TSTP Solution File: SWV043+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWV043+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n021.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 13:38:21 EDT 2022
% Result : Theorem 12.90s 2.66s
% Output : Proof 12.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SWV043+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.11 % Command : goeland -dmt -presko -proof %s
% 0.11/0.31 % Computer : n021.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun Sep 4 01:07:00 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.31 [DMT] DMT loaded with preskolemization
% 0.16/0.31 [EQ] equality loaded.
% 0.16/0.31 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.16/0.34 Conjecture not found
% 0.16/0.34 Start search
% 0.16/0.35 nb_step : 1 - limit : 77
% 0.16/0.35 Launch Gotab with destructive = true
% 12.90/2.63 % SZS output start Proof for theBenchmark.p
% 12.90/2.66 [0] ALPHA_AND : ((! [X27_27, Y28_28] : (((gt(X27_27, Y28_28) | gt(Y28_28, X27_27)) | =(X27_27, Y28_28))) & ! [X29_29, Y30_30, Z31_31] : (((gt(X29_29, Y30_30) & gt(Y30_30, Z31_31)) => gt(X29_29, Z31_31))) & ! [X32_32] : (~gt(X32_32, X32_32)) & ! [X33_33] : (leq(X33_33, X33_33)) & ! [X34_34, Y35_35, Z36_36] : (((leq(X34_34, Y35_35) & leq(Y35_35, Z36_36)) => leq(X34_34, Z36_36))) & ! [X37_37, Y38_38] : ((lt(X37_37, Y38_38) <=> gt(Y38_38, X37_37))) & ! [X39_39, Y40_40] : ((geq(X39_39, Y40_40) <=> leq(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((gt(Y42_42, X41_41) => leq(X41_41, Y42_42))) & ! [X43_43, Y44_44] : (((leq(X43_43, Y44_44) & ~=(X43_43, Y44_44)) => gt(Y44_44, X43_43))) & ! [X45_45, Y46_46] : ((leq(X45_45, pred(Y46_46)) <=> gt(Y46_46, X45_45))) & ! [X47_47] : (gt(succ(X47_47), X47_47)) & ! [X48_48, Y49_49] : ((leq(X48_48, Y49_49) => leq(X48_48, succ(Y49_49)))) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) <=> gt(succ(Y51_51), X50_50))) & ! [X52_52, C53_53] : ((leq(n0, X52_52) => leq(uniform_int_rnd(C53_53, X52_52), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(n0, uniform_int_rnd(C55_55, X54_54)))) & ! [I56_56, L57_57, U58_58, Val59_59] : (((leq(L57_57, I56_56) & leq(I56_56, U58_58)) => =(a_select2(tptp_const_array1(dim(L57_57, U58_58), Val59_59), I56_56), Val59_59))) & ! [I60_60, L161_61, U162_62, J63_63, L264_64, U265_65, Val66_66] : (((((leq(L161_61, I60_60) & leq(I60_60, U162_62)) & leq(L264_64, J63_63)) & leq(J63_63, U265_65)) => =(a_select3(tptp_const_array2(dim(L161_61, U162_62), dim(L264_64, U265_65), Val66_66), I60_60, J63_63), Val66_66))) & ! [A67_67, N68_68] : ((! [I69_69, J70_70] : (((((leq(n0, I69_69) & leq(I69_69, N68_68)) & leq(n0, J70_70)) & leq(J70_70, N68_68)) => =(a_select3(A67_67, I69_69, J70_70), a_select3(A67_67, J70_70, I69_69)))) => ! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N68_68)) & leq(n0, J72_72)) & leq(J72_72, N68_68)) => =(a_select3(trans(A67_67), I71_71, J72_72), a_select3(trans(A67_67), J72_72, I71_71)))))) & ! [A73_73, N74_74] : ((! [I75_75, J76_76] : (((((leq(n0, I75_75) & leq(I75_75, N74_74)) & leq(n0, J76_76)) & leq(J76_76, N74_74)) => =(a_select3(A73_73, I75_75, J76_76), a_select3(A73_73, J76_76, I75_75)))) => ! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N74_74)) & leq(n0, J78_78)) & leq(J78_78, N74_74)) => =(a_select3(inv(A73_73), I77_77, J78_78), a_select3(inv(A73_73), J78_78, I77_77)))))) & ! [A79_79, N80_80] : ((! [I81_81, J82_82] : (((((leq(n0, I81_81) & leq(I81_81, N80_80)) & leq(n0, J82_82)) & leq(J82_82, N80_80)) => =(a_select3(A79_79, I81_81, J82_82), a_select3(A79_79, J82_82, I81_81)))) => ! [I83_83, J84_84, K85_85, VAL86_86] : (((((((leq(n0, I83_83) & leq(I83_83, N80_80)) & leq(n0, J84_84)) & leq(J84_84, N80_80)) & leq(n0, K85_85)) & leq(K85_85, N80_80)) => =(a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), I83_83, J84_84), a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), J84_84, I83_83)))))) & ! [A87_87, B88_88, N89_89] : (((! [I90_90, J91_91] : (((((leq(n0, I90_90) & leq(I90_90, N89_89)) & leq(n0, J91_91)) & leq(J91_91, N89_89)) => =(a_select3(A87_87, I90_90, J91_91), a_select3(A87_87, J91_91, I90_90)))) & ! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N89_89)) & leq(n0, J93_93)) & leq(J93_93, N89_89)) => =(a_select3(B88_88, I92_92, J93_93), a_select3(B88_88, J93_93, I92_92))))) => ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N89_89)) & leq(n0, J95_95)) & leq(J95_95, N89_89)) => =(a_select3(tptp_madd(A87_87, B88_88), I94_94, J95_95), a_select3(tptp_madd(A87_87, B88_88), J95_95, I94_94)))))) & ! [A96_96, B97_97, N98_98] : (((! [I99_99, J100_100] : (((((leq(n0, I99_99) & leq(I99_99, N98_98)) & leq(n0, J100_100)) & leq(J100_100, N98_98)) => =(a_select3(A96_96, I99_99, J100_100), a_select3(A96_96, J100_100, I99_99)))) & ! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N98_98)) & leq(n0, J102_102)) & leq(J102_102, N98_98)) => =(a_select3(B97_97, I101_101, J102_102), a_select3(B97_97, J102_102, I101_101))))) => ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N98_98)) & leq(n0, J104_104)) & leq(J104_104, N98_98)) => =(a_select3(tptp_msub(A96_96, B97_97), I103_103, J104_104), a_select3(tptp_msub(A96_96, B97_97), J104_104, I103_103)))))) & ! [A105_105, B106_106, N107_107] : ((! [I108_108, J109_109] : (((((leq(n0, I108_108) & leq(I108_108, N107_107)) & leq(n0, J109_109)) & leq(J109_109, N107_107)) => =(a_select3(B106_106, I108_108, J109_109), a_select3(B106_106, J109_109, I108_108)))) => ! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N107_107)) & leq(n0, J111_111)) & leq(J111_111, N107_107)) => =(a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), I110_110, J111_111), a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), J111_111, I110_110)))))) & ! [A112_112, B113_113, N114_114, M115_115] : ((! [I116_116, J117_117] : (((((leq(n0, I116_116) & leq(I116_116, M115_115)) & leq(n0, J117_117)) & leq(J117_117, M115_115)) => =(a_select3(B113_113, I116_116, J117_117), a_select3(B113_113, J117_117, I116_116)))) => ! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, N114_114)) & leq(n0, J119_119)) & leq(J119_119, N114_114)) => =(a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), I118_118, J119_119), a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), J119_119, I118_118)))))) & ! [A120_120, B121_121, C122_122, D123_123, E124_124, F125_125, N126_126, M127_127] : ((((! [I128_128, J129_129] : (((((leq(n0, I128_128) & leq(I128_128, M127_127)) & leq(n0, J129_129)) & leq(J129_129, M127_127)) => =(a_select3(D123_123, I128_128, J129_129), a_select3(D123_123, J129_129, I128_128)))) & ! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, N126_126)) & leq(n0, J131_131)) & leq(J131_131, N126_126)) => =(a_select3(A120_120, I130_130, J131_131), a_select3(A120_120, J131_131, I130_130))))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N126_126)) & leq(n0, J133_133)) & leq(J133_133, N126_126)) => =(a_select3(F125_125, I132_132, J133_133), a_select3(F125_125, J133_133, I132_132))))) => ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N126_126)) & leq(n0, J135_135)) & leq(J135_135, N126_126)) => =(a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), I134_134, J135_135), a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), J135_135, I134_134)))))) & ! [Body136_136] : (=(sum(n0, tptp_minus_1, Body136_136), n0)) & ! [Body137_137] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body137_137))) & =(succ(tptp_minus_1), n0) & ! [X138_138] : (=(plus(X138_138, n1), succ(X138_138))) & ! [X139_139] : (=(plus(n1, X139_139), succ(X139_139))) & ! [X140_140] : (=(plus(X140_140, n2), succ(succ(X140_140)))) & ! [X141_141] : (=(plus(n2, X141_141), succ(succ(X141_141)))) & ! [X142_142] : (=(plus(X142_142, n3), succ(succ(succ(X142_142))))) & ! [X143_143] : (=(plus(n3, X143_143), succ(succ(succ(X143_143))))) & ! [X144_144] : (=(plus(X144_144, n4), succ(succ(succ(succ(X144_144)))))) & ! [X145_145] : (=(plus(n4, X145_145), succ(succ(succ(succ(X145_145)))))) & ! [X146_146] : (=(plus(X146_146, n5), succ(succ(succ(succ(succ(X146_146))))))) & ! [X147_147] : (=(plus(n5, X147_147), succ(succ(succ(succ(succ(X147_147))))))) & ! [X148_148] : (=(minus(X148_148, n1), pred(X148_148))) & ! [X149_149] : (=(pred(succ(X149_149)), X149_149)) & ! [X150_150] : (=(succ(pred(X150_150)), X150_150)) & ! [X151_151, Y152_152] : ((leq(succ(X151_151), succ(Y152_152)) <=> leq(X151_151, Y152_152))) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), Y154_154) => gt(Y154_154, X153_153))) & ! [X155_155, Y156_156] : ((leq(minus(X155_155, Y156_156), X155_155) => leq(n0, Y156_156))) & ! [X157_157, U158_158, V159_159, VAL160_160] : (=(a_select3(tptp_update3(X157_157, U158_158, V159_159, VAL160_160), U158_158, V159_159), VAL160_160)) & ! [I161_161, J162_162, U163_163, V164_164, X165_165, VAL166_166, VAL2167_167] : ((((~=(I161_161, U163_163) & =(J162_162, V164_164)) & =(a_select3(X165_165, U163_163, V164_164), VAL166_166)) => =(a_select3(tptp_update3(X165_165, I161_161, J162_162, VAL2167_167), U163_163, V164_164), VAL166_166))) & ! [I168_168, J169_169, U170_170, V171_171, X172_172, VAL173_173] : ((((((! [I0174_174, J0175_175] : (((((leq(n0, I0174_174) & leq(n0, J0175_175)) & leq(I0174_174, U170_170)) & leq(J0175_175, V171_171)) => =(a_select3(X172_172, I0174_174, J0175_175), VAL173_173))) & leq(n0, I168_168)) & leq(I168_168, U170_170)) & leq(n0, J169_169)) & leq(J169_169, V171_171)) => =(a_select3(tptp_update3(X172_172, U170_170, V171_171, VAL173_173), I168_168, J169_169), VAL173_173))) & ! [X176_176, U177_177, VAL178_178] : (=(a_select2(tptp_update2(X176_176, U177_177, VAL178_178), U177_177), VAL178_178)) & ! [I179_179, U180_180, X181_181, VAL182_182, VAL2183_183] : (((~=(I179_179, U180_180) & =(a_select2(X181_181, U180_180), VAL182_182)) => =(a_select2(tptp_update2(X181_181, I179_179, VAL2183_183), U180_180), VAL182_182))) & ! [I184_184, U185_185, X186_186, VAL187_187] : ((((! [I0188_188] : (((leq(n0, I0188_188) & leq(I0188_188, U185_185)) => =(a_select2(X186_186, I0188_188), VAL187_187))) & leq(n0, I184_184)) & leq(I184_184, U185_185)) => =(a_select2(tptp_update2(X186_186, U185_185, VAL187_187), I184_184), VAL187_187))) & true & ~=(def, use)) & gt(n5, n4) & gt(n4, tptp_minus_1) & gt(n5, 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(n1, n0) & gt(n2, n0) & gt(n3, n0) & gt(n4, n1) & gt(n5, n1) & gt(n2, n1) & gt(n3, n1) & gt(n4, n2) & gt(n5, n2) & gt(n3, n2) & gt(n4, n3) & gt(n5, n3) & ! [X189_189] : (((leq(n0, X189_189) & leq(X189_189, n4)) => ((((=(X189_189, n0) | =(X189_189, n1)) | =(X189_189, n2)) | =(X189_189, n3)) | =(X189_189, n4)))) & ! [X190_190] : (((leq(n0, X190_190) & leq(X190_190, n5)) => (((((=(X190_190, n0) | =(X190_190, n1)) | =(X190_190, n2)) | =(X190_190, n3)) | =(X190_190, n4)) | =(X190_190, n5)))) & ! [X191_191] : (((leq(n0, X191_191) & leq(X191_191, n0)) => =(X191_191, n0))) & ! [X192_192] : (((leq(n0, X192_192) & leq(X192_192, n1)) => (=(X192_192, n0) | =(X192_192, n1)))) & ! [X193_193] : (((leq(n0, X193_193) & leq(X193_193, n2)) => ((=(X193_193, n0) | =(X193_193, n1)) | =(X193_193, n2)))) & ! [X194_194] : (((leq(n0, X194_194) & leq(X194_194, n3)) => (((=(X194_194, n0) | =(X194_194, n1)) | =(X194_194, n2)) | =(X194_194, 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) & ~(true => true))
% 12.90/2.66 -> [1] (! [X27_27, Y28_28] : (((gt(X27_27, Y28_28) | gt(Y28_28, X27_27)) | =(X27_27, Y28_28))) & ! [X29_29, Y30_30, Z31_31] : (((gt(X29_29, Y30_30) & gt(Y30_30, Z31_31)) => gt(X29_29, Z31_31))) & ! [X32_32] : (~gt(X32_32, X32_32)) & ! [X33_33] : (leq(X33_33, X33_33)) & ! [X34_34, Y35_35, Z36_36] : (((leq(X34_34, Y35_35) & leq(Y35_35, Z36_36)) => leq(X34_34, Z36_36))) & ! [X37_37, Y38_38] : ((lt(X37_37, Y38_38) <=> gt(Y38_38, X37_37))) & ! [X39_39, Y40_40] : ((geq(X39_39, Y40_40) <=> leq(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((gt(Y42_42, X41_41) => leq(X41_41, Y42_42))) & ! [X43_43, Y44_44] : (((leq(X43_43, Y44_44) & ~=(X43_43, Y44_44)) => gt(Y44_44, X43_43))) & ! [X45_45, Y46_46] : ((leq(X45_45, pred(Y46_46)) <=> gt(Y46_46, X45_45))) & ! [X47_47] : (gt(succ(X47_47), X47_47)) & ! [X48_48, Y49_49] : ((leq(X48_48, Y49_49) => leq(X48_48, succ(Y49_49)))) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) <=> gt(succ(Y51_51), X50_50))) & ! [X52_52, C53_53] : ((leq(n0, X52_52) => leq(uniform_int_rnd(C53_53, X52_52), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(n0, uniform_int_rnd(C55_55, X54_54)))) & ! [I56_56, L57_57, U58_58, Val59_59] : (((leq(L57_57, I56_56) & leq(I56_56, U58_58)) => =(a_select2(tptp_const_array1(dim(L57_57, U58_58), Val59_59), I56_56), Val59_59))) & ! [I60_60, L161_61, U162_62, J63_63, L264_64, U265_65, Val66_66] : (((((leq(L161_61, I60_60) & leq(I60_60, U162_62)) & leq(L264_64, J63_63)) & leq(J63_63, U265_65)) => =(a_select3(tptp_const_array2(dim(L161_61, U162_62), dim(L264_64, U265_65), Val66_66), I60_60, J63_63), Val66_66))) & ! [A67_67, N68_68] : ((! [I69_69, J70_70] : (((((leq(n0, I69_69) & leq(I69_69, N68_68)) & leq(n0, J70_70)) & leq(J70_70, N68_68)) => =(a_select3(A67_67, I69_69, J70_70), a_select3(A67_67, J70_70, I69_69)))) => ! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N68_68)) & leq(n0, J72_72)) & leq(J72_72, N68_68)) => =(a_select3(trans(A67_67), I71_71, J72_72), a_select3(trans(A67_67), J72_72, I71_71)))))) & ! [A73_73, N74_74] : ((! [I75_75, J76_76] : (((((leq(n0, I75_75) & leq(I75_75, N74_74)) & leq(n0, J76_76)) & leq(J76_76, N74_74)) => =(a_select3(A73_73, I75_75, J76_76), a_select3(A73_73, J76_76, I75_75)))) => ! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N74_74)) & leq(n0, J78_78)) & leq(J78_78, N74_74)) => =(a_select3(inv(A73_73), I77_77, J78_78), a_select3(inv(A73_73), J78_78, I77_77)))))) & ! [A79_79, N80_80] : ((! [I81_81, J82_82] : (((((leq(n0, I81_81) & leq(I81_81, N80_80)) & leq(n0, J82_82)) & leq(J82_82, N80_80)) => =(a_select3(A79_79, I81_81, J82_82), a_select3(A79_79, J82_82, I81_81)))) => ! [I83_83, J84_84, K85_85, VAL86_86] : (((((((leq(n0, I83_83) & leq(I83_83, N80_80)) & leq(n0, J84_84)) & leq(J84_84, N80_80)) & leq(n0, K85_85)) & leq(K85_85, N80_80)) => =(a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), I83_83, J84_84), a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), J84_84, I83_83)))))) & ! [A87_87, B88_88, N89_89] : (((! [I90_90, J91_91] : (((((leq(n0, I90_90) & leq(I90_90, N89_89)) & leq(n0, J91_91)) & leq(J91_91, N89_89)) => =(a_select3(A87_87, I90_90, J91_91), a_select3(A87_87, J91_91, I90_90)))) & ! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N89_89)) & leq(n0, J93_93)) & leq(J93_93, N89_89)) => =(a_select3(B88_88, I92_92, J93_93), a_select3(B88_88, J93_93, I92_92))))) => ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N89_89)) & leq(n0, J95_95)) & leq(J95_95, N89_89)) => =(a_select3(tptp_madd(A87_87, B88_88), I94_94, J95_95), a_select3(tptp_madd(A87_87, B88_88), J95_95, I94_94)))))) & ! [A96_96, B97_97, N98_98] : (((! [I99_99, J100_100] : (((((leq(n0, I99_99) & leq(I99_99, N98_98)) & leq(n0, J100_100)) & leq(J100_100, N98_98)) => =(a_select3(A96_96, I99_99, J100_100), a_select3(A96_96, J100_100, I99_99)))) & ! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N98_98)) & leq(n0, J102_102)) & leq(J102_102, N98_98)) => =(a_select3(B97_97, I101_101, J102_102), a_select3(B97_97, J102_102, I101_101))))) => ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N98_98)) & leq(n0, J104_104)) & leq(J104_104, N98_98)) => =(a_select3(tptp_msub(A96_96, B97_97), I103_103, J104_104), a_select3(tptp_msub(A96_96, B97_97), J104_104, I103_103)))))) & ! [A105_105, B106_106, N107_107] : ((! [I108_108, J109_109] : (((((leq(n0, I108_108) & leq(I108_108, N107_107)) & leq(n0, J109_109)) & leq(J109_109, N107_107)) => =(a_select3(B106_106, I108_108, J109_109), a_select3(B106_106, J109_109, I108_108)))) => ! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N107_107)) & leq(n0, J111_111)) & leq(J111_111, N107_107)) => =(a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), I110_110, J111_111), a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), J111_111, I110_110)))))) & ! [A112_112, B113_113, N114_114, M115_115] : ((! [I116_116, J117_117] : (((((leq(n0, I116_116) & leq(I116_116, M115_115)) & leq(n0, J117_117)) & leq(J117_117, M115_115)) => =(a_select3(B113_113, I116_116, J117_117), a_select3(B113_113, J117_117, I116_116)))) => ! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, N114_114)) & leq(n0, J119_119)) & leq(J119_119, N114_114)) => =(a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), I118_118, J119_119), a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), J119_119, I118_118)))))) & ! [A120_120, B121_121, C122_122, D123_123, E124_124, F125_125, N126_126, M127_127] : ((((! [I128_128, J129_129] : (((((leq(n0, I128_128) & leq(I128_128, M127_127)) & leq(n0, J129_129)) & leq(J129_129, M127_127)) => =(a_select3(D123_123, I128_128, J129_129), a_select3(D123_123, J129_129, I128_128)))) & ! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, N126_126)) & leq(n0, J131_131)) & leq(J131_131, N126_126)) => =(a_select3(A120_120, I130_130, J131_131), a_select3(A120_120, J131_131, I130_130))))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N126_126)) & leq(n0, J133_133)) & leq(J133_133, N126_126)) => =(a_select3(F125_125, I132_132, J133_133), a_select3(F125_125, J133_133, I132_132))))) => ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N126_126)) & leq(n0, J135_135)) & leq(J135_135, N126_126)) => =(a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), I134_134, J135_135), a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), J135_135, I134_134)))))) & ! [Body136_136] : (=(sum(n0, tptp_minus_1, Body136_136), n0)) & ! [Body137_137] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body137_137))) & =(succ(tptp_minus_1), n0) & ! [X138_138] : (=(plus(X138_138, n1), succ(X138_138))) & ! [X139_139] : (=(plus(n1, X139_139), succ(X139_139))) & ! [X140_140] : (=(plus(X140_140, n2), succ(succ(X140_140)))) & ! [X141_141] : (=(plus(n2, X141_141), succ(succ(X141_141)))) & ! [X142_142] : (=(plus(X142_142, n3), succ(succ(succ(X142_142))))) & ! [X143_143] : (=(plus(n3, X143_143), succ(succ(succ(X143_143))))) & ! [X144_144] : (=(plus(X144_144, n4), succ(succ(succ(succ(X144_144)))))) & ! [X145_145] : (=(plus(n4, X145_145), succ(succ(succ(succ(X145_145)))))) & ! [X146_146] : (=(plus(X146_146, n5), succ(succ(succ(succ(succ(X146_146))))))) & ! [X147_147] : (=(plus(n5, X147_147), succ(succ(succ(succ(succ(X147_147))))))) & ! [X148_148] : (=(minus(X148_148, n1), pred(X148_148))) & ! [X149_149] : (=(pred(succ(X149_149)), X149_149)) & ! [X150_150] : (=(succ(pred(X150_150)), X150_150)) & ! [X151_151, Y152_152] : ((leq(succ(X151_151), succ(Y152_152)) <=> leq(X151_151, Y152_152))) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), Y154_154) => gt(Y154_154, X153_153))) & ! [X155_155, Y156_156] : ((leq(minus(X155_155, Y156_156), X155_155) => leq(n0, Y156_156))) & ! [X157_157, U158_158, V159_159, VAL160_160] : (=(a_select3(tptp_update3(X157_157, U158_158, V159_159, VAL160_160), U158_158, V159_159), VAL160_160)) & ! [I161_161, J162_162, U163_163, V164_164, X165_165, VAL166_166, VAL2167_167] : ((((~=(I161_161, U163_163) & =(J162_162, V164_164)) & =(a_select3(X165_165, U163_163, V164_164), VAL166_166)) => =(a_select3(tptp_update3(X165_165, I161_161, J162_162, VAL2167_167), U163_163, V164_164), VAL166_166))) & ! [I168_168, J169_169, U170_170, V171_171, X172_172, VAL173_173] : ((((((! [I0174_174, J0175_175] : (((((leq(n0, I0174_174) & leq(n0, J0175_175)) & leq(I0174_174, U170_170)) & leq(J0175_175, V171_171)) => =(a_select3(X172_172, I0174_174, J0175_175), VAL173_173))) & leq(n0, I168_168)) & leq(I168_168, U170_170)) & leq(n0, J169_169)) & leq(J169_169, V171_171)) => =(a_select3(tptp_update3(X172_172, U170_170, V171_171, VAL173_173), I168_168, J169_169), VAL173_173))) & ! [X176_176, U177_177, VAL178_178] : (=(a_select2(tptp_update2(X176_176, U177_177, VAL178_178), U177_177), VAL178_178)) & ! [I179_179, U180_180, X181_181, VAL182_182, VAL2183_183] : (((~=(I179_179, U180_180) & =(a_select2(X181_181, U180_180), VAL182_182)) => =(a_select2(tptp_update2(X181_181, I179_179, VAL2183_183), U180_180), VAL182_182))) & ! [I184_184, U185_185, X186_186, VAL187_187] : ((((! [I0188_188] : (((leq(n0, I0188_188) & leq(I0188_188, U185_185)) => =(a_select2(X186_186, I0188_188), VAL187_187))) & leq(n0, I184_184)) & leq(I184_184, U185_185)) => =(a_select2(tptp_update2(X186_186, U185_185, VAL187_187), I184_184), VAL187_187))) & true & ~=(def, use)), gt(n5, n4), gt(n4, tptp_minus_1), gt(n5, 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(n1, n0), gt(n2, n0), gt(n3, n0), gt(n4, n1), gt(n5, n1), gt(n2, n1), gt(n3, n1), gt(n4, n2), gt(n5, n2), gt(n3, n2), gt(n4, n3), gt(n5, n3), ! [X189_189] : (((leq(n0, X189_189) & leq(X189_189, n4)) => ((((=(X189_189, n0) | =(X189_189, n1)) | =(X189_189, n2)) | =(X189_189, n3)) | =(X189_189, n4)))), ! [X190_190] : (((leq(n0, X190_190) & leq(X190_190, n5)) => (((((=(X190_190, n0) | =(X190_190, n1)) | =(X190_190, n2)) | =(X190_190, n3)) | =(X190_190, n4)) | =(X190_190, n5)))), ! [X191_191] : (((leq(n0, X191_191) & leq(X191_191, n0)) => =(X191_191, n0))), ! [X192_192] : (((leq(n0, X192_192) & leq(X192_192, n1)) => (=(X192_192, n0) | =(X192_192, n1)))), ! [X193_193] : (((leq(n0, X193_193) & leq(X193_193, n2)) => ((=(X193_193, n0) | =(X193_193, n1)) | =(X193_193, n2)))), ! [X194_194] : (((leq(n0, X194_194) & leq(X194_194, n3)) => (((=(X194_194, n0) | =(X194_194, n1)) | =(X194_194, n2)) | =(X194_194, 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), ~(true => true)
% 12.90/2.66
% 12.90/2.66 [1] ALPHA_AND : (! [X27_27, Y28_28] : (((gt(X27_27, Y28_28) | gt(Y28_28, X27_27)) | =(X27_27, Y28_28))) & ! [X29_29, Y30_30, Z31_31] : (((gt(X29_29, Y30_30) & gt(Y30_30, Z31_31)) => gt(X29_29, Z31_31))) & ! [X32_32] : (~gt(X32_32, X32_32)) & ! [X33_33] : (leq(X33_33, X33_33)) & ! [X34_34, Y35_35, Z36_36] : (((leq(X34_34, Y35_35) & leq(Y35_35, Z36_36)) => leq(X34_34, Z36_36))) & ! [X37_37, Y38_38] : ((lt(X37_37, Y38_38) <=> gt(Y38_38, X37_37))) & ! [X39_39, Y40_40] : ((geq(X39_39, Y40_40) <=> leq(Y40_40, X39_39))) & ! [X41_41, Y42_42] : ((gt(Y42_42, X41_41) => leq(X41_41, Y42_42))) & ! [X43_43, Y44_44] : (((leq(X43_43, Y44_44) & ~=(X43_43, Y44_44)) => gt(Y44_44, X43_43))) & ! [X45_45, Y46_46] : ((leq(X45_45, pred(Y46_46)) <=> gt(Y46_46, X45_45))) & ! [X47_47] : (gt(succ(X47_47), X47_47)) & ! [X48_48, Y49_49] : ((leq(X48_48, Y49_49) => leq(X48_48, succ(Y49_49)))) & ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) <=> gt(succ(Y51_51), X50_50))) & ! [X52_52, C53_53] : ((leq(n0, X52_52) => leq(uniform_int_rnd(C53_53, X52_52), X52_52))) & ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(n0, uniform_int_rnd(C55_55, X54_54)))) & ! [I56_56, L57_57, U58_58, Val59_59] : (((leq(L57_57, I56_56) & leq(I56_56, U58_58)) => =(a_select2(tptp_const_array1(dim(L57_57, U58_58), Val59_59), I56_56), Val59_59))) & ! [I60_60, L161_61, U162_62, J63_63, L264_64, U265_65, Val66_66] : (((((leq(L161_61, I60_60) & leq(I60_60, U162_62)) & leq(L264_64, J63_63)) & leq(J63_63, U265_65)) => =(a_select3(tptp_const_array2(dim(L161_61, U162_62), dim(L264_64, U265_65), Val66_66), I60_60, J63_63), Val66_66))) & ! [A67_67, N68_68] : ((! [I69_69, J70_70] : (((((leq(n0, I69_69) & leq(I69_69, N68_68)) & leq(n0, J70_70)) & leq(J70_70, N68_68)) => =(a_select3(A67_67, I69_69, J70_70), a_select3(A67_67, J70_70, I69_69)))) => ! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N68_68)) & leq(n0, J72_72)) & leq(J72_72, N68_68)) => =(a_select3(trans(A67_67), I71_71, J72_72), a_select3(trans(A67_67), J72_72, I71_71)))))) & ! [A73_73, N74_74] : ((! [I75_75, J76_76] : (((((leq(n0, I75_75) & leq(I75_75, N74_74)) & leq(n0, J76_76)) & leq(J76_76, N74_74)) => =(a_select3(A73_73, I75_75, J76_76), a_select3(A73_73, J76_76, I75_75)))) => ! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N74_74)) & leq(n0, J78_78)) & leq(J78_78, N74_74)) => =(a_select3(inv(A73_73), I77_77, J78_78), a_select3(inv(A73_73), J78_78, I77_77)))))) & ! [A79_79, N80_80] : ((! [I81_81, J82_82] : (((((leq(n0, I81_81) & leq(I81_81, N80_80)) & leq(n0, J82_82)) & leq(J82_82, N80_80)) => =(a_select3(A79_79, I81_81, J82_82), a_select3(A79_79, J82_82, I81_81)))) => ! [I83_83, J84_84, K85_85, VAL86_86] : (((((((leq(n0, I83_83) & leq(I83_83, N80_80)) & leq(n0, J84_84)) & leq(J84_84, N80_80)) & leq(n0, K85_85)) & leq(K85_85, N80_80)) => =(a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), I83_83, J84_84), a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), J84_84, I83_83)))))) & ! [A87_87, B88_88, N89_89] : (((! [I90_90, J91_91] : (((((leq(n0, I90_90) & leq(I90_90, N89_89)) & leq(n0, J91_91)) & leq(J91_91, N89_89)) => =(a_select3(A87_87, I90_90, J91_91), a_select3(A87_87, J91_91, I90_90)))) & ! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N89_89)) & leq(n0, J93_93)) & leq(J93_93, N89_89)) => =(a_select3(B88_88, I92_92, J93_93), a_select3(B88_88, J93_93, I92_92))))) => ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N89_89)) & leq(n0, J95_95)) & leq(J95_95, N89_89)) => =(a_select3(tptp_madd(A87_87, B88_88), I94_94, J95_95), a_select3(tptp_madd(A87_87, B88_88), J95_95, I94_94)))))) & ! [A96_96, B97_97, N98_98] : (((! [I99_99, J100_100] : (((((leq(n0, I99_99) & leq(I99_99, N98_98)) & leq(n0, J100_100)) & leq(J100_100, N98_98)) => =(a_select3(A96_96, I99_99, J100_100), a_select3(A96_96, J100_100, I99_99)))) & ! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N98_98)) & leq(n0, J102_102)) & leq(J102_102, N98_98)) => =(a_select3(B97_97, I101_101, J102_102), a_select3(B97_97, J102_102, I101_101))))) => ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N98_98)) & leq(n0, J104_104)) & leq(J104_104, N98_98)) => =(a_select3(tptp_msub(A96_96, B97_97), I103_103, J104_104), a_select3(tptp_msub(A96_96, B97_97), J104_104, I103_103)))))) & ! [A105_105, B106_106, N107_107] : ((! [I108_108, J109_109] : (((((leq(n0, I108_108) & leq(I108_108, N107_107)) & leq(n0, J109_109)) & leq(J109_109, N107_107)) => =(a_select3(B106_106, I108_108, J109_109), a_select3(B106_106, J109_109, I108_108)))) => ! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N107_107)) & leq(n0, J111_111)) & leq(J111_111, N107_107)) => =(a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), I110_110, J111_111), a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), J111_111, I110_110)))))) & ! [A112_112, B113_113, N114_114, M115_115] : ((! [I116_116, J117_117] : (((((leq(n0, I116_116) & leq(I116_116, M115_115)) & leq(n0, J117_117)) & leq(J117_117, M115_115)) => =(a_select3(B113_113, I116_116, J117_117), a_select3(B113_113, J117_117, I116_116)))) => ! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, N114_114)) & leq(n0, J119_119)) & leq(J119_119, N114_114)) => =(a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), I118_118, J119_119), a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), J119_119, I118_118)))))) & ! [A120_120, B121_121, C122_122, D123_123, E124_124, F125_125, N126_126, M127_127] : ((((! [I128_128, J129_129] : (((((leq(n0, I128_128) & leq(I128_128, M127_127)) & leq(n0, J129_129)) & leq(J129_129, M127_127)) => =(a_select3(D123_123, I128_128, J129_129), a_select3(D123_123, J129_129, I128_128)))) & ! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, N126_126)) & leq(n0, J131_131)) & leq(J131_131, N126_126)) => =(a_select3(A120_120, I130_130, J131_131), a_select3(A120_120, J131_131, I130_130))))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N126_126)) & leq(n0, J133_133)) & leq(J133_133, N126_126)) => =(a_select3(F125_125, I132_132, J133_133), a_select3(F125_125, J133_133, I132_132))))) => ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N126_126)) & leq(n0, J135_135)) & leq(J135_135, N126_126)) => =(a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), I134_134, J135_135), a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), J135_135, I134_134)))))) & ! [Body136_136] : (=(sum(n0, tptp_minus_1, Body136_136), n0)) & ! [Body137_137] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body137_137))) & =(succ(tptp_minus_1), n0) & ! [X138_138] : (=(plus(X138_138, n1), succ(X138_138))) & ! [X139_139] : (=(plus(n1, X139_139), succ(X139_139))) & ! [X140_140] : (=(plus(X140_140, n2), succ(succ(X140_140)))) & ! [X141_141] : (=(plus(n2, X141_141), succ(succ(X141_141)))) & ! [X142_142] : (=(plus(X142_142, n3), succ(succ(succ(X142_142))))) & ! [X143_143] : (=(plus(n3, X143_143), succ(succ(succ(X143_143))))) & ! [X144_144] : (=(plus(X144_144, n4), succ(succ(succ(succ(X144_144)))))) & ! [X145_145] : (=(plus(n4, X145_145), succ(succ(succ(succ(X145_145)))))) & ! [X146_146] : (=(plus(X146_146, n5), succ(succ(succ(succ(succ(X146_146))))))) & ! [X147_147] : (=(plus(n5, X147_147), succ(succ(succ(succ(succ(X147_147))))))) & ! [X148_148] : (=(minus(X148_148, n1), pred(X148_148))) & ! [X149_149] : (=(pred(succ(X149_149)), X149_149)) & ! [X150_150] : (=(succ(pred(X150_150)), X150_150)) & ! [X151_151, Y152_152] : ((leq(succ(X151_151), succ(Y152_152)) <=> leq(X151_151, Y152_152))) & ! [X153_153, Y154_154] : ((leq(succ(X153_153), Y154_154) => gt(Y154_154, X153_153))) & ! [X155_155, Y156_156] : ((leq(minus(X155_155, Y156_156), X155_155) => leq(n0, Y156_156))) & ! [X157_157, U158_158, V159_159, VAL160_160] : (=(a_select3(tptp_update3(X157_157, U158_158, V159_159, VAL160_160), U158_158, V159_159), VAL160_160)) & ! [I161_161, J162_162, U163_163, V164_164, X165_165, VAL166_166, VAL2167_167] : ((((~=(I161_161, U163_163) & =(J162_162, V164_164)) & =(a_select3(X165_165, U163_163, V164_164), VAL166_166)) => =(a_select3(tptp_update3(X165_165, I161_161, J162_162, VAL2167_167), U163_163, V164_164), VAL166_166))) & ! [I168_168, J169_169, U170_170, V171_171, X172_172, VAL173_173] : ((((((! [I0174_174, J0175_175] : (((((leq(n0, I0174_174) & leq(n0, J0175_175)) & leq(I0174_174, U170_170)) & leq(J0175_175, V171_171)) => =(a_select3(X172_172, I0174_174, J0175_175), VAL173_173))) & leq(n0, I168_168)) & leq(I168_168, U170_170)) & leq(n0, J169_169)) & leq(J169_169, V171_171)) => =(a_select3(tptp_update3(X172_172, U170_170, V171_171, VAL173_173), I168_168, J169_169), VAL173_173))) & ! [X176_176, U177_177, VAL178_178] : (=(a_select2(tptp_update2(X176_176, U177_177, VAL178_178), U177_177), VAL178_178)) & ! [I179_179, U180_180, X181_181, VAL182_182, VAL2183_183] : (((~=(I179_179, U180_180) & =(a_select2(X181_181, U180_180), VAL182_182)) => =(a_select2(tptp_update2(X181_181, I179_179, VAL2183_183), U180_180), VAL182_182))) & ! [I184_184, U185_185, X186_186, VAL187_187] : ((((! [I0188_188] : (((leq(n0, I0188_188) & leq(I0188_188, U185_185)) => =(a_select2(X186_186, I0188_188), VAL187_187))) & leq(n0, I184_184)) & leq(I184_184, U185_185)) => =(a_select2(tptp_update2(X186_186, U185_185, VAL187_187), I184_184), VAL187_187))) & true & ~=(def, use))
% 12.90/2.66 -> [2] ! [X27_27, Y28_28] : (((gt(X27_27, Y28_28) | gt(Y28_28, X27_27)) | =(X27_27, Y28_28))), ! [X29_29, Y30_30, Z31_31] : (((gt(X29_29, Y30_30) & gt(Y30_30, Z31_31)) => gt(X29_29, Z31_31))), ! [X32_32] : (~gt(X32_32, X32_32)), ! [X33_33] : (leq(X33_33, X33_33)), ! [X34_34, Y35_35, Z36_36] : (((leq(X34_34, Y35_35) & leq(Y35_35, Z36_36)) => leq(X34_34, Z36_36))), ! [X37_37, Y38_38] : ((lt(X37_37, Y38_38) <=> gt(Y38_38, X37_37))), ! [X39_39, Y40_40] : ((geq(X39_39, Y40_40) <=> leq(Y40_40, X39_39))), ! [X41_41, Y42_42] : ((gt(Y42_42, X41_41) => leq(X41_41, Y42_42))), ! [X43_43, Y44_44] : (((leq(X43_43, Y44_44) & ~=(X43_43, Y44_44)) => gt(Y44_44, X43_43))), ! [X45_45, Y46_46] : ((leq(X45_45, pred(Y46_46)) <=> gt(Y46_46, X45_45))), ! [X47_47] : (gt(succ(X47_47), X47_47)), ! [X48_48, Y49_49] : ((leq(X48_48, Y49_49) => leq(X48_48, succ(Y49_49)))), ! [X50_50, Y51_51] : ((leq(X50_50, Y51_51) <=> gt(succ(Y51_51), X50_50))), ! [X52_52, C53_53] : ((leq(n0, X52_52) => leq(uniform_int_rnd(C53_53, X52_52), X52_52))), ! [X54_54, C55_55] : ((leq(n0, X54_54) => leq(n0, uniform_int_rnd(C55_55, X54_54)))), ! [I56_56, L57_57, U58_58, Val59_59] : (((leq(L57_57, I56_56) & leq(I56_56, U58_58)) => =(a_select2(tptp_const_array1(dim(L57_57, U58_58), Val59_59), I56_56), Val59_59))), ! [I60_60, L161_61, U162_62, J63_63, L264_64, U265_65, Val66_66] : (((((leq(L161_61, I60_60) & leq(I60_60, U162_62)) & leq(L264_64, J63_63)) & leq(J63_63, U265_65)) => =(a_select3(tptp_const_array2(dim(L161_61, U162_62), dim(L264_64, U265_65), Val66_66), I60_60, J63_63), Val66_66))), ! [A67_67, N68_68] : ((! [I69_69, J70_70] : (((((leq(n0, I69_69) & leq(I69_69, N68_68)) & leq(n0, J70_70)) & leq(J70_70, N68_68)) => =(a_select3(A67_67, I69_69, J70_70), a_select3(A67_67, J70_70, I69_69)))) => ! [I71_71, J72_72] : (((((leq(n0, I71_71) & leq(I71_71, N68_68)) & leq(n0, J72_72)) & leq(J72_72, N68_68)) => =(a_select3(trans(A67_67), I71_71, J72_72), a_select3(trans(A67_67), J72_72, I71_71)))))), ! [A73_73, N74_74] : ((! [I75_75, J76_76] : (((((leq(n0, I75_75) & leq(I75_75, N74_74)) & leq(n0, J76_76)) & leq(J76_76, N74_74)) => =(a_select3(A73_73, I75_75, J76_76), a_select3(A73_73, J76_76, I75_75)))) => ! [I77_77, J78_78] : (((((leq(n0, I77_77) & leq(I77_77, N74_74)) & leq(n0, J78_78)) & leq(J78_78, N74_74)) => =(a_select3(inv(A73_73), I77_77, J78_78), a_select3(inv(A73_73), J78_78, I77_77)))))), ! [A79_79, N80_80] : ((! [I81_81, J82_82] : (((((leq(n0, I81_81) & leq(I81_81, N80_80)) & leq(n0, J82_82)) & leq(J82_82, N80_80)) => =(a_select3(A79_79, I81_81, J82_82), a_select3(A79_79, J82_82, I81_81)))) => ! [I83_83, J84_84, K85_85, VAL86_86] : (((((((leq(n0, I83_83) & leq(I83_83, N80_80)) & leq(n0, J84_84)) & leq(J84_84, N80_80)) & leq(n0, K85_85)) & leq(K85_85, N80_80)) => =(a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), I83_83, J84_84), a_select3(tptp_update3(A79_79, K85_85, K85_85, VAL86_86), J84_84, I83_83)))))), ! [A87_87, B88_88, N89_89] : (((! [I90_90, J91_91] : (((((leq(n0, I90_90) & leq(I90_90, N89_89)) & leq(n0, J91_91)) & leq(J91_91, N89_89)) => =(a_select3(A87_87, I90_90, J91_91), a_select3(A87_87, J91_91, I90_90)))) & ! [I92_92, J93_93] : (((((leq(n0, I92_92) & leq(I92_92, N89_89)) & leq(n0, J93_93)) & leq(J93_93, N89_89)) => =(a_select3(B88_88, I92_92, J93_93), a_select3(B88_88, J93_93, I92_92))))) => ! [I94_94, J95_95] : (((((leq(n0, I94_94) & leq(I94_94, N89_89)) & leq(n0, J95_95)) & leq(J95_95, N89_89)) => =(a_select3(tptp_madd(A87_87, B88_88), I94_94, J95_95), a_select3(tptp_madd(A87_87, B88_88), J95_95, I94_94)))))), ! [A96_96, B97_97, N98_98] : (((! [I99_99, J100_100] : (((((leq(n0, I99_99) & leq(I99_99, N98_98)) & leq(n0, J100_100)) & leq(J100_100, N98_98)) => =(a_select3(A96_96, I99_99, J100_100), a_select3(A96_96, J100_100, I99_99)))) & ! [I101_101, J102_102] : (((((leq(n0, I101_101) & leq(I101_101, N98_98)) & leq(n0, J102_102)) & leq(J102_102, N98_98)) => =(a_select3(B97_97, I101_101, J102_102), a_select3(B97_97, J102_102, I101_101))))) => ! [I103_103, J104_104] : (((((leq(n0, I103_103) & leq(I103_103, N98_98)) & leq(n0, J104_104)) & leq(J104_104, N98_98)) => =(a_select3(tptp_msub(A96_96, B97_97), I103_103, J104_104), a_select3(tptp_msub(A96_96, B97_97), J104_104, I103_103)))))), ! [A105_105, B106_106, N107_107] : ((! [I108_108, J109_109] : (((((leq(n0, I108_108) & leq(I108_108, N107_107)) & leq(n0, J109_109)) & leq(J109_109, N107_107)) => =(a_select3(B106_106, I108_108, J109_109), a_select3(B106_106, J109_109, I108_108)))) => ! [I110_110, J111_111] : (((((leq(n0, I110_110) & leq(I110_110, N107_107)) & leq(n0, J111_111)) & leq(J111_111, N107_107)) => =(a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), I110_110, J111_111), a_select3(tptp_mmul(A105_105, tptp_mmul(B106_106, trans(A105_105))), J111_111, I110_110)))))), ! [A112_112, B113_113, N114_114, M115_115] : ((! [I116_116, J117_117] : (((((leq(n0, I116_116) & leq(I116_116, M115_115)) & leq(n0, J117_117)) & leq(J117_117, M115_115)) => =(a_select3(B113_113, I116_116, J117_117), a_select3(B113_113, J117_117, I116_116)))) => ! [I118_118, J119_119] : (((((leq(n0, I118_118) & leq(I118_118, N114_114)) & leq(n0, J119_119)) & leq(J119_119, N114_114)) => =(a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), I118_118, J119_119), a_select3(tptp_mmul(A112_112, tptp_mmul(B113_113, trans(A112_112))), J119_119, I118_118)))))), ! [A120_120, B121_121, C122_122, D123_123, E124_124, F125_125, N126_126, M127_127] : ((((! [I128_128, J129_129] : (((((leq(n0, I128_128) & leq(I128_128, M127_127)) & leq(n0, J129_129)) & leq(J129_129, M127_127)) => =(a_select3(D123_123, I128_128, J129_129), a_select3(D123_123, J129_129, I128_128)))) & ! [I130_130, J131_131] : (((((leq(n0, I130_130) & leq(I130_130, N126_126)) & leq(n0, J131_131)) & leq(J131_131, N126_126)) => =(a_select3(A120_120, I130_130, J131_131), a_select3(A120_120, J131_131, I130_130))))) & ! [I132_132, J133_133] : (((((leq(n0, I132_132) & leq(I132_132, N126_126)) & leq(n0, J133_133)) & leq(J133_133, N126_126)) => =(a_select3(F125_125, I132_132, J133_133), a_select3(F125_125, J133_133, I132_132))))) => ! [I134_134, J135_135] : (((((leq(n0, I134_134) & leq(I134_134, N126_126)) & leq(n0, J135_135)) & leq(J135_135, N126_126)) => =(a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), I134_134, J135_135), a_select3(tptp_madd(A120_120, tptp_mmul(B121_121, tptp_mmul(tptp_madd(tptp_mmul(C122_122, tptp_mmul(D123_123, trans(C122_122))), tptp_mmul(E124_124, tptp_mmul(F125_125, trans(E124_124)))), trans(B121_121)))), J135_135, I134_134)))))), ! [Body136_136] : (=(sum(n0, tptp_minus_1, Body136_136), n0)), ! [Body137_137] : (=(tptp_float_0_0, sum(n0, tptp_minus_1, Body137_137))), =(succ(tptp_minus_1), n0), ! [X138_138] : (=(plus(X138_138, n1), succ(X138_138))), ! [X139_139] : (=(plus(n1, X139_139), succ(X139_139))), ! [X140_140] : (=(plus(X140_140, n2), succ(succ(X140_140)))), ! [X141_141] : (=(plus(n2, X141_141), succ(succ(X141_141)))), ! [X142_142] : (=(plus(X142_142, n3), succ(succ(succ(X142_142))))), ! [X143_143] : (=(plus(n3, X143_143), succ(succ(succ(X143_143))))), ! [X144_144] : (=(plus(X144_144, n4), succ(succ(succ(succ(X144_144)))))), ! [X145_145] : (=(plus(n4, X145_145), succ(succ(succ(succ(X145_145)))))), ! [X146_146] : (=(plus(X146_146, n5), succ(succ(succ(succ(succ(X146_146))))))), ! [X147_147] : (=(plus(n5, X147_147), succ(succ(succ(succ(succ(X147_147))))))), ! [X148_148] : (=(minus(X148_148, n1), pred(X148_148))), ! [X149_149] : (=(pred(succ(X149_149)), X149_149)), ! [X150_150] : (=(succ(pred(X150_150)), X150_150)), ! [X151_151, Y152_152] : ((leq(succ(X151_151), succ(Y152_152)) <=> leq(X151_151, Y152_152))), ! [X153_153, Y154_154] : ((leq(succ(X153_153), Y154_154) => gt(Y154_154, X153_153))), ! [X155_155, Y156_156] : ((leq(minus(X155_155, Y156_156), X155_155) => leq(n0, Y156_156))), ! [X157_157, U158_158, V159_159, VAL160_160] : (=(a_select3(tptp_update3(X157_157, U158_158, V159_159, VAL160_160), U158_158, V159_159), VAL160_160)), ! [I161_161, J162_162, U163_163, V164_164, X165_165, VAL166_166, VAL2167_167] : ((((~=(I161_161, U163_163) & =(J162_162, V164_164)) & =(a_select3(X165_165, U163_163, V164_164), VAL166_166)) => =(a_select3(tptp_update3(X165_165, I161_161, J162_162, VAL2167_167), U163_163, V164_164), VAL166_166))), ! [I168_168, J169_169, U170_170, V171_171, X172_172, VAL173_173] : ((((((! [I0174_174, J0175_175] : (((((leq(n0, I0174_174) & leq(n0, J0175_175)) & leq(I0174_174, U170_170)) & leq(J0175_175, V171_171)) => =(a_select3(X172_172, I0174_174, J0175_175), VAL173_173))) & leq(n0, I168_168)) & leq(I168_168, U170_170)) & leq(n0, J169_169)) & leq(J169_169, V171_171)) => =(a_select3(tptp_update3(X172_172, U170_170, V171_171, VAL173_173), I168_168, J169_169), VAL173_173))), ! [X176_176, U177_177, VAL178_178] : (=(a_select2(tptp_update2(X176_176, U177_177, VAL178_178), U177_177), VAL178_178)), ! [I179_179, U180_180, X181_181, VAL182_182, VAL2183_183] : (((~=(I179_179, U180_180) & =(a_select2(X181_181, U180_180), VAL182_182)) => =(a_select2(tptp_update2(X181_181, I179_179, VAL2183_183), U180_180), VAL182_182))), ! [I184_184, U185_185, X186_186, VAL187_187] : ((((! [I0188_188] : (((leq(n0, I0188_188) & leq(I0188_188, U185_185)) => =(a_select2(X186_186, I0188_188), VAL187_187))) & leq(n0, I184_184)) & leq(I184_184, U185_185)) => =(a_select2(tptp_update2(X186_186, U185_185, VAL187_187), I184_184), VAL187_187))), true, ~=(def, use)
% 12.90/2.66
% 12.90/2.66 [2] ALPHA_NOT_IMPLY : ~(true => true)
% 12.90/2.66 -> [3] true, ~true
% 12.90/2.66
% 12.90/2.66 [3] CLOSURE : true
% 12.90/2.66
% 12.90/2.66 % SZS output end Proof for theBenchmark.p
% 12.90/2.66 [2.344901s][1][Res] 18591 goroutines created
% 12.90/2.66 ==== Result ====
% 12.90/2.66 [2.344948s][1][Res] VALID
% 12.90/2.66 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------