TSTP Solution File: SEU160+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:55:38 EDT 2022
% Result : Theorem 0.18s 0.56s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 09:10:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 95
% 0.12/0.35 Launch Gotab with destructive = true
% 0.18/0.55 % SZS output start Proof for theBenchmark.p
% 0.18/0.56 [0] ALPHA_AND : (! [A6_6, B7_7] : ((in(A6_6, B7_7) => ~in(B7_7, A6_6))) & ! [A8_8, B9_9] : ((proper_subset(A8_8, B9_9) => ~proper_subset(B9_9, A8_8))) & ! [A10_10, B11_11] : (=(unordered_pair(A10_10, B11_11), unordered_pair(B11_11, A10_10))) & ! [A12_12, B13_13] : (=(set_union2(A12_12, B13_13), set_union2(B13_13, A12_12))) & ! [A14_14, B15_15] : (=(set_intersection2(A14_14, B15_15), set_intersection2(B15_15, A14_14))) & ! [A16_16, B17_17] : ((=(A16_16, B17_17) <=> (subset(A16_16, B17_17) & subset(B17_17, A16_16)))) & ! [A18_18, B19_19] : ((=(B19_19, singleton(A18_18)) <=> ! [C20_20] : ((in(C20_20, B19_19) <=> =(C20_20, A18_18))))) & ! [A21_21] : ((=(A21_21, empty_set) <=> ! [B22_22] : (~in(B22_22, A21_21)))) & ! [A23_23, B24_24] : ((=(B24_24, powerset(A23_23)) <=> ! [C25_25] : ((in(C25_25, B24_24) <=> subset(C25_25, A23_23))))) & ! [A26_26, B27_27, C28_28] : ((=(C28_28, unordered_pair(A26_26, B27_27)) <=> ! [D29_29] : ((in(D29_29, C28_28) <=> (=(D29_29, A26_26) | =(D29_29, B27_27)))))) & ! [A30_30, B31_31, C32_32] : ((=(C32_32, set_union2(A30_30, B31_31)) <=> ! [D33_33] : ((in(D33_33, C32_32) <=> (in(D33_33, A30_30) | in(D33_33, B31_31)))))) & ! [A34_34, B35_35, C36_36] : ((=(C36_36, cartesian_product2(A34_34, B35_35)) <=> ! [D37_37] : ((in(D37_37, C36_36) <=> ? [E38_38, F39_39] : (((in(E38_38, A34_34) & in(F39_39, B35_35)) & =(D37_37, ordered_pair(E38_38, F39_39)))))))) & ! [A43_43, B44_44, C45_45] : ((=(C45_45, set_intersection2(A43_43, B44_44)) <=> ! [D46_46] : ((in(D46_46, C45_45) <=> (in(D46_46, A43_43) & in(D46_46, B44_44)))))) & ! [A47_47, B48_48] : ((=(B48_48, union(A47_47)) <=> ! [C49_49] : ((in(C49_49, B48_48) <=> ? [D50_50] : ((in(C49_49, D50_50) & in(D50_50, A47_47))))))) & ! [A51_51, B52_52, C53_53] : ((=(C53_53, set_difference(A51_51, B52_52)) <=> ! [D54_54] : ((in(D54_54, C53_53) <=> (in(D54_54, A51_51) & ~in(D54_54, B52_52)))))) & ! [A55_55, B56_56] : (=(ordered_pair(A55_55, B56_56), unordered_pair(unordered_pair(A55_55, B56_56), singleton(A55_55)))) & ! [A57_57, B58_58] : ((disjoint(A57_57, B58_58) <=> =(set_intersection2(A57_57, B58_58), empty_set))) & $true & $true & $true & $true & $true & $true & $true & $true & $true & $true & empty(empty_set) & ! [A61_61, B62_62] : (~empty(ordered_pair(A61_61, B62_62))) & ! [A63_63, B64_64] : ((~empty(A63_63) => ~empty(set_union2(A63_63, B64_64)))) & ! [A65_65, B66_66] : ((~empty(A65_65) => ~empty(set_union2(B66_66, A65_65)))) & ! [A67_67, B68_68] : (=(set_union2(A67_67, A67_67), A67_67)) & ! [A69_69, B70_70] : (=(set_intersection2(A69_69, A69_69), A69_69)) & ! [A71_71, B72_72] : (~proper_subset(A71_71, A71_71)) & ! [A73_73] : (~=(singleton(A73_73), empty_set)) & ! [A74_74, B75_75] : ((in(A74_74, B75_75) => =(set_union2(singleton(A74_74), B75_75), B75_75))) & ! [A76_76, B77_77] : (~(disjoint(singleton(A76_76), B77_77) & in(A76_76, B77_77))) & ! [A78_78, B79_79] : ((~in(A78_78, B79_79) => disjoint(singleton(A78_78), B79_79))) & ! [A80_80, B81_81] : ((subset(singleton(A80_80), B81_81) <=> in(A80_80, B81_81))) & ! [A82_82, B83_83] : ((=(set_difference(A82_82, B83_83), empty_set) <=> subset(A82_82, B83_83))) & ! [A84_84, B85_85, C86_86] : ((subset(A84_84, B85_85) => (in(C86_86, A84_84) | subset(A84_84, set_difference(B85_85, singleton(C86_86)))))) & ! [A89_89, B90_90] : ((in(A89_89, B90_90) => subset(A89_89, union(B90_90)))) & ? [A95_95] : (empty(A95_95)) & ? [A96_96] : (~empty(A96_96)) & ! [A97_97, B98_98] : (subset(A97_97, A97_97)) & ! [A99_99, B100_100] : ((disjoint(A99_99, B100_100) => disjoint(B100_100, A99_99))) & ! [A101_101, B102_102, C103_103, D104_104] : (~((=(unordered_pair(A101_101, B102_102), unordered_pair(C103_103, D104_104)) & ~=(A101_101, C103_103)) & ~=(A101_101, D104_104))) & ! [A105_105, B106_106] : ((subset(A105_105, B106_106) => =(set_union2(A105_105, B106_106), B106_106))) & ! [A107_107, B108_108] : (subset(set_intersection2(A107_107, B108_108), A107_107)) & ! [A109_109, B110_110, C111_111] : (((subset(A109_109, B110_110) & subset(A109_109, C111_111)) => subset(A109_109, set_intersection2(B110_110, C111_111)))) & ! [A112_112] : (=(set_union2(A112_112, empty_set), A112_112)) & ! [A113_113, B114_114, C115_115] : (((subset(A113_113, B114_114) & subset(B114_114, C115_115)) => subset(A113_113, C115_115))) & =(powerset(empty_set), singleton(empty_set)) & ! [A116_116, B117_117, C118_118] : ((subset(A116_116, B117_117) => subset(set_intersection2(A116_116, C118_118), set_intersection2(B117_117, C118_118)))) & ! [A119_119, B120_120] : ((subset(A119_119, B120_120) => =(set_intersection2(A119_119, B120_120), A119_119))) & ! [A121_121] : (=(set_intersection2(A121_121, empty_set), empty_set)) & ! [A122_122, B123_123] : ((! [C124_124] : ((in(C124_124, A122_122) <=> in(C124_124, B123_123))) => =(A122_122, B123_123))) & ! [A125_125] : (subset(empty_set, A125_125)) & ! [A126_126, B127_127, C128_128] : ((subset(A126_126, B127_127) => subset(set_difference(A126_126, C128_128), set_difference(B127_127, C128_128)))) & ! [A129_129, B130_130, C131_131, D132_132] : ((=(ordered_pair(A129_129, B130_130), ordered_pair(C131_131, D132_132)) => (=(A129_129, C131_131) & =(B130_130, D132_132)))) & ! [A133_133, B134_134] : (subset(set_difference(A133_133, B134_134), A133_133)) & ! [A135_135, B136_136] : ((=(set_difference(A135_135, B136_136), empty_set) <=> subset(A135_135, B136_136))) & ! [A137_137, B138_138] : ((subset(singleton(A137_137), B138_138) <=> in(A137_137, B138_138))) & ! [A142_142, B143_143] : (=(set_union2(A142_142, set_difference(B143_143, A142_142)), set_union2(A142_142, B143_143))) & ! [A146_146] : (=(set_difference(A146_146, empty_set), A146_146)) & ! [A147_147, B148_148] : ((~(~disjoint(A147_147, B148_148) & ! [C149_149] : (~(in(C149_149, A147_147) & in(C149_149, B148_148)))) & ~(? [C150_150] : ((in(C150_150, A147_147) & in(C150_150, B148_148))) & disjoint(A147_147, B148_148)))) & ! [A151_151] : ((subset(A151_151, empty_set) => =(A151_151, empty_set))) & ! [A152_152, B153_153] : (=(set_difference(set_union2(A152_152, B153_153), B153_153), set_difference(A152_152, B153_153))) & ! [A154_154, B155_155] : ((subset(A154_154, B155_155) => =(B155_155, set_union2(A154_154, set_difference(B155_155, A154_154))))) & ! [A156_156, B157_157] : (=(set_difference(A156_156, set_difference(A156_156, B157_157)), set_intersection2(A156_156, B157_157))) & ! [A158_158] : (=(set_difference(empty_set, A158_158), empty_set)) & ! [A159_159, B160_160] : ((~(~disjoint(A159_159, B160_160) & ! [C161_161] : (~in(C161_161, set_intersection2(A159_159, B160_160)))) & ~(? [C162_162] : (in(C162_162, set_intersection2(A159_159, B160_160))) & disjoint(A159_159, B160_160)))) & ! [A163_163, B164_164] : (~(subset(A163_163, B164_164) & proper_subset(B164_164, A163_163))) & ! [A165_165, B166_166, C167_167] : (((subset(A165_165, B166_166) & disjoint(B166_166, C167_167)) => disjoint(A165_165, C167_167))) & ! [A168_168] : (=(unordered_pair(A168_168, A168_168), singleton(A168_168))) & ! [A169_169] : ((empty(A169_169) => =(A169_169, empty_set))) & ! [A170_170, B171_171] : ((subset(singleton(A170_170), singleton(B171_171)) => =(A170_170, B171_171))) & ! [A172_172, B173_173] : (~(in(A172_172, B173_173) & empty(B173_173))) & ! [A174_174, B175_175] : (subset(A174_174, set_union2(A174_174, B175_175))) & ! [A176_176, B177_177] : ((disjoint(A176_176, B177_177) <=> =(set_difference(A176_176, B177_177), A176_176))) & ! [A178_178, B179_179] : (~((empty(A178_178) & ~=(A178_178, B179_179)) & empty(B179_179))) & ! [A180_180, B181_181, C182_182] : (((subset(A180_180, B181_181) & subset(C182_182, B181_181)) => subset(set_union2(A180_180, C182_182), B181_181))) & ! [A183_183, B184_184, C185_185] : ((=(singleton(A183_183), unordered_pair(B184_184, C185_185)) => =(A183_183, B184_184))) & ! [A186_186, B187_187, C188_188] : ((=(singleton(A186_186), unordered_pair(B187_187, C188_188)) => =(B187_187, C188_188))) & ~! [A144_144, B145_145] : ((subset(A144_144, singleton(B145_145)) <=> (=(A144_144, empty_set) | =(A144_144, singleton(B145_145))))))
% 0.18/0.56 -> [1] ! [A6_6, B7_7] : ((in(A6_6, B7_7) => ~in(B7_7, A6_6))), ! [A8_8, B9_9] : ((proper_subset(A8_8, B9_9) => ~proper_subset(B9_9, A8_8))), ! [A10_10, B11_11] : (=(unordered_pair(A10_10, B11_11), unordered_pair(B11_11, A10_10))), ! [A12_12, B13_13] : (=(set_union2(A12_12, B13_13), set_union2(B13_13, A12_12))), ! [A14_14, B15_15] : (=(set_intersection2(A14_14, B15_15), set_intersection2(B15_15, A14_14))), ! [A16_16, B17_17] : ((=(A16_16, B17_17) <=> (subset(A16_16, B17_17) & subset(B17_17, A16_16)))), ! [A18_18, B19_19] : ((=(B19_19, singleton(A18_18)) <=> ! [C20_20] : ((in(C20_20, B19_19) <=> =(C20_20, A18_18))))), ! [A21_21] : ((=(A21_21, empty_set) <=> ! [B22_22] : (~in(B22_22, A21_21)))), ! [A23_23, B24_24] : ((=(B24_24, powerset(A23_23)) <=> ! [C25_25] : ((in(C25_25, B24_24) <=> subset(C25_25, A23_23))))), ! [A26_26, B27_27, C28_28] : ((=(C28_28, unordered_pair(A26_26, B27_27)) <=> ! [D29_29] : ((in(D29_29, C28_28) <=> (=(D29_29, A26_26) | =(D29_29, B27_27)))))), ! [A30_30, B31_31, C32_32] : ((=(C32_32, set_union2(A30_30, B31_31)) <=> ! [D33_33] : ((in(D33_33, C32_32) <=> (in(D33_33, A30_30) | in(D33_33, B31_31)))))), ! [A34_34, B35_35, C36_36] : ((=(C36_36, cartesian_product2(A34_34, B35_35)) <=> ! [D37_37] : ((in(D37_37, C36_36) <=> ? [E38_38, F39_39] : (((in(E38_38, A34_34) & in(F39_39, B35_35)) & =(D37_37, ordered_pair(E38_38, F39_39)))))))), ! [A43_43, B44_44, C45_45] : ((=(C45_45, set_intersection2(A43_43, B44_44)) <=> ! [D46_46] : ((in(D46_46, C45_45) <=> (in(D46_46, A43_43) & in(D46_46, B44_44)))))), ! [A47_47, B48_48] : ((=(B48_48, union(A47_47)) <=> ! [C49_49] : ((in(C49_49, B48_48) <=> ? [D50_50] : ((in(C49_49, D50_50) & in(D50_50, A47_47))))))), ! [A51_51, B52_52, C53_53] : ((=(C53_53, set_difference(A51_51, B52_52)) <=> ! [D54_54] : ((in(D54_54, C53_53) <=> (in(D54_54, A51_51) & ~in(D54_54, B52_52)))))), ! [A55_55, B56_56] : (=(ordered_pair(A55_55, B56_56), unordered_pair(unordered_pair(A55_55, B56_56), singleton(A55_55)))), ! [A57_57, B58_58] : ((disjoint(A57_57, B58_58) <=> =(set_intersection2(A57_57, B58_58), empty_set))), $true, empty(empty_set), ! [A61_61, B62_62] : (~empty(ordered_pair(A61_61, B62_62))), ! [A63_63, B64_64] : ((~empty(A63_63) => ~empty(set_union2(A63_63, B64_64)))), ! [A65_65, B66_66] : ((~empty(A65_65) => ~empty(set_union2(B66_66, A65_65)))), ! [A67_67, B68_68] : (=(set_union2(A67_67, A67_67), A67_67)), ! [A69_69, B70_70] : (=(set_intersection2(A69_69, A69_69), A69_69)), ! [A71_71, B72_72] : (~proper_subset(A71_71, A71_71)), ! [A73_73] : (~=(singleton(A73_73), empty_set)), ! [A74_74, B75_75] : ((in(A74_74, B75_75) => =(set_union2(singleton(A74_74), B75_75), B75_75))), ! [A76_76, B77_77] : (~(disjoint(singleton(A76_76), B77_77) & in(A76_76, B77_77))), ! [A78_78, B79_79] : ((~in(A78_78, B79_79) => disjoint(singleton(A78_78), B79_79))), ! [A80_80, B81_81] : ((subset(singleton(A80_80), B81_81) <=> in(A80_80, B81_81))), ! [A82_82, B83_83] : ((=(set_difference(A82_82, B83_83), empty_set) <=> subset(A82_82, B83_83))), ! [A84_84, B85_85, C86_86] : ((subset(A84_84, B85_85) => (in(C86_86, A84_84) | subset(A84_84, set_difference(B85_85, singleton(C86_86)))))), ! [A89_89, B90_90] : ((in(A89_89, B90_90) => subset(A89_89, union(B90_90)))), ? [A95_95] : (empty(A95_95)), ? [A96_96] : (~empty(A96_96)), ! [A97_97, B98_98] : (subset(A97_97, A97_97)), ! [A99_99, B100_100] : ((disjoint(A99_99, B100_100) => disjoint(B100_100, A99_99))), ! [A101_101, B102_102, C103_103, D104_104] : (~((=(unordered_pair(A101_101, B102_102), unordered_pair(C103_103, D104_104)) & ~=(A101_101, C103_103)) & ~=(A101_101, D104_104))), ! [A105_105, B106_106] : ((subset(A105_105, B106_106) => =(set_union2(A105_105, B106_106), B106_106))), ! [A107_107, B108_108] : (subset(set_intersection2(A107_107, B108_108), A107_107)), ! [A109_109, B110_110, C111_111] : (((subset(A109_109, B110_110) & subset(A109_109, C111_111)) => subset(A109_109, set_intersection2(B110_110, C111_111)))), ! [A112_112] : (=(set_union2(A112_112, empty_set), A112_112)), ! [A113_113, B114_114, C115_115] : (((subset(A113_113, B114_114) & subset(B114_114, C115_115)) => subset(A113_113, C115_115))), =(powerset(empty_set), singleton(empty_set)), ! [A116_116, B117_117, C118_118] : ((subset(A116_116, B117_117) => subset(set_intersection2(A116_116, C118_118), set_intersection2(B117_117, C118_118)))), ! [A119_119, B120_120] : ((subset(A119_119, B120_120) => =(set_intersection2(A119_119, B120_120), A119_119))), ! [A121_121] : (=(set_intersection2(A121_121, empty_set), empty_set)), ! [A122_122, B123_123] : ((! [C124_124] : ((in(C124_124, A122_122) <=> in(C124_124, B123_123))) => =(A122_122, B123_123))), ! [A125_125] : (subset(empty_set, A125_125)), ! [A126_126, B127_127, C128_128] : ((subset(A126_126, B127_127) => subset(set_difference(A126_126, C128_128), set_difference(B127_127, C128_128)))), ! [A129_129, B130_130, C131_131, D132_132] : ((=(ordered_pair(A129_129, B130_130), ordered_pair(C131_131, D132_132)) => (=(A129_129, C131_131) & =(B130_130, D132_132)))), ! [A133_133, B134_134] : (subset(set_difference(A133_133, B134_134), A133_133)), ! [A135_135, B136_136] : ((=(set_difference(A135_135, B136_136), empty_set) <=> subset(A135_135, B136_136))), ! [A137_137, B138_138] : ((subset(singleton(A137_137), B138_138) <=> in(A137_137, B138_138))), ! [A142_142, B143_143] : (=(set_union2(A142_142, set_difference(B143_143, A142_142)), set_union2(A142_142, B143_143))), ! [A146_146] : (=(set_difference(A146_146, empty_set), A146_146)), ! [A147_147, B148_148] : ((~(~disjoint(A147_147, B148_148) & ! [C149_149] : (~(in(C149_149, A147_147) & in(C149_149, B148_148)))) & ~(? [C150_150] : ((in(C150_150, A147_147) & in(C150_150, B148_148))) & disjoint(A147_147, B148_148)))), ! [A151_151] : ((subset(A151_151, empty_set) => =(A151_151, empty_set))), ! [A152_152, B153_153] : (=(set_difference(set_union2(A152_152, B153_153), B153_153), set_difference(A152_152, B153_153))), ! [A154_154, B155_155] : ((subset(A154_154, B155_155) => =(B155_155, set_union2(A154_154, set_difference(B155_155, A154_154))))), ! [A156_156, B157_157] : (=(set_difference(A156_156, set_difference(A156_156, B157_157)), set_intersection2(A156_156, B157_157))), ! [A158_158] : (=(set_difference(empty_set, A158_158), empty_set)), ! [A159_159, B160_160] : ((~(~disjoint(A159_159, B160_160) & ! [C161_161] : (~in(C161_161, set_intersection2(A159_159, B160_160)))) & ~(? [C162_162] : (in(C162_162, set_intersection2(A159_159, B160_160))) & disjoint(A159_159, B160_160)))), ! [A163_163, B164_164] : (~(subset(A163_163, B164_164) & proper_subset(B164_164, A163_163))), ! [A165_165, B166_166, C167_167] : (((subset(A165_165, B166_166) & disjoint(B166_166, C167_167)) => disjoint(A165_165, C167_167))), ! [A168_168] : (=(unordered_pair(A168_168, A168_168), singleton(A168_168))), ! [A169_169] : ((empty(A169_169) => =(A169_169, empty_set))), ! [A170_170, B171_171] : ((subset(singleton(A170_170), singleton(B171_171)) => =(A170_170, B171_171))), ! [A172_172, B173_173] : (~(in(A172_172, B173_173) & empty(B173_173))), ! [A174_174, B175_175] : (subset(A174_174, set_union2(A174_174, B175_175))), ! [A176_176, B177_177] : ((disjoint(A176_176, B177_177) <=> =(set_difference(A176_176, B177_177), A176_176))), ! [A178_178, B179_179] : (~((empty(A178_178) & ~=(A178_178, B179_179)) & empty(B179_179))), ! [A180_180, B181_181, C182_182] : (((subset(A180_180, B181_181) & subset(C182_182, B181_181)) => subset(set_union2(A180_180, C182_182), B181_181))), ! [A183_183, B184_184, C185_185] : ((=(singleton(A183_183), unordered_pair(B184_184, C185_185)) => =(A183_183, B184_184))), ! [A186_186, B187_187, C188_188] : ((=(singleton(A186_186), unordered_pair(B187_187, C188_188)) => =(B187_187, C188_188))), ~! [A144_144, B145_145] : ((subset(A144_144, singleton(B145_145)) <=> (=(A144_144, empty_set) | =(A144_144, singleton(B145_145)))))
% 0.18/0.56
% 0.18/0.56 [1] DELTA_EXISTS : ? [A95_95] : (empty(A95_95))
% 0.18/0.56 -> [2] empty(skolem_A9595)
% 0.18/0.56
% 0.18/0.56 [2] DELTA_EXISTS : ? [A96_96] : (~empty(A96_96))
% 0.18/0.56 -> [3] ~empty(skolem_A9696)
% 0.18/0.56
% 0.18/0.56 [3] DELTA_NOT_FORALL : ~! [A144_144, B145_145] : ((subset(A144_144, singleton(B145_145)) <=> (=(A144_144, empty_set) | =(A144_144, singleton(B145_145)))))
% 0.18/0.56 -> [4] ~(subset(skolem_A144144, singleton(skolem_B145145)) <=> (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145))))
% 0.18/0.56
% 0.18/0.56 [4] BETA_NOT_EQUIV : ~(subset(skolem_A144144, singleton(skolem_B145145)) <=> (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145))))
% 0.18/0.56 -> [5] ~subset(skolem_A144144, singleton(skolem_B145145)), (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56 -> [6] subset(skolem_A144144, singleton(skolem_B145145)), ~(=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56
% 0.18/0.56 [6] Rewrite : subset(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56 -> [7] (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56
% 0.18/0.56 [7] ALPHA_NOT_OR : ~(=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56 -> [10] ~=(skolem_A144144, empty_set), ~=(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 [10] BETA_OR : (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56 -> [13] =(skolem_A144144, empty_set)
% 0.18/0.56 -> [14] =(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 [13] CLOSURE : =(skolem_A144144, empty_set)
% 0.18/0.56
% 0.18/0.56 [14] CLOSURE : =(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 [5] Rewrite : ~subset(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56 -> [8] ~(=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56
% 0.18/0.56 [8] ALPHA_NOT_OR : ~(=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56 -> [9] ~=(skolem_A144144, empty_set), ~=(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 [9] BETA_OR : (=(skolem_A144144, empty_set) | =(skolem_A144144, singleton(skolem_B145145)))
% 0.18/0.56 -> [11] =(skolem_A144144, empty_set)
% 0.18/0.56 -> [12] =(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 [11] CLOSURE : =(skolem_A144144, empty_set)
% 0.18/0.56
% 0.18/0.56 [12] CLOSURE : =(skolem_A144144, singleton(skolem_B145145))
% 0.18/0.56
% 0.18/0.56 % SZS output end Proof for theBenchmark.p
% 0.18/0.56 [0.219180s][1][Res] 436 goroutines created
% 0.18/0.56 ==== Result ====
% 0.18/0.56 [0.219218s][1][Res] VALID
% 0.18/0.56 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------