TSTP Solution File: SWV128+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWV128+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 13:38:37 EDT 2022
% Result : Theorem 12.95s 2.76s
% Output : Proof 12.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV128+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n004.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 : Sun Sep 4 01:28:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.37 Conjecture not found
% 0.12/0.37 Start search
% 0.12/0.38 nb_step : 1 - limit : 82
% 0.12/0.38 Launch Gotab with destructive = true
% 12.95/2.73 % SZS output start Proof for theBenchmark.p
% 12.95/2.76 [0] ALPHA_AND : ((! [X29_29, Y30_30] : (((gt(X29_29, Y30_30) | gt(Y30_30, X29_29)) | =(X29_29, Y30_30))) & ! [X31_31, Y32_32, Z33_33] : (((gt(X31_31, Y32_32) & gt(Y32_32, Z33_33)) => gt(X31_31, Z33_33))) & ! [X34_34] : (~gt(X34_34, X34_34)) & ! [X35_35] : (leq(X35_35, X35_35)) & ! [X36_36, Y37_37, Z38_38] : (((leq(X36_36, Y37_37) & leq(Y37_37, Z38_38)) => leq(X36_36, Z38_38))) & ! [X39_39, Y40_40] : ((lt(X39_39, Y40_40) <=> gt(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((geq(X41_41, Y42_42) <=> leq(Y42_42, X41_41))) & ! [X43_43, Y44_44] : ((gt(Y44_44, X43_43) => leq(X43_43, Y44_44))) & ! [X45_45, Y46_46] : (((leq(X45_45, Y46_46) & ~=(X45_45, Y46_46)) => gt(Y46_46, X45_45))) & ! [X47_47, Y48_48] : ((leq(X47_47, pred(Y48_48)) <=> gt(Y48_48, X47_47))) & ! [X49_49] : (gt(succ(X49_49), X49_49)) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) => leq(X50_50, succ(Y51_51)))) & ! [X52_52, Y53_53] : ((leq(X52_52, Y53_53) <=> gt(succ(Y53_53), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(uniform_int_rnd(C55_55, X54_54), X54_54))) & ! [X56_56, C57_57] : ((leq(n0, X56_56) => leq(n0, uniform_int_rnd(C57_57, X56_56)))) & ! [I58_58, L59_59, U60_60, Val61_61] : (((leq(L59_59, I58_58) & leq(I58_58, U60_60)) => =(a_select2(tptp_const_array1(dim(L59_59, U60_60), Val61_61), I58_58), Val61_61))) & ! [I62_62, L163_63, U164_64, J65_65, L266_66, U267_67, Val68_68] : (((((leq(L163_63, I62_62) & leq(I62_62, U164_64)) & leq(L266_66, J65_65)) & leq(J65_65, U267_67)) => =(a_select3(tptp_const_array2(dim(L163_63, U164_64), dim(L266_66, U267_67), Val68_68), I62_62, J65_65), Val68_68))) & ! [A69_69, N70_70] : ((! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N70_70)) & leq(n0, J72_72)) & leq(J72_72, N70_70)) => =(a_select3(A69_69, I71_71, J72_72), a_select3(A69_69, J72_72, I71_71)))) => ! [I73_73, J74_74] : (((((leq(n0, I73_73) & leq(I73_73, N70_70)) & leq(n0, J74_74)) & leq(J74_74, N70_70)) => =(a_select3(trans(A69_69), I73_73, J74_74), a_select3(trans(A69_69), J74_74, I73_73)))))) & ! [A75_75, N76_76] : ((! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N76_76)) & leq(n0, J78_78)) & leq(J78_78, N76_76)) => =(a_select3(A75_75, I77_77, J78_78), a_select3(A75_75, J78_78, I77_77)))) => ! [I79_79, J80_80] : (((((leq(n0, I79_79) & leq(I79_79, N76_76)) & leq(n0, J80_80)) & leq(J80_80, N76_76)) => =(a_select3(inv(A75_75), I79_79, J80_80), a_select3(inv(A75_75), J80_80, I79_79)))))) & ! [A81_81, N82_82] : ((! [I83_83, J84_84] : (((((leq(n0, I83_83) & leq(I83_83, N82_82)) & leq(n0, J84_84)) & leq(J84_84, N82_82)) => =(a_select3(A81_81, I83_83, J84_84), a_select3(A81_81, J84_84, I83_83)))) => ! [I85_85, J86_86, K87_87, VAL88_88] : (((((((leq(n0, I85_85) & leq(I85_85, N82_82)) & leq(n0, J86_86)) & leq(J86_86, N82_82)) & leq(n0, K87_87)) & leq(K87_87, N82_82)) => =(a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), I85_85, J86_86), a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), J86_86, I85_85)))))) & ! [A89_89, B90_90, N91_91] : (((! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N91_91)) & leq(n0, J93_93)) & leq(J93_93, N91_91)) => =(a_select3(A89_89, I92_92, J93_93), a_select3(A89_89, J93_93, I92_92)))) & ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N91_91)) & leq(n0, J95_95)) & leq(J95_95, N91_91)) => =(a_select3(B90_90, I94_94, J95_95), a_select3(B90_90, J95_95, I94_94))))) => ! [I96_96, J97_97] : (((((leq(n0, I96_96) & leq(I96_96, N91_91)) & leq(n0, J97_97)) & leq(J97_97, N91_91)) => =(a_select3(tptp_madd(A89_89, B90_90), I96_96, J97_97), a_select3(tptp_madd(A89_89, B90_90), J97_97, I96_96)))))) & ! [A98_98, B99_99, N100_100] : (((! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N100_100)) & leq(n0, J102_102)) & leq(J102_102, N100_100)) => =(a_select3(A98_98, I101_101, J102_102), a_select3(A98_98, J102_102, I101_101)))) & ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N100_100)) & leq(n0, J104_104)) & leq(J104_104, N100_100)) => =(a_select3(B99_99, I103_103, J104_104), a_select3(B99_99, J104_104, I103_103))))) => ! [I105_105, J106_106] : (((((leq(n0, I105_105) & leq(I105_105, N100_100)) & leq(n0, J106_106)) & leq(J106_106, N100_100)) => =(a_select3(tptp_msub(A98_98, B99_99), I105_105, J106_106), a_select3(tptp_msub(A98_98, B99_99), J106_106, I105_105)))))) & ! [A107_107, B108_108, N109_109] : ((! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N109_109)) & leq(n0, J111_111)) & leq(J111_111, N109_109)) => =(a_select3(B108_108, I110_110, J111_111), a_select3(B108_108, J111_111, I110_110)))) => ! [I112_112, J113_113] : (((((leq(n0, I112_112) & leq(I112_112, N109_109)) & leq(n0, J113_113)) & leq(J113_113, N109_109)) => =(a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), I112_112, J113_113), a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), J113_113, I112_112)))))) & ! [A114_114, B115_115, N116_116, M117_117] : ((! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, M117_117)) & leq(n0, J119_119)) & leq(J119_119, M117_117)) => =(a_select3(B115_115, I118_118, J119_119), a_select3(B115_115, J119_119, I118_118)))) => ! [I120_120, J121_121] : (((((leq(n0, I120_120) & leq(I120_120, N116_116)) & leq(n0, J121_121)) & leq(J121_121, N116_116)) => =(a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), I120_120, J121_121), a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), J121_121, I120_120)))))) & ! [A122_122, B123_123, C124_124, D125_125, E126_126, F127_127, N128_128, M129_129] : ((((! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, M129_129)) & leq(n0, J131_131)) & leq(J131_131, M129_129)) => =(a_select3(D125_125, I130_130, J131_131), a_select3(D125_125, J131_131, I130_130)))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N128_128)) & leq(n0, J133_133)) & leq(J133_133, N128_128)) => =(a_select3(A122_122, I132_132, J133_133), a_select3(A122_122, J133_133, I132_132))))) & ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N128_128)) & leq(n0, J135_135)) & leq(J135_135, N128_128)) => =(a_select3(F127_127, I134_134, J135_135), a_select3(F127_127, J135_135, I134_134))))) => ! [I136_136, J137_137] : (((((leq(n0, I136_136) & leq(I136_136, N128_128)) & leq(n0, J137_137)) & leq(J137_137, N128_128)) => =(a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), I136_136, J137_137), a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), J137_137, I136_136)))))) & ! [Body138_138] : (=(sum(n0, tptp_minus_1, Body138_138), n0)) & ! [Body139_139] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body139_139))) & =(succ(tptp_minus_1), n0) & ! [X140_140] : (=(plus(X140_140, n1), succ(X140_140))) & ! [X141_141] : (=(plus(n1, X141_141), succ(X141_141))) & ! [X142_142] : (=(plus(X142_142, n2), succ(succ(X142_142)))) & ! [X143_143] : (=(plus(n2, X143_143), succ(succ(X143_143)))) & ! [X144_144] : (=(plus(X144_144, n3), succ(succ(succ(X144_144))))) & ! [X145_145] : (=(plus(n3, X145_145), succ(succ(succ(X145_145))))) & ! [X146_146] : (=(plus(X146_146, n4), succ(succ(succ(succ(X146_146)))))) & ! [X147_147] : (=(plus(n4, X147_147), succ(succ(succ(succ(X147_147)))))) & ! [X148_148] : (=(plus(X148_148, n5), succ(succ(succ(succ(succ(X148_148))))))) & ! [X149_149] : (=(plus(n5, X149_149), succ(succ(succ(succ(succ(X149_149))))))) & ! [X150_150] : (=(minus(X150_150, n1), pred(X150_150))) & ! [X151_151] : (=(pred(succ(X151_151)), X151_151)) & ! [X152_152] : (=(succ(pred(X152_152)), X152_152)) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), succ(Y154_154)) <=> leq(X153_153, Y154_154))) & ! [X155_155, Y156_156] : ((leq(succ(X155_155), Y156_156) => gt(Y156_156, X155_155))) & ! [X157_157, Y158_158] : ((leq(minus(X157_157, Y158_158), X157_157) => leq(n0, Y158_158))) & ! [X159_159, U160_160, V161_161, VAL162_162] : (=(a_select3(tptp_update3(X159_159, U160_160, V161_161, VAL162_162), U160_160, V161_161), VAL162_162)) & ! [I163_163, J164_164, U165_165, V166_166, X167_167, VAL168_168, VAL2169_169] : ((((~=(I163_163, U165_165) & =(J164_164, V166_166)) & =(a_select3(X167_167, U165_165, V166_166), VAL168_168)) => =(a_select3(tptp_update3(X167_167, I163_163, J164_164, VAL2169_169), U165_165, V166_166), VAL168_168))) & ! [I170_170, J171_171, U172_172, V173_173, X174_174, VAL175_175] : ((((((! [I0176_176, J0177_177] : (((((leq(n0, I0176_176) & leq(n0, J0177_177)) & leq(I0176_176, U172_172)) & leq(J0177_177, V173_173)) => =(a_select3(X174_174, I0176_176, J0177_177), VAL175_175))) & leq(n0, I170_170)) & leq(I170_170, U172_172)) & leq(n0, J171_171)) & leq(J171_171, V173_173)) => =(a_select3(tptp_update3(X174_174, U172_172, V173_173, VAL175_175), I170_170, J171_171), VAL175_175))) & ! [X178_178, U179_179, VAL180_180] : (=(a_select2(tptp_update2(X178_178, U179_179, VAL180_180), U179_179), VAL180_180)) & ! [I181_181, U182_182, X183_183, VAL184_184, VAL2185_185] : (((~=(I181_181, U182_182) & =(a_select2(X183_183, U182_182), VAL184_184)) => =(a_select2(tptp_update2(X183_183, I181_181, VAL2185_185), U182_182), VAL184_184))) & ! [I186_186, U187_187, X188_188, VAL189_189] : ((((! [I0190_190] : (((leq(n0, I0190_190) & leq(I0190_190, U187_187)) => =(a_select2(X188_188, I0190_190), VAL189_189))) & leq(n0, I186_186)) & leq(I186_186, U187_187)) => =(a_select2(tptp_update2(X188_188, U187_187, VAL189_189), I186_186), VAL189_189))) & true & ~=(def, use)) & gt(n5, n4) & gt(n7, n4) & gt(n7, n5) & gt(n4, tptp_minus_1) & gt(n5, tptp_minus_1) & gt(n7, tptp_minus_1) & gt(n0, tptp_minus_1) & gt(n1, tptp_minus_1) & gt(n2, tptp_minus_1) & gt(n3, tptp_minus_1) & gt(n4, n0) & gt(n5, n0) & gt(n7, n0) & gt(n1, n0) & gt(n2, n0) & gt(n3, n0) & gt(n4, n1) & gt(n5, n1) & gt(n7, n1) & gt(n2, n1) & gt(n3, n1) & gt(n4, n2) & gt(n5, n2) & gt(n7, n2) & gt(n3, n2) & gt(n4, n3) & gt(n5, n3) & gt(n7, n3) & ! [X199_199] : (((leq(n0, X199_199) & leq(X199_199, n4)) => ((((=(X199_199, n0) | =(X199_199, n1)) | =(X199_199, n2)) | =(X199_199, n3)) | =(X199_199, n4)))) & ! [X200_200] : (((leq(n0, X200_200) & leq(X200_200, n5)) => (((((=(X200_200, n0) | =(X200_200, n1)) | =(X200_200, n2)) | =(X200_200, n3)) | =(X200_200, n4)) | =(X200_200, n5)))) & ! [X201_201] : (((leq(n0, X201_201) & leq(X201_201, n0)) => =(X201_201, n0))) & ! [X202_202] : (((leq(n0, X202_202) & leq(X202_202, n1)) => (=(X202_202, n0) | =(X202_202, n1)))) & ! [X203_203] : (((leq(n0, X203_203) & leq(X203_203, n2)) => ((=(X203_203, n0) | =(X203_203, n1)) | =(X203_203, n2)))) & ! [X204_204] : (((leq(n0, X204_204) & leq(X204_204, n3)) => (((=(X204_204, n0) | =(X204_204, n1)) | =(X204_204, n2)) | =(X204_204, n3)))) & =(succ(succ(succ(succ(n0)))), n4) & =(succ(succ(succ(succ(succ(n0))))), n5) & =(succ(n0), n1) & =(succ(succ(n0)), n2) & =(succ(succ(succ(n0))), n3) & ~(((((((=(t_defuse, use) & =(tvar_defuse, use)) & ! [A191_191, B192_192] : (((((leq(n0, A191_191) & leq(n0, B192_192)) & leq(A191_191, minus(m_measvars, n1))) & leq(B192_192, minus(n_steps, n1))) => =(a_select3(rho_defuse, A191_191, B192_192), use)))) & ! [C193_193, D194_194] : (((((leq(n0, C193_193) & leq(n0, D194_194)) & leq(C193_193, n7)) & leq(D194_194, minus(n_steps, n1))) => =(a_select3(tr_defuse, C193_193, D194_194), use)))) & ! [E195_195] : (((leq(n0, E195_195) & leq(E195_195, minus(n_statevars, n1))) => =(a_select2(xinit_defuse, E195_195), use)))) & ! [F196_196] : (((leq(n0, F196_196) & leq(F196_196, minus(n_statevars, n1))) => =(a_select2(xinit_mean_defuse, F196_196), use)))) & ! [G197_197, H198_198] : (((((leq(n0, G197_197) & leq(n0, H198_198)) & leq(G197_197, minus(m_measvars, n1))) & leq(H198_198, minus(n_steps, n1))) => =(a_select3(z_defuse, G197_197, H198_198), use)))) => true))
% 12.95/2.76 -> [1] (! [X29_29, Y30_30] : (((gt(X29_29, Y30_30) | gt(Y30_30, X29_29)) | =(X29_29, Y30_30))) & ! [X31_31, Y32_32, Z33_33] : (((gt(X31_31, Y32_32) & gt(Y32_32, Z33_33)) => gt(X31_31, Z33_33))) & ! [X34_34] : (~gt(X34_34, X34_34)) & ! [X35_35] : (leq(X35_35, X35_35)) & ! [X36_36, Y37_37, Z38_38] : (((leq(X36_36, Y37_37) & leq(Y37_37, Z38_38)) => leq(X36_36, Z38_38))) & ! [X39_39, Y40_40] : ((lt(X39_39, Y40_40) <=> gt(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((geq(X41_41, Y42_42) <=> leq(Y42_42, X41_41))) & ! [X43_43, Y44_44] : ((gt(Y44_44, X43_43) => leq(X43_43, Y44_44))) & ! [X45_45, Y46_46] : (((leq(X45_45, Y46_46) & ~=(X45_45, Y46_46)) => gt(Y46_46, X45_45))) & ! [X47_47, Y48_48] : ((leq(X47_47, pred(Y48_48)) <=> gt(Y48_48, X47_47))) & ! [X49_49] : (gt(succ(X49_49), X49_49)) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) => leq(X50_50, succ(Y51_51)))) & ! [X52_52, Y53_53] : ((leq(X52_52, Y53_53) <=> gt(succ(Y53_53), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(uniform_int_rnd(C55_55, X54_54), X54_54))) & ! [X56_56, C57_57] : ((leq(n0, X56_56) => leq(n0, uniform_int_rnd(C57_57, X56_56)))) & ! [I58_58, L59_59, U60_60, Val61_61] : (((leq(L59_59, I58_58) & leq(I58_58, U60_60)) => =(a_select2(tptp_const_array1(dim(L59_59, U60_60), Val61_61), I58_58), Val61_61))) & ! [I62_62, L163_63, U164_64, J65_65, L266_66, U267_67, Val68_68] : (((((leq(L163_63, I62_62) & leq(I62_62, U164_64)) & leq(L266_66, J65_65)) & leq(J65_65, U267_67)) => =(a_select3(tptp_const_array2(dim(L163_63, U164_64), dim(L266_66, U267_67), Val68_68), I62_62, J65_65), Val68_68))) & ! [A69_69, N70_70] : ((! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N70_70)) & leq(n0, J72_72)) & leq(J72_72, N70_70)) => =(a_select3(A69_69, I71_71, J72_72), a_select3(A69_69, J72_72, I71_71)))) => ! [I73_73, J74_74] : (((((leq(n0, I73_73) & leq(I73_73, N70_70)) & leq(n0, J74_74)) & leq(J74_74, N70_70)) => =(a_select3(trans(A69_69), I73_73, J74_74), a_select3(trans(A69_69), J74_74, I73_73)))))) & ! [A75_75, N76_76] : ((! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N76_76)) & leq(n0, J78_78)) & leq(J78_78, N76_76)) => =(a_select3(A75_75, I77_77, J78_78), a_select3(A75_75, J78_78, I77_77)))) => ! [I79_79, J80_80] : (((((leq(n0, I79_79) & leq(I79_79, N76_76)) & leq(n0, J80_80)) & leq(J80_80, N76_76)) => =(a_select3(inv(A75_75), I79_79, J80_80), a_select3(inv(A75_75), J80_80, I79_79)))))) & ! [A81_81, N82_82] : ((! [I83_83, J84_84] : (((((leq(n0, I83_83) & leq(I83_83, N82_82)) & leq(n0, J84_84)) & leq(J84_84, N82_82)) => =(a_select3(A81_81, I83_83, J84_84), a_select3(A81_81, J84_84, I83_83)))) => ! [I85_85, J86_86, K87_87, VAL88_88] : (((((((leq(n0, I85_85) & leq(I85_85, N82_82)) & leq(n0, J86_86)) & leq(J86_86, N82_82)) & leq(n0, K87_87)) & leq(K87_87, N82_82)) => =(a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), I85_85, J86_86), a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), J86_86, I85_85)))))) & ! [A89_89, B90_90, N91_91] : (((! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N91_91)) & leq(n0, J93_93)) & leq(J93_93, N91_91)) => =(a_select3(A89_89, I92_92, J93_93), a_select3(A89_89, J93_93, I92_92)))) & ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N91_91)) & leq(n0, J95_95)) & leq(J95_95, N91_91)) => =(a_select3(B90_90, I94_94, J95_95), a_select3(B90_90, J95_95, I94_94))))) => ! [I96_96, J97_97] : (((((leq(n0, I96_96) & leq(I96_96, N91_91)) & leq(n0, J97_97)) & leq(J97_97, N91_91)) => =(a_select3(tptp_madd(A89_89, B90_90), I96_96, J97_97), a_select3(tptp_madd(A89_89, B90_90), J97_97, I96_96)))))) & ! [A98_98, B99_99, N100_100] : (((! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N100_100)) & leq(n0, J102_102)) & leq(J102_102, N100_100)) => =(a_select3(A98_98, I101_101, J102_102), a_select3(A98_98, J102_102, I101_101)))) & ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N100_100)) & leq(n0, J104_104)) & leq(J104_104, N100_100)) => =(a_select3(B99_99, I103_103, J104_104), a_select3(B99_99, J104_104, I103_103))))) => ! [I105_105, J106_106] : (((((leq(n0, I105_105) & leq(I105_105, N100_100)) & leq(n0, J106_106)) & leq(J106_106, N100_100)) => =(a_select3(tptp_msub(A98_98, B99_99), I105_105, J106_106), a_select3(tptp_msub(A98_98, B99_99), J106_106, I105_105)))))) & ! [A107_107, B108_108, N109_109] : ((! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N109_109)) & leq(n0, J111_111)) & leq(J111_111, N109_109)) => =(a_select3(B108_108, I110_110, J111_111), a_select3(B108_108, J111_111, I110_110)))) => ! [I112_112, J113_113] : (((((leq(n0, I112_112) & leq(I112_112, N109_109)) & leq(n0, J113_113)) & leq(J113_113, N109_109)) => =(a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), I112_112, J113_113), a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), J113_113, I112_112)))))) & ! [A114_114, B115_115, N116_116, M117_117] : ((! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, M117_117)) & leq(n0, J119_119)) & leq(J119_119, M117_117)) => =(a_select3(B115_115, I118_118, J119_119), a_select3(B115_115, J119_119, I118_118)))) => ! [I120_120, J121_121] : (((((leq(n0, I120_120) & leq(I120_120, N116_116)) & leq(n0, J121_121)) & leq(J121_121, N116_116)) => =(a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), I120_120, J121_121), a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), J121_121, I120_120)))))) & ! [A122_122, B123_123, C124_124, D125_125, E126_126, F127_127, N128_128, M129_129] : ((((! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, M129_129)) & leq(n0, J131_131)) & leq(J131_131, M129_129)) => =(a_select3(D125_125, I130_130, J131_131), a_select3(D125_125, J131_131, I130_130)))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N128_128)) & leq(n0, J133_133)) & leq(J133_133, N128_128)) => =(a_select3(A122_122, I132_132, J133_133), a_select3(A122_122, J133_133, I132_132))))) & ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N128_128)) & leq(n0, J135_135)) & leq(J135_135, N128_128)) => =(a_select3(F127_127, I134_134, J135_135), a_select3(F127_127, J135_135, I134_134))))) => ! [I136_136, J137_137] : (((((leq(n0, I136_136) & leq(I136_136, N128_128)) & leq(n0, J137_137)) & leq(J137_137, N128_128)) => =(a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), I136_136, J137_137), a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), J137_137, I136_136)))))) & ! [Body138_138] : (=(sum(n0, tptp_minus_1, Body138_138), n0)) & ! [Body139_139] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body139_139))) & =(succ(tptp_minus_1), n0) & ! [X140_140] : (=(plus(X140_140, n1), succ(X140_140))) & ! [X141_141] : (=(plus(n1, X141_141), succ(X141_141))) & ! [X142_142] : (=(plus(X142_142, n2), succ(succ(X142_142)))) & ! [X143_143] : (=(plus(n2, X143_143), succ(succ(X143_143)))) & ! [X144_144] : (=(plus(X144_144, n3), succ(succ(succ(X144_144))))) & ! [X145_145] : (=(plus(n3, X145_145), succ(succ(succ(X145_145))))) & ! [X146_146] : (=(plus(X146_146, n4), succ(succ(succ(succ(X146_146)))))) & ! [X147_147] : (=(plus(n4, X147_147), succ(succ(succ(succ(X147_147)))))) & ! [X148_148] : (=(plus(X148_148, n5), succ(succ(succ(succ(succ(X148_148))))))) & ! [X149_149] : (=(plus(n5, X149_149), succ(succ(succ(succ(succ(X149_149))))))) & ! [X150_150] : (=(minus(X150_150, n1), pred(X150_150))) & ! [X151_151] : (=(pred(succ(X151_151)), X151_151)) & ! [X152_152] : (=(succ(pred(X152_152)), X152_152)) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), succ(Y154_154)) <=> leq(X153_153, Y154_154))) & ! [X155_155, Y156_156] : ((leq(succ(X155_155), Y156_156) => gt(Y156_156, X155_155))) & ! [X157_157, Y158_158] : ((leq(minus(X157_157, Y158_158), X157_157) => leq(n0, Y158_158))) & ! [X159_159, U160_160, V161_161, VAL162_162] : (=(a_select3(tptp_update3(X159_159, U160_160, V161_161, VAL162_162), U160_160, V161_161), VAL162_162)) & ! [I163_163, J164_164, U165_165, V166_166, X167_167, VAL168_168, VAL2169_169] : ((((~=(I163_163, U165_165) & =(J164_164, V166_166)) & =(a_select3(X167_167, U165_165, V166_166), VAL168_168)) => =(a_select3(tptp_update3(X167_167, I163_163, J164_164, VAL2169_169), U165_165, V166_166), VAL168_168))) & ! [I170_170, J171_171, U172_172, V173_173, X174_174, VAL175_175] : ((((((! [I0176_176, J0177_177] : (((((leq(n0, I0176_176) & leq(n0, J0177_177)) & leq(I0176_176, U172_172)) & leq(J0177_177, V173_173)) => =(a_select3(X174_174, I0176_176, J0177_177), VAL175_175))) & leq(n0, I170_170)) & leq(I170_170, U172_172)) & leq(n0, J171_171)) & leq(J171_171, V173_173)) => =(a_select3(tptp_update3(X174_174, U172_172, V173_173, VAL175_175), I170_170, J171_171), VAL175_175))) & ! [X178_178, U179_179, VAL180_180] : (=(a_select2(tptp_update2(X178_178, U179_179, VAL180_180), U179_179), VAL180_180)) & ! [I181_181, U182_182, X183_183, VAL184_184, VAL2185_185] : (((~=(I181_181, U182_182) & =(a_select2(X183_183, U182_182), VAL184_184)) => =(a_select2(tptp_update2(X183_183, I181_181, VAL2185_185), U182_182), VAL184_184))) & ! [I186_186, U187_187, X188_188, VAL189_189] : ((((! [I0190_190] : (((leq(n0, I0190_190) & leq(I0190_190, U187_187)) => =(a_select2(X188_188, I0190_190), VAL189_189))) & leq(n0, I186_186)) & leq(I186_186, U187_187)) => =(a_select2(tptp_update2(X188_188, U187_187, VAL189_189), I186_186), VAL189_189))) & true & ~=(def, use)), gt(n5, n4), gt(n7, n4), gt(n7, n5), gt(n4, tptp_minus_1), gt(n5, tptp_minus_1), gt(n7, tptp_minus_1), gt(n0, tptp_minus_1), gt(n1, tptp_minus_1), gt(n2, tptp_minus_1), gt(n3, tptp_minus_1), gt(n4, n0), gt(n5, n0), gt(n7, n0), gt(n1, n0), gt(n2, n0), gt(n3, n0), gt(n4, n1), gt(n5, n1), gt(n7, n1), gt(n2, n1), gt(n3, n1), gt(n4, n2), gt(n5, n2), gt(n7, n2), gt(n3, n2), gt(n4, n3), gt(n5, n3), gt(n7, n3), ! [X199_199] : (((leq(n0, X199_199) & leq(X199_199, n4)) => ((((=(X199_199, n0) | =(X199_199, n1)) | =(X199_199, n2)) | =(X199_199, n3)) | =(X199_199, n4)))), ! [X200_200] : (((leq(n0, X200_200) & leq(X200_200, n5)) => (((((=(X200_200, n0) | =(X200_200, n1)) | =(X200_200, n2)) | =(X200_200, n3)) | =(X200_200, n4)) | =(X200_200, n5)))), ! [X201_201] : (((leq(n0, X201_201) & leq(X201_201, n0)) => =(X201_201, n0))), ! [X202_202] : (((leq(n0, X202_202) & leq(X202_202, n1)) => (=(X202_202, n0) | =(X202_202, n1)))), ! [X203_203] : (((leq(n0, X203_203) & leq(X203_203, n2)) => ((=(X203_203, n0) | =(X203_203, n1)) | =(X203_203, n2)))), ! [X204_204] : (((leq(n0, X204_204) & leq(X204_204, n3)) => (((=(X204_204, n0) | =(X204_204, n1)) | =(X204_204, n2)) | =(X204_204, n3)))), =(succ(succ(succ(succ(n0)))), n4), =(succ(succ(succ(succ(succ(n0))))), n5), =(succ(n0), n1), =(succ(succ(n0)), n2), =(succ(succ(succ(n0))), n3), ~(((((((=(t_defuse, use) & =(tvar_defuse, use)) & ! [A191_191, B192_192] : (((((leq(n0, A191_191) & leq(n0, B192_192)) & leq(A191_191, minus(m_measvars, n1))) & leq(B192_192, minus(n_steps, n1))) => =(a_select3(rho_defuse, A191_191, B192_192), use)))) & ! [C193_193, D194_194] : (((((leq(n0, C193_193) & leq(n0, D194_194)) & leq(C193_193, n7)) & leq(D194_194, minus(n_steps, n1))) => =(a_select3(tr_defuse, C193_193, D194_194), use)))) & ! [E195_195] : (((leq(n0, E195_195) & leq(E195_195, minus(n_statevars, n1))) => =(a_select2(xinit_defuse, E195_195), use)))) & ! [F196_196] : (((leq(n0, F196_196) & leq(F196_196, minus(n_statevars, n1))) => =(a_select2(xinit_mean_defuse, F196_196), use)))) & ! [G197_197, H198_198] : (((((leq(n0, G197_197) & leq(n0, H198_198)) & leq(G197_197, minus(m_measvars, n1))) & leq(H198_198, minus(n_steps, n1))) => =(a_select3(z_defuse, G197_197, H198_198), use)))) => true)
% 12.95/2.76
% 12.95/2.76 [1] ALPHA_AND : (! [X29_29, Y30_30] : (((gt(X29_29, Y30_30) | gt(Y30_30, X29_29)) | =(X29_29, Y30_30))) & ! [X31_31, Y32_32, Z33_33] : (((gt(X31_31, Y32_32) & gt(Y32_32, Z33_33)) => gt(X31_31, Z33_33))) & ! [X34_34] : (~gt(X34_34, X34_34)) & ! [X35_35] : (leq(X35_35, X35_35)) & ! [X36_36, Y37_37, Z38_38] : (((leq(X36_36, Y37_37) & leq(Y37_37, Z38_38)) => leq(X36_36, Z38_38))) & ! [X39_39, Y40_40] : ((lt(X39_39, Y40_40) <=> gt(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((geq(X41_41, Y42_42) <=> leq(Y42_42, X41_41))) & ! [X43_43, Y44_44] : ((gt(Y44_44, X43_43) => leq(X43_43, Y44_44))) & ! [X45_45, Y46_46] : (((leq(X45_45, Y46_46) & ~=(X45_45, Y46_46)) => gt(Y46_46, X45_45))) & ! [X47_47, Y48_48] : ((leq(X47_47, pred(Y48_48)) <=> gt(Y48_48, X47_47))) & ! [X49_49] : (gt(succ(X49_49), X49_49)) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) => leq(X50_50, succ(Y51_51)))) & ! [X52_52, Y53_53] : ((leq(X52_52, Y53_53) <=> gt(succ(Y53_53), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(uniform_int_rnd(C55_55, X54_54), X54_54))) & ! [X56_56, C57_57] : ((leq(n0, X56_56) => leq(n0, uniform_int_rnd(C57_57, X56_56)))) & ! [I58_58, L59_59, U60_60, Val61_61] : (((leq(L59_59, I58_58) & leq(I58_58, U60_60)) => =(a_select2(tptp_const_array1(dim(L59_59, U60_60), Val61_61), I58_58), Val61_61))) & ! [I62_62, L163_63, U164_64, J65_65, L266_66, U267_67, Val68_68] : (((((leq(L163_63, I62_62) & leq(I62_62, U164_64)) & leq(L266_66, J65_65)) & leq(J65_65, U267_67)) => =(a_select3(tptp_const_array2(dim(L163_63, U164_64), dim(L266_66, U267_67), Val68_68), I62_62, J65_65), Val68_68))) & ! [A69_69, N70_70] : ((! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N70_70)) & leq(n0, J72_72)) & leq(J72_72, N70_70)) => =(a_select3(A69_69, I71_71, J72_72), a_select3(A69_69, J72_72, I71_71)))) => ! [I73_73, J74_74] : (((((leq(n0, I73_73) & leq(I73_73, N70_70)) & leq(n0, J74_74)) & leq(J74_74, N70_70)) => =(a_select3(trans(A69_69), I73_73, J74_74), a_select3(trans(A69_69), J74_74, I73_73)))))) & ! [A75_75, N76_76] : ((! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N76_76)) & leq(n0, J78_78)) & leq(J78_78, N76_76)) => =(a_select3(A75_75, I77_77, J78_78), a_select3(A75_75, J78_78, I77_77)))) => ! [I79_79, J80_80] : (((((leq(n0, I79_79) & leq(I79_79, N76_76)) & leq(n0, J80_80)) & leq(J80_80, N76_76)) => =(a_select3(inv(A75_75), I79_79, J80_80), a_select3(inv(A75_75), J80_80, I79_79)))))) & ! [A81_81, N82_82] : ((! [I83_83, J84_84] : (((((leq(n0, I83_83) & leq(I83_83, N82_82)) & leq(n0, J84_84)) & leq(J84_84, N82_82)) => =(a_select3(A81_81, I83_83, J84_84), a_select3(A81_81, J84_84, I83_83)))) => ! [I85_85, J86_86, K87_87, VAL88_88] : (((((((leq(n0, I85_85) & leq(I85_85, N82_82)) & leq(n0, J86_86)) & leq(J86_86, N82_82)) & leq(n0, K87_87)) & leq(K87_87, N82_82)) => =(a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), I85_85, J86_86), a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), J86_86, I85_85)))))) & ! [A89_89, B90_90, N91_91] : (((! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N91_91)) & leq(n0, J93_93)) & leq(J93_93, N91_91)) => =(a_select3(A89_89, I92_92, J93_93), a_select3(A89_89, J93_93, I92_92)))) & ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N91_91)) & leq(n0, J95_95)) & leq(J95_95, N91_91)) => =(a_select3(B90_90, I94_94, J95_95), a_select3(B90_90, J95_95, I94_94))))) => ! [I96_96, J97_97] : (((((leq(n0, I96_96) & leq(I96_96, N91_91)) & leq(n0, J97_97)) & leq(J97_97, N91_91)) => =(a_select3(tptp_madd(A89_89, B90_90), I96_96, J97_97), a_select3(tptp_madd(A89_89, B90_90), J97_97, I96_96)))))) & ! [A98_98, B99_99, N100_100] : (((! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N100_100)) & leq(n0, J102_102)) & leq(J102_102, N100_100)) => =(a_select3(A98_98, I101_101, J102_102), a_select3(A98_98, J102_102, I101_101)))) & ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N100_100)) & leq(n0, J104_104)) & leq(J104_104, N100_100)) => =(a_select3(B99_99, I103_103, J104_104), a_select3(B99_99, J104_104, I103_103))))) => ! [I105_105, J106_106] : (((((leq(n0, I105_105) & leq(I105_105, N100_100)) & leq(n0, J106_106)) & leq(J106_106, N100_100)) => =(a_select3(tptp_msub(A98_98, B99_99), I105_105, J106_106), a_select3(tptp_msub(A98_98, B99_99), J106_106, I105_105)))))) & ! [A107_107, B108_108, N109_109] : ((! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N109_109)) & leq(n0, J111_111)) & leq(J111_111, N109_109)) => =(a_select3(B108_108, I110_110, J111_111), a_select3(B108_108, J111_111, I110_110)))) => ! [I112_112, J113_113] : (((((leq(n0, I112_112) & leq(I112_112, N109_109)) & leq(n0, J113_113)) & leq(J113_113, N109_109)) => =(a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), I112_112, J113_113), a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), J113_113, I112_112)))))) & ! [A114_114, B115_115, N116_116, M117_117] : ((! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, M117_117)) & leq(n0, J119_119)) & leq(J119_119, M117_117)) => =(a_select3(B115_115, I118_118, J119_119), a_select3(B115_115, J119_119, I118_118)))) => ! [I120_120, J121_121] : (((((leq(n0, I120_120) & leq(I120_120, N116_116)) & leq(n0, J121_121)) & leq(J121_121, N116_116)) => =(a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), I120_120, J121_121), a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), J121_121, I120_120)))))) & ! [A122_122, B123_123, C124_124, D125_125, E126_126, F127_127, N128_128, M129_129] : ((((! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, M129_129)) & leq(n0, J131_131)) & leq(J131_131, M129_129)) => =(a_select3(D125_125, I130_130, J131_131), a_select3(D125_125, J131_131, I130_130)))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N128_128)) & leq(n0, J133_133)) & leq(J133_133, N128_128)) => =(a_select3(A122_122, I132_132, J133_133), a_select3(A122_122, J133_133, I132_132))))) & ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N128_128)) & leq(n0, J135_135)) & leq(J135_135, N128_128)) => =(a_select3(F127_127, I134_134, J135_135), a_select3(F127_127, J135_135, I134_134))))) => ! [I136_136, J137_137] : (((((leq(n0, I136_136) & leq(I136_136, N128_128)) & leq(n0, J137_137)) & leq(J137_137, N128_128)) => =(a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), I136_136, J137_137), a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), J137_137, I136_136)))))) & ! [Body138_138] : (=(sum(n0, tptp_minus_1, Body138_138), n0)) & ! [Body139_139] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body139_139))) & =(succ(tptp_minus_1), n0) & ! [X140_140] : (=(plus(X140_140, n1), succ(X140_140))) & ! [X141_141] : (=(plus(n1, X141_141), succ(X141_141))) & ! [X142_142] : (=(plus(X142_142, n2), succ(succ(X142_142)))) & ! [X143_143] : (=(plus(n2, X143_143), succ(succ(X143_143)))) & ! [X144_144] : (=(plus(X144_144, n3), succ(succ(succ(X144_144))))) & ! [X145_145] : (=(plus(n3, X145_145), succ(succ(succ(X145_145))))) & ! [X146_146] : (=(plus(X146_146, n4), succ(succ(succ(succ(X146_146)))))) & ! [X147_147] : (=(plus(n4, X147_147), succ(succ(succ(succ(X147_147)))))) & ! [X148_148] : (=(plus(X148_148, n5), succ(succ(succ(succ(succ(X148_148))))))) & ! [X149_149] : (=(plus(n5, X149_149), succ(succ(succ(succ(succ(X149_149))))))) & ! [X150_150] : (=(minus(X150_150, n1), pred(X150_150))) & ! [X151_151] : (=(pred(succ(X151_151)), X151_151)) & ! [X152_152] : (=(succ(pred(X152_152)), X152_152)) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), succ(Y154_154)) <=> leq(X153_153, Y154_154))) & ! [X155_155, Y156_156] : ((leq(succ(X155_155), Y156_156) => gt(Y156_156, X155_155))) & ! [X157_157, Y158_158] : ((leq(minus(X157_157, Y158_158), X157_157) => leq(n0, Y158_158))) & ! [X159_159, U160_160, V161_161, VAL162_162] : (=(a_select3(tptp_update3(X159_159, U160_160, V161_161, VAL162_162), U160_160, V161_161), VAL162_162)) & ! [I163_163, J164_164, U165_165, V166_166, X167_167, VAL168_168, VAL2169_169] : ((((~=(I163_163, U165_165) & =(J164_164, V166_166)) & =(a_select3(X167_167, U165_165, V166_166), VAL168_168)) => =(a_select3(tptp_update3(X167_167, I163_163, J164_164, VAL2169_169), U165_165, V166_166), VAL168_168))) & ! [I170_170, J171_171, U172_172, V173_173, X174_174, VAL175_175] : ((((((! [I0176_176, J0177_177] : (((((leq(n0, I0176_176) & leq(n0, J0177_177)) & leq(I0176_176, U172_172)) & leq(J0177_177, V173_173)) => =(a_select3(X174_174, I0176_176, J0177_177), VAL175_175))) & leq(n0, I170_170)) & leq(I170_170, U172_172)) & leq(n0, J171_171)) & leq(J171_171, V173_173)) => =(a_select3(tptp_update3(X174_174, U172_172, V173_173, VAL175_175), I170_170, J171_171), VAL175_175))) & ! [X178_178, U179_179, VAL180_180] : (=(a_select2(tptp_update2(X178_178, U179_179, VAL180_180), U179_179), VAL180_180)) & ! [I181_181, U182_182, X183_183, VAL184_184, VAL2185_185] : (((~=(I181_181, U182_182) & =(a_select2(X183_183, U182_182), VAL184_184)) => =(a_select2(tptp_update2(X183_183, I181_181, VAL2185_185), U182_182), VAL184_184))) & ! [I186_186, U187_187, X188_188, VAL189_189] : ((((! [I0190_190] : (((leq(n0, I0190_190) & leq(I0190_190, U187_187)) => =(a_select2(X188_188, I0190_190), VAL189_189))) & leq(n0, I186_186)) & leq(I186_186, U187_187)) => =(a_select2(tptp_update2(X188_188, U187_187, VAL189_189), I186_186), VAL189_189))) & true & ~=(def, use))
% 12.95/2.76 -> [2] ! [X29_29, Y30_30] : (((gt(X29_29, Y30_30) | gt(Y30_30, X29_29)) | =(X29_29, Y30_30))), ! [X31_31, Y32_32, Z33_33] : (((gt(X31_31, Y32_32) & gt(Y32_32, Z33_33)) => gt(X31_31, Z33_33))), ! [X34_34] : (~gt(X34_34, X34_34)), ! [X35_35] : (leq(X35_35, X35_35)), ! [X36_36, Y37_37, Z38_38] : (((leq(X36_36, Y37_37) & leq(Y37_37, Z38_38)) => leq(X36_36, Z38_38))), ! [X39_39, Y40_40] : ((lt(X39_39, Y40_40) <=> gt(Y40_40, X39_39))), ! [X41_41, Y42_42] : ((geq(X41_41, Y42_42) <=> leq(Y42_42, X41_41))), ! [X43_43, Y44_44] : ((gt(Y44_44, X43_43) => leq(X43_43, Y44_44))), ! [X45_45, Y46_46] : (((leq(X45_45, Y46_46) & ~=(X45_45, Y46_46)) => gt(Y46_46, X45_45))), ! [X47_47, Y48_48] : ((leq(X47_47, pred(Y48_48)) <=> gt(Y48_48, X47_47))), ! [X49_49] : (gt(succ(X49_49), X49_49)), ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) => leq(X50_50, succ(Y51_51)))), ! [X52_52, Y53_53] : ((leq(X52_52, Y53_53) <=> gt(succ(Y53_53), X52_52))), ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(uniform_int_rnd(C55_55, X54_54), X54_54))), ! [X56_56, C57_57] : ((leq(n0, X56_56) => leq(n0, uniform_int_rnd(C57_57, X56_56)))), ! [I58_58, L59_59, U60_60, Val61_61] : (((leq(L59_59, I58_58) & leq(I58_58, U60_60)) => =(a_select2(tptp_const_array1(dim(L59_59, U60_60), Val61_61), I58_58), Val61_61))), ! [I62_62, L163_63, U164_64, J65_65, L266_66, U267_67, Val68_68] : (((((leq(L163_63, I62_62) & leq(I62_62, U164_64)) & leq(L266_66, J65_65)) & leq(J65_65, U267_67)) => =(a_select3(tptp_const_array2(dim(L163_63, U164_64), dim(L266_66, U267_67), Val68_68), I62_62, J65_65), Val68_68))), ! [A69_69, N70_70] : ((! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N70_70)) & leq(n0, J72_72)) & leq(J72_72, N70_70)) => =(a_select3(A69_69, I71_71, J72_72), a_select3(A69_69, J72_72, I71_71)))) => ! [I73_73, J74_74] : (((((leq(n0, I73_73) & leq(I73_73, N70_70)) & leq(n0, J74_74)) & leq(J74_74, N70_70)) => =(a_select3(trans(A69_69), I73_73, J74_74), a_select3(trans(A69_69), J74_74, I73_73)))))), ! [A75_75, N76_76] : ((! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N76_76)) & leq(n0, J78_78)) & leq(J78_78, N76_76)) => =(a_select3(A75_75, I77_77, J78_78), a_select3(A75_75, J78_78, I77_77)))) => ! [I79_79, J80_80] : (((((leq(n0, I79_79) & leq(I79_79, N76_76)) & leq(n0, J80_80)) & leq(J80_80, N76_76)) => =(a_select3(inv(A75_75), I79_79, J80_80), a_select3(inv(A75_75), J80_80, I79_79)))))), ! [A81_81, N82_82] : ((! [I83_83, J84_84] : (((((leq(n0, I83_83) & leq(I83_83, N82_82)) & leq(n0, J84_84)) & leq(J84_84, N82_82)) => =(a_select3(A81_81, I83_83, J84_84), a_select3(A81_81, J84_84, I83_83)))) => ! [I85_85, J86_86, K87_87, VAL88_88] : (((((((leq(n0, I85_85) & leq(I85_85, N82_82)) & leq(n0, J86_86)) & leq(J86_86, N82_82)) & leq(n0, K87_87)) & leq(K87_87, N82_82)) => =(a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), I85_85, J86_86), a_select3(tptp_update3(A81_81, K87_87, K87_87, VAL88_88), J86_86, I85_85)))))), ! [A89_89, B90_90, N91_91] : (((! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N91_91)) & leq(n0, J93_93)) & leq(J93_93, N91_91)) => =(a_select3(A89_89, I92_92, J93_93), a_select3(A89_89, J93_93, I92_92)))) & ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N91_91)) & leq(n0, J95_95)) & leq(J95_95, N91_91)) => =(a_select3(B90_90, I94_94, J95_95), a_select3(B90_90, J95_95, I94_94))))) => ! [I96_96, J97_97] : (((((leq(n0, I96_96) & leq(I96_96, N91_91)) & leq(n0, J97_97)) & leq(J97_97, N91_91)) => =(a_select3(tptp_madd(A89_89, B90_90), I96_96, J97_97), a_select3(tptp_madd(A89_89, B90_90), J97_97, I96_96)))))), ! [A98_98, B99_99, N100_100] : (((! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N100_100)) & leq(n0, J102_102)) & leq(J102_102, N100_100)) => =(a_select3(A98_98, I101_101, J102_102), a_select3(A98_98, J102_102, I101_101)))) & ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N100_100)) & leq(n0, J104_104)) & leq(J104_104, N100_100)) => =(a_select3(B99_99, I103_103, J104_104), a_select3(B99_99, J104_104, I103_103))))) => ! [I105_105, J106_106] : (((((leq(n0, I105_105) & leq(I105_105, N100_100)) & leq(n0, J106_106)) & leq(J106_106, N100_100)) => =(a_select3(tptp_msub(A98_98, B99_99), I105_105, J106_106), a_select3(tptp_msub(A98_98, B99_99), J106_106, I105_105)))))), ! [A107_107, B108_108, N109_109] : ((! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N109_109)) & leq(n0, J111_111)) & leq(J111_111, N109_109)) => =(a_select3(B108_108, I110_110, J111_111), a_select3(B108_108, J111_111, I110_110)))) => ! [I112_112, J113_113] : (((((leq(n0, I112_112) & leq(I112_112, N109_109)) & leq(n0, J113_113)) & leq(J113_113, N109_109)) => =(a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), I112_112, J113_113), a_select3(tptp_mmul(A107_107, tptp_mmul(B108_108, trans(A107_107))), J113_113, I112_112)))))), ! [A114_114, B115_115, N116_116, M117_117] : ((! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, M117_117)) & leq(n0, J119_119)) & leq(J119_119, M117_117)) => =(a_select3(B115_115, I118_118, J119_119), a_select3(B115_115, J119_119, I118_118)))) => ! [I120_120, J121_121] : (((((leq(n0, I120_120) & leq(I120_120, N116_116)) & leq(n0, J121_121)) & leq(J121_121, N116_116)) => =(a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), I120_120, J121_121), a_select3(tptp_mmul(A114_114, tptp_mmul(B115_115, trans(A114_114))), J121_121, I120_120)))))), ! [A122_122, B123_123, C124_124, D125_125, E126_126, F127_127, N128_128, M129_129] : ((((! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, M129_129)) & leq(n0, J131_131)) & leq(J131_131, M129_129)) => =(a_select3(D125_125, I130_130, J131_131), a_select3(D125_125, J131_131, I130_130)))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N128_128)) & leq(n0, J133_133)) & leq(J133_133, N128_128)) => =(a_select3(A122_122, I132_132, J133_133), a_select3(A122_122, J133_133, I132_132))))) & ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N128_128)) & leq(n0, J135_135)) & leq(J135_135, N128_128)) => =(a_select3(F127_127, I134_134, J135_135), a_select3(F127_127, J135_135, I134_134))))) => ! [I136_136, J137_137] : (((((leq(n0, I136_136) & leq(I136_136, N128_128)) & leq(n0, J137_137)) & leq(J137_137, N128_128)) => =(a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), I136_136, J137_137), a_select3(tptp_madd(A122_122, tptp_mmul(B123_123, tptp_mmul(tptp_madd(tptp_mmul(C124_124, tptp_mmul(D125_125, trans(C124_124))), tptp_mmul(E126_126, tptp_mmul(F127_127, trans(E126_126)))), trans(B123_123)))), J137_137, I136_136)))))), ! [Body138_138] : (=(sum(n0, tptp_minus_1, Body138_138), n0)), ! [Body139_139] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body139_139))), =(succ(tptp_minus_1), n0), ! [X140_140] : (=(plus(X140_140, n1), succ(X140_140))), ! [X141_141] : (=(plus(n1, X141_141), succ(X141_141))), ! [X142_142] : (=(plus(X142_142, n2), succ(succ(X142_142)))), ! [X143_143] : (=(plus(n2, X143_143), succ(succ(X143_143)))), ! [X144_144] : (=(plus(X144_144, n3), succ(succ(succ(X144_144))))), ! [X145_145] : (=(plus(n3, X145_145), succ(succ(succ(X145_145))))), ! [X146_146] : (=(plus(X146_146, n4), succ(succ(succ(succ(X146_146)))))), ! [X147_147] : (=(plus(n4, X147_147), succ(succ(succ(succ(X147_147)))))), ! [X148_148] : (=(plus(X148_148, n5), succ(succ(succ(succ(succ(X148_148))))))), ! [X149_149] : (=(plus(n5, X149_149), succ(succ(succ(succ(succ(X149_149))))))), ! [X150_150] : (=(minus(X150_150, n1), pred(X150_150))), ! [X151_151] : (=(pred(succ(X151_151)), X151_151)), ! [X152_152] : (=(succ(pred(X152_152)), X152_152)), ! [X153_153, Y154_154] : ((leq(succ(X153_153), succ(Y154_154)) <=> leq(X153_153, Y154_154))), ! [X155_155, Y156_156] : ((leq(succ(X155_155), Y156_156) => gt(Y156_156, X155_155))), ! [X157_157, Y158_158] : ((leq(minus(X157_157, Y158_158), X157_157) => leq(n0, Y158_158))), ! [X159_159, U160_160, V161_161, VAL162_162] : (=(a_select3(tptp_update3(X159_159, U160_160, V161_161, VAL162_162), U160_160, V161_161), VAL162_162)), ! [I163_163, J164_164, U165_165, V166_166, X167_167, VAL168_168, VAL2169_169] : ((((~=(I163_163, U165_165) & =(J164_164, V166_166)) & =(a_select3(X167_167, U165_165, V166_166), VAL168_168)) => =(a_select3(tptp_update3(X167_167, I163_163, J164_164, VAL2169_169), U165_165, V166_166), VAL168_168))), ! [I170_170, J171_171, U172_172, V173_173, X174_174, VAL175_175] : ((((((! [I0176_176, J0177_177] : (((((leq(n0, I0176_176) & leq(n0, J0177_177)) & leq(I0176_176, U172_172)) & leq(J0177_177, V173_173)) => =(a_select3(X174_174, I0176_176, J0177_177), VAL175_175))) & leq(n0, I170_170)) & leq(I170_170, U172_172)) & leq(n0, J171_171)) & leq(J171_171, V173_173)) => =(a_select3(tptp_update3(X174_174, U172_172, V173_173, VAL175_175), I170_170, J171_171), VAL175_175))), ! [X178_178, U179_179, VAL180_180] : (=(a_select2(tptp_update2(X178_178, U179_179, VAL180_180), U179_179), VAL180_180)), ! [I181_181, U182_182, X183_183, VAL184_184, VAL2185_185] : (((~=(I181_181, U182_182) & =(a_select2(X183_183, U182_182), VAL184_184)) => =(a_select2(tptp_update2(X183_183, I181_181, VAL2185_185), U182_182), VAL184_184))), ! [I186_186, U187_187, X188_188, VAL189_189] : ((((! [I0190_190] : (((leq(n0, I0190_190) & leq(I0190_190, U187_187)) => =(a_select2(X188_188, I0190_190), VAL189_189))) & leq(n0, I186_186)) & leq(I186_186, U187_187)) => =(a_select2(tptp_update2(X188_188, U187_187, VAL189_189), I186_186), VAL189_189))), true, ~=(def, use)
% 12.95/2.76
% 12.95/2.76 [2] ALPHA_NOT_IMPLY : ~(((((((=(t_defuse, use) & =(tvar_defuse, use)) & ! [A191_191, B192_192] : (((((leq(n0, A191_191) & leq(n0, B192_192)) & leq(A191_191, minus(m_measvars, n1))) & leq(B192_192, minus(n_steps, n1))) => =(a_select3(rho_defuse, A191_191, B192_192), use)))) & ! [C193_193, D194_194] : (((((leq(n0, C193_193) & leq(n0, D194_194)) & leq(C193_193, n7)) & leq(D194_194, minus(n_steps, n1))) => =(a_select3(tr_defuse, C193_193, D194_194), use)))) & ! [E195_195] : (((leq(n0, E195_195) & leq(E195_195, minus(n_statevars, n1))) => =(a_select2(xinit_defuse, E195_195), use)))) & ! [F196_196] : (((leq(n0, F196_196) & leq(F196_196, minus(n_statevars, n1))) => =(a_select2(xinit_mean_defuse, F196_196), use)))) & ! [G197_197, H198_198] : (((((leq(n0, G197_197) & leq(n0, H198_198)) & leq(G197_197, minus(m_measvars, n1))) & leq(H198_198, minus(n_steps, n1))) => =(a_select3(z_defuse, G197_197, H198_198), use)))) => true)
% 12.95/2.76 -> [3] ((((((=(t_defuse, use) & =(tvar_defuse, use)) & ! [A191_191, B192_192] : (((((leq(n0, A191_191) & leq(n0, B192_192)) & leq(A191_191, minus(m_measvars, n1))) & leq(B192_192, minus(n_steps, n1))) => =(a_select3(rho_defuse, A191_191, B192_192), use)))) & ! [C193_193, D194_194] : (((((leq(n0, C193_193) & leq(n0, D194_194)) & leq(C193_193, n7)) & leq(D194_194, minus(n_steps, n1))) => =(a_select3(tr_defuse, C193_193, D194_194), use)))) & ! [E195_195] : (((leq(n0, E195_195) & leq(E195_195, minus(n_statevars, n1))) => =(a_select2(xinit_defuse, E195_195), use)))) & ! [F196_196] : (((leq(n0, F196_196) & leq(F196_196, minus(n_statevars, n1))) => =(a_select2(xinit_mean_defuse, F196_196), use)))) & ! [G197_197, H198_198] : (((((leq(n0, G197_197) & leq(n0, H198_198)) & leq(G197_197, minus(m_measvars, n1))) & leq(H198_198, minus(n_steps, n1))) => =(a_select3(z_defuse, G197_197, H198_198), use)))), ~true
% 12.95/2.76
% 12.95/2.76 [3] CLOSURE : ~true
% 12.95/2.76
% 12.95/2.76 % SZS output end Proof for theBenchmark.p
% 12.95/2.76 [2.420435s][1][Res] 18592 goroutines created
% 12.95/2.76 ==== Result ====
% 12.95/2.76 [2.420466s][1][Res] VALID
% 12.95/2.76 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------