TSTP Solution File: SWC040+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.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 11:18:13 EDT 2022
% Result : Theorem 2.55s 1.77s
% Output : Proof 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 21:16:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.35 Conjecture not found
% 0.19/0.35 Start search
% 0.19/0.36 nb_step : 1 - limit : 209
% 0.19/0.36 Launch Gotab with destructive = true
% 2.55/1.74 % SZS output start Proof for theBenchmark.p
% 2.55/1.77 [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)) | =(nil, U209_209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))))))))
% 2.55/1.77 -> [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)) | =(nil, U209_209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))))))
% 2.55/1.77
% 2.55/1.77 [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)))))))))
% 2.55/1.77 -> [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))))))))
% 2.55/1.77
% 2.55/1.77 [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)) | =(nil, U209_209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))))))
% 2.55/1.77 -> [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))))))
% 2.55/1.77
% 2.55/1.77 [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))))))
% 2.55/1.77 -> [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))))
% 2.55/1.77
% 2.55/1.77 [4] DELTA_EXISTS : ? [U8_8] : ((ssItem(U8_8) & ? [V9_9] : ((ssItem(V9_9) & ~=(U8_8, V9_9)))))
% 2.55/1.77 -> [5] (ssItem(skolem_U88) & ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9))))
% 2.55/1.77
% 2.55/1.77 [5] ALPHA_AND : (ssItem(skolem_U88) & ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9))))
% 2.55/1.77 -> [6] ssItem(skolem_U88), ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9)))
% 2.55/1.77
% 2.55/1.77 [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))))
% 2.55/1.77 -> [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))))
% 2.55/1.77
% 2.55/1.77 [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))))
% 2.55/1.77 -> [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))
% 2.55/1.77
% 2.55/1.77 [8] DELTA_EXISTS : ? [V9_9] : ((ssItem(V9_9) & ~=(skolem_U88, V9_9)))
% 2.55/1.77 -> [9] (ssItem(skolem_V99) & ~=(skolem_U88, skolem_V99))
% 2.55/1.77
% 2.55/1.77 [9] ALPHA_AND : (ssItem(skolem_V99) & ~=(skolem_U88, skolem_V99))
% 2.55/1.77 -> [10] ssItem(skolem_V99), ~=(skolem_U88, skolem_V99)
% 2.55/1.77
% 2.55/1.77 [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)) | =(nil, skolem_U209209)) | (~=(nil, W211_211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), W211_211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))))
% 2.55/1.77 -> [11] ~(ssList(skolem_W211211) => ! [X212_212] : ((ssList(X212_212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))
% 2.55/1.77
% 2.55/1.77 [11] ALPHA_NOT_IMPLY : ~(ssList(skolem_W211211) => ! [X212_212] : ((ssList(X212_212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil))))))
% 2.55/1.77 -> [12] ssList(skolem_W211211), ~! [X212_212] : ((ssList(X212_212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))
% 2.55/1.77
% 2.55/1.77 [12] DELTA_NOT_FORALL : ~! [X212_212] : ((ssList(X212_212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, X212_212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, X212_212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), X212_212)))))) & neq(X212_212, nil)))))
% 2.55/1.77 -> [13] ~(ssList(skolem_X212212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil))))
% 2.55/1.77
% 2.55/1.77 [13] ALPHA_NOT_IMPLY : ~(ssList(skolem_X212212) => (((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil))))
% 2.55/1.77 -> [14] ssList(skolem_X212212), ~(((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil)))
% 2.55/1.77
% 2.55/1.77 [14] ALPHA_NOT_OR : ~(((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212))) | (! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil)))
% 2.55/1.77 -> [15] ~((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212))), ~(! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil))
% 2.55/1.77
% 2.55/1.77 [15] ALPHA_NOT_OR : ~((((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)) | (~=(nil, skolem_W211211) & =(nil, skolem_X212212)))
% 2.55/1.77 -> [16] ~(((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209)), ~(~=(nil, skolem_W211211) & =(nil, skolem_X212212))
% 2.55/1.77
% 2.55/1.77 [16] ALPHA_NOT_OR : ~(((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)) | =(nil, skolem_U209209))
% 2.55/1.77 -> [17] ~((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211)), ~=(nil, skolem_U209209)
% 2.55/1.77
% 2.55/1.77 [17] ALPHA_NOT_OR : ~((~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)) | ~=(skolem_U209209, skolem_W211211))
% 2.55/1.77 -> [18] ~(~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212)), ~~=(skolem_U209209, skolem_W211211)
% 2.55/1.77
% 2.55/1.77 [18] ALPHA_NOT_OR : ~(~=(nil, skolem_V210210) | ~=(skolem_V210210, skolem_X212212))
% 2.55/1.77 -> [19] ~~=(nil, skolem_V210210), ~~=(skolem_V210210, skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [19] ALPHA_NOT_NOT : ~~=(skolem_U209209, skolem_W211211)
% 2.55/1.77 -> [20] =(skolem_U209209, skolem_W211211)
% 2.55/1.77
% 2.55/1.77 [20] ALPHA_NOT_NOT : ~~=(nil, skolem_V210210)
% 2.55/1.77 -> [21] =(nil, skolem_V210210)
% 2.55/1.77
% 2.55/1.77 [21] ALPHA_NOT_NOT : ~~=(skolem_V210210, skolem_X212212)
% 2.55/1.77 -> [22] =(skolem_V210210, skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [22] BETA_NOT_AND : ~(! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212)))))) & neq(skolem_X212212, nil))
% 2.55/1.77 -> [23] ~! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212))))))
% 2.55/1.77 -> [24] ~neq(skolem_X212212, nil)
% 2.55/1.77
% 2.55/1.77 [24] BETA_NOT_AND : ~(~=(nil, skolem_W211211) & =(nil, skolem_X212212))
% 2.55/1.77 -> [27] ~~=(nil, skolem_W211211)
% 2.55/1.77 -> [28] ~=(nil, skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [28] CLOSURE : =
% 2.55/1.77
% 2.55/1.77 [27] ALPHA_NOT_NOT : ~~=(nil, skolem_W211211)
% 2.55/1.77 -> [29] =(nil, skolem_W211211)
% 2.55/1.77
% 2.55/1.77 [29] CLOSURE : =
% 2.55/1.77
% 2.55/1.77 [23] DELTA_NOT_FORALL : ~! [Y213_213] : ((ssItem(Y213_213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(Y213_213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(Y213_213, nil)), skolem_X212212))))))
% 2.55/1.77 -> [25] ~(ssItem(skolem_Y213213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(skolem_Y213213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(skolem_Y213213, nil)), skolem_X212212)))))
% 2.55/1.77
% 2.55/1.77 [25] ALPHA_NOT_IMPLY : ~(ssItem(skolem_Y213213) => ! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(skolem_Y213213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(skolem_Y213213, nil)), skolem_X212212)))))
% 2.55/1.77 -> [26] ssItem(skolem_Y213213), ~! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(skolem_Y213213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(skolem_Y213213, nil)), skolem_X212212))))
% 2.55/1.77
% 2.55/1.77 [26] DELTA_NOT_FORALL : ~! [Z214_214] : ((ssList(Z214_214) => (~=(app(cons(skolem_Y213213, nil), Z214_214), skolem_W211211) | ~=(app(Z214_214, cons(skolem_Y213213, nil)), skolem_X212212))))
% 2.55/1.77 -> [30] ~(ssList(skolem_Z214214) => (~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211) | ~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212)))
% 2.55/1.77
% 2.55/1.77 [30] ALPHA_NOT_IMPLY : ~(ssList(skolem_Z214214) => (~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211) | ~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212)))
% 2.55/1.77 -> [31] ssList(skolem_Z214214), ~(~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211) | ~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212))
% 2.55/1.77
% 2.55/1.77 [31] ALPHA_NOT_OR : ~(~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211) | ~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212))
% 2.55/1.77 -> [32] ~~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211), ~~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [32] ALPHA_NOT_NOT : ~~=(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211)
% 2.55/1.77 -> [33] =(app(cons(skolem_Y213213, nil), skolem_Z214214), skolem_W211211)
% 2.55/1.77
% 2.55/1.77 [33] ALPHA_NOT_NOT : ~~=(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212)
% 2.55/1.77 -> [34] =(app(skolem_Z214214, cons(skolem_Y213213, nil)), skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [34] BETA_NOT_AND : ~(~=(nil, skolem_W211211) & =(nil, skolem_X212212))
% 2.55/1.77 -> [35] ~~=(nil, skolem_W211211)
% 2.55/1.77 -> [36] ~=(nil, skolem_X212212)
% 2.55/1.77
% 2.55/1.77 [36] CLOSURE : =
% 2.55/1.77
% 2.55/1.77 [35] ALPHA_NOT_NOT : ~~=(nil, skolem_W211211)
% 2.55/1.77 -> [37] =(nil, skolem_W211211)
% 2.55/1.77
% 2.55/1.77 [37] CLOSURE : =
% 2.55/1.77
% 2.55/1.77 % SZS output end Proof for theBenchmark.p
% 2.55/1.77 [1.432273s][1][Res] 4071 goroutines created
% 2.55/1.77 ==== Result ====
% 2.55/1.77 [1.432327s][1][Res] VALID
% 2.55/1.77 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------