TSTP Solution File: SEU165+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n015.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 05:55:41 EDT 2022
% Result : Theorem 0.54s 0.59s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 10:00:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.36 Start search
% 0.13/0.37 nb_step : 1 - limit : 100
% 0.13/0.37 Launch Gotab with destructive = true
% 0.19/0.58 % SZS output start Proof for theBenchmark.p
% 0.54/0.59 [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))) & ! [A105_105, B106_106, C107_107, D108_108] : (~((=(unordered_pair(A105_105, B106_106), unordered_pair(C107_107, D108_108)) & ~=(A105_105, C107_107)) & ~=(A105_105, D108_108))) & ! [A109_109, B110_110] : ((subset(A109_109, B110_110) => =(set_union2(A109_109, B110_110), B110_110))) & ! [A111_111, B112_112] : (subset(set_intersection2(A111_111, B112_112), A111_111)) & ! [A113_113, B114_114, C115_115] : (((subset(A113_113, B114_114) & subset(A113_113, C115_115)) => subset(A113_113, set_intersection2(B114_114, C115_115)))) & ! [A116_116] : (=(set_union2(A116_116, empty_set), A116_116)) & ! [A117_117, B118_118, C119_119] : (((subset(A117_117, B118_118) & subset(B118_118, C119_119)) => subset(A117_117, C119_119))) & =(powerset(empty_set), singleton(empty_set)) & ! [A120_120, B121_121, C122_122] : ((subset(A120_120, B121_121) => subset(set_intersection2(A120_120, C122_122), set_intersection2(B121_121, C122_122)))) & ! [A123_123, B124_124] : ((subset(A123_123, B124_124) => =(set_intersection2(A123_123, B124_124), A123_123))) & ! [A125_125] : (=(set_intersection2(A125_125, empty_set), empty_set)) & ! [A126_126, B127_127] : ((! [C128_128] : ((in(C128_128, A126_126) <=> in(C128_128, B127_127))) => =(A126_126, B127_127))) & ! [A129_129] : (subset(empty_set, A129_129)) & ! [A130_130, B131_131, C132_132] : ((subset(A130_130, B131_131) => subset(set_difference(A130_130, C132_132), set_difference(B131_131, C132_132)))) & ! [A133_133, B134_134, C135_135, D136_136] : ((=(ordered_pair(A133_133, B134_134), ordered_pair(C135_135, D136_136)) => (=(A133_133, C135_135) & =(B134_134, D136_136)))) & ! [A137_137, B138_138] : (subset(set_difference(A137_137, B138_138), A137_137)) & ! [A139_139, B140_140] : ((=(set_difference(A139_139, B140_140), empty_set) <=> subset(A139_139, B140_140))) & ! [A141_141, B142_142] : ((subset(singleton(A141_141), B142_142) <=> in(A141_141, B142_142))) & ! [A146_146, B147_147] : (=(set_union2(A146_146, set_difference(B147_147, A146_146)), set_union2(A146_146, B147_147))) & ! [A150_150] : (=(set_difference(A150_150, empty_set), A150_150)) & ! [A151_151, B152_152] : ((~(~disjoint(A151_151, B152_152) & ! [C153_153] : (~(in(C153_153, A151_151) & in(C153_153, B152_152)))) & ~(? [C154_154] : ((in(C154_154, A151_151) & in(C154_154, B152_152))) & disjoint(A151_151, B152_152)))) & ! [A155_155] : ((subset(A155_155, empty_set) => =(A155_155, empty_set))) & ! [A156_156, B157_157] : (=(set_difference(set_union2(A156_156, B157_157), B157_157), set_difference(A156_156, B157_157))) & ! [A158_158, B159_159] : ((subset(A158_158, B159_159) => =(B159_159, set_union2(A158_158, set_difference(B159_159, A158_158))))) & ! [A160_160, B161_161] : ((in(A160_160, B161_161) => =(set_union2(singleton(A160_160), B161_161), B161_161))) & ! [A162_162, B163_163] : (=(set_difference(A162_162, set_difference(A162_162, B163_163)), set_intersection2(A162_162, B163_163))) & ! [A164_164] : (=(set_difference(empty_set, A164_164), empty_set)) & ! [A165_165, B166_166] : ((~(~disjoint(A165_165, B166_166) & ! [C167_167] : (~in(C167_167, set_intersection2(A165_165, B166_166)))) & ~(? [C168_168] : (in(C168_168, set_intersection2(A165_165, B166_166))) & disjoint(A165_165, B166_166)))) & ! [A169_169, B170_170] : (~(subset(A169_169, B170_170) & proper_subset(B170_170, A169_169))) & ! [A171_171, B172_172, C173_173] : (((subset(A171_171, B172_172) & disjoint(B172_172, C173_173)) => disjoint(A171_171, C173_173))) & ! [A174_174, B175_175] : ((=(set_difference(A174_174, singleton(B175_175)), A174_174) <=> ~in(B175_175, A174_174))) & ! [A176_176] : (=(unordered_pair(A176_176, A176_176), singleton(A176_176))) & ! [A177_177] : ((empty(A177_177) => =(A177_177, empty_set))) & ! [A178_178, B179_179] : ((subset(singleton(A178_178), singleton(B179_179)) => =(A178_178, B179_179))) & ! [A180_180, B181_181] : (~(in(A180_180, B181_181) & empty(B181_181))) & ! [A182_182, B183_183] : (subset(A182_182, set_union2(A182_182, B183_183))) & ! [A184_184, B185_185] : ((disjoint(A184_184, B185_185) <=> =(set_difference(A184_184, B185_185), A184_184))) & ! [A186_186, B187_187] : (~((empty(A186_186) & ~=(A186_186, B187_187)) & empty(B187_187))) & ! [A188_188, B189_189, C190_190] : (((subset(A188_188, B189_189) & subset(C190_190, B189_189)) => subset(set_union2(A188_188, C190_190), B189_189))) & ! [A191_191, B192_192, C193_193] : ((=(singleton(A191_191), unordered_pair(B192_192, C193_193)) => =(A191_191, B192_192))) & ! [A194_194, B195_195] : ((in(A194_194, B195_195) => subset(A194_194, union(B195_195)))) & ! [A196_196] : (=(union(powerset(A196_196)), A196_196)) & ! [A197_197, B198_198, C199_199] : ((=(singleton(A197_197), unordered_pair(B198_198, C199_199)) => =(B198_198, C199_199))) & ~! [A101_101, B102_102, C103_103, D104_104] : ((in(ordered_pair(A101_101, B102_102), cartesian_product2(C103_103, D104_104)) <=> (in(A101_101, C103_103) & in(B102_102, D104_104)))))
% 0.54/0.59 -> [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))), ! [A105_105, B106_106, C107_107, D108_108] : (~((=(unordered_pair(A105_105, B106_106), unordered_pair(C107_107, D108_108)) & ~=(A105_105, C107_107)) & ~=(A105_105, D108_108))), ! [A109_109, B110_110] : ((subset(A109_109, B110_110) => =(set_union2(A109_109, B110_110), B110_110))), ! [A111_111, B112_112] : (subset(set_intersection2(A111_111, B112_112), A111_111)), ! [A113_113, B114_114, C115_115] : (((subset(A113_113, B114_114) & subset(A113_113, C115_115)) => subset(A113_113, set_intersection2(B114_114, C115_115)))), ! [A116_116] : (=(set_union2(A116_116, empty_set), A116_116)), ! [A117_117, B118_118, C119_119] : (((subset(A117_117, B118_118) & subset(B118_118, C119_119)) => subset(A117_117, C119_119))), =(powerset(empty_set), singleton(empty_set)), ! [A120_120, B121_121, C122_122] : ((subset(A120_120, B121_121) => subset(set_intersection2(A120_120, C122_122), set_intersection2(B121_121, C122_122)))), ! [A123_123, B124_124] : ((subset(A123_123, B124_124) => =(set_intersection2(A123_123, B124_124), A123_123))), ! [A125_125] : (=(set_intersection2(A125_125, empty_set), empty_set)), ! [A126_126, B127_127] : ((! [C128_128] : ((in(C128_128, A126_126) <=> in(C128_128, B127_127))) => =(A126_126, B127_127))), ! [A129_129] : (subset(empty_set, A129_129)), ! [A130_130, B131_131, C132_132] : ((subset(A130_130, B131_131) => subset(set_difference(A130_130, C132_132), set_difference(B131_131, C132_132)))), ! [A133_133, B134_134, C135_135, D136_136] : ((=(ordered_pair(A133_133, B134_134), ordered_pair(C135_135, D136_136)) => (=(A133_133, C135_135) & =(B134_134, D136_136)))), ! [A137_137, B138_138] : (subset(set_difference(A137_137, B138_138), A137_137)), ! [A139_139, B140_140] : ((=(set_difference(A139_139, B140_140), empty_set) <=> subset(A139_139, B140_140))), ! [A141_141, B142_142] : ((subset(singleton(A141_141), B142_142) <=> in(A141_141, B142_142))), ! [A146_146, B147_147] : (=(set_union2(A146_146, set_difference(B147_147, A146_146)), set_union2(A146_146, B147_147))), ! [A150_150] : (=(set_difference(A150_150, empty_set), A150_150)), ! [A151_151, B152_152] : ((~(~disjoint(A151_151, B152_152) & ! [C153_153] : (~(in(C153_153, A151_151) & in(C153_153, B152_152)))) & ~(? [C154_154] : ((in(C154_154, A151_151) & in(C154_154, B152_152))) & disjoint(A151_151, B152_152)))), ! [A155_155] : ((subset(A155_155, empty_set) => =(A155_155, empty_set))), ! [A156_156, B157_157] : (=(set_difference(set_union2(A156_156, B157_157), B157_157), set_difference(A156_156, B157_157))), ! [A158_158, B159_159] : ((subset(A158_158, B159_159) => =(B159_159, set_union2(A158_158, set_difference(B159_159, A158_158))))), ! [A160_160, B161_161] : ((in(A160_160, B161_161) => =(set_union2(singleton(A160_160), B161_161), B161_161))), ! [A162_162, B163_163] : (=(set_difference(A162_162, set_difference(A162_162, B163_163)), set_intersection2(A162_162, B163_163))), ! [A164_164] : (=(set_difference(empty_set, A164_164), empty_set)), ! [A165_165, B166_166] : ((~(~disjoint(A165_165, B166_166) & ! [C167_167] : (~in(C167_167, set_intersection2(A165_165, B166_166)))) & ~(? [C168_168] : (in(C168_168, set_intersection2(A165_165, B166_166))) & disjoint(A165_165, B166_166)))), ! [A169_169, B170_170] : (~(subset(A169_169, B170_170) & proper_subset(B170_170, A169_169))), ! [A171_171, B172_172, C173_173] : (((subset(A171_171, B172_172) & disjoint(B172_172, C173_173)) => disjoint(A171_171, C173_173))), ! [A174_174, B175_175] : ((=(set_difference(A174_174, singleton(B175_175)), A174_174) <=> ~in(B175_175, A174_174))), ! [A176_176] : (=(unordered_pair(A176_176, A176_176), singleton(A176_176))), ! [A177_177] : ((empty(A177_177) => =(A177_177, empty_set))), ! [A178_178, B179_179] : ((subset(singleton(A178_178), singleton(B179_179)) => =(A178_178, B179_179))), ! [A180_180, B181_181] : (~(in(A180_180, B181_181) & empty(B181_181))), ! [A182_182, B183_183] : (subset(A182_182, set_union2(A182_182, B183_183))), ! [A184_184, B185_185] : ((disjoint(A184_184, B185_185) <=> =(set_difference(A184_184, B185_185), A184_184))), ! [A186_186, B187_187] : (~((empty(A186_186) & ~=(A186_186, B187_187)) & empty(B187_187))), ! [A188_188, B189_189, C190_190] : (((subset(A188_188, B189_189) & subset(C190_190, B189_189)) => subset(set_union2(A188_188, C190_190), B189_189))), ! [A191_191, B192_192, C193_193] : ((=(singleton(A191_191), unordered_pair(B192_192, C193_193)) => =(A191_191, B192_192))), ! [A194_194, B195_195] : ((in(A194_194, B195_195) => subset(A194_194, union(B195_195)))), ! [A196_196] : (=(union(powerset(A196_196)), A196_196)), ! [A197_197, B198_198, C199_199] : ((=(singleton(A197_197), unordered_pair(B198_198, C199_199)) => =(B198_198, C199_199))), ~! [A101_101, B102_102, C103_103, D104_104] : ((in(ordered_pair(A101_101, B102_102), cartesian_product2(C103_103, D104_104)) <=> (in(A101_101, C103_103) & in(B102_102, D104_104))))
% 0.54/0.59
% 0.54/0.59 [1] DELTA_EXISTS : ? [A95_95] : (empty(A95_95))
% 0.54/0.59 -> [2] empty(skolem_A9595)
% 0.54/0.59
% 0.54/0.59 [2] DELTA_EXISTS : ? [A96_96] : (~empty(A96_96))
% 0.54/0.59 -> [3] ~empty(skolem_A9696)
% 0.54/0.59
% 0.54/0.59 [3] DELTA_NOT_FORALL : ~! [A101_101, B102_102, C103_103, D104_104] : ((in(ordered_pair(A101_101, B102_102), cartesian_product2(C103_103, D104_104)) <=> (in(A101_101, C103_103) & in(B102_102, D104_104))))
% 0.54/0.59 -> [4] ~(in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104)) <=> (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104)))
% 0.54/0.59
% 0.54/0.59 [4] BETA_NOT_EQUIV : ~(in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104)) <=> (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104)))
% 0.54/0.59 -> [5] ~in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104)), (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59 -> [6] in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104)), ~(in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59
% 0.54/0.59 [6] Rewrite : in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104))
% 0.54/0.59 -> [7] (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59
% 0.54/0.59 [7] ALPHA_AND : (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59 -> [8] in(skolem_A101101, skolem_C103103), in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 [8] BETA_NOT_AND : ~(in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59 -> [11] ~in(skolem_A101101, skolem_C103103)
% 0.54/0.59 -> [12] ~in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 [11] CLOSURE : ~in(skolem_A101101, skolem_C103103)
% 0.54/0.59
% 0.54/0.59 [12] CLOSURE : ~in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 [5] Rewrite : ~in(ordered_pair(skolem_A101101, skolem_B102102), cartesian_product2(skolem_C103103, skolem_D104104))
% 0.54/0.59 -> [9] ~(in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59
% 0.54/0.59 [9] ALPHA_AND : (in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59 -> [10] in(skolem_A101101, skolem_C103103), in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 [10] BETA_NOT_AND : ~(in(skolem_A101101, skolem_C103103) & in(skolem_B102102, skolem_D104104))
% 0.54/0.59 -> [13] ~in(skolem_A101101, skolem_C103103)
% 0.54/0.59 -> [14] ~in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 [13] CLOSURE : ~in(skolem_A101101, skolem_C103103)
% 0.54/0.59
% 0.54/0.59 [14] CLOSURE : ~in(skolem_B102102, skolem_D104104)
% 0.54/0.59
% 0.54/0.59 % SZS output end Proof for theBenchmark.p
% 0.54/0.59 [0.240320s][1][Res] 292 goroutines created
% 0.54/0.59 ==== Result ====
% 0.54/0.59 [0.240358s][1][Res] VALID
% 0.54/0.59 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------