201) => (=(U200_200, V201_201) | lt(U200_200, V201_201))))))) & ! [U202_202] : ((ssItem(U202_202) => ! [V203_203] : ((ssItem(V203_203) => (lt(U202_202, V203_203) <=> (~=(U202_202, V203_203) & leq(U202_202, V203_203))))))) & ! [U204_204] : ((ssItem(U204_204) => ! [V205_205] : ((ssItem(V205_205) => (gt(U204_204, V205_205) => ~gt(V205_205, U204_204)))))) & ! [U206_206] : ((ssItem(U206_206) => ! [V207_207] : ((ssItem(V207_207) => ! [W208_208] : ((ssItem(W208_208) => ((gt(U206_206, V207_207) & gt(V207_207, W208_208)) => gt(U206_206, W208_208))))))))) & ~! [U209_209] : ((ssList(U209_209) => ! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(U209_209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, U209_209)))))))))))
% 44.71/8.59 -> [1] (! [U6_6] : ((ssItem(U6_6) => ! [V7_7] : ((ssItem(V7_7) => (neq(U6_6, V7_7) <=> ~=(U6_6, V7_7)))))) & ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9))))) & ! [U10_10] : ((ssList(U10_10) => ! [V11_11] : ((ssItem(V11_11) => (memberP(U10_10, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), U10_10)))))))))) & ! [U14_14] : ((ssList(U14_14) => (singletonP(U14_14) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), U14_14)))))) & ! [U16_16] : ((ssList(U16_16) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(U16_16, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), U16_16)))))))) & ! [U19_19] : ((ssList(U19_19) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(U19_19, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), U19_19)))))))) & ! [U22_22] : ((ssList(U22_22) => ! [V23_23] : ((ssList(V23_23) => (segmentP(U22_22, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), U22_22)))))))))) & ! [U26_26] : ((ssList(U26_26) => (cyclefreeP(U26_26) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), U26_26) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))) & ! [U32_32] : ((ssList(U32_32) => (totalorderP(U32_32) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), U32_32) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))) & ! [U38_38] : ((ssList(U38_38) => (strictorderP(U38_38) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), U38_38) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))) & ! [U44_44] : ((ssList(U44_44) => (totalorderedP(U44_44) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), U44_44) => leq(V45_45, W46_46))))))))))))))) & ! [U50_50] : ((ssList(U50_50) => (strictorderedP(U50_50) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), U50_50) => lt(V51_51, W52_52))))))))))))))) & ! [U56_56] : ((ssList(U56_56) => (duplicatefreeP(U56_56) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), U56_56) => ~=(V57_57, W58_58))))))))))))))) & ! [U62_62] : ((ssList(U62_62) => (equalelemsP(U62_62) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), U62_62) => =(V63_63, W64_64))))))))))))) & ! [U67_67] : ((ssList(U67_67) => ! [V68_68] : ((ssList(V68_68) => (neq(U67_67, V68_68) <=> ~=(U67_67, V68_68)))))) & ! [U69_69] : ((ssList(U69_69) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, U69_69)))))) & ssList(nil) & ! [U71_71] : ((ssList(U71_71) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, U71_71), U71_71))))) & ! [U73_73] : ((ssList(U73_73) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, U73_73), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, U73_73))))))))))) & ! [U77_77] : ((ssList(U77_77) => (=(nil, U77_77) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), U77_77)))))))) & ! [U80_80] : ((ssList(U80_80) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, U80_80)))))) & ! [U82_82] : ((ssList(U82_82) => (~=(nil, U82_82) => ssItem(hd(U82_82))))) & ! [U83_83] : ((ssList(U83_83) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, U83_83)), V84_84))))) & ! [U85_85] : ((ssList(U85_85) => (~=(nil, U85_85) => ssList(tl(U85_85))))) & ! [U86_86] : ((ssList(U86_86) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, U86_86)), U86_86))))) & ! [U88_88] : ((ssList(U88_88) => ! [V89_89] : ((ssList(V89_89) => ssList(app(U88_88, V89_89)))))) & ! [U90_90] : ((ssList(U90_90) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, U90_90)), app(cons(W92_92, V91_91), U90_90)))))))) & ! [U93_93] : ((ssList(U93_93) => =(app(nil, U93_93), U93_93))) & ! [U94_94] : ((ssItem(U94_94) => ! [V95_95] : ((ssItem(V95_95) => ((leq(U94_94, V95_95) & leq(V95_95, U94_94)) => =(U94_94, V95_95)))))) & ! [U96_96] : ((ssItem(U96_96) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(U96_96, V97_97) & leq(V97_97, W98_98)) => leq(U96_96, W98_98)))))))) & ! [U99_99] : ((ssItem(U99_99) => leq(U99_99, U99_99))) & ! [U100_100] : ((ssItem(U100_100) => ! [V101_101] : ((ssItem(V101_101) => (geq(U100_100, V101_101) <=> leq(V101_101, U100_100)))))) & ! [U102_102] : ((ssItem(U102_102) => ! [V103_103] : ((ssItem(V103_103) => (lt(U102_102, V103_103) => ~lt(V103_103, U102_102)))))) & ! [U104_104] : ((ssItem(U104_104) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(U104_104, V105_105) & lt(V105_105, W106_106)) => lt(U104_104, W106_106)))))))) & ! [U107_107] : ((ssItem(U107_107) => ! [V108_108] : ((ssItem(V108_108) => (gt(U107_107, V108_108) <=> lt(V108_108, U107_107)))))) & ! [U109_109] : ((ssItem(U109_109) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), U109_109) <=> (memberP(V110_110, U109_109) | memberP(W111_111, U109_109))))))))) & ! [U112_112] : ((ssItem(U112_112) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), U112_112) <=> (=(U112_112, V113_113) | memberP(W114_114, U112_112))))))))) & ! [U115_115] : ((ssItem(U115_115) => ~memberP(nil, U115_115))) & ~singletonP(nil) & ! [U116_116] : ((ssList(U116_116) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(U116_116, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(U116_116, W118_118)))))))) & ! [U119_119] : ((ssList(U119_119) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(U119_119, V120_120) & frontsegP(V120_120, U119_119)) => =(U119_119, V120_120)))))) & ! [U121_121] : ((ssList(U121_121) => frontsegP(U121_121, U121_121))) & ! [U122_122] : ((ssList(U122_122) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(U122_122, V123_123) => frontsegP(app(U122_122, W124_124), V123_123)))))))) & ! [U125_125] : ((ssItem(U125_125) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(U125_125, W127_127), cons(V126_126, X128_128)) <=> (=(U125_125, V126_126) & frontsegP(W127_127, X128_128))))))))))) & ! [U129_129] : ((ssList(U129_129) => frontsegP(U129_129, nil))) & ! [U130_130] : ((ssList(U130_130) => (frontsegP(nil, U130_130) <=> =(nil, U130_130)))) & ! [U131_131] : ((ssList(U131_131) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(U131_131, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(U131_131, W133_133)))))))) & ! [U134_134] : ((ssList(U134_134) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(U134_134, V135_135) & rearsegP(V135_135, U134_134)) => =(U134_134, V135_135)))))) & ! [U136_136] : ((ssList(U136_136) => rearsegP(U136_136, U136_136))) & ! [U137_137] : ((ssList(U137_137) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(U137_137, V138_138) => rearsegP(app(W139_139, U137_137), V138_138)))))))) & ! [U140_140] : ((ssList(U140_140) => rearsegP(U140_140, nil))) & ! [U141_141] : ((ssList(U141_141) => (rearsegP(nil, U141_141) <=> =(nil, U141_141)))) & ! [U142_142] : ((ssList(U142_142) => ! [V143_143] : ((ssList(V143_143) => ! [W144_144] : ((ssList(W144_144) => ((segmentP(U142_142, V143_143) & segmentP(V143_143, W144_144)) => segmentP(U142_142, W144_144)))))))) & ! [U145_145] : ((ssList(U145_145) => ! [V146_146] : ((ssList(V146_146) => ((segmentP(U145_145, V146_146) & segmentP(V146_146, U145_145)) => =(U145_145, V146_146)))))) & ! [U147_147] : ((ssList(U147_147) => segmentP(U147_147, U147_147))) & ! [U148_148] : ((ssList(U148_148) => ! [V149_149] : ((ssList(V149_149) => ! [W150_150] : ((ssList(W150_150) => ! [X151_151] : ((ssList(X151_151) => (segmentP(U148_148, V149_149) => segmentP(app(app(W150_150, U148_148), X151_151), V149_149)))))))))) & ! [U152_152] : ((ssList(U152_152) => segmentP(U152_152, nil))) & ! [U153_153] : ((ssList(U153_153) => (segmentP(nil, U153_153) <=> =(nil, U153_153)))) & ! [U154_154] : ((ssItem(U154_154) => cyclefreeP(cons(U154_154, nil)))) & cyclefreeP(nil) & ! [U155_155] : ((ssItem(U155_155) => totalorderP(cons(U155_155, nil)))) & totalorderP(nil) & ! [U156_156] : ((ssItem(U156_156) => strictorderP(cons(U156_156, nil)))) & strictorderP(nil) & ! [U157_157] : ((ssItem(U157_157) => totalorderedP(cons(U157_157, nil)))) & totalorderedP(nil) & ! [U158_158] : ((ssItem(U158_158) => ! [V159_159] : ((ssList(V159_159) => (totalorderedP(cons(U158_158, V159_159)) <=> (=(nil, V159_159) | ((~=(nil, V159_159) & totalorderedP(V159_159)) & leq(U158_158, hd(V159_159))))))))) & ! [U160_160] : ((ssItem(U160_160) => strictorderedP(cons(U160_160, nil)))) & strictorderedP(nil) & ! [U161_161] : ((ssItem(U161_161) => ! [V162_162] : ((ssList(V162_162) => (strictorderedP(cons(U161_161, V162_162)) <=> (=(nil, V162_162) | ((~=(nil, V162_162) & strictorderedP(V162_162)) & lt(U161_161, hd(V162_162))))))))) & ! [U163_163] : ((ssItem(U163_163) => duplicatefreeP(cons(U163_163, nil)))) & duplicatefreeP(nil) & ! [U164_164] : ((ssItem(U164_164) => equalelemsP(cons(U164_164, nil)))) & equalelemsP(nil) & ! [U165_165] : ((ssList(U165_165) => (~=(nil, U165_165) => ? [V166_166] : ((ssItem(V166_166) & =(hd(U165_165), V166_166)))))) & ! [U167_167] : ((ssList(U167_167) => (~=(nil, U167_167) => ? [V168_168] : ((ssList(V168_168) & =(tl(U167_167), V168_168)))))) & ! [U169_169] : ((ssList(U169_169) => ! [V170_170] : ((ssList(V170_170) => ((((~=(nil, V170_170) & ~=(nil, U169_169)) & =(hd(V170_170), hd(U169_169))) & =(tl(V170_170), tl(U169_169))) => =(V170_170, U169_169)))))) & ! [U171_171] : ((ssList(U171_171) => (~=(nil, U171_171) => =(cons(hd(U171_171), tl(U171_171)), U171_171)))) & ! [U172_172] : ((ssList(U172_172) => ! [V173_173] : ((ssList(V173_173) => ! [W174_174] : ((ssList(W174_174) => (=(app(W174_174, V173_173), app(U172_172, V173_173)) => =(W174_174, U172_172)))))))) & ! [U175_175] : ((ssList(U175_175) => ! [V176_176] : ((ssList(V176_176) => ! [W177_177] : ((ssList(W177_177) => (=(app(V176_176, W177_177), app(V176_176, U175_175)) => =(W177_177, U175_175)))))))) & ! [U178_178] : ((ssList(U178_178) => ! [V179_179] : ((ssItem(V179_179) => =(cons(V179_179, U178_178), app(cons(V179_179, nil), U178_178)))))) & ! [U180_180] : ((ssList(U180_180) => ! [V181_181] : ((ssList(V181_181) => ! [W182_182] : ((ssList(W182_182) => =(app(app(U180_180, V181_181), W182_182), app(U180_180, app(V181_181, W182_182))))))))) & ! [U183_183] : ((ssList(U183_183) => ! [V184_184] : ((ssList(V184_184) => (=(nil, app(U183_183, V184_184)) <=> (=(nil, V184_184) & =(nil, U183_183))))))) & ! [U185_185] : ((ssList(U185_185) => =(app(U185_185, nil), U185_185))) & ! [U186_186] : ((ssList(U186_186) => ! [V187_187] : ((ssList(V187_187) => (~=(nil, U186_186) => =(hd(app(U186_186, V187_187)), hd(U186_186))))))) & ! [U188_188] : ((ssList(U188_188) => ! [V189_189] : ((ssList(V189_189) => (~=(nil, U188_188) => =(tl(app(U188_188, V189_189)), app(tl(U188_188), V189_189))))))) & ! [U190_190] : ((ssItem(U190_190) => ! [V191_191] : ((ssItem(V191_191) => ((geq(U190_190, V191_191) & geq(V191_191, U190_190)) => =(U190_190, V191_191)))))) & ! [U192_192] : ((ssItem(U192_192) => ! [V193_193] : ((ssItem(V193_193) => ! [W194_194] : ((ssItem(W194_194) => ((geq(U192_192, V193_193) & geq(V193_193, W194_194)) => geq(U192_192, W194_194)))))))) & ! [U195_195] : ((ssItem(U195_195) => geq(U195_195, U195_195))) & ! [U196_196] : ((ssItem(U196_196) => ~lt(U196_196, U196_196))) & ! [U197_197] : ((ssItem(U197_197) => ! [V198_198] : ((ssItem(V198_198) => ! [W199_199] : ((ssItem(W199_199) => ((leq(U197_197, V198_198) & lt(V198_198, W199_199)) => lt(U197_197, W199_199)))))))) & ! [U200_200] : ((ssItem(U200_200) => ! [V201_201] : ((ssItem(V201_201) => (leq(U200_200, V201_201) => (=(U200_200, V201_201) | lt(U200_200, V201_201))))))) & ! [U202_202] : ((ssItem(U202_202) => ! [V203_203] : ((ssItem(V203_203) => (lt(U202_202, V203_203) <=> (~=(U202_202, V203_203) & leq(U202_202, V203_203))))))) & ! [U204_204] : ((ssItem(U204_204) => ! [V205_205] : ((ssItem(V205_205) => (gt(U204_204, V205_205) => ~gt(V205_205, U204_204)))))) & ! [U206_206] : ((ssItem(U206_206) => ! [V207_207] : ((ssItem(V207_207) => ! [W208_208] : ((ssItem(W208_208) => ((gt(U206_206, V207_207) & gt(V207_207, W208_208)) => gt(U206_206, W208_208))))))))), ~! [U209_209] : ((ssList(U209_209) => ! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(U209_209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, U209_209))))))))))
% 44.71/8.59
% 44.71/8.59 [1] ALPHA_AND : (! [U6_6] : ((ssItem(U6_6) => ! [V7_7] : ((ssItem(V7_7) => (neq(U6_6, V7_7) <=> ~=(U6_6, V7_7)))))) & ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9))))) & ! [U10_10] : ((ssList(U10_10) => ! [V11_11] : ((ssItem(V11_11) => (memberP(U10_10, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), U10_10)))))))))) & ! [U14_14] : ((ssList(U14_14) => (singletonP(U14_14) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), U14_14)))))) & ! [U16_16] : ((ssList(U16_16) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(U16_16, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), U16_16)))))))) & ! [U19_19] : ((ssList(U19_19) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(U19_19, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), U19_19)))))))) & ! [U22_22] : ((ssList(U22_22) => ! [V23_23] : ((ssList(V23_23) => (segmentP(U22_22, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), U22_22)))))))))) & ! [U26_26] : ((ssList(U26_26) => (cyclefreeP(U26_26) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), U26_26) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))) & ! [U32_32] : ((ssList(U32_32) => (totalorderP(U32_32) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), U32_32) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))) & ! [U38_38] : ((ssList(U38_38) => (strictorderP(U38_38) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), U38_38) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))) & ! [U44_44] : ((ssList(U44_44) => (totalorderedP(U44_44) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), U44_44) => leq(V45_45, W46_46))))))))))))))) & ! [U50_50] : ((ssList(U50_50) => (strictorderedP(U50_50) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), U50_50) => lt(V51_51, W52_52))))))))))))))) & ! [U56_56] : ((ssList(U56_56) => (duplicatefreeP(U56_56) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), U56_56) => ~=(V57_57, W58_58))))))))))))))) & ! [U62_62] : ((ssList(U62_62) => (equalelemsP(U62_62) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), U62_62) => =(V63_63, W64_64))))))))))))) & ! [U67_67] : ((ssList(U67_67) => ! [V68_68] : ((ssList(V68_68) => (neq(U67_67, V68_68) <=> ~=(U67_67, V68_68)))))) & ! [U69_69] : ((ssList(U69_69) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, U69_69)))))) & ssList(nil) & ! [U71_71] : ((ssList(U71_71) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, U71_71), U71_71))))) & ! [U73_73] : ((ssList(U73_73) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, U73_73), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, U73_73))))))))))) & ! [U77_77] : ((ssList(U77_77) => (=(nil, U77_77) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), U77_77)))))))) & ! [U80_80] : ((ssList(U80_80) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, U80_80)))))) & ! [U82_82] : ((ssList(U82_82) => (~=(nil, U82_82) => ssItem(hd(U82_82))))) & ! [U83_83] : ((ssList(U83_83) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, U83_83)), V84_84))))) & ! [U85_85] : ((ssList(U85_85) => (~=(nil, U85_85) => ssList(tl(U85_85))))) & ! [U86_86] : ((ssList(U86_86) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, U86_86)), U86_86))))) & ! [U88_88] : ((ssList(U88_88) => ! [V89_89] : ((ssList(V89_89) => ssList(app(U88_88, V89_89)))))) & ! [U90_90] : ((ssList(U90_90) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, U90_90)), app(cons(W92_92, V91_91), U90_90)))))))) & ! [U93_93] : ((ssList(U93_93) => =(app(nil, U93_93), U93_93))) & ! [U94_94] : ((ssItem(U94_94) => ! [V95_95] : ((ssItem(V95_95) => ((leq(U94_94, V95_95) & leq(V95_95, U94_94)) => =(U94_94, V95_95)))))) & ! [U96_96] : ((ssItem(U96_96) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(U96_96, V97_97) & leq(V97_97, W98_98)) => leq(U96_96, W98_98)))))))) & ! [U99_99] : ((ssItem(U99_99) => leq(U99_99, U99_99))) & ! [U100_100] : ((ssItem(U100_100) => ! [V101_101] : ((ssItem(V101_101) => (geq(U100_100, V101_101) <=> leq(V101_101, U100_100)))))) & ! [U102_102] : ((ssItem(U102_102) => ! [V103_103] : ((ssItem(V103_103) => (lt(U102_102, V103_103) => ~lt(V103_103, U102_102)))))) & ! [U104_104] : ((ssItem(U104_104) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(U104_104, V105_105) & lt(V105_105, W106_106)) => lt(U104_104, W106_106)))))))) & ! [U107_107] : ((ssItem(U107_107) => ! [V108_108] : ((ssItem(V108_108) => (gt(U107_107, V108_108) <=> lt(V108_108, U107_107)))))) & ! [U109_109] : ((ssItem(U109_109) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), U109_109) <=> (memberP(V110_110, U109_109) | memberP(W111_111, U109_109))))))))) & ! [U112_112] : ((ssItem(U112_112) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), U112_112) <=> (=(U112_112, V113_113) | memberP(W114_114, U112_112))))))))) & ! [U115_115] : ((ssItem(U115_115) => ~memberP(nil, U115_115))) & ~singletonP(nil) & ! [U116_116] : ((ssList(U116_116) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(U116_116, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(U116_116, W118_118)))))))) & ! [U119_119] : ((ssList(U119_119) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(U119_119, V120_120) & frontsegP(V120_120, U119_119)) => =(U119_119, V120_120)))))) & ! [U121_121] : ((ssList(U121_121) => frontsegP(U121_121, U121_121))) & ! [U122_122] : ((ssList(U122_122) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(U122_122, V123_123) => frontsegP(app(U122_122, W124_124), V123_123)))))))) & ! [U125_125] : ((ssItem(U125_125) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(U125_125, W127_127), cons(V126_126, X128_128)) <=> (=(U125_125, V126_126) & frontsegP(W127_127, X128_128))))))))))) & ! [U129_129] : ((ssList(U129_129) => frontsegP(U129_129, nil))) & ! [U130_130] : ((ssList(U130_130) => (frontsegP(nil, U130_130) <=> =(nil, U130_130)))) & ! [U131_131] : ((ssList(U131_131) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(U131_131, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(U131_131, W133_133)))))))) & ! [U134_134] : ((ssList(U134_134) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(U134_134, V135_135) & rearsegP(V135_135, U134_134)) => =(U134_134, V135_135)))))) & ! [U136_136] : ((ssList(U136_136) => rearsegP(U136_136, U136_136))) & ! [U137_137] : ((ssList(U137_137) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(U137_137, V138_138) => rearsegP(app(W139_139, U137_137), V138_138)))))))) & ! [U140_140] : ((ssList(U140_140) => rearsegP(U140_140, nil))) & ! [U141_141] : ((ssList(U141_141) => (rearsegP(nil, U141_141) <=> =(nil, U141_141)))) & ! [U142_142] : ((ssList(U142_142) => ! [V143_143] : ((ssList(V143_143) => ! [W144_144] : ((ssList(W144_144) => ((segmentP(U142_142, V143_143) & segmentP(V143_143, W144_144)) => segmentP(U142_142, W144_144)))))))) & ! [U145_145] : ((ssList(U145_145) => ! [V146_146] : ((ssList(V146_146) => ((segmentP(U145_145, V146_146) & segmentP(V146_146, U145_145)) => =(U145_145, V146_146)))))) & ! [U147_147] : ((ssList(U147_147) => segmentP(U147_147, U147_147))) & ! [U148_148] : ((ssList(U148_148) => ! [V149_149] : ((ssList(V149_149) => ! [W150_150] : ((ssList(W150_150) => ! [X151_151] : ((ssList(X151_151) => (segmentP(U148_148, V149_149) => segmentP(app(app(W150_150, U148_148), X151_151), V149_149)))))))))) & ! [U152_152] : ((ssList(U152_152) => segmentP(U152_152, nil))) & ! [U153_153] : ((ssList(U153_153) => (segmentP(nil, U153_153) <=> =(nil, U153_153)))) & ! [U154_154] : ((ssItem(U154_154) => cyclefreeP(cons(U154_154, nil)))) & cyclefreeP(nil) & ! [U155_155] : ((ssItem(U155_155) => totalorderP(cons(U155_155, nil)))) & totalorderP(nil) & ! [U156_156] : ((ssItem(U156_156) => strictorderP(cons(U156_156, nil)))) & strictorderP(nil) & ! [U157_157] : ((ssItem(U157_157) => totalorderedP(cons(U157_157, nil)))) & totalorderedP(nil) & ! [U158_158] : ((ssItem(U158_158) => ! [V159_159] : ((ssList(V159_159) => (totalorderedP(cons(U158_158, V159_159)) <=> (=(nil, V159_159) | ((~=(nil, V159_159) & totalorderedP(V159_159)) & leq(U158_158, hd(V159_159))))))))) & ! [U160_160] : ((ssItem(U160_160) => strictorderedP(cons(U160_160, nil)))) & strictorderedP(nil) & ! [U161_161] : ((ssItem(U161_161) => ! [V162_162] : ((ssList(V162_162) => (strictorderedP(cons(U161_161, V162_162)) <=> (=(nil, V162_162) | ((~=(nil, V162_162) & strictorderedP(V162_162)) & lt(U161_161, hd(V162_162))))))))) & ! [U163_163] : ((ssItem(U163_163) => duplicatefreeP(cons(U163_163, nil)))) & duplicatefreeP(nil) & ! [U164_164] : ((ssItem(U164_164) => equalelemsP(cons(U164_164, nil)))) & equalelemsP(nil) & ! [U165_165] : ((ssList(U165_165) => (~=(nil, U165_165) => ? [V166_166] : ((ssItem(V166_166) & =(hd(U165_165), V166_166)))))) & ! [U167_167] : ((ssList(U167_167) => (~=(nil, U167_167) => ? [V168_168] : ((ssList(V168_168) & =(tl(U167_167), V168_168)))))) & ! [U169_169] : ((ssList(U169_169) => ! [V170_170] : ((ssList(V170_170) => ((((~=(nil, V170_170) & ~=(nil, U169_169)) & =(hd(V170_170), hd(U169_169))) & =(tl(V170_170), tl(U169_169))) => =(V170_170, U169_169)))))) & ! [U171_171] : ((ssList(U171_171) => (~=(nil, U171_171) => =(cons(hd(U171_171), tl(U171_171)), U171_171)))) & ! [U172_172] : ((ssList(U172_172) => ! [V173_173] : ((ssList(V173_173) => ! [W174_174] : ((ssList(W174_174) => (=(app(W174_174, V173_173), app(U172_172, V173_173)) => =(W174_174, U172_172)))))))) & ! [U175_175] : ((ssList(U175_175) => ! [V176_176] : ((ssList(V176_176) => ! [W177_177] : ((ssList(W177_177) => (=(app(V176_176, W177_177), app(V176_176, U175_175)) => =(W177_177, U175_175)))))))) & ! [U178_178] : ((ssList(U178_178) => ! [V179_179] : ((ssItem(V179_179) => =(cons(V179_179, U178_178), app(cons(V179_179, nil), U178_178)))))) & ! [U180_180] : ((ssList(U180_180) => ! [V181_181] : ((ssList(V181_181) => ! [W182_182] : ((ssList(W182_182) => =(app(app(U180_180, V181_181), W182_182), app(U180_180, app(V181_181, W182_182))))))))) & ! [U183_183] : ((ssList(U183_183) => ! [V184_184] : ((ssList(V184_184) => (=(nil, app(U183_183, V184_184)) <=> (=(nil, V184_184) & =(nil, U183_183))))))) & ! [U185_185] : ((ssList(U185_185) => =(app(U185_185, nil), U185_185))) & ! [U186_186] : ((ssList(U186_186) => ! [V187_187] : ((ssList(V187_187) => (~=(nil, U186_186) => =(hd(app(U186_186, V187_187)), hd(U186_186))))))) & ! [U188_188] : ((ssList(U188_188) => ! [V189_189] : ((ssList(V189_189) => (~=(nil, U188_188) => =(tl(app(U188_188, V189_189)), app(tl(U188_188), V189_189))))))) & ! [U190_190] : ((ssItem(U190_190) => ! [V191_191] : ((ssItem(V191_191) => ((geq(U190_190, V191_191) & geq(V191_191, U190_190)) => =(U190_190, V191_191)))))) & ! [U192_192] : ((ssItem(U192_192) => ! [V193_193] : ((ssItem(V193_193) => ! [W194_194] : ((ssItem(W194_194) => ((geq(U192_192, V193_193) & geq(V193_193, W194_194)) => geq(U192_192, W194_194)))))))) & ! [U195_195] : ((ssItem(U195_195) => geq(U195_195, U195_195))) & ! [U196_196] : ((ssItem(U196_196) => ~lt(U196_196, U196_196))) & ! [U197_197] : ((ssItem(U197_197) => ! [V198_198] : ((ssItem(V198_198) => ! [W199_199] : ((ssItem(W199_199) => ((leq(U197_197, V198_198) & lt(V198_198, W199_199)) => lt(U197_197, W199_199)))))))) & ! [U200_200] : ((ssItem(U200_200) => ! [V201_201] : ((ssItem(V201_201) => (leq(U200_200, V201_201) => (=(U200_200, V201_201) | lt(U200_200, V201_201))))))) & ! [U202_202] : ((ssItem(U202_202) => ! [V203_203] : ((ssItem(V203_203) => (lt(U202_202, V203_203) <=> (~=(U202_202, V203_203) & leq(U202_202, V203_203))))))) & ! [U204_204] : ((ssItem(U204_204) => ! [V205_205] : ((ssItem(V205_205) => (gt(U204_204, V205_205) => ~gt(V205_205, U204_204)))))) & ! [U206_206] : ((ssItem(U206_206) => ! [V207_207] : ((ssItem(V207_207) => ! [W208_208] : ((ssItem(W208_208) => ((gt(U206_206, V207_207) & gt(V207_207, W208_208)) => gt(U206_206, W208_208)))))))))
% 44.71/8.59 -> [2] ! [U6_6] : ((ssItem(U6_6) => ! [V7_7] : ((ssItem(V7_7) => (neq(U6_6, V7_7) <=> ~=(U6_6, V7_7)))))), ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9))))), ! [U10_10] : ((ssList(U10_10) => ! [V11_11] : ((ssItem(V11_11) => (memberP(U10_10, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), U10_10)))))))))), ! [U14_14] : ((ssList(U14_14) => (singletonP(U14_14) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), U14_14)))))), ! [U16_16] : ((ssList(U16_16) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(U16_16, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), U16_16)))))))), ! [U19_19] : ((ssList(U19_19) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(U19_19, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), U19_19)))))))), ! [U22_22] : ((ssList(U22_22) => ! [V23_23] : ((ssList(V23_23) => (segmentP(U22_22, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), U22_22)))))))))), ! [U26_26] : ((ssList(U26_26) => (cyclefreeP(U26_26) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), U26_26) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))), ! [U32_32] : ((ssList(U32_32) => (totalorderP(U32_32) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), U32_32) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))), ! [U38_38] : ((ssList(U38_38) => (strictorderP(U38_38) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), U38_38) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))), ! [U44_44] : ((ssList(U44_44) => (totalorderedP(U44_44) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), U44_44) => leq(V45_45, W46_46))))))))))))))), ! [U50_50] : ((ssList(U50_50) => (strictorderedP(U50_50) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), U50_50) => lt(V51_51, W52_52))))))))))))))), ! [U56_56] : ((ssList(U56_56) => (duplicatefreeP(U56_56) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), U56_56) => ~=(V57_57, W58_58))))))))))))))), ! [U62_62] : ((ssList(U62_62) => (equalelemsP(U62_62) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), U62_62) => =(V63_63, W64_64))))))))))))), ! [U67_67] : ((ssList(U67_67) => ! [V68_68] : ((ssList(V68_68) => (neq(U67_67, V68_68) <=> ~=(U67_67, V68_68)))))), ! [U69_69] : ((ssList(U69_69) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, U69_69)))))), ssList(nil), ! [U71_71] : ((ssList(U71_71) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, U71_71), U71_71))))), ! [U73_73] : ((ssList(U73_73) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, U73_73), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, U73_73))))))))))), ! [U77_77] : ((ssList(U77_77) => (=(nil, U77_77) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), U77_77)))))))), ! [U80_80] : ((ssList(U80_80) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, U80_80)))))), ! [U82_82] : ((ssList(U82_82) => (~=(nil, U82_82) => ssItem(hd(U82_82))))), ! [U83_83] : ((ssList(U83_83) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, U83_83)), V84_84))))), ! [U85_85] : ((ssList(U85_85) => (~=(nil, U85_85) => ssList(tl(U85_85))))), ! [U86_86] : ((ssList(U86_86) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, U86_86)), U86_86))))), ! [U88_88] : ((ssList(U88_88) => ! [V89_89] : ((ssList(V89_89) => ssList(app(U88_88, V89_89)))))), ! [U90_90] : ((ssList(U90_90) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, U90_90)), app(cons(W92_92, V91_91), U90_90)))))))), ! [U93_93] : ((ssList(U93_93) => =(app(nil, U93_93), U93_93))), ! [U94_94] : ((ssItem(U94_94) => ! [V95_95] : ((ssItem(V95_95) => ((leq(U94_94, V95_95) & leq(V95_95, U94_94)) => =(U94_94, V95_95)))))), ! [U96_96] : ((ssItem(U96_96) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(U96_96, V97_97) & leq(V97_97, W98_98)) => leq(U96_96, W98_98)))))))), ! [U99_99] : ((ssItem(U99_99) => leq(U99_99, U99_99))), ! [U100_100] : ((ssItem(U100_100) => ! [V101_101] : ((ssItem(V101_101) => (geq(U100_100, V101_101) <=> leq(V101_101, U100_100)))))), ! [U102_102] : ((ssItem(U102_102) => ! [V103_103] : ((ssItem(V103_103) => (lt(U102_102, V103_103) => ~lt(V103_103, U102_102)))))), ! [U104_104] : ((ssItem(U104_104) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(U104_104, V105_105) & lt(V105_105, W106_106)) => lt(U104_104, W106_106)))))))), ! [U107_107] : ((ssItem(U107_107) => ! [V108_108] : ((ssItem(V108_108) => (gt(U107_107, V108_108) <=> lt(V108_108, U107_107)))))), ! [U109_109] : ((ssItem(U109_109) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), U109_109) <=> (memberP(V110_110, U109_109) | memberP(W111_111, U109_109))))))))), ! [U112_112] : ((ssItem(U112_112) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), U112_112) <=> (=(U112_112, V113_113) | memberP(W114_114, U112_112))))))))), ! [U115_115] : ((ssItem(U115_115) => ~memberP(nil, U115_115))), ~singletonP(nil), ! [U116_116] : ((ssList(U116_116) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(U116_116, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(U116_116, W118_118)))))))), ! [U119_119] : ((ssList(U119_119) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(U119_119, V120_120) & frontsegP(V120_120, U119_119)) => =(U119_119, V120_120)))))), ! [U121_121] : ((ssList(U121_121) => frontsegP(U121_121, U121_121))), ! [U122_122] : ((ssList(U122_122) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(U122_122, V123_123) => frontsegP(app(U122_122, W124_124), V123_123)))))))), ! [U125_125] : ((ssItem(U125_125) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(U125_125, W127_127), cons(V126_126, X128_128)) <=> (=(U125_125, V126_126) & frontsegP(W127_127, X128_128))))))))))), ! [U129_129] : ((ssList(U129_129) => frontsegP(U129_129, nil))), ! [U130_130] : ((ssList(U130_130) => (frontsegP(nil, U130_130) <=> =(nil, U130_130)))), ! [U131_131] : ((ssList(U131_131) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(U131_131, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(U131_131, W133_133)))))))), ! [U134_134] : ((ssList(U134_134) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(U134_134, V135_135) & rearsegP(V135_135, U134_134)) => =(U134_134, V135_135)))))), ! [U136_136] : ((ssList(U136_136) => rearsegP(U136_136, U136_136))), ! [U137_137] : ((ssList(U137_137) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(U137_137, V138_138) => rearsegP(app(W139_139, U137_137), V138_138)))))))), ! [U140_140] : ((ssList(U140_140) => rearsegP(U140_140, nil))), ! [U141_141] : ((ssList(U141_141) => (rearsegP(nil, U141_141) <=> =(nil, U141_141)))), ! [U142_142] : ((ssList(U142_142) => ! [V143_143] : ((ssList(V143_143) => ! [W144_144] : ((ssList(W144_144) => ((segmentP(U142_142, V143_143) & segmentP(V143_143, W144_144)) => segmentP(U142_142, W144_144)))))))), ! [U145_145] : ((ssList(U145_145) => ! [V146_146] : ((ssList(V146_146) => ((segmentP(U145_145, V146_146) & segmentP(V146_146, U145_145)) => =(U145_145, V146_146)))))), ! [U147_147] : ((ssList(U147_147) => segmentP(U147_147, U147_147))), ! [U148_148] : ((ssList(U148_148) => ! [V149_149] : ((ssList(V149_149) => ! [W150_150] : ((ssList(W150_150) => ! [X151_151] : ((ssList(X151_151) => (segmentP(U148_148, V149_149) => segmentP(app(app(W150_150, U148_148), X151_151), V149_149)))))))))), ! [U152_152] : ((ssList(U152_152) => segmentP(U152_152, nil))), ! [U153_153] : ((ssList(U153_153) => (segmentP(nil, U153_153) <=> =(nil, U153_153)))), ! [U154_154] : ((ssItem(U154_154) => cyclefreeP(cons(U154_154, nil)))), cyclefreeP(nil), ! [U155_155] : ((ssItem(U155_155) => totalorderP(cons(U155_155, nil)))), totalorderP(nil), ! [U156_156] : ((ssItem(U156_156) => strictorderP(cons(U156_156, nil)))), strictorderP(nil), ! [U157_157] : ((ssItem(U157_157) => totalorderedP(cons(U157_157, nil)))), totalorderedP(nil), ! [U158_158] : ((ssItem(U158_158) => ! [V159_159] : ((ssList(V159_159) => (totalorderedP(cons(U158_158, V159_159)) <=> (=(nil, V159_159) | ((~=(nil, V159_159) & totalorderedP(V159_159)) & leq(U158_158, hd(V159_159))))))))), ! [U160_160] : ((ssItem(U160_160) => strictorderedP(cons(U160_160, nil)))), strictorderedP(nil), ! [U161_161] : ((ssItem(U161_161) => ! [V162_162] : ((ssList(V162_162) => (strictorderedP(cons(U161_161, V162_162)) <=> (=(nil, V162_162) | ((~=(nil, V162_162) & strictorderedP(V162_162)) & lt(U161_161, hd(V162_162))))))))), ! [U163_163] : ((ssItem(U163_163) => duplicatefreeP(cons(U163_163, nil)))), duplicatefreeP(nil), ! [U164_164] : ((ssItem(U164_164) => equalelemsP(cons(U164_164, nil)))), equalelemsP(nil), ! [U165_165] : ((ssList(U165_165) => (~=(nil, U165_165) => ? [V166_166] : ((ssItem(V166_166) & =(hd(U165_165), V166_166)))))), ! [U167_167] : ((ssList(U167_167) => (~=(nil, U167_167) => ? [V168_168] : ((ssList(V168_168) & =(tl(U167_167), V168_168)))))), ! [U169_169] : ((ssList(U169_169) => ! [V170_170] : ((ssList(V170_170) => ((((~=(nil, V170_170) & ~=(nil, U169_169)) & =(hd(V170_170), hd(U169_169))) & =(tl(V170_170), tl(U169_169))) => =(V170_170, U169_169)))))), ! [U171_171] : ((ssList(U171_171) => (~=(nil, U171_171) => =(cons(hd(U171_171), tl(U171_171)), U171_171)))), ! [U172_172] : ((ssList(U172_172) => ! [V173_173] : ((ssList(V173_173) => ! [W174_174] : ((ssList(W174_174) => (=(app(W174_174, V173_173), app(U172_172, V173_173)) => =(W174_174, U172_172)))))))), ! [U175_175] : ((ssList(U175_175) => ! [V176_176] : ((ssList(V176_176) => ! [W177_177] : ((ssList(W177_177) => (=(app(V176_176, W177_177), app(V176_176, U175_175)) => =(W177_177, U175_175)))))))), ! [U178_178] : ((ssList(U178_178) => ! [V179_179] : ((ssItem(V179_179) => =(cons(V179_179, U178_178), app(cons(V179_179, nil), U178_178)))))), ! [U180_180] : ((ssList(U180_180) => ! [V181_181] : ((ssList(V181_181) => ! [W182_182] : ((ssList(W182_182) => =(app(app(U180_180, V181_181), W182_182), app(U180_180, app(V181_181, W182_182))))))))), ! [U183_183] : ((ssList(U183_183) => ! [V184_184] : ((ssList(V184_184) => (=(nil, app(U183_183, V184_184)) <=> (=(nil, V184_184) & =(nil, U183_183))))))), ! [U185_185] : ((ssList(U185_185) => =(app(U185_185, nil), U185_185))), ! [U186_186] : ((ssList(U186_186) => ! [V187_187] : ((ssList(V187_187) => (~=(nil, U186_186) => =(hd(app(U186_186, V187_187)), hd(U186_186))))))), ! [U188_188] : ((ssList(U188_188) => ! [V189_189] : ((ssList(V189_189) => (~=(nil, U188_188) => =(tl(app(U188_188, V189_189)), app(tl(U188_188), V189_189))))))), ! [U190_190] : ((ssItem(U190_190) => ! [V191_191] : ((ssItem(V191_191) => ((geq(U190_190, V191_191) & geq(V191_191, U190_190)) => =(U190_190, V191_191)))))), ! [U192_192] : ((ssItem(U192_192) => ! [V193_193] : ((ssItem(V193_193) => ! [W194_194] : ((ssItem(W194_194) => ((geq(U192_192, V193_193) & geq(V193_193, W194_194)) => geq(U192_192, W194_194)))))))), ! [U195_195] : ((ssItem(U195_195) => geq(U195_195, U195_195))), ! [U196_196] : ((ssItem(U196_196) => ~lt(U196_196, U196_196))), ! [U197_197] : ((ssItem(U197_197) => ! [V198_198] : ((ssItem(V198_198) => ! [W199_199] : ((ssItem(W199_199) => ((leq(U197_197, V198_198) & lt(V198_198, W199_199)) => lt(U197_197, W199_199)))))))), ! [U200_200] : ((ssItem(U200_200) => ! [V201_201] : ((ssItem(V201_201) => (leq(U200_200, V201_201) => (=(U200_200, V201_201) | lt(U200_200, V201_201))))))), ! [U202_202] : ((ssItem(U202_202) => ! [V203_203] : ((ssItem(V203_203) => (lt(U202_202, V203_203) <=> (~=(U202_202, V203_203) & leq(U202_202, V203_203))))))), ! [U204_204] : ((ssItem(U204_204) => ! [V205_205] : ((ssItem(V205_205) => (gt(U204_204, V205_205) => ~gt(V205_205, U204_204)))))), ! [U206_206] : ((ssItem(U206_206) => ! [V207_207] : ((ssItem(V207_207) => ! [W208_208] : ((ssItem(W208_208) => ((gt(U206_206, V207_207) & gt(V207_207, W208_208)) => gt(U206_206, W208_208))))))))
% 44.71/8.59
% 44.71/8.59 [2] DELTA_NOT_FORALL : ~! [U209_209] : ((ssList(U209_209) => ! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(U209_209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, U209_209))))))))))
% 44.71/8.59 -> [3] ~(ssList(skolem_U209209) => ! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209)))))))))
% 44.71/8.59
% 44.71/8.59 [3] ALPHA_NOT_IMPLY : ~(ssList(skolem_U209209) => ! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209)))))))))
% 44.71/8.59 -> [4] ssList(skolem_U209209), ~! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209))))))))
% 44.71/8.59
% 44.71/8.59 [4] DELTA_EXISTS : ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9)))))
% 44.71/8.59 -> [5] (ssItem(skolem_U88) & ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9))))
% 44.71/8.59
% 44.71/8.59 [5] ALPHA_AND : (ssItem(skolem_U88) & ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9))))
% 44.71/8.59 -> [6] ssItem(skolem_U88), ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9)))
% 44.71/8.59
% 44.71/8.59 [6] DELTA_NOT_FORALL : ~! [V210_210] : ((ssList(V210_210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, V210_210) | ~=(V210_210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209))))))))
% 44.71/8.59 -> [7] ~(ssList(skolem_V210210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209)))))))
% 44.71/8.59
% 44.71/8.59 [7] ALPHA_NOT_IMPLY : ~(ssList(skolem_V210210) => ! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209)))))))
% 44.71/8.59 -> [8] ssList(skolem_V210210), ~! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209))))))
% 44.71/8.59
% 44.71/8.59 [8] DELTA_EXISTS : ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9)))
% 44.71/8.59 -> [9] (ssItem(skolem_V99) & ~=(skolem_U88, skolem_V99))
% 44.71/8.59
% 44.71/8.59 [9] ALPHA_AND : (ssItem(skolem_V99) & ~=(skolem_U88, skolem_V99))
% 44.71/8.59 -> [10] ssItem(skolem_V99), ~=(skolem_U88, skolem_V99)
% 44.71/8.59
% 44.71/8.59 [10] DELTA_NOT_FORALL : ~! [W211_211] : ((ssList(W211_211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, W211_211)) | ~rearsegP(X212_212, W211_211)) | =(nil, skolem_U209209))))))
% 44.71/8.59 -> [11] ~(ssList(skolem_W211211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(X212_212, skolem_W211211)) | =(nil, skolem_U209209)))))
% 44.71/8.59
% 44.71/8.59 [11] ALPHA_NOT_IMPLY : ~(ssList(skolem_W211211) => ! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(X212_212, skolem_W211211)) | =(nil, skolem_U209209)))))
% 44.71/8.59 -> [12] ssList(skolem_W211211), ~! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(X212_212, skolem_W211211)) | =(nil, skolem_U209209))))
% 44.71/8.59
% 44.71/8.59 [12] DELTA_NOT_FORALL : ~! [X212_212] : ((ssList(X212_212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(X212_212, skolem_W211211)) | =(nil, skolem_U209209))))
% 44.71/8.59 -> [13] ~(ssList(skolem_X212212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211)) | =(nil, skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [13] ALPHA_NOT_IMPLY : ~(ssList(skolem_X212212) => ((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211)) | =(nil, skolem_U209209)))
% 44.71/8.59 -> [14] ssList(skolem_X212212), ~((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211)) | =(nil, skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [14] ALPHA_NOT_OR : ~((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211)) | =(nil, skolem_U209209))
% 44.71/8.59 -> [15] ~(((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211)), ~=(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [15] ALPHA_NOT_OR : ~(((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | ~rearsegP(skolem_X212212, skolem_W211211))
% 44.71/8.59 -> [16] ~((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)), ~~rearsegP(skolem_X212212, skolem_W211211)
% 44.71/8.59
% 44.71/8.59 [16] ALPHA_NOT_OR : ~((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211))
% 44.71/8.59 -> [17] ~(~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)), ~~=(skolem_U209209, skolem_W211211)
% 44.71/8.59
% 44.71/8.59 [17] ALPHA_NOT_NOT : ~~rearsegP(skolem_X212212, skolem_W211211)
% 44.71/8.59 -> [18] rearsegP(skolem_X212212, skolem_W211211)
% 44.71/8.59
% 44.71/8.59 [18] ALPHA_NOT_OR : ~(~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212))
% 44.71/8.59 -> [19] ~~=(nil, skolem_V210210), ~~=(skolem_V210210, skolem_X212212)
% 44.71/8.59
% 44.71/8.59 [19] ALPHA_NOT_NOT : ~~=(skolem_U209209, skolem_W211211)
% 44.71/8.59 -> [20] =(skolem_U209209, skolem_W211211)
% 44.71/8.59
% 44.71/8.59 [20] ALPHA_NOT_NOT : ~~=(nil, skolem_V210210)
% 44.71/8.59 -> [21] =(nil, skolem_V210210)
% 44.71/8.59
% 44.71/8.59 [21] ALPHA_NOT_NOT : ~~=(skolem_V210210, skolem_X212212)
% 44.71/8.59 -> [22] =(skolem_V210210, skolem_X212212)
% 44.71/8.59
% 44.71/8.59 [22] GAMMA_FORALL : ! [U6_6] : ((ssItem(U6_6) => ! [V7_7] : ((ssItem(V7_7) => (neq(U6_6, V7_7) <=> ~=(U6_6, V7_7))))))
% 44.71/8.59 -> [23] (ssItem(skolem_V99) => ! [V7_7] : ((ssItem(V7_7) => (neq(skolem_V99, V7_7) <=> ~=(skolem_V99, V7_7)))))
% 44.71/8.59
% 44.71/8.59 [23] BETA_IMPLY : (ssItem(skolem_V99) => ! [V7_7] : ((ssItem(V7_7) => (neq(skolem_V99, V7_7) <=> ~=(skolem_V99, V7_7)))))
% 44.71/8.59 -> [24] ~ssItem(skolem_V99)
% 44.71/8.59 -> [25] ! [V7_7] : ((ssItem(V7_7) => (neq(skolem_V99, V7_7) <=> ~=(skolem_V99, V7_7))))
% 44.71/8.59
% 44.71/8.59 [24] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [25] GAMMA_FORALL : ! [U10_10] : ((ssList(U10_10) => ! [V11_11] : ((ssItem(V11_11) => (memberP(U10_10, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), U10_10))))))))))
% 44.71/8.59 -> [26] (ssList(nil) => ! [V11_11] : ((ssItem(V11_11) => (memberP(nil, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), nil)))))))))
% 44.71/8.59
% 44.71/8.59 [26] BETA_IMPLY : (ssList(nil) => ! [V11_11] : ((ssItem(V11_11) => (memberP(nil, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), nil)))))))))
% 44.71/8.59 -> [27] ~ssList(nil)
% 44.71/8.59 -> [28] ! [V11_11] : ((ssItem(V11_11) => (memberP(nil, V11_11) <=> ? [W12_12] : ((ssList(W12_12) & ? [X13_13] : ((ssList(X13_13) & =(app(W12_12, cons(V11_11, X13_13)), nil))))))))
% 44.71/8.59
% 44.71/8.59 [27] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [28] GAMMA_FORALL : ! [U14_14] : ((ssList(U14_14) => (singletonP(U14_14) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), U14_14))))))
% 44.71/8.59 -> [29] (ssList(nil) => (singletonP(nil) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil)))))
% 44.71/8.59
% 44.71/8.59 [29] BETA_IMPLY : (ssList(nil) => (singletonP(nil) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil)))))
% 44.71/8.59 -> [30] ~ssList(nil)
% 44.71/8.59 -> [31] (singletonP(nil) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil))))
% 44.71/8.59
% 44.71/8.59 [30] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [31] BETA_EQUIV : (singletonP(nil) <=> ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil))))
% 44.71/8.59 -> [32] ~singletonP(nil), ~? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil)))
% 44.71/8.59 -> [33] singletonP(nil), ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil)))
% 44.71/8.59
% 44.71/8.59 [33] DELTA_EXISTS : ? [V15_15] : ((ssItem(V15_15) & =(cons(V15_15, nil), nil)))
% 44.71/8.59 -> [34] (ssItem(skolem_V1515(nil)) & =(cons(skolem_V1515(nil), nil), nil))
% 44.71/8.59
% 44.71/8.59 [34] ALPHA_AND : (ssItem(skolem_V1515(nil)) & =(cons(skolem_V1515(nil), nil), nil))
% 44.71/8.59 -> [35] ssItem(skolem_V1515(nil)), =(cons(skolem_V1515(nil), nil), nil)
% 44.71/8.59
% 44.71/8.59 [35] CLOSURE : (ssItem(skolem_V1515(nil)) & =(cons(skolem_V1515(nil), nil), nil))
% 44.71/8.59
% 44.71/8.59 [32] GAMMA_FORALL : ! [U16_16] : ((ssList(U16_16) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(U16_16, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), U16_16))))))))
% 44.71/8.59 -> [36] (ssList(nil) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(nil, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), nil)))))))
% 44.71/8.59
% 44.71/8.59 [36] BETA_IMPLY : (ssList(nil) => ! [V17_17] : ((ssList(V17_17) => (frontsegP(nil, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), nil)))))))
% 44.71/8.59 -> [37] ~ssList(nil)
% 44.71/8.59 -> [38] ! [V17_17] : ((ssList(V17_17) => (frontsegP(nil, V17_17) <=> ? [W18_18] : ((ssList(W18_18) & =(app(V17_17, W18_18), nil))))))
% 44.71/8.59
% 44.71/8.59 [37] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [38] GAMMA_FORALL : ! [U19_19] : ((ssList(U19_19) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(U19_19, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), U19_19))))))))
% 44.71/8.59 -> [39] (ssList(nil) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(nil, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), nil)))))))
% 44.71/8.59
% 44.71/8.59 [39] BETA_IMPLY : (ssList(nil) => ! [V20_20] : ((ssList(V20_20) => (rearsegP(nil, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), nil)))))))
% 44.71/8.59 -> [40] ~ssList(nil)
% 44.71/8.59 -> [41] ! [V20_20] : ((ssList(V20_20) => (rearsegP(nil, V20_20) <=> ? [W21_21] : ((ssList(W21_21) & =(app(W21_21, V20_20), nil))))))
% 44.71/8.59
% 44.71/8.59 [40] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [41] GAMMA_FORALL : ! [U22_22] : ((ssList(U22_22) => ! [V23_23] : ((ssList(V23_23) => (segmentP(U22_22, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), U22_22))))))))))
% 44.71/8.59 -> [42] (ssList(nil) => ! [V23_23] : ((ssList(V23_23) => (segmentP(nil, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), nil)))))))))
% 44.71/8.59
% 44.71/8.59 [42] BETA_IMPLY : (ssList(nil) => ! [V23_23] : ((ssList(V23_23) => (segmentP(nil, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), nil)))))))))
% 44.71/8.59 -> [43] ~ssList(nil)
% 44.71/8.59 -> [44] ! [V23_23] : ((ssList(V23_23) => (segmentP(nil, V23_23) <=> ? [W24_24] : ((ssList(W24_24) & ? [X25_25] : ((ssList(X25_25) & =(app(app(W24_24, V23_23), X25_25), nil))))))))
% 44.71/8.59
% 44.71/8.59 [43] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [44] GAMMA_FORALL : ! [U26_26] : ((ssList(U26_26) => (cyclefreeP(U26_26) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), U26_26) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27))))))))))))))))
% 44.71/8.59 -> [45] (ssList(nil) => (cyclefreeP(nil) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))
% 44.71/8.59
% 44.71/8.59 [45] BETA_IMPLY : (ssList(nil) => (cyclefreeP(nil) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))))
% 44.71/8.59 -> [46] ~ssList(nil)
% 44.71/8.59 -> [47] (cyclefreeP(nil) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27))))))))))))))
% 44.71/8.59
% 44.71/8.59 [46] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [47] BETA_EQUIV : (cyclefreeP(nil) <=> ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27))))))))))))))
% 44.71/8.59 -> [48] ~cyclefreeP(nil), ~! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))
% 44.71/8.59 -> [49] cyclefreeP(nil), ! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))
% 44.71/8.59
% 44.71/8.59 [48] DELTA_NOT_FORALL : ~! [V27_27] : ((ssItem(V27_27) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(V27_27, Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(V27_27, W28_28) & leq(W28_28, V27_27)))))))))))))
% 44.71/8.59 -> [50] ~(ssItem(skolem_V2727(nil)) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(skolem_V2727(nil), W28_28) & leq(W28_28, skolem_V2727(nil)))))))))))))
% 44.71/8.59
% 44.71/8.59 [50] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V2727(nil)) => ! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(skolem_V2727(nil), W28_28) & leq(W28_28, skolem_V2727(nil)))))))))))))
% 44.71/8.59 -> [51] ssItem(skolem_V2727(nil)), ~! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(skolem_V2727(nil), W28_28) & leq(W28_28, skolem_V2727(nil))))))))))))
% 44.71/8.59
% 44.71/8.59 [51] DELTA_NOT_FORALL : ~! [W28_28] : ((ssItem(W28_28) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(W28_28, Z31_31)), nil) => ~(leq(skolem_V2727(nil), W28_28) & leq(W28_28, skolem_V2727(nil))))))))))))
% 44.71/8.59 -> [57] ~(ssItem(skolem_W2828(nil)) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))))))
% 44.71/8.59
% 44.71/8.59 [57] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W2828(nil)) => ! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))))))
% 44.71/8.59 -> [58] ssItem(skolem_W2828(nil)), ~! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [58] DELTA_NOT_FORALL : ~! [X29_29] : ((ssList(X29_29) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(X29_29, cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))))))
% 44.71/8.59 -> [62] ~(ssList(skolem_X2929(nil)) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [62] ALPHA_NOT_IMPLY : ~(ssList(skolem_X2929(nil)) => ! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))))
% 44.71/8.59 -> [65] ssList(skolem_X2929(nil)), ~! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))))
% 44.71/8.59
% 44.71/8.59 [65] DELTA_NOT_FORALL : ~! [Y30_30] : ((ssList(Y30_30) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), Y30_30)), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))))
% 44.71/8.59 -> [72] ~(ssList(skolem_Y3030(nil)) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))
% 44.71/8.59
% 44.71/8.59 [72] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y3030(nil)) => ! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))))
% 44.71/8.59 -> [74] ssList(skolem_Y3030(nil)), ~! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))
% 44.71/8.59
% 44.71/8.59 [74] DELTA_NOT_FORALL : ~! [Z31_31] : ((ssList(Z31_31) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), Z31_31)), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))))
% 44.71/8.59 -> [86] ~(ssList(skolem_Z3131(nil)) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), skolem_Z3131(nil))), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))
% 44.71/8.59
% 44.71/8.59 [86] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z3131(nil)) => (=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), skolem_Z3131(nil))), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))))
% 44.71/8.59 -> [89] ssList(skolem_Z3131(nil)), ~(=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), skolem_Z3131(nil))), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))
% 44.71/8.59
% 44.71/8.59 [89] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), skolem_Z3131(nil))), nil) => ~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil))))
% 44.71/8.59 -> [110] =(app(app(skolem_X2929(nil), cons(skolem_V2727(nil), skolem_Y3030(nil))), cons(skolem_W2828(nil), skolem_Z3131(nil))), nil), ~~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))
% 44.71/8.59
% 44.71/8.59 [110] ALPHA_NOT_NOT : ~~(leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))
% 44.71/8.59 -> [136] (leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))
% 44.71/8.59
% 44.71/8.59 [136] ALPHA_AND : (leq(skolem_V2727(nil), skolem_W2828(nil)) & leq(skolem_W2828(nil), skolem_V2727(nil)))
% 44.71/8.59 -> [137] leq(skolem_V2727(nil), skolem_W2828(nil)), leq(skolem_W2828(nil), skolem_V2727(nil))
% 44.71/8.59
% 44.71/8.59 [137] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [49] GAMMA_FORALL : ! [U32_32] : ((ssList(U32_32) => (totalorderP(U32_32) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), U32_32) => (leq(V33_33, W34_34) | leq(W34_34, V33_33))))))))))))))))
% 44.71/8.59 -> [52] (ssList(nil) => (totalorderP(nil) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))
% 44.71/8.59
% 44.71/8.59 [52] BETA_IMPLY : (ssList(nil) => (totalorderP(nil) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))))
% 44.71/8.59 -> [53] ~ssList(nil)
% 44.71/8.59 -> [54] (totalorderP(nil) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33))))))))))))))
% 44.71/8.59
% 44.71/8.59 [53] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [54] BETA_EQUIV : (totalorderP(nil) <=> ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33))))))))))))))
% 44.71/8.59 -> [55] ~totalorderP(nil), ~! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))
% 44.71/8.59 -> [56] totalorderP(nil), ! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))
% 44.71/8.59
% 44.71/8.59 [55] DELTA_NOT_FORALL : ~! [V33_33] : ((ssItem(V33_33) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(V33_33, Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(V33_33, W34_34) | leq(W34_34, V33_33)))))))))))))
% 44.71/8.59 -> [59] ~(ssItem(skolem_V3333(nil)) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(skolem_V3333(nil), W34_34) | leq(W34_34, skolem_V3333(nil)))))))))))))
% 44.71/8.59
% 44.71/8.59 [59] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V3333(nil)) => ! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(skolem_V3333(nil), W34_34) | leq(W34_34, skolem_V3333(nil)))))))))))))
% 44.71/8.59 -> [60] ssItem(skolem_V3333(nil)), ~! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(skolem_V3333(nil), W34_34) | leq(W34_34, skolem_V3333(nil))))))))))))
% 44.71/8.59
% 44.71/8.59 [60] DELTA_NOT_FORALL : ~! [W34_34] : ((ssItem(W34_34) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(W34_34, Z37_37)), nil) => (leq(skolem_V3333(nil), W34_34) | leq(W34_34, skolem_V3333(nil))))))))))))
% 44.71/8.59 -> [68] ~(ssItem(skolem_W3434(nil)) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))))))
% 44.71/8.59
% 44.71/8.59 [68] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W3434(nil)) => ! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))))))
% 44.71/8.59 -> [69] ssItem(skolem_W3434(nil)), ~! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [69] DELTA_NOT_FORALL : ~! [X35_35] : ((ssList(X35_35) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(X35_35, cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))))))
% 44.71/8.59 -> [79] ~(ssList(skolem_X3535(nil)) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [79] ALPHA_NOT_IMPLY : ~(ssList(skolem_X3535(nil)) => ! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))))
% 44.71/8.59 -> [80] ssList(skolem_X3535(nil)), ~! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))))
% 44.71/8.59
% 44.71/8.59 [80] DELTA_NOT_FORALL : ~! [Y36_36] : ((ssList(Y36_36) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), Y36_36)), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))))
% 44.71/8.59 -> [90] ~(ssList(skolem_Y3636(nil)) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))
% 44.71/8.59
% 44.71/8.59 [90] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y3636(nil)) => ! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))))
% 44.71/8.59 -> [93] ssList(skolem_Y3636(nil)), ~! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))
% 44.71/8.59
% 44.71/8.59 [93] DELTA_NOT_FORALL : ~! [Z37_37] : ((ssList(Z37_37) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), Z37_37)), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))))
% 44.71/8.59 -> [105] ~(ssList(skolem_Z3737(nil)) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), skolem_Z3737(nil))), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))
% 44.71/8.59
% 44.71/8.59 [105] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z3737(nil)) => (=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), skolem_Z3737(nil))), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))))
% 44.71/8.59 -> [108] ssList(skolem_Z3737(nil)), ~(=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), skolem_Z3737(nil))), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))
% 44.71/8.59
% 44.71/8.59 [108] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), skolem_Z3737(nil))), nil) => (leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil))))
% 44.71/8.59 -> [129] =(app(app(skolem_X3535(nil), cons(skolem_V3333(nil), skolem_Y3636(nil))), cons(skolem_W3434(nil), skolem_Z3737(nil))), nil), ~(leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))
% 44.71/8.59
% 44.71/8.59 [129] ALPHA_NOT_OR : ~(leq(skolem_V3333(nil), skolem_W3434(nil)) | leq(skolem_W3434(nil), skolem_V3333(nil)))
% 44.71/8.59 -> [162] ~leq(skolem_V3333(nil), skolem_W3434(nil)), ~leq(skolem_W3434(nil), skolem_V3333(nil))
% 44.71/8.59
% 44.71/8.59 [162] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [56] GAMMA_FORALL : ! [U38_38] : ((ssList(U38_38) => (strictorderP(U38_38) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), U38_38) => (lt(V39_39, W40_40) | lt(W40_40, V39_39))))))))))))))))
% 44.71/8.59 -> [61] (ssList(nil) => (strictorderP(nil) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))
% 44.71/8.59
% 44.71/8.59 [61] BETA_IMPLY : (ssList(nil) => (strictorderP(nil) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))))
% 44.71/8.59 -> [63] ~ssList(nil)
% 44.71/8.59 -> [64] (strictorderP(nil) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39))))))))))))))
% 44.71/8.59
% 44.71/8.59 [63] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [64] BETA_EQUIV : (strictorderP(nil) <=> ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39))))))))))))))
% 44.71/8.59 -> [66] ~strictorderP(nil), ~! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))
% 44.71/8.59 -> [67] strictorderP(nil), ! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))
% 44.71/8.59
% 44.71/8.59 [66] DELTA_NOT_FORALL : ~! [V39_39] : ((ssItem(V39_39) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(V39_39, Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(V39_39, W40_40) | lt(W40_40, V39_39)))))))))))))
% 44.71/8.59 -> [70] ~(ssItem(skolem_V3939(nil)) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(skolem_V3939(nil), W40_40) | lt(W40_40, skolem_V3939(nil)))))))))))))
% 44.71/8.59
% 44.71/8.59 [70] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V3939(nil)) => ! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(skolem_V3939(nil), W40_40) | lt(W40_40, skolem_V3939(nil)))))))))))))
% 44.71/8.59 -> [71] ssItem(skolem_V3939(nil)), ~! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(skolem_V3939(nil), W40_40) | lt(W40_40, skolem_V3939(nil))))))))))))
% 44.71/8.59
% 44.71/8.59 [71] DELTA_NOT_FORALL : ~! [W40_40] : ((ssItem(W40_40) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(W40_40, Z43_43)), nil) => (lt(skolem_V3939(nil), W40_40) | lt(W40_40, skolem_V3939(nil))))))))))))
% 44.71/8.59 -> [81] ~(ssItem(skolem_W4040(nil)) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))))))
% 44.71/8.59
% 44.71/8.59 [81] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W4040(nil)) => ! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))))))
% 44.71/8.59 -> [82] ssItem(skolem_W4040(nil)), ~! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [82] DELTA_NOT_FORALL : ~! [X41_41] : ((ssList(X41_41) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(X41_41, cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))))))
% 44.71/8.59 -> [94] ~(ssList(skolem_X4141(nil)) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [94] ALPHA_NOT_IMPLY : ~(ssList(skolem_X4141(nil)) => ! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))))
% 44.71/8.59 -> [95] ssList(skolem_X4141(nil)), ~! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))))
% 44.71/8.59
% 44.71/8.59 [95] DELTA_NOT_FORALL : ~! [Y42_42] : ((ssList(Y42_42) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), Y42_42)), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))))
% 44.71/8.59 -> [106] ~(ssList(skolem_Y4242(nil)) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))
% 44.71/8.59
% 44.71/8.59 [106] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y4242(nil)) => ! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))))
% 44.71/8.59 -> [109] ssList(skolem_Y4242(nil)), ~! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))
% 44.71/8.59
% 44.71/8.59 [109] DELTA_NOT_FORALL : ~! [Z43_43] : ((ssList(Z43_43) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), Z43_43)), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))))
% 44.71/8.59 -> [123] ~(ssList(skolem_Z4343(nil)) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), skolem_Z4343(nil))), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))
% 44.71/8.59
% 44.71/8.59 [123] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z4343(nil)) => (=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), skolem_Z4343(nil))), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))))
% 44.71/8.59 -> [125] ssList(skolem_Z4343(nil)), ~(=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), skolem_Z4343(nil))), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))
% 44.71/8.59
% 44.71/8.59 [125] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), skolem_Z4343(nil))), nil) => (lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil))))
% 44.71/8.59 -> [161] =(app(app(skolem_X4141(nil), cons(skolem_V3939(nil), skolem_Y4242(nil))), cons(skolem_W4040(nil), skolem_Z4343(nil))), nil), ~(lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))
% 44.71/8.59
% 44.71/8.59 [161] ALPHA_NOT_OR : ~(lt(skolem_V3939(nil), skolem_W4040(nil)) | lt(skolem_W4040(nil), skolem_V3939(nil)))
% 44.71/8.59 -> [172] ~lt(skolem_V3939(nil), skolem_W4040(nil)), ~lt(skolem_W4040(nil), skolem_V3939(nil))
% 44.71/8.59
% 44.71/8.59 [172] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [67] GAMMA_FORALL : ! [U44_44] : ((ssList(U44_44) => (totalorderedP(U44_44) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), U44_44) => leq(V45_45, W46_46)))))))))))))))
% 44.71/8.59 -> [73] (ssList(nil) => (totalorderedP(nil) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46))))))))))))))
% 44.71/8.59
% 44.71/8.59 [73] BETA_IMPLY : (ssList(nil) => (totalorderedP(nil) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46))))))))))))))
% 44.71/8.59 -> [75] ~ssList(nil)
% 44.71/8.59 -> [76] (totalorderedP(nil) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46)))))))))))))
% 44.71/8.59
% 44.71/8.59 [75] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [76] BETA_EQUIV : (totalorderedP(nil) <=> ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46)))))))))))))
% 44.71/8.59 -> [77] ~totalorderedP(nil), ~! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46))))))))))))
% 44.71/8.59 -> [78] totalorderedP(nil), ! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46))))))))))))
% 44.71/8.59
% 44.71/8.59 [77] DELTA_NOT_FORALL : ~! [V45_45] : ((ssItem(V45_45) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(V45_45, Y48_48)), cons(W46_46, Z49_49)), nil) => leq(V45_45, W46_46))))))))))))
% 44.71/8.59 -> [83] ~(ssItem(skolem_V4545(nil)) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(W46_46, Z49_49)), nil) => leq(skolem_V4545(nil), W46_46)))))))))))
% 44.71/8.59
% 44.71/8.59 [83] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V4545(nil)) => ! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(W46_46, Z49_49)), nil) => leq(skolem_V4545(nil), W46_46)))))))))))
% 44.71/8.59 -> [84] ssItem(skolem_V4545(nil)), ~! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(W46_46, Z49_49)), nil) => leq(skolem_V4545(nil), W46_46))))))))))
% 44.71/8.59
% 44.71/8.59 [84] DELTA_NOT_FORALL : ~! [W46_46] : ((ssItem(W46_46) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(W46_46, Z49_49)), nil) => leq(skolem_V4545(nil), W46_46))))))))))
% 44.71/8.59 -> [96] ~(ssItem(skolem_W4646(nil)) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [96] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W4646(nil)) => ! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))))))
% 44.71/8.59 -> [97] ssItem(skolem_W4646(nil)), ~! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [97] DELTA_NOT_FORALL : ~! [X47_47] : ((ssList(X47_47) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(X47_47, cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))))))
% 44.71/8.59 -> [107] ~(ssList(skolem_X4747(nil)) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))))
% 44.71/8.59
% 44.71/8.59 [107] ALPHA_NOT_IMPLY : ~(ssList(skolem_X4747(nil)) => ! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))))
% 44.71/8.59 -> [111] ssList(skolem_X4747(nil)), ~! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))))
% 44.71/8.59
% 44.71/8.59 [111] DELTA_NOT_FORALL : ~! [Y48_48] : ((ssList(Y48_48) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), Y48_48)), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))))
% 44.71/8.59 -> [121] ~(ssList(skolem_Y4848(nil)) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))
% 44.71/8.59
% 44.71/8.59 [121] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y4848(nil)) => ! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))))
% 44.71/8.59 -> [122] ssList(skolem_Y4848(nil)), ~! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))
% 44.71/8.59
% 44.71/8.59 [122] DELTA_NOT_FORALL : ~! [Z49_49] : ((ssList(Z49_49) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), Z49_49)), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))))
% 44.71/8.59 -> [153] ~(ssList(skolem_Z4949(nil)) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), skolem_Z4949(nil))), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))
% 44.71/8.59
% 44.71/8.59 [153] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z4949(nil)) => (=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), skolem_Z4949(nil))), nil) => leq(skolem_V4545(nil), skolem_W4646(nil))))
% 44.71/8.59 -> [154] ssList(skolem_Z4949(nil)), ~(=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), skolem_Z4949(nil))), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))
% 44.71/8.59
% 44.71/8.59 [154] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), skolem_Z4949(nil))), nil) => leq(skolem_V4545(nil), skolem_W4646(nil)))
% 44.71/8.59 -> [163] =(app(app(skolem_X4747(nil), cons(skolem_V4545(nil), skolem_Y4848(nil))), cons(skolem_W4646(nil), skolem_Z4949(nil))), nil), ~leq(skolem_V4545(nil), skolem_W4646(nil))
% 44.71/8.59
% 44.71/8.59 [163] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [78] GAMMA_FORALL : ! [U50_50] : ((ssList(U50_50) => (strictorderedP(U50_50) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), U50_50) => lt(V51_51, W52_52)))))))))))))))
% 44.71/8.59 -> [85] (ssList(nil) => (strictorderedP(nil) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52))))))))))))))
% 44.71/8.59
% 44.71/8.59 [85] BETA_IMPLY : (ssList(nil) => (strictorderedP(nil) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52))))))))))))))
% 44.71/8.59 -> [87] ~ssList(nil)
% 44.71/8.59 -> [88] (strictorderedP(nil) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52)))))))))))))
% 44.71/8.59
% 44.71/8.59 [87] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [88] BETA_EQUIV : (strictorderedP(nil) <=> ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52)))))))))))))
% 44.71/8.59 -> [91] ~strictorderedP(nil), ~! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52))))))))))))
% 44.71/8.59 -> [92] strictorderedP(nil), ! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52))))))))))))
% 44.71/8.59
% 44.71/8.59 [91] DELTA_NOT_FORALL : ~! [V51_51] : ((ssItem(V51_51) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(V51_51, Y54_54)), cons(W52_52, Z55_55)), nil) => lt(V51_51, W52_52))))))))))))
% 44.71/8.59 -> [98] ~(ssItem(skolem_V5151(nil)) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(W52_52, Z55_55)), nil) => lt(skolem_V5151(nil), W52_52)))))))))))
% 44.71/8.59
% 44.71/8.59 [98] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V5151(nil)) => ! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(W52_52, Z55_55)), nil) => lt(skolem_V5151(nil), W52_52)))))))))))
% 44.71/8.59 -> [99] ssItem(skolem_V5151(nil)), ~! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(W52_52, Z55_55)), nil) => lt(skolem_V5151(nil), W52_52))))))))))
% 44.71/8.59
% 44.71/8.59 [99] DELTA_NOT_FORALL : ~! [W52_52] : ((ssItem(W52_52) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(W52_52, Z55_55)), nil) => lt(skolem_V5151(nil), W52_52))))))))))
% 44.71/8.59 -> [112] ~(ssItem(skolem_W5252(nil)) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [112] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W5252(nil)) => ! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))))))
% 44.71/8.59 -> [113] ssItem(skolem_W5252(nil)), ~! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [113] DELTA_NOT_FORALL : ~! [X53_53] : ((ssList(X53_53) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(X53_53, cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))))))
% 44.71/8.59 -> [124] ~(ssList(skolem_X5353(nil)) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))))
% 44.71/8.59
% 44.71/8.59 [124] ALPHA_NOT_IMPLY : ~(ssList(skolem_X5353(nil)) => ! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))))
% 44.71/8.59 -> [126] ssList(skolem_X5353(nil)), ~! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))))
% 44.71/8.59
% 44.71/8.59 [126] DELTA_NOT_FORALL : ~! [Y54_54] : ((ssList(Y54_54) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), Y54_54)), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))))
% 44.71/8.59 -> [157] ~(ssList(skolem_Y5454(nil)) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))
% 44.71/8.59
% 44.71/8.59 [157] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y5454(nil)) => ! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))))
% 44.71/8.59 -> [160] ssList(skolem_Y5454(nil)), ~! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))
% 44.71/8.59
% 44.71/8.59 [160] DELTA_NOT_FORALL : ~! [Z55_55] : ((ssList(Z55_55) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), Z55_55)), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))))
% 44.71/8.59 -> [168] ~(ssList(skolem_Z5555(nil)) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), skolem_Z5555(nil))), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))
% 44.71/8.59
% 44.71/8.59 [168] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z5555(nil)) => (=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), skolem_Z5555(nil))), nil) => lt(skolem_V5151(nil), skolem_W5252(nil))))
% 44.71/8.59 -> [169] ssList(skolem_Z5555(nil)), ~(=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), skolem_Z5555(nil))), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))
% 44.71/8.59
% 44.71/8.59 [169] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), skolem_Z5555(nil))), nil) => lt(skolem_V5151(nil), skolem_W5252(nil)))
% 44.71/8.59 -> [177] =(app(app(skolem_X5353(nil), cons(skolem_V5151(nil), skolem_Y5454(nil))), cons(skolem_W5252(nil), skolem_Z5555(nil))), nil), ~lt(skolem_V5151(nil), skolem_W5252(nil))
% 44.71/8.59
% 44.71/8.59 [177] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [92] GAMMA_FORALL : ! [U56_56] : ((ssList(U56_56) => (duplicatefreeP(U56_56) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), U56_56) => ~=(V57_57, W58_58)))))))))))))))
% 44.71/8.59 -> [100] (ssList(nil) => (duplicatefreeP(nil) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58))))))))))))))
% 44.71/8.59
% 44.71/8.59 [100] BETA_IMPLY : (ssList(nil) => (duplicatefreeP(nil) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58))))))))))))))
% 44.71/8.59 -> [101] ~ssList(nil)
% 44.71/8.59 -> [102] (duplicatefreeP(nil) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58)))))))))))))
% 44.71/8.59
% 44.71/8.59 [101] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [102] BETA_EQUIV : (duplicatefreeP(nil) <=> ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58)))))))))))))
% 44.71/8.59 -> [103] ~duplicatefreeP(nil), ~! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58))))))))))))
% 44.71/8.59 -> [104] duplicatefreeP(nil), ! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58))))))))))))
% 44.71/8.59
% 44.71/8.59 [103] DELTA_NOT_FORALL : ~! [V57_57] : ((ssItem(V57_57) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(V57_57, Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(V57_57, W58_58))))))))))))
% 44.71/8.59 -> [114] ~(ssItem(skolem_V5757(nil)) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(skolem_V5757(nil), W58_58)))))))))))
% 44.71/8.59
% 44.71/8.59 [114] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V5757(nil)) => ! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(skolem_V5757(nil), W58_58)))))))))))
% 44.71/8.59 -> [115] ssItem(skolem_V5757(nil)), ~! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(skolem_V5757(nil), W58_58))))))))))
% 44.71/8.59
% 44.71/8.59 [115] DELTA_NOT_FORALL : ~! [W58_58] : ((ssItem(W58_58) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(W58_58, Z61_61)), nil) => ~=(skolem_V5757(nil), W58_58))))))))))
% 44.71/8.59 -> [127] ~(ssItem(skolem_W5858(nil)) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))))))
% 44.71/8.59
% 44.71/8.59 [127] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W5858(nil)) => ! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))))))
% 44.71/8.59 -> [128] ssItem(skolem_W5858(nil)), ~! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))))))
% 44.71/8.59
% 44.71/8.59 [128] DELTA_NOT_FORALL : ~! [X59_59] : ((ssList(X59_59) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(X59_59, cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))))))
% 44.71/8.59 -> [141] ~(ssList(skolem_X5959(nil)) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))))
% 44.71/8.59
% 44.71/8.59 [141] ALPHA_NOT_IMPLY : ~(ssList(skolem_X5959(nil)) => ! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))))
% 44.71/8.59 -> [144] ssList(skolem_X5959(nil)), ~! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))))
% 44.71/8.59
% 44.71/8.59 [144] DELTA_NOT_FORALL : ~! [Y60_60] : ((ssList(Y60_60) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), Y60_60)), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))))
% 44.71/8.59 -> [166] ~(ssList(skolem_Y6060(nil)) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))
% 44.71/8.59
% 44.71/8.59 [166] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y6060(nil)) => ! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))))
% 44.71/8.59 -> [167] ssList(skolem_Y6060(nil)), ~! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))
% 44.71/8.59
% 44.71/8.59 [167] DELTA_NOT_FORALL : ~! [Z61_61] : ((ssList(Z61_61) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), Z61_61)), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))))
% 44.71/8.59 -> [175] ~(ssList(skolem_Z6161(nil)) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), skolem_Z6161(nil))), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))
% 44.71/8.59
% 44.71/8.59 [175] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z6161(nil)) => (=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), skolem_Z6161(nil))), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil))))
% 44.71/8.59 -> [176] ssList(skolem_Z6161(nil)), ~(=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), skolem_Z6161(nil))), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))
% 44.71/8.59
% 44.71/8.59 [176] ALPHA_NOT_IMPLY : ~(=(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), skolem_Z6161(nil))), nil) => ~=(skolem_V5757(nil), skolem_W5858(nil)))
% 44.71/8.59 -> [188] =(app(app(skolem_X5959(nil), cons(skolem_V5757(nil), skolem_Y6060(nil))), cons(skolem_W5858(nil), skolem_Z6161(nil))), nil), ~~=(skolem_V5757(nil), skolem_W5858(nil))
% 44.71/8.59
% 44.71/8.59 [188] ALPHA_NOT_NOT : ~~=(skolem_V5757(nil), skolem_W5858(nil))
% 44.71/8.59 -> [198] =(skolem_V5757(nil), skolem_W5858(nil))
% 44.71/8.59
% 44.71/8.59 [198] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [104] GAMMA_FORALL : ! [U62_62] : ((ssList(U62_62) => (equalelemsP(U62_62) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), U62_62) => =(V63_63, W64_64)))))))))))))
% 44.71/8.59 -> [116] (ssList(nil) => (equalelemsP(nil) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64))))))))))))
% 44.71/8.59
% 44.71/8.59 [116] BETA_IMPLY : (ssList(nil) => (equalelemsP(nil) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64))))))))))))
% 44.71/8.59 -> [117] ~ssList(nil)
% 44.71/8.59 -> [118] (equalelemsP(nil) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64)))))))))))
% 44.71/8.59
% 44.71/8.59 [117] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [118] BETA_EQUIV : (equalelemsP(nil) <=> ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64)))))))))))
% 44.71/8.59 -> [119] ~equalelemsP(nil), ~! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64))))))))))
% 44.71/8.59 -> [120] equalelemsP(nil), ! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64))))))))))
% 44.71/8.59
% 44.71/8.59 [119] DELTA_NOT_FORALL : ~! [V63_63] : ((ssItem(V63_63) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(V63_63, cons(W64_64, Y66_66))), nil) => =(V63_63, W64_64))))))))))
% 44.71/8.59 -> [130] ~(ssItem(skolem_V6363(nil)) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(W64_64, Y66_66))), nil) => =(skolem_V6363(nil), W64_64)))))))))
% 44.71/8.59
% 44.71/8.59 [130] ALPHA_NOT_IMPLY : ~(ssItem(skolem_V6363(nil)) => ! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(W64_64, Y66_66))), nil) => =(skolem_V6363(nil), W64_64)))))))))
% 44.71/8.59 -> [131] ssItem(skolem_V6363(nil)), ~! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(W64_64, Y66_66))), nil) => =(skolem_V6363(nil), W64_64))))))))
% 44.71/8.59
% 44.71/8.59 [131] DELTA_NOT_FORALL : ~! [W64_64] : ((ssItem(W64_64) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(W64_64, Y66_66))), nil) => =(skolem_V6363(nil), W64_64))))))))
% 44.71/8.59 -> [158] ~(ssItem(skolem_W6464(nil)) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))))))
% 44.71/8.59
% 44.71/8.59 [158] ALPHA_NOT_IMPLY : ~(ssItem(skolem_W6464(nil)) => ! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))))))
% 44.71/8.59 -> [159] ssItem(skolem_W6464(nil)), ~! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))))))
% 44.71/8.59
% 44.71/8.59 [159] DELTA_NOT_FORALL : ~! [X65_65] : ((ssList(X65_65) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(X65_65, cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))))))
% 44.71/8.59 -> [164] ~(ssList(skolem_X6565(nil)) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))))
% 44.71/8.59
% 44.71/8.59 [164] ALPHA_NOT_IMPLY : ~(ssList(skolem_X6565(nil)) => ! [Y66_66] : ((ssList(Y66_66) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))))
% 44.71/8.59 -> [165] ssList(skolem_X6565(nil)), ~! [Y66_66] : ((ssList(Y66_66) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))))
% 44.71/8.59
% 44.71/8.59 [165] DELTA_NOT_FORALL : ~! [Y66_66] : ((ssList(Y66_66) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), Y66_66))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))))
% 44.71/8.59 -> [173] ~(ssList(skolem_Y6666(nil)) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), skolem_Y6666(nil)))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))
% 44.71/8.59
% 44.71/8.59 [173] ALPHA_NOT_IMPLY : ~(ssList(skolem_Y6666(nil)) => (=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), skolem_Y6666(nil)))), nil) => =(skolem_V6363(nil), skolem_W6464(nil))))
% 44.71/8.59 -> [174] ssList(skolem_Y6666(nil)), ~(=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), skolem_Y6666(nil)))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))
% 44.71/8.59
% 44.71/8.59 [174] ALPHA_NOT_IMPLY : ~(=(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), skolem_Y6666(nil)))), nil) => =(skolem_V6363(nil), skolem_W6464(nil)))
% 44.71/8.59 -> [187] =(app(skolem_X6565(nil), cons(skolem_V6363(nil), cons(skolem_W6464(nil), skolem_Y6666(nil)))), nil), ~=(skolem_V6363(nil), skolem_W6464(nil))
% 44.71/8.59
% 44.71/8.59 [187] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [120] GAMMA_FORALL : ! [U67_67] : ((ssList(U67_67) => ! [V68_68] : ((ssList(V68_68) => (neq(U67_67, V68_68) <=> ~=(U67_67, V68_68))))))
% 44.71/8.59 -> [132] (ssList(skolem_X212212) => ! [V68_68] : ((ssList(V68_68) => (neq(skolem_X212212, V68_68) <=> ~=(skolem_X212212, V68_68)))))
% 44.71/8.59
% 44.71/8.59 [132] BETA_IMPLY : (ssList(skolem_X212212) => ! [V68_68] : ((ssList(V68_68) => (neq(skolem_X212212, V68_68) <=> ~=(skolem_X212212, V68_68)))))
% 44.71/8.59 -> [133] ~ssList(skolem_X212212)
% 44.71/8.59 -> [134] ! [V68_68] : ((ssList(V68_68) => (neq(skolem_X212212, V68_68) <=> ~=(skolem_X212212, V68_68))))
% 44.71/8.59
% 44.71/8.59 [133] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [134] GAMMA_FORALL : ! [U69_69] : ((ssList(U69_69) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, U69_69))))))
% 44.71/8.59 -> [135] (ssList(skolem_X212212) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, skolem_X212212)))))
% 44.71/8.59
% 44.71/8.59 [135] BETA_IMPLY : (ssList(skolem_X212212) => ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, skolem_X212212)))))
% 44.71/8.59 -> [138] ~ssList(skolem_X212212)
% 44.71/8.59 -> [139] ! [V70_70] : ((ssItem(V70_70) => ssList(cons(V70_70, skolem_X212212))))
% 44.71/8.59
% 44.71/8.59 [138] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [139] GAMMA_FORALL : ! [U71_71] : ((ssList(U71_71) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, U71_71), U71_71)))))
% 44.71/8.59 -> [140] (ssList(skolem_X212212) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, skolem_X212212), skolem_X212212))))
% 44.71/8.59
% 44.71/8.59 [140] BETA_IMPLY : (ssList(skolem_X212212) => ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, skolem_X212212), skolem_X212212))))
% 44.71/8.59 -> [142] ~ssList(skolem_X212212)
% 44.71/8.59 -> [143] ! [V72_72] : ((ssItem(V72_72) => ~=(cons(V72_72, skolem_X212212), skolem_X212212)))
% 44.71/8.59
% 44.71/8.59 [142] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [143] GAMMA_FORALL : ! [U73_73] : ((ssList(U73_73) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, U73_73), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, U73_73)))))))))))
% 44.71/8.59 -> [145] (ssList(nil) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, nil), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, nil))))))))))
% 44.71/8.59
% 44.71/8.59 [145] BETA_IMPLY : (ssList(nil) => ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, nil), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, nil))))))))))
% 44.71/8.59 -> [146] ~ssList(nil)
% 44.71/8.59 -> [147] ! [V74_74] : ((ssList(V74_74) => ! [W75_75] : ((ssItem(W75_75) => ! [X76_76] : ((ssItem(X76_76) => (=(cons(W75_75, nil), cons(X76_76, V74_74)) => (=(W75_75, X76_76) & =(V74_74, nil)))))))))
% 44.71/8.59
% 44.71/8.59 [146] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [147] GAMMA_FORALL : ! [U77_77] : ((ssList(U77_77) => (=(nil, U77_77) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), U77_77))))))))
% 44.71/8.59 -> [148] (ssList(skolem_U209209) => (=(nil, skolem_U209209) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209)))))))
% 44.71/8.59
% 44.71/8.59 [148] BETA_IMPLY : (ssList(skolem_U209209) => (=(nil, skolem_U209209) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209)))))))
% 44.71/8.59 -> [149] ~ssList(skolem_U209209)
% 44.71/8.59 -> [150] (=(nil, skolem_U209209) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209))))))
% 44.71/8.59
% 44.71/8.59 [149] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [150] BETA_OR : (=(nil, skolem_U209209) | ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209))))))
% 44.71/8.59 -> [151] =(nil, skolem_U209209)
% 44.71/8.59 -> [152] ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209)))))
% 44.71/8.59
% 44.71/8.59 [151] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [152] DELTA_EXISTS : ? [V78_78] : ((ssList(V78_78) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, V78_78), skolem_U209209)))))
% 44.71/8.59 -> [155] (ssList(skolem_V7878(skolem_U209209)) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, skolem_V7878(skolem_U209209)), skolem_U209209))))
% 44.71/8.59
% 44.71/8.59 [155] ALPHA_AND : (ssList(skolem_V7878(skolem_U209209)) & ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, skolem_V7878(skolem_U209209)), skolem_U209209))))
% 44.71/8.59 -> [156] ssList(skolem_V7878(skolem_U209209)), ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, skolem_V7878(skolem_U209209)), skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [156] DELTA_EXISTS : ? [W79_79] : ((ssItem(W79_79) & =(cons(W79_79, skolem_V7878(skolem_U209209)), skolem_U209209)))
% 44.71/8.59 -> [170] (ssItem(skolem_W7979(skolem_U209209)) & =(cons(skolem_W7979(skolem_U209209), skolem_V7878(skolem_U209209)), skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [170] ALPHA_AND : (ssItem(skolem_W7979(skolem_U209209)) & =(cons(skolem_W7979(skolem_U209209), skolem_V7878(skolem_U209209)), skolem_U209209))
% 44.71/8.59 -> [171] ssItem(skolem_W7979(skolem_U209209)), =(cons(skolem_W7979(skolem_U209209), skolem_V7878(skolem_U209209)), skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [171] GAMMA_FORALL : ! [U80_80] : ((ssList(U80_80) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, U80_80))))))
% 44.71/8.59 -> [178] (ssList(skolem_V210210) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, skolem_V210210)))))
% 44.71/8.59
% 44.71/8.59 [178] BETA_IMPLY : (ssList(skolem_V210210) => ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, skolem_V210210)))))
% 44.71/8.59 -> [179] ~ssList(skolem_V210210)
% 44.71/8.59 -> [180] ! [V81_81] : ((ssItem(V81_81) => ~=(nil, cons(V81_81, skolem_V210210))))
% 44.71/8.59
% 44.71/8.59 [179] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [180] GAMMA_FORALL : ! [U82_82] : ((ssList(U82_82) => (~=(nil, U82_82) => ssItem(hd(U82_82)))))
% 44.71/8.59 -> [181] (ssList(skolem_U209209) => (~=(nil, skolem_U209209) => ssItem(hd(skolem_U209209))))
% 44.71/8.59
% 44.71/8.59 [181] BETA_IMPLY : (ssList(skolem_U209209) => (~=(nil, skolem_U209209) => ssItem(hd(skolem_U209209))))
% 44.71/8.59 -> [182] ~ssList(skolem_U209209)
% 44.71/8.59 -> [183] (~=(nil, skolem_U209209) => ssItem(hd(skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [182] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [183] BETA_IMPLY : (~=(nil, skolem_U209209) => ssItem(hd(skolem_U209209)))
% 44.71/8.59 -> [184] ~~=(nil, skolem_U209209)
% 44.71/8.59 -> [185] ssItem(hd(skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [184] ALPHA_NOT_NOT : ~~=(nil, skolem_U209209)
% 44.71/8.59 -> [186] =(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [186] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [185] GAMMA_FORALL : ! [U83_83] : ((ssList(U83_83) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, U83_83)), V84_84)))))
% 44.71/8.59 -> [189] (ssList(skolem_V7878(skolem_U209209)) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, skolem_V7878(skolem_U209209))), V84_84))))
% 44.71/8.59
% 44.71/8.59 [189] BETA_IMPLY : (ssList(skolem_V7878(skolem_U209209)) => ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, skolem_V7878(skolem_U209209))), V84_84))))
% 44.71/8.59 -> [190] ~ssList(skolem_V7878(skolem_U209209))
% 44.71/8.59 -> [191] ! [V84_84] : ((ssItem(V84_84) => =(hd(cons(V84_84, skolem_V7878(skolem_U209209))), V84_84)))
% 44.71/8.59
% 44.71/8.59 [190] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [191] GAMMA_FORALL : ! [U85_85] : ((ssList(U85_85) => (~=(nil, U85_85) => ssList(tl(U85_85)))))
% 44.71/8.59 -> [192] (ssList(skolem_U209209) => (~=(nil, skolem_U209209) => ssList(tl(skolem_U209209))))
% 44.71/8.59
% 44.71/8.59 [192] BETA_IMPLY : (ssList(skolem_U209209) => (~=(nil, skolem_U209209) => ssList(tl(skolem_U209209))))
% 44.71/8.59 -> [193] ~ssList(skolem_U209209)
% 44.71/8.59 -> [194] (~=(nil, skolem_U209209) => ssList(tl(skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [193] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [194] BETA_IMPLY : (~=(nil, skolem_U209209) => ssList(tl(skolem_U209209)))
% 44.71/8.59 -> [195] ~~=(nil, skolem_U209209)
% 44.71/8.59 -> [196] ssList(tl(skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [195] ALPHA_NOT_NOT : ~~=(nil, skolem_U209209)
% 44.71/8.59 -> [197] =(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [197] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [196] GAMMA_FORALL : ! [U86_86] : ((ssList(U86_86) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, U86_86)), U86_86)))))
% 44.71/8.59 -> [199] (ssList(tl(skolem_U209209)) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, tl(skolem_U209209))), tl(skolem_U209209)))))
% 44.71/8.59
% 44.71/8.59 [199] BETA_IMPLY : (ssList(tl(skolem_U209209)) => ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, tl(skolem_U209209))), tl(skolem_U209209)))))
% 44.71/8.59 -> [200] ~ssList(tl(skolem_U209209))
% 44.71/8.59 -> [201] ! [V87_87] : ((ssItem(V87_87) => =(tl(cons(V87_87, tl(skolem_U209209))), tl(skolem_U209209))))
% 44.71/8.59
% 44.71/8.59 [200] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [201] GAMMA_FORALL : ! [U88_88] : ((ssList(U88_88) => ! [V89_89] : ((ssList(V89_89) => ssList(app(U88_88, V89_89))))))
% 44.71/8.59 -> [202] (ssList(skolem_U209209) => ! [V89_89] : ((ssList(V89_89) => ssList(app(skolem_U209209, V89_89)))))
% 44.71/8.59
% 44.71/8.59 [202] BETA_IMPLY : (ssList(skolem_U209209) => ! [V89_89] : ((ssList(V89_89) => ssList(app(skolem_U209209, V89_89)))))
% 44.71/8.59 -> [203] ~ssList(skolem_U209209)
% 44.71/8.59 -> [204] ! [V89_89] : ((ssList(V89_89) => ssList(app(skolem_U209209, V89_89))))
% 44.71/8.59
% 44.71/8.59 [203] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [204] GAMMA_FORALL : ! [U90_90] : ((ssList(U90_90) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, U90_90)), app(cons(W92_92, V91_91), U90_90))))))))
% 44.71/8.59 -> [205] (ssList(skolem_W211211) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, skolem_W211211)), app(cons(W92_92, V91_91), skolem_W211211)))))))
% 44.71/8.59
% 44.71/8.59 [205] BETA_IMPLY : (ssList(skolem_W211211) => ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, skolem_W211211)), app(cons(W92_92, V91_91), skolem_W211211)))))))
% 44.71/8.59 -> [206] ~ssList(skolem_W211211)
% 44.71/8.59 -> [207] ! [V91_91] : ((ssList(V91_91) => ! [W92_92] : ((ssItem(W92_92) => =(cons(W92_92, app(V91_91, skolem_W211211)), app(cons(W92_92, V91_91), skolem_W211211))))))
% 44.71/8.59
% 44.71/8.59 [206] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [207] GAMMA_FORALL : ! [U93_93] : ((ssList(U93_93) => =(app(nil, U93_93), U93_93)))
% 44.71/8.59 -> [208] (ssList(skolem_W211211) => =(app(nil, skolem_W211211), skolem_W211211))
% 44.71/8.59
% 44.71/8.59 [208] BETA_IMPLY : (ssList(skolem_W211211) => =(app(nil, skolem_W211211), skolem_W211211))
% 44.71/8.59 -> [209] ~ssList(skolem_W211211)
% 44.71/8.59 -> [210] =(app(nil, skolem_W211211), skolem_W211211)
% 44.71/8.59
% 44.71/8.59 [209] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [210] GAMMA_FORALL : ! [U94_94] : ((ssItem(U94_94) => ! [V95_95] : ((ssItem(V95_95) => ((leq(U94_94, V95_95) & leq(V95_95, U94_94)) => =(U94_94, V95_95))))))
% 44.71/8.59 -> [211] (ssItem(skolem_V99) => ! [V95_95] : ((ssItem(V95_95) => ((leq(skolem_V99, V95_95) & leq(V95_95, skolem_V99)) => =(skolem_V99, V95_95)))))
% 44.71/8.59
% 44.71/8.59 [211] BETA_IMPLY : (ssItem(skolem_V99) => ! [V95_95] : ((ssItem(V95_95) => ((leq(skolem_V99, V95_95) & leq(V95_95, skolem_V99)) => =(skolem_V99, V95_95)))))
% 44.71/8.59 -> [212] ~ssItem(skolem_V99)
% 44.71/8.59 -> [213] ! [V95_95] : ((ssItem(V95_95) => ((leq(skolem_V99, V95_95) & leq(V95_95, skolem_V99)) => =(skolem_V99, V95_95))))
% 44.71/8.59
% 44.71/8.59 [212] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [213] GAMMA_FORALL : ! [U96_96] : ((ssItem(U96_96) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(U96_96, V97_97) & leq(V97_97, W98_98)) => leq(U96_96, W98_98))))))))
% 44.71/8.59 -> [214] (ssItem(hd(skolem_U209209)) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(hd(skolem_U209209), V97_97) & leq(V97_97, W98_98)) => leq(hd(skolem_U209209), W98_98)))))))
% 44.71/8.59
% 44.71/8.59 [214] BETA_IMPLY : (ssItem(hd(skolem_U209209)) => ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(hd(skolem_U209209), V97_97) & leq(V97_97, W98_98)) => leq(hd(skolem_U209209), W98_98)))))))
% 44.71/8.59 -> [215] ~ssItem(hd(skolem_U209209))
% 44.71/8.59 -> [216] ! [V97_97] : ((ssItem(V97_97) => ! [W98_98] : ((ssItem(W98_98) => ((leq(hd(skolem_U209209), V97_97) & leq(V97_97, W98_98)) => leq(hd(skolem_U209209), W98_98))))))
% 44.71/8.59
% 44.71/8.59 [215] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [216] GAMMA_FORALL : ! [U99_99] : ((ssItem(U99_99) => leq(U99_99, U99_99)))
% 44.71/8.59 -> [217] (ssItem(skolem_U88) => leq(skolem_U88, skolem_U88))
% 44.71/8.59
% 44.71/8.59 [217] BETA_IMPLY : (ssItem(skolem_U88) => leq(skolem_U88, skolem_U88))
% 44.71/8.59 -> [218] ~ssItem(skolem_U88)
% 44.71/8.59 -> [219] leq(skolem_U88, skolem_U88)
% 44.71/8.59
% 44.71/8.59 [218] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [219] GAMMA_FORALL : ! [U100_100] : ((ssItem(U100_100) => ! [V101_101] : ((ssItem(V101_101) => (geq(U100_100, V101_101) <=> leq(V101_101, U100_100))))))
% 44.71/8.59 -> [220] (ssItem(skolem_U88) => ! [V101_101] : ((ssItem(V101_101) => (geq(skolem_U88, V101_101) <=> leq(V101_101, skolem_U88)))))
% 44.71/8.59
% 44.71/8.59 [220] BETA_IMPLY : (ssItem(skolem_U88) => ! [V101_101] : ((ssItem(V101_101) => (geq(skolem_U88, V101_101) <=> leq(V101_101, skolem_U88)))))
% 44.71/8.59 -> [221] ~ssItem(skolem_U88)
% 44.71/8.59 -> [222] ! [V101_101] : ((ssItem(V101_101) => (geq(skolem_U88, V101_101) <=> leq(V101_101, skolem_U88))))
% 44.71/8.59
% 44.71/8.59 [221] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [222] GAMMA_FORALL : ! [U102_102] : ((ssItem(U102_102) => ! [V103_103] : ((ssItem(V103_103) => (lt(U102_102, V103_103) => ~lt(V103_103, U102_102))))))
% 44.71/8.59 -> [223] (ssItem(skolem_V99) => ! [V103_103] : ((ssItem(V103_103) => (lt(skolem_V99, V103_103) => ~lt(V103_103, skolem_V99)))))
% 44.71/8.59
% 44.71/8.59 [223] BETA_IMPLY : (ssItem(skolem_V99) => ! [V103_103] : ((ssItem(V103_103) => (lt(skolem_V99, V103_103) => ~lt(V103_103, skolem_V99)))))
% 44.71/8.59 -> [224] ~ssItem(skolem_V99)
% 44.71/8.59 -> [225] ! [V103_103] : ((ssItem(V103_103) => (lt(skolem_V99, V103_103) => ~lt(V103_103, skolem_V99))))
% 44.71/8.59
% 44.71/8.59 [224] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [225] GAMMA_FORALL : ! [U104_104] : ((ssItem(U104_104) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(U104_104, V105_105) & lt(V105_105, W106_106)) => lt(U104_104, W106_106))))))))
% 44.71/8.59 -> [226] (ssItem(skolem_V99) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(skolem_V99, V105_105) & lt(V105_105, W106_106)) => lt(skolem_V99, W106_106)))))))
% 44.71/8.59
% 44.71/8.59 [226] BETA_IMPLY : (ssItem(skolem_V99) => ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(skolem_V99, V105_105) & lt(V105_105, W106_106)) => lt(skolem_V99, W106_106)))))))
% 44.71/8.59 -> [227] ~ssItem(skolem_V99)
% 44.71/8.59 -> [228] ! [V105_105] : ((ssItem(V105_105) => ! [W106_106] : ((ssItem(W106_106) => ((lt(skolem_V99, V105_105) & lt(V105_105, W106_106)) => lt(skolem_V99, W106_106))))))
% 44.71/8.59
% 44.71/8.59 [227] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [228] GAMMA_FORALL : ! [U107_107] : ((ssItem(U107_107) => ! [V108_108] : ((ssItem(V108_108) => (gt(U107_107, V108_108) <=> lt(V108_108, U107_107))))))
% 44.71/8.59 -> [229] (ssItem(skolem_V99) => ! [V108_108] : ((ssItem(V108_108) => (gt(skolem_V99, V108_108) <=> lt(V108_108, skolem_V99)))))
% 44.71/8.59
% 44.71/8.59 [229] BETA_IMPLY : (ssItem(skolem_V99) => ! [V108_108] : ((ssItem(V108_108) => (gt(skolem_V99, V108_108) <=> lt(V108_108, skolem_V99)))))
% 44.71/8.59 -> [230] ~ssItem(skolem_V99)
% 44.71/8.59 -> [231] ! [V108_108] : ((ssItem(V108_108) => (gt(skolem_V99, V108_108) <=> lt(V108_108, skolem_V99))))
% 44.71/8.59
% 44.71/8.59 [230] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [231] GAMMA_FORALL : ! [U109_109] : ((ssItem(U109_109) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), U109_109) <=> (memberP(V110_110, U109_109) | memberP(W111_111, U109_109)))))))))
% 44.71/8.59 -> [232] (ssItem(hd(skolem_U209209)) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), hd(skolem_U209209)) <=> (memberP(V110_110, hd(skolem_U209209)) | memberP(W111_111, hd(skolem_U209209)))))))))
% 44.71/8.59
% 44.71/8.59 [232] BETA_IMPLY : (ssItem(hd(skolem_U209209)) => ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), hd(skolem_U209209)) <=> (memberP(V110_110, hd(skolem_U209209)) | memberP(W111_111, hd(skolem_U209209)))))))))
% 44.71/8.59 -> [233] ~ssItem(hd(skolem_U209209))
% 44.71/8.59 -> [234] ! [V110_110] : ((ssList(V110_110) => ! [W111_111] : ((ssList(W111_111) => (memberP(app(V110_110, W111_111), hd(skolem_U209209)) <=> (memberP(V110_110, hd(skolem_U209209)) | memberP(W111_111, hd(skolem_U209209))))))))
% 44.71/8.59
% 44.71/8.59 [233] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [234] GAMMA_FORALL : ! [U112_112] : ((ssItem(U112_112) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), U112_112) <=> (=(U112_112, V113_113) | memberP(W114_114, U112_112)))))))))
% 44.71/8.59 -> [235] (ssItem(hd(skolem_U209209)) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), hd(skolem_U209209)) <=> (=(hd(skolem_U209209), V113_113) | memberP(W114_114, hd(skolem_U209209)))))))))
% 44.71/8.59
% 44.71/8.59 [235] BETA_IMPLY : (ssItem(hd(skolem_U209209)) => ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), hd(skolem_U209209)) <=> (=(hd(skolem_U209209), V113_113) | memberP(W114_114, hd(skolem_U209209)))))))))
% 44.71/8.59 -> [236] ~ssItem(hd(skolem_U209209))
% 44.71/8.59 -> [237] ! [V113_113] : ((ssItem(V113_113) => ! [W114_114] : ((ssList(W114_114) => (memberP(cons(V113_113, W114_114), hd(skolem_U209209)) <=> (=(hd(skolem_U209209), V113_113) | memberP(W114_114, hd(skolem_U209209))))))))
% 44.71/8.59
% 44.71/8.59 [236] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [237] GAMMA_FORALL : ! [U115_115] : ((ssItem(U115_115) => ~memberP(nil, U115_115)))
% 44.71/8.59 -> [238] (ssItem(hd(skolem_U209209)) => ~memberP(nil, hd(skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [238] BETA_IMPLY : (ssItem(hd(skolem_U209209)) => ~memberP(nil, hd(skolem_U209209)))
% 44.71/8.59 -> [239] ~ssItem(hd(skolem_U209209))
% 44.71/8.59 -> [240] ~memberP(nil, hd(skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [239] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [240] GAMMA_FORALL : ! [U116_116] : ((ssList(U116_116) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(U116_116, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(U116_116, W118_118))))))))
% 44.71/8.59 -> [241] (ssList(nil) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(nil, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(nil, W118_118)))))))
% 44.71/8.59
% 44.71/8.59 [241] BETA_IMPLY : (ssList(nil) => ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(nil, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(nil, W118_118)))))))
% 44.71/8.59 -> [242] ~ssList(nil)
% 44.71/8.59 -> [243] ! [V117_117] : ((ssList(V117_117) => ! [W118_118] : ((ssList(W118_118) => ((frontsegP(nil, V117_117) & frontsegP(V117_117, W118_118)) => frontsegP(nil, W118_118))))))
% 44.71/8.59
% 44.71/8.59 [242] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [243] GAMMA_FORALL : ! [U119_119] : ((ssList(U119_119) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(U119_119, V120_120) & frontsegP(V120_120, U119_119)) => =(U119_119, V120_120))))))
% 44.71/8.59 -> [244] (ssList(skolem_U209209) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(skolem_U209209, V120_120) & frontsegP(V120_120, skolem_U209209)) => =(skolem_U209209, V120_120)))))
% 44.71/8.59
% 44.71/8.59 [244] BETA_IMPLY : (ssList(skolem_U209209) => ! [V120_120] : ((ssList(V120_120) => ((frontsegP(skolem_U209209, V120_120) & frontsegP(V120_120, skolem_U209209)) => =(skolem_U209209, V120_120)))))
% 44.71/8.59 -> [245] ~ssList(skolem_U209209)
% 44.71/8.59 -> [246] ! [V120_120] : ((ssList(V120_120) => ((frontsegP(skolem_U209209, V120_120) & frontsegP(V120_120, skolem_U209209)) => =(skolem_U209209, V120_120))))
% 44.71/8.59
% 44.71/8.59 [245] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [246] GAMMA_FORALL : ! [U121_121] : ((ssList(U121_121) => frontsegP(U121_121, U121_121)))
% 44.71/8.59 -> [247] (ssList(skolem_X212212) => frontsegP(skolem_X212212, skolem_X212212))
% 44.71/8.59
% 44.71/8.59 [247] BETA_IMPLY : (ssList(skolem_X212212) => frontsegP(skolem_X212212, skolem_X212212))
% 44.71/8.59 -> [248] ~ssList(skolem_X212212)
% 44.71/8.59 -> [249] frontsegP(skolem_X212212, skolem_X212212)
% 44.71/8.59
% 44.71/8.59 [248] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [249] GAMMA_FORALL : ! [U122_122] : ((ssList(U122_122) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(U122_122, V123_123) => frontsegP(app(U122_122, W124_124), V123_123))))))))
% 44.71/8.59 -> [250] (ssList(skolem_X212212) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(skolem_X212212, V123_123) => frontsegP(app(skolem_X212212, W124_124), V123_123)))))))
% 44.71/8.59
% 44.71/8.59 [250] BETA_IMPLY : (ssList(skolem_X212212) => ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(skolem_X212212, V123_123) => frontsegP(app(skolem_X212212, W124_124), V123_123)))))))
% 44.71/8.59 -> [251] ~ssList(skolem_X212212)
% 44.71/8.59 -> [252] ! [V123_123] : ((ssList(V123_123) => ! [W124_124] : ((ssList(W124_124) => (frontsegP(skolem_X212212, V123_123) => frontsegP(app(skolem_X212212, W124_124), V123_123))))))
% 44.71/8.59
% 44.71/8.59 [251] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [252] GAMMA_FORALL : ! [U125_125] : ((ssItem(U125_125) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(U125_125, W127_127), cons(V126_126, X128_128)) <=> (=(U125_125, V126_126) & frontsegP(W127_127, X128_128)))))))))))
% 44.71/8.59 -> [253] (ssItem(skolem_V99) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(skolem_V99, W127_127), cons(V126_126, X128_128)) <=> (=(skolem_V99, V126_126) & frontsegP(W127_127, X128_128))))))))))
% 44.71/8.59
% 44.71/8.59 [253] BETA_IMPLY : (ssItem(skolem_V99) => ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(skolem_V99, W127_127), cons(V126_126, X128_128)) <=> (=(skolem_V99, V126_126) & frontsegP(W127_127, X128_128))))))))))
% 44.71/8.59 -> [254] ~ssItem(skolem_V99)
% 44.71/8.59 -> [255] ! [V126_126] : ((ssItem(V126_126) => ! [W127_127] : ((ssList(W127_127) => ! [X128_128] : ((ssList(X128_128) => (frontsegP(cons(skolem_V99, W127_127), cons(V126_126, X128_128)) <=> (=(skolem_V99, V126_126) & frontsegP(W127_127, X128_128)))))))))
% 44.71/8.59
% 44.71/8.59 [254] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [255] GAMMA_FORALL : ! [U129_129] : ((ssList(U129_129) => frontsegP(U129_129, nil)))
% 44.71/8.59 -> [256] (ssList(skolem_U209209) => frontsegP(skolem_U209209, nil))
% 44.71/8.59
% 44.71/8.59 [256] BETA_IMPLY : (ssList(skolem_U209209) => frontsegP(skolem_U209209, nil))
% 44.71/8.59 -> [257] ~ssList(skolem_U209209)
% 44.71/8.59 -> [258] frontsegP(skolem_U209209, nil)
% 44.71/8.59
% 44.71/8.59 [257] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [258] GAMMA_FORALL : ! [U130_130] : ((ssList(U130_130) => (frontsegP(nil, U130_130) <=> =(nil, U130_130))))
% 44.71/8.59 -> [259] (ssList(skolem_U209209) => (frontsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [259] BETA_IMPLY : (ssList(skolem_U209209) => (frontsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209)))
% 44.71/8.59 -> [260] ~ssList(skolem_U209209)
% 44.71/8.59 -> [261] (frontsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [260] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [261] BETA_EQUIV : (frontsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209))
% 44.71/8.59 -> [284] ~frontsegP(nil, skolem_U209209), ~=(nil, skolem_U209209)
% 44.71/8.59 -> [285] frontsegP(nil, skolem_U209209), =(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [285] CLOSURE : =(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [284] GAMMA_FORALL : ! [U131_131] : ((ssList(U131_131) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(U131_131, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(U131_131, W133_133))))))))
% 44.71/8.59 -> [286] (ssList(skolem_V210210) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(skolem_V210210, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(skolem_V210210, W133_133)))))))
% 44.71/8.59
% 44.71/8.59 [286] BETA_IMPLY : (ssList(skolem_V210210) => ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(skolem_V210210, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(skolem_V210210, W133_133)))))))
% 44.71/8.59 -> [287] ~ssList(skolem_V210210)
% 44.71/8.59 -> [288] ! [V132_132] : ((ssList(V132_132) => ! [W133_133] : ((ssList(W133_133) => ((rearsegP(skolem_V210210, V132_132) & rearsegP(V132_132, W133_133)) => rearsegP(skolem_V210210, W133_133))))))
% 44.71/8.59
% 44.71/8.59 [287] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [288] GAMMA_FORALL : ! [U134_134] : ((ssList(U134_134) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(U134_134, V135_135) & rearsegP(V135_135, U134_134)) => =(U134_134, V135_135))))))
% 44.71/8.59 -> [289] (ssList(nil) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(nil, V135_135) & rearsegP(V135_135, nil)) => =(nil, V135_135)))))
% 44.71/8.59
% 44.71/8.59 [289] BETA_IMPLY : (ssList(nil) => ! [V135_135] : ((ssList(V135_135) => ((rearsegP(nil, V135_135) & rearsegP(V135_135, nil)) => =(nil, V135_135)))))
% 44.71/8.59 -> [290] ~ssList(nil)
% 44.71/8.59 -> [291] ! [V135_135] : ((ssList(V135_135) => ((rearsegP(nil, V135_135) & rearsegP(V135_135, nil)) => =(nil, V135_135))))
% 44.71/8.59
% 44.71/8.59 [290] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [291] GAMMA_FORALL : ! [U136_136] : ((ssList(U136_136) => rearsegP(U136_136, U136_136)))
% 44.71/8.59 -> [292] (ssList(skolem_U209209) => rearsegP(skolem_U209209, skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [292] BETA_IMPLY : (ssList(skolem_U209209) => rearsegP(skolem_U209209, skolem_U209209))
% 44.71/8.59 -> [293] ~ssList(skolem_U209209)
% 44.71/8.59 -> [294] rearsegP(skolem_U209209, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [293] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [294] GAMMA_FORALL : ! [U137_137] : ((ssList(U137_137) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(U137_137, V138_138) => rearsegP(app(W139_139, U137_137), V138_138))))))))
% 44.71/8.59 -> [295] (ssList(nil) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(nil, V138_138) => rearsegP(app(W139_139, nil), V138_138)))))))
% 44.71/8.59
% 44.71/8.59 [295] BETA_IMPLY : (ssList(nil) => ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(nil, V138_138) => rearsegP(app(W139_139, nil), V138_138)))))))
% 44.71/8.59 -> [296] ~ssList(nil)
% 44.71/8.59 -> [297] ! [V138_138] : ((ssList(V138_138) => ! [W139_139] : ((ssList(W139_139) => (rearsegP(nil, V138_138) => rearsegP(app(W139_139, nil), V138_138))))))
% 44.71/8.59
% 44.71/8.59 [296] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [297] GAMMA_FORALL : ! [U140_140] : ((ssList(U140_140) => rearsegP(U140_140, nil)))
% 44.71/8.59 -> [298] (ssList(nil) => rearsegP(nil, nil))
% 44.71/8.59
% 44.71/8.59 [298] BETA_IMPLY : (ssList(nil) => rearsegP(nil, nil))
% 44.71/8.59 -> [299] ~ssList(nil)
% 44.71/8.59 -> [300] rearsegP(nil, nil)
% 44.71/8.59
% 44.71/8.59 [299] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [300] GAMMA_FORALL : ! [U141_141] : ((ssList(U141_141) => (rearsegP(nil, U141_141) <=> =(nil, U141_141))))
% 44.71/8.59 -> [301] (ssList(skolem_U209209) => (rearsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209)))
% 44.71/8.59
% 44.71/8.59 [301] BETA_IMPLY : (ssList(skolem_U209209) => (rearsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209)))
% 44.71/8.59 -> [302] ~ssList(skolem_U209209)
% 44.71/8.59 -> [303] (rearsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209))
% 44.71/8.59
% 44.71/8.59 [302] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [303] BETA_EQUIV : (rearsegP(nil, skolem_U209209) <=> =(nil, skolem_U209209))
% 44.71/8.59 -> [304] ~rearsegP(nil, skolem_U209209), ~=(nil, skolem_U209209)
% 44.71/8.59 -> [305] rearsegP(nil, skolem_U209209), =(nil, skolem_U209209)
% 44.71/8.59
% 44.71/8.59 [304] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 [305] CLOSURE : =
% 44.71/8.59
% 44.71/8.59 % SZS output end Proof for theBenchmark.p
% 44.71/8.59 [8.242771s][1][Res] 89552 goroutines created
% 44.71/8.59 ==== Result ====
% 44.71/8.59 [8.242814s][1][Res] VALID
% 44.71/8.59 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------