TSTP Solution File: NUM849+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 : Sun Sep 18 10:20:55 EDT 2022
% Result : Theorem 93.45s 13.49s
% Output : Proof 93.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 15:33:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 63
% 0.13/0.35 Launch Gotab with destructive = true
% 93.45/13.49 % SZS output start Proof for theBenchmark.p
% 93.45/13.49 [0] ALPHA_AND : (! [Vd45193_93] : ((=(vmul(vmul(vd448, vd449), Vd45193_93), vmul(vd448, vmul(vd449, Vd45193_93))) => =(vmul(vd448, vplus(vmul(vd449, Vd45193_93), vd449)), vmul(vd448, vmul(vd449, vsucc(Vd45193_93)))))) & ! [Vd45194_94] : ((=(vmul(vmul(vd448, vd449), Vd45194_94), vmul(vd448, vmul(vd449, Vd45194_94))) => =(vplus(vmul(vd448, vmul(vd449, Vd45194_94)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, Vd45194_94), vd449))))) & ! [Vd45195_95] : ((=(vmul(vmul(vd448, vd449), Vd45195_95), vmul(vd448, vmul(vd449, Vd45195_95))) => =(vplus(vmul(vmul(vd448, vd449), Vd45195_95), vmul(vd448, vd449)), vplus(vmul(vd448, vmul(vd449, Vd45195_95)), vmul(vd448, vd449))))) & ! [Vd45196_96] : ((=(vmul(vmul(vd448, vd449), Vd45196_96), vmul(vd448, vmul(vd449, Vd45196_96))) => =(vmul(vmul(vd448, vd449), vsucc(Vd45196_96)), vplus(vmul(vmul(vd448, vd449), Vd45196_96), vmul(vd448, vd449))))) & =(vmul(vd448, vd449), vmul(vd448, vmul(vd449, v1))) & =(vmul(vmul(vd448, vd449), v1), vmul(vd448, vd449)) & ! [Vd43297_97, Vd43398_98, Vd43499_99] : (=(vmul(Vd43297_97, vplus(Vd43398_98, Vd43499_99)), vplus(vmul(Vd43297_97, Vd43398_98), vmul(Vd43297_97, Vd43499_99)))) & ! [Vd418100_100, Vd419101_101] : (=(vmul(Vd418100_100, Vd419101_101), vmul(Vd419101_101, Vd418100_100))) & ! [Vd408102_102, Vd409103_103] : (=(vmul(vsucc(Vd408102_102), Vd409103_103), vplus(vmul(Vd408102_102, Vd409103_103), Vd409103_103))) & ! [Vd400104_104] : (=(vmul(v1, Vd400104_104), Vd400104_104)) & ! [Vd396105_105, Vd397106_106] : ((=(vmul(Vd396105_105, vsucc(Vd397106_106)), vplus(vmul(Vd396105_105, Vd397106_106), Vd396105_105)) & =(vmul(Vd396105_105, v1), Vd396105_105))) & ! [Vd386107_107, Vd387108_108] : ((less(Vd386107_107, vplus(Vd387108_108, v1)) => leq(Vd386107_107, Vd387108_108))) & ! [Vd375109_109, Vd376110_110] : ((greater(Vd375109_109, Vd376110_110) => geq(Vd375109_109, vplus(Vd376110_110, v1)))) & ! [Vd369111_111] : (geq(Vd369111_111, v1)) & ! [Vd362112_112, Vd363113_113, Vd365114_114, Vd366115_115] : (((geq(Vd365114_114, Vd366115_115) & geq(Vd362112_112, Vd363113_113)) => geq(vplus(Vd362112_112, Vd365114_114), vplus(Vd363113_113, Vd366115_115)))) & ! [Vd353116_116, Vd354117_117, Vd355118_118, Vd356119_119] : ((((greater(Vd355118_118, Vd356119_119) & geq(Vd353116_116, Vd354117_117)) | (geq(Vd355118_118, Vd356119_119) & greater(Vd353116_116, Vd354117_117))) => greater(vplus(Vd353116_116, Vd355118_118), vplus(Vd354117_117, Vd356119_119)))) & ! [Vd337120_120, Vd338121_121, Vd340122_122, Vd341123_123] : (((greater(Vd340122_122, Vd341123_123) & greater(Vd337120_120, Vd338121_121)) => greater(vplus(Vd337120_120, Vd340122_122), vplus(Vd338121_121, Vd341123_123)))) & ! [Vd328124_124, Vd329125_125, Vd330126_126] : ((less(vplus(Vd328124_124, Vd330126_126), vplus(Vd329125_125, Vd330126_126)) => less(Vd328124_124, Vd329125_125))) & ! [Vd328127_127, Vd329128_128, Vd330129_129] : ((=(vplus(Vd328127_127, Vd330129_129), vplus(Vd329128_128, Vd330129_129)) => =(Vd328127_127, Vd329128_128))) & ! [Vd328130_130, Vd329131_131, Vd330132_132] : ((greater(vplus(Vd328130_130, Vd330132_132), vplus(Vd329131_131, Vd330132_132)) => greater(Vd328130_130, Vd329131_131))) & ! [Vd301133_133, Vd302134_134, Vd303135_135] : ((less(Vd301133_133, Vd302134_134) => less(vplus(Vd301133_133, Vd303135_135), vplus(Vd302134_134, Vd303135_135)))) & ! [Vd301136_136, Vd302137_137, Vd303138_138] : ((=(Vd301136_136, Vd302137_137) => =(vplus(Vd301136_136, Vd303138_138), vplus(Vd302137_137, Vd303138_138)))) & ! [Vd301139_139, Vd302140_140, Vd303141_141] : ((greater(Vd301139_139, Vd302140_140) => greater(vplus(Vd301139_139, Vd303141_141), vplus(Vd302140_140, Vd303141_141)))) & ! [Vd295142_142, Vd296143_143] : (greater(vplus(Vd295142_142, Vd296143_143), Vd295142_142)) & ! [Vd289144_144, Vd290145_145, Vd292146_146] : (((leq(Vd290145_145, Vd292146_146) & leq(Vd289144_144, Vd290145_145)) => leq(Vd289144_144, Vd292146_146))) & ! [Vd281147_147, Vd282148_148, Vd283149_149] : ((((less(Vd282148_148, Vd283149_149) & leq(Vd281147_147, Vd282148_148)) | (leq(Vd282148_148, Vd283149_149) & less(Vd281147_147, Vd282148_148))) => less(Vd281147_147, Vd283149_149))) & ! [Vd262150_150, Vd263151_151, Vd265152_152] : (((less(Vd263151_151, Vd265152_152) & less(Vd262150_150, Vd263151_151)) => less(Vd262150_150, Vd265152_152))) & ! [Vd258153_153, Vd259154_154] : ((leq(Vd258153_153, Vd259154_154) => geq(Vd259154_154, Vd258153_153))) & ! [Vd254155_155, Vd255156_156] : ((geq(Vd254155_155, Vd255156_156) => leq(Vd255156_156, Vd254155_155))) & ! [Vd226161_161, Vd227162_162] : ((less(Vd226161_161, Vd227162_162) => greater(Vd227162_162, Vd226161_161))) & ! [Vd208163_163, Vd209164_164] : ((greater(Vd208163_163, Vd209164_164) => less(Vd209164_164, Vd208163_163))) & ! [Vd203165_165, Vd204166_166] : (((=(Vd203165_165, Vd204166_166) | greater(Vd203165_165, Vd204166_166)) | less(Vd203165_165, Vd204166_166))) & ! [Vd203167_167, Vd204168_168] : ((~=(Vd203167_167, Vd204168_168) | ~less(Vd203167_167, Vd204168_168))) & ! [Vd203169_169, Vd204170_170] : ((~greater(Vd203169_169, Vd204170_170) | ~less(Vd203169_169, Vd204170_170))) & ! [Vd203171_171, Vd204172_172] : ((~=(Vd203171_171, Vd204172_172) | ~greater(Vd203171_171, Vd204172_172))) & ! [Vd120179_179, Vd121180_180] : (((=(Vd120179_179, Vd121180_180) | ? [Vd123181_181] : (=(Vd120179_179, vplus(Vd121180_180, Vd123181_181)))) | ? [Vd125182_182] : (=(Vd121180_180, vplus(Vd120179_179, Vd125182_182))))) & ! [Vd120183_183, Vd121184_184] : ((~=(Vd120183_183, Vd121184_184) | ~? [Vd125185_185] : (=(Vd121184_184, vplus(Vd120183_183, Vd125185_185))))) & ! [Vd120186_186, Vd121187_187] : ((~? [Vd123188_188] : (=(Vd120186_186, vplus(Vd121187_187, Vd123188_188))) | ~? [Vd125189_189] : (=(Vd121187_187, vplus(Vd120186_186, Vd125189_189))))) & ! [Vd120190_190, Vd121191_191] : ((~=(Vd120190_190, Vd121191_191) | ~? [Vd123192_192] : (=(Vd120190_190, vplus(Vd121191_191, Vd123192_192))))) & ! [Vd104193_193, Vd105194_194] : ((~=(Vd104193_193, Vd105194_194) => ! [Vd107195_195] : (~=(vplus(Vd107195_195, Vd104193_193), vplus(Vd107195_195, Vd105194_194))))) & ! [Vd92196_196, Vd93197_197] : (~=(Vd93197_197, vplus(Vd92196_196, Vd93197_197))) & ! [Vd78198_198, Vd79199_199] : (=(vplus(Vd79199_199, Vd78198_198), vplus(Vd78198_198, Vd79199_199))) & ! [Vd68200_200, Vd69201_201] : (=(vplus(vsucc(Vd68200_200), Vd69201_201), vsucc(vplus(Vd68200_200, Vd69201_201)))) & ! [Vd59202_202] : (=(vplus(v1, Vd59202_202), vsucc(Vd59202_202))) & ! [Vd46203_203, Vd47204_204, Vd48205_205] : (=(vplus(vplus(Vd46203_203, Vd47204_204), Vd48205_205), vplus(Vd46203_203, vplus(Vd47204_204, Vd48205_205)))) & ! [Vd42206_206, Vd43207_207] : ((=(vplus(Vd42206_206, vsucc(Vd43207_207)), vsucc(vplus(Vd42206_206, Vd43207_207))) & =(vplus(Vd42206_206, v1), vsucc(Vd42206_206)))) & ! [Vd24208_208] : ((~=(Vd24208_208, v1) => =(Vd24208_208, vsucc(vskolem2(Vd24208_208))))) & ! [Vd16209_209] : (~=(vsucc(Vd16209_209), Vd16209_209)) & ! [Vd7210_210, Vd8211_211] : ((~=(Vd7210_210, Vd8211_211) => ~=(vsucc(Vd7210_210), vsucc(Vd8211_211)))) & ! [Vd3212_212, Vd4213_213] : ((=(vsucc(Vd3212_212), vsucc(Vd4213_213)) => =(Vd3212_212, Vd4213_213))) & ! [Vd1214_214] : (~=(vsucc(Vd1214_214), v1)) & ~! [Vd45492_92] : ((=(vmul(vmul(vd448, vd449), Vd45492_92), vmul(vd448, vmul(vd449, Vd45492_92))) => =(vmul(vmul(vd448, vd449), vsucc(Vd45492_92)), vmul(vd448, vmul(vd449, vsucc(Vd45492_92)))))))
% 93.45/13.49 -> [1] ! [Vd45193_93] : ((=(vmul(vmul(vd448, vd449), Vd45193_93), vmul(vd448, vmul(vd449, Vd45193_93))) => =(vmul(vd448, vplus(vmul(vd449, Vd45193_93), vd449)), vmul(vd448, vmul(vd449, vsucc(Vd45193_93)))))), ! [Vd45194_94] : ((=(vmul(vmul(vd448, vd449), Vd45194_94), vmul(vd448, vmul(vd449, Vd45194_94))) => =(vplus(vmul(vd448, vmul(vd449, Vd45194_94)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, Vd45194_94), vd449))))), ! [Vd45195_95] : ((=(vmul(vmul(vd448, vd449), Vd45195_95), vmul(vd448, vmul(vd449, Vd45195_95))) => =(vplus(vmul(vmul(vd448, vd449), Vd45195_95), vmul(vd448, vd449)), vplus(vmul(vd448, vmul(vd449, Vd45195_95)), vmul(vd448, vd449))))), ! [Vd45196_96] : ((=(vmul(vmul(vd448, vd449), Vd45196_96), vmul(vd448, vmul(vd449, Vd45196_96))) => =(vmul(vmul(vd448, vd449), vsucc(Vd45196_96)), vplus(vmul(vmul(vd448, vd449), Vd45196_96), vmul(vd448, vd449))))), =(vmul(vd448, vd449), vmul(vd448, vmul(vd449, v1))), =(vmul(vmul(vd448, vd449), v1), vmul(vd448, vd449)), ! [Vd43297_97, Vd43398_98, Vd43499_99] : (=(vmul(Vd43297_97, vplus(Vd43398_98, Vd43499_99)), vplus(vmul(Vd43297_97, Vd43398_98), vmul(Vd43297_97, Vd43499_99)))), ! [Vd418100_100, Vd419101_101] : (=(vmul(Vd418100_100, Vd419101_101), vmul(Vd419101_101, Vd418100_100))), ! [Vd408102_102, Vd409103_103] : (=(vmul(vsucc(Vd408102_102), Vd409103_103), vplus(vmul(Vd408102_102, Vd409103_103), Vd409103_103))), ! [Vd400104_104] : (=(vmul(v1, Vd400104_104), Vd400104_104)), ! [Vd396105_105, Vd397106_106] : ((=(vmul(Vd396105_105, vsucc(Vd397106_106)), vplus(vmul(Vd396105_105, Vd397106_106), Vd396105_105)) & =(vmul(Vd396105_105, v1), Vd396105_105))), ! [Vd386107_107, Vd387108_108] : ((less(Vd386107_107, vplus(Vd387108_108, v1)) => leq(Vd386107_107, Vd387108_108))), ! [Vd375109_109, Vd376110_110] : ((greater(Vd375109_109, Vd376110_110) => geq(Vd375109_109, vplus(Vd376110_110, v1)))), ! [Vd369111_111] : (geq(Vd369111_111, v1)), ! [Vd362112_112, Vd363113_113, Vd365114_114, Vd366115_115] : (((geq(Vd365114_114, Vd366115_115) & geq(Vd362112_112, Vd363113_113)) => geq(vplus(Vd362112_112, Vd365114_114), vplus(Vd363113_113, Vd366115_115)))), ! [Vd353116_116, Vd354117_117, Vd355118_118, Vd356119_119] : ((((greater(Vd355118_118, Vd356119_119) & geq(Vd353116_116, Vd354117_117)) | (geq(Vd355118_118, Vd356119_119) & greater(Vd353116_116, Vd354117_117))) => greater(vplus(Vd353116_116, Vd355118_118), vplus(Vd354117_117, Vd356119_119)))), ! [Vd337120_120, Vd338121_121, Vd340122_122, Vd341123_123] : (((greater(Vd340122_122, Vd341123_123) & greater(Vd337120_120, Vd338121_121)) => greater(vplus(Vd337120_120, Vd340122_122), vplus(Vd338121_121, Vd341123_123)))), ! [Vd328124_124, Vd329125_125, Vd330126_126] : ((less(vplus(Vd328124_124, Vd330126_126), vplus(Vd329125_125, Vd330126_126)) => less(Vd328124_124, Vd329125_125))), ! [Vd328127_127, Vd329128_128, Vd330129_129] : ((=(vplus(Vd328127_127, Vd330129_129), vplus(Vd329128_128, Vd330129_129)) => =(Vd328127_127, Vd329128_128))), ! [Vd328130_130, Vd329131_131, Vd330132_132] : ((greater(vplus(Vd328130_130, Vd330132_132), vplus(Vd329131_131, Vd330132_132)) => greater(Vd328130_130, Vd329131_131))), ! [Vd301133_133, Vd302134_134, Vd303135_135] : ((less(Vd301133_133, Vd302134_134) => less(vplus(Vd301133_133, Vd303135_135), vplus(Vd302134_134, Vd303135_135)))), ! [Vd301136_136, Vd302137_137, Vd303138_138] : ((=(Vd301136_136, Vd302137_137) => =(vplus(Vd301136_136, Vd303138_138), vplus(Vd302137_137, Vd303138_138)))), ! [Vd301139_139, Vd302140_140, Vd303141_141] : ((greater(Vd301139_139, Vd302140_140) => greater(vplus(Vd301139_139, Vd303141_141), vplus(Vd302140_140, Vd303141_141)))), ! [Vd295142_142, Vd296143_143] : (greater(vplus(Vd295142_142, Vd296143_143), Vd295142_142)), ! [Vd289144_144, Vd290145_145, Vd292146_146] : (((leq(Vd290145_145, Vd292146_146) & leq(Vd289144_144, Vd290145_145)) => leq(Vd289144_144, Vd292146_146))), ! [Vd281147_147, Vd282148_148, Vd283149_149] : ((((less(Vd282148_148, Vd283149_149) & leq(Vd281147_147, Vd282148_148)) | (leq(Vd282148_148, Vd283149_149) & less(Vd281147_147, Vd282148_148))) => less(Vd281147_147, Vd283149_149))), ! [Vd262150_150, Vd263151_151, Vd265152_152] : (((less(Vd263151_151, Vd265152_152) & less(Vd262150_150, Vd263151_151)) => less(Vd262150_150, Vd265152_152))), ! [Vd258153_153, Vd259154_154] : ((leq(Vd258153_153, Vd259154_154) => geq(Vd259154_154, Vd258153_153))), ! [Vd254155_155, Vd255156_156] : ((geq(Vd254155_155, Vd255156_156) => leq(Vd255156_156, Vd254155_155))), ! [Vd226161_161, Vd227162_162] : ((less(Vd226161_161, Vd227162_162) => greater(Vd227162_162, Vd226161_161))), ! [Vd208163_163, Vd209164_164] : ((greater(Vd208163_163, Vd209164_164) => less(Vd209164_164, Vd208163_163))), ! [Vd203165_165, Vd204166_166] : (((=(Vd203165_165, Vd204166_166) | greater(Vd203165_165, Vd204166_166)) | less(Vd203165_165, Vd204166_166))), ! [Vd203167_167, Vd204168_168] : ((~=(Vd203167_167, Vd204168_168) | ~less(Vd203167_167, Vd204168_168))), ! [Vd203169_169, Vd204170_170] : ((~greater(Vd203169_169, Vd204170_170) | ~less(Vd203169_169, Vd204170_170))), ! [Vd203171_171, Vd204172_172] : ((~=(Vd203171_171, Vd204172_172) | ~greater(Vd203171_171, Vd204172_172))), ! [Vd120179_179, Vd121180_180] : (((=(Vd120179_179, Vd121180_180) | ? [Vd123181_181] : (=(Vd120179_179, vplus(Vd121180_180, Vd123181_181)))) | ? [Vd125182_182] : (=(Vd121180_180, vplus(Vd120179_179, Vd125182_182))))), ! [Vd120183_183, Vd121184_184] : ((~=(Vd120183_183, Vd121184_184) | ~? [Vd125185_185] : (=(Vd121184_184, vplus(Vd120183_183, Vd125185_185))))), ! [Vd120186_186, Vd121187_187] : ((~? [Vd123188_188] : (=(Vd120186_186, vplus(Vd121187_187, Vd123188_188))) | ~? [Vd125189_189] : (=(Vd121187_187, vplus(Vd120186_186, Vd125189_189))))), ! [Vd120190_190, Vd121191_191] : ((~=(Vd120190_190, Vd121191_191) | ~? [Vd123192_192] : (=(Vd120190_190, vplus(Vd121191_191, Vd123192_192))))), ! [Vd104193_193, Vd105194_194] : ((~=(Vd104193_193, Vd105194_194) => ! [Vd107195_195] : (~=(vplus(Vd107195_195, Vd104193_193), vplus(Vd107195_195, Vd105194_194))))), ! [Vd92196_196, Vd93197_197] : (~=(Vd93197_197, vplus(Vd92196_196, Vd93197_197))), ! [Vd78198_198, Vd79199_199] : (=(vplus(Vd79199_199, Vd78198_198), vplus(Vd78198_198, Vd79199_199))), ! [Vd68200_200, Vd69201_201] : (=(vplus(vsucc(Vd68200_200), Vd69201_201), vsucc(vplus(Vd68200_200, Vd69201_201)))), ! [Vd59202_202] : (=(vplus(v1, Vd59202_202), vsucc(Vd59202_202))), ! [Vd46203_203, Vd47204_204, Vd48205_205] : (=(vplus(vplus(Vd46203_203, Vd47204_204), Vd48205_205), vplus(Vd46203_203, vplus(Vd47204_204, Vd48205_205)))), ! [Vd42206_206, Vd43207_207] : ((=(vplus(Vd42206_206, vsucc(Vd43207_207)), vsucc(vplus(Vd42206_206, Vd43207_207))) & =(vplus(Vd42206_206, v1), vsucc(Vd42206_206)))), ! [Vd24208_208] : ((~=(Vd24208_208, v1) => =(Vd24208_208, vsucc(vskolem2(Vd24208_208))))), ! [Vd16209_209] : (~=(vsucc(Vd16209_209), Vd16209_209)), ! [Vd7210_210, Vd8211_211] : ((~=(Vd7210_210, Vd8211_211) => ~=(vsucc(Vd7210_210), vsucc(Vd8211_211)))), ! [Vd3212_212, Vd4213_213] : ((=(vsucc(Vd3212_212), vsucc(Vd4213_213)) => =(Vd3212_212, Vd4213_213))), ! [Vd1214_214] : (~=(vsucc(Vd1214_214), v1)), ~! [Vd45492_92] : ((=(vmul(vmul(vd448, vd449), Vd45492_92), vmul(vd448, vmul(vd449, Vd45492_92))) => =(vmul(vmul(vd448, vd449), vsucc(Vd45492_92)), vmul(vd448, vmul(vd449, vsucc(Vd45492_92))))))
% 93.45/13.49
% 93.45/13.49 [1] DELTA_NOT_FORALL : ~! [Vd45492_92] : ((=(vmul(vmul(vd448, vd449), Vd45492_92), vmul(vd448, vmul(vd449, Vd45492_92))) => =(vmul(vmul(vd448, vd449), vsucc(Vd45492_92)), vmul(vd448, vmul(vd449, vsucc(Vd45492_92))))))
% 93.45/13.49 -> [2] ~(=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vmul(vmul(vd448, vd449), vsucc(skolem_Vd4549292)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292)))))
% 93.45/13.49
% 93.45/13.49 [2] ALPHA_NOT_IMPLY : ~(=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vmul(vmul(vd448, vd449), vsucc(skolem_Vd4549292)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292)))))
% 93.45/13.49 -> [3] =(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))), ~=(vmul(vmul(vd448, vd449), vsucc(skolem_Vd4549292)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292))))
% 93.45/13.49
% 93.45/13.49 [3] GAMMA_FORALL : ! [Vd45193_93] : ((=(vmul(vmul(vd448, vd449), Vd45193_93), vmul(vd448, vmul(vd449, Vd45193_93))) => =(vmul(vd448, vplus(vmul(vd449, Vd45193_93), vd449)), vmul(vd448, vmul(vd449, vsucc(Vd45193_93))))))
% 93.45/13.49 -> [4] (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292)))))
% 93.45/13.49
% 93.45/13.49 [4] BETA_IMPLY : (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292)))))
% 93.45/13.49 -> [5] ~=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292)))
% 93.45/13.49 -> [6] =(vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449)), vmul(vd448, vmul(vd449, vsucc(skolem_Vd4549292))))
% 93.45/13.49
% 93.45/13.49 [5] CLOSURE : =
% 93.45/13.49
% 93.45/13.49 [6] GAMMA_FORALL : ! [Vd45194_94] : ((=(vmul(vmul(vd448, vd449), Vd45194_94), vmul(vd448, vmul(vd449, Vd45194_94))) => =(vplus(vmul(vd448, vmul(vd449, Vd45194_94)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, Vd45194_94), vd449)))))
% 93.45/13.49 -> [7] (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vplus(vmul(vd448, vmul(vd449, skolem_Vd4549292)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449))))
% 93.45/13.49
% 93.45/13.49 [7] BETA_IMPLY : (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vplus(vmul(vd448, vmul(vd449, skolem_Vd4549292)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449))))
% 93.45/13.49 -> [8] ~=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292)))
% 93.45/13.49 -> [9] =(vplus(vmul(vd448, vmul(vd449, skolem_Vd4549292)), vmul(vd448, vd449)), vmul(vd448, vplus(vmul(vd449, skolem_Vd4549292), vd449)))
% 93.45/13.49
% 93.45/13.49 [8] CLOSURE : =
% 93.45/13.49
% 93.45/13.49 [10] BETA_IMPLY : (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vplus(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vd449)), vplus(vmul(vd448, vmul(vd449, skolem_Vd4549292)), vmul(vd448, vd449))))
% 93.45/13.49 -> [18] ~=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292)))
% 93.45/13.49 -> [19] =(vplus(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vd449)), vplus(vmul(vd448, vmul(vd449, skolem_Vd4549292)), vmul(vd448, vd449)))
% 93.45/13.49
% 93.45/13.49 [18] CLOSURE : =
% 93.45/13.49
% 93.45/13.49 [20] BETA_IMPLY : (=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292))) => =(vmul(vmul(vd448, vd449), vsucc(skolem_Vd4549292)), vplus(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vd449))))
% 93.45/13.49 -> [23] ~=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292)))
% 93.45/13.49 -> [24] =(vmul(vmul(vd448, vd449), vsucc(skolem_Vd4549292)), vplus(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vd449)))
% 93.45/13.49
% 93.45/13.49 [24] CLOSURE : =
% 93.45/13.49
% 93.45/13.49 [23] CLOSURE : ~=(vmul(vmul(vd448, vd449), skolem_Vd4549292), vmul(vd448, vmul(vd449, skolem_Vd4549292)))
% 93.45/13.49
% 93.45/13.49 % SZS output end Proof for theBenchmark.p
% 93.45/13.49 [13.148598s][1][Res] 157294 goroutines created
% 93.45/13.49 ==== Result ====
% 93.45/13.49 [13.148658s][1][Res] VALID
% 93.45/13.49 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------