TSTP Solution File: SEU295+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU295+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.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 05:56:21 EDT 2022
% Result : Theorem 64.02s 28.30s
% Output : Proof 64.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU295+3 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n023.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 12:03:48 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 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 64
% 0.12/0.35 Launch Gotab with destructive = true
% 64.02/28.28 % SZS output start Proof for theBenchmark.p
% 64.02/28.30 [0] ALPHA_AND : (! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3))) & ! [A5_5] : ((ordinal(A5_5) => ! [B6_6] : ((element(B6_6, A5_5) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))) & ! [A7_7] : ((empty(A7_7) => finite(A7_7))) & ! [A8_8] : ((empty(A8_8) => function(A8_8))) & ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9)))) & ! [A10_10] : ((empty(A10_10) => relation(A10_10))) & ! [A11_11] : (((empty(A11_11) & ordinal(A11_11)) => (((epsilon_transitive(A11_11) & epsilon_connected(A11_11)) & ordinal(A11_11)) & natural(A11_11)))) & ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13))))) & ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14)))) & ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15))) & ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16)))) & ! [A17_17] : ((element(A17_17, positive_rationals) => (ordinal(A17_17) => (((epsilon_transitive(A17_17) & epsilon_connected(A17_17)) & ordinal(A17_17)) & natural(A17_17))))) & ! [A18_18, B19_19] : (=(set_intersection2(A18_18, B19_19), set_intersection2(B19_19, A18_18))) & ! [A20_20] : (? [B21_21] : (element(B21_21, A20_20))) & ! [A22_22, B23_23] : ((finite(B23_23) => finite(set_intersection2(A22_22, B23_23)))) & ! [A24_24, B25_25] : ((finite(A24_24) => finite(set_intersection2(A24_24, B25_25)))) & ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)) & ! [A26_26, B27_27] : (((relation(A26_26) & relation(B27_27)) => relation(set_intersection2(A26_26, B27_27)))) & ! [A28_28] : (~empty(powerset(A28_28))) & empty(empty_set) & (((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)) & ordinal(empty_set)) & (empty(empty_set) & relation(empty_set)) & ~empty(positive_rationals) & ! [A29_29, B30_30] : (=(set_intersection2(A29_29, A29_29), A29_29)) & ? [A31_31] : (((((~empty(A31_31) & epsilon_transitive(A31_31)) & epsilon_connected(A31_31)) & ordinal(A31_31)) & natural(A31_31))) & ? [A32_32] : ((~empty(A32_32) & finite(A32_32))) & ? [A33_33] : (((relation(A33_33) & function(A33_33)) & function_yielding(A33_33))) & ? [A34_34] : ((relation(A34_34) & function(A34_34))) & ? [A35_35] : (((epsilon_transitive(A35_35) & epsilon_connected(A35_35)) & ordinal(A35_35))) & ? [A36_36] : ((((epsilon_transitive(A36_36) & epsilon_connected(A36_36)) & ordinal(A36_36)) & being_limit_ordinal(A36_36))) & ? [A37_37] : ((empty(A37_37) & relation(A37_37))) & ! [A38_38] : ((~empty(A38_38) => ? [B39_39] : ((element(B39_39, powerset(A38_38)) & ~empty(B39_39))))) & ? [A40_40] : (empty(A40_40)) & ? [A41_41] : (((((element(A41_41, positive_rationals) & ~empty(A41_41)) & epsilon_transitive(A41_41)) & epsilon_connected(A41_41)) & ordinal(A41_41))) & ! [A42_42] : (? [B43_43] : ((((((((((element(B43_43, powerset(A42_42)) & empty(B43_43)) & relation(B43_43)) & function(B43_43)) & one_to_one(B43_43)) & epsilon_transitive(B43_43)) & epsilon_connected(B43_43)) & ordinal(B43_43)) & natural(B43_43)) & finite(B43_43)))) & ? [A44_44] : (((relation(A44_44) & empty(A44_44)) & function(A44_44))) & ? [A45_45] : (((((((relation(A45_45) & function(A45_45)) & one_to_one(A45_45)) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45))) & ? [A46_46] : ((((relation(A46_46) & function(A46_46)) & transfinite_sequence(A46_46)) & ordinal_yielding(A46_46))) & ? [A47_47] : ((~empty(A47_47) & relation(A47_47))) & ! [A48_48] : (? [B49_49] : ((element(B49_49, powerset(A48_48)) & empty(B49_49)))) & ? [A50_50] : (~empty(A50_50)) & ? [A51_51] : ((((((element(A51_51, positive_rationals) & empty(A51_51)) & epsilon_transitive(A51_51)) & epsilon_connected(A51_51)) & ordinal(A51_51)) & natural(A51_51))) & ! [A52_52] : ((~empty(A52_52) => ? [B53_53] : (((element(B53_53, powerset(A52_52)) & ~empty(B53_53)) & finite(B53_53))))) & ? [A54_54] : (((relation(A54_54) & function(A54_54)) & one_to_one(A54_54))) & ? [A55_55] : ((((~empty(A55_55) & epsilon_transitive(A55_55)) & epsilon_connected(A55_55)) & ordinal(A55_55))) & ? [A56_56] : ((relation(A56_56) & relation_empty_yielding(A56_56))) & ? [A57_57] : (((relation(A57_57) & relation_empty_yielding(A57_57)) & function(A57_57))) & ? [A58_58] : (((relation(A58_58) & function(A58_58)) & transfinite_sequence(A58_58))) & ? [A59_59] : (((relation(A59_59) & relation_non_empty(A59_59)) & function(A59_59))) & ! [A60_60, B61_61] : (subset(A60_60, A60_60)) & ! [A62_62, B63_63] : (((subset(A62_62, B63_63) & finite(B63_63)) => finite(A62_62))) & ! [A66_66, B67_67] : (subset(set_intersection2(A66_66, B67_67), A66_66)) & ! [A68_68, B69_69] : ((in(A68_68, B69_69) => element(A68_68, B69_69))) & ! [A70_70] : (=(set_intersection2(A70_70, empty_set), empty_set)) & ! [A71_71, B72_72] : ((element(A71_71, B72_72) => (empty(B72_72) | in(A71_71, B72_72)))) & ! [A73_73, B74_74] : ((element(A73_73, powerset(B74_74)) <=> subset(A73_73, B74_74))) & ! [A75_75, B76_76, C77_77] : (((in(A75_75, B76_76) & element(B76_76, powerset(C77_77))) => element(A75_75, C77_77))) & ! [A78_78, B79_79, C80_80] : (~((in(A78_78, B79_79) & element(B79_79, powerset(C80_80))) & empty(C80_80))) & ! [A81_81] : ((empty(A81_81) => =(A81_81, empty_set))) & ! [A82_82, B83_83] : (~(in(A82_82, B83_83) & empty(B83_83))) & ! [A84_84, B85_85] : (~((empty(A84_84) & ~=(A84_84, B85_85)) & empty(B85_85))) & ~! [A64_64, B65_65] : ((finite(A64_64) => finite(set_intersection2(A64_64, B65_65)))))
% 64.02/28.30 -> [1] ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3))), ! [A5_5] : ((ordinal(A5_5) => ! [B6_6] : ((element(B6_6, A5_5) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))), ! [A7_7] : ((empty(A7_7) => finite(A7_7))), ! [A8_8] : ((empty(A8_8) => function(A8_8))), ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9)))), ! [A10_10] : ((empty(A10_10) => relation(A10_10))), ! [A11_11] : (((empty(A11_11) & ordinal(A11_11)) => (((epsilon_transitive(A11_11) & epsilon_connected(A11_11)) & ordinal(A11_11)) & natural(A11_11)))), ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13))))), ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14)))), ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15))), ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16)))), ! [A17_17] : ((element(A17_17, positive_rationals) => (ordinal(A17_17) => (((epsilon_transitive(A17_17) & epsilon_connected(A17_17)) & ordinal(A17_17)) & natural(A17_17))))), ! [A18_18, B19_19] : (=(set_intersection2(A18_18, B19_19), set_intersection2(B19_19, A18_18))), ! [A20_20] : (? [B21_21] : (element(B21_21, A20_20))), ! [A22_22, B23_23] : ((finite(B23_23) => finite(set_intersection2(A22_22, B23_23)))), ! [A24_24, B25_25] : ((finite(A24_24) => finite(set_intersection2(A24_24, B25_25)))), ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), ! [A26_26, B27_27] : (((relation(A26_26) & relation(B27_27)) => relation(set_intersection2(A26_26, B27_27)))), ! [A28_28] : (~empty(powerset(A28_28))), empty(empty_set), (((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)) & ordinal(empty_set)), (empty(empty_set) & relation(empty_set)), ~empty(positive_rationals), ! [A29_29, B30_30] : (=(set_intersection2(A29_29, A29_29), A29_29)), ? [A31_31] : (((((~empty(A31_31) & epsilon_transitive(A31_31)) & epsilon_connected(A31_31)) & ordinal(A31_31)) & natural(A31_31))), ? [A32_32] : ((~empty(A32_32) & finite(A32_32))), ? [A33_33] : (((relation(A33_33) & function(A33_33)) & function_yielding(A33_33))), ? [A34_34] : ((relation(A34_34) & function(A34_34))), ? [A35_35] : (((epsilon_transitive(A35_35) & epsilon_connected(A35_35)) & ordinal(A35_35))), ? [A36_36] : ((((epsilon_transitive(A36_36) & epsilon_connected(A36_36)) & ordinal(A36_36)) & being_limit_ordinal(A36_36))), ? [A37_37] : ((empty(A37_37) & relation(A37_37))), ! [A38_38] : ((~empty(A38_38) => ? [B39_39] : ((element(B39_39, powerset(A38_38)) & ~empty(B39_39))))), ? [A40_40] : (empty(A40_40)), ? [A41_41] : (((((element(A41_41, positive_rationals) & ~empty(A41_41)) & epsilon_transitive(A41_41)) & epsilon_connected(A41_41)) & ordinal(A41_41))), ! [A42_42] : (? [B43_43] : ((((((((((element(B43_43, powerset(A42_42)) & empty(B43_43)) & relation(B43_43)) & function(B43_43)) & one_to_one(B43_43)) & epsilon_transitive(B43_43)) & epsilon_connected(B43_43)) & ordinal(B43_43)) & natural(B43_43)) & finite(B43_43)))), ? [A44_44] : (((relation(A44_44) & empty(A44_44)) & function(A44_44))), ? [A45_45] : (((((((relation(A45_45) & function(A45_45)) & one_to_one(A45_45)) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45))), ? [A46_46] : ((((relation(A46_46) & function(A46_46)) & transfinite_sequence(A46_46)) & ordinal_yielding(A46_46))), ? [A47_47] : ((~empty(A47_47) & relation(A47_47))), ! [A48_48] : (? [B49_49] : ((element(B49_49, powerset(A48_48)) & empty(B49_49)))), ? [A50_50] : (~empty(A50_50)), ? [A51_51] : ((((((element(A51_51, positive_rationals) & empty(A51_51)) & epsilon_transitive(A51_51)) & epsilon_connected(A51_51)) & ordinal(A51_51)) & natural(A51_51))), ! [A52_52] : ((~empty(A52_52) => ? [B53_53] : (((element(B53_53, powerset(A52_52)) & ~empty(B53_53)) & finite(B53_53))))), ? [A54_54] : (((relation(A54_54) & function(A54_54)) & one_to_one(A54_54))), ? [A55_55] : ((((~empty(A55_55) & epsilon_transitive(A55_55)) & epsilon_connected(A55_55)) & ordinal(A55_55))), ? [A56_56] : ((relation(A56_56) & relation_empty_yielding(A56_56))), ? [A57_57] : (((relation(A57_57) & relation_empty_yielding(A57_57)) & function(A57_57))), ? [A58_58] : (((relation(A58_58) & function(A58_58)) & transfinite_sequence(A58_58))), ? [A59_59] : (((relation(A59_59) & relation_non_empty(A59_59)) & function(A59_59))), ! [A60_60, B61_61] : (subset(A60_60, A60_60)), ! [A62_62, B63_63] : (((subset(A62_62, B63_63) & finite(B63_63)) => finite(A62_62))), ! [A66_66, B67_67] : (subset(set_intersection2(A66_66, B67_67), A66_66)), ! [A68_68, B69_69] : ((in(A68_68, B69_69) => element(A68_68, B69_69))), ! [A70_70] : (=(set_intersection2(A70_70, empty_set), empty_set)), ! [A71_71, B72_72] : ((element(A71_71, B72_72) => (empty(B72_72) | in(A71_71, B72_72)))), ! [A73_73, B74_74] : ((element(A73_73, powerset(B74_74)) <=> subset(A73_73, B74_74))), ! [A75_75, B76_76, C77_77] : (((in(A75_75, B76_76) & element(B76_76, powerset(C77_77))) => element(A75_75, C77_77))), ! [A78_78, B79_79, C80_80] : (~((in(A78_78, B79_79) & element(B79_79, powerset(C80_80))) & empty(C80_80))), ! [A81_81] : ((empty(A81_81) => =(A81_81, empty_set))), ! [A82_82, B83_83] : (~(in(A82_82, B83_83) & empty(B83_83))), ! [A84_84, B85_85] : (~((empty(A84_84) & ~=(A84_84, B85_85)) & empty(B85_85))), ~! [A64_64, B65_65] : ((finite(A64_64) => finite(set_intersection2(A64_64, B65_65))))
% 64.02/28.30
% 64.02/28.30 [1] ALPHA_AND : ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set))
% 64.02/28.30 -> [2] (empty(empty_set) & relation(empty_set)), relation_empty_yielding(empty_set)
% 64.02/28.30
% 64.02/28.30 [2] ALPHA_AND : (((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)) & ordinal(empty_set))
% 64.02/28.30 -> [3] ((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)), ordinal(empty_set)
% 64.02/28.30
% 64.02/28.30 [3] ALPHA_AND : (empty(empty_set) & relation(empty_set))
% 64.02/28.30 -> [4] empty(empty_set), relation(empty_set)
% 64.02/28.30
% 64.02/28.30 [4] ALPHA_AND : ((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set))
% 64.02/28.30 -> [5] (((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)), epsilon_connected(empty_set)
% 64.02/28.30
% 64.02/28.30 [5] ALPHA_AND : (((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set))
% 64.02/28.30 -> [6] ((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)), epsilon_transitive(empty_set)
% 64.02/28.30
% 64.02/28.30 [6] ALPHA_AND : ((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set))
% 64.02/28.30 -> [7] (((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)), empty(empty_set)
% 64.02/28.30
% 64.02/28.30 [7] ALPHA_AND : (((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set))
% 64.02/28.30 -> [8] ((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)), one_to_one(empty_set)
% 64.02/28.30
% 64.02/28.30 [8] ALPHA_AND : ((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set))
% 64.02/28.30 -> [9] (relation(empty_set) & relation_empty_yielding(empty_set)), function(empty_set)
% 64.02/28.30
% 64.02/28.30 [9] ALPHA_AND : (relation(empty_set) & relation_empty_yielding(empty_set))
% 64.02/28.30 -> [10] relation(empty_set), relation_empty_yielding(empty_set)
% 64.02/28.30
% 64.02/28.30 [10] DELTA_EXISTS : ? [A31_31] : (((((~empty(A31_31) & epsilon_transitive(A31_31)) & epsilon_connected(A31_31)) & ordinal(A31_31)) & natural(A31_31)))
% 64.02/28.30 -> [11] ((((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131)) & ordinal(skolem_A3131)) & natural(skolem_A3131))
% 64.02/28.30
% 64.02/28.30 [11] ALPHA_AND : ((((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131)) & ordinal(skolem_A3131)) & natural(skolem_A3131))
% 64.02/28.30 -> [12] (((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131)) & ordinal(skolem_A3131)), natural(skolem_A3131)
% 64.02/28.30
% 64.02/28.30 [12] ALPHA_AND : (((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131)) & ordinal(skolem_A3131))
% 64.02/28.30 -> [13] ((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131)), ordinal(skolem_A3131)
% 64.02/28.30
% 64.02/28.30 [13] ALPHA_AND : ((~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)) & epsilon_connected(skolem_A3131))
% 64.02/28.30 -> [14] (~empty(skolem_A3131) & epsilon_transitive(skolem_A3131)), epsilon_connected(skolem_A3131)
% 64.02/28.30
% 64.02/28.30 [14] ALPHA_AND : (~empty(skolem_A3131) & epsilon_transitive(skolem_A3131))
% 64.02/28.30 -> [15] ~empty(skolem_A3131), epsilon_transitive(skolem_A3131)
% 64.02/28.30
% 64.02/28.30 [15] DELTA_EXISTS : ? [A32_32] : ((~empty(A32_32) & finite(A32_32)))
% 64.02/28.30 -> [16] (~empty(skolem_A3232) & finite(skolem_A3232))
% 64.02/28.30
% 64.02/28.30 [16] ALPHA_AND : (~empty(skolem_A3232) & finite(skolem_A3232))
% 64.02/28.30 -> [17] ~empty(skolem_A3232), finite(skolem_A3232)
% 64.02/28.30
% 64.02/28.30 [17] DELTA_EXISTS : ? [A33_33] : (((relation(A33_33) & function(A33_33)) & function_yielding(A33_33)))
% 64.02/28.30 -> [18] ((relation(skolem_A3333) & function(skolem_A3333)) & function_yielding(skolem_A3333))
% 64.02/28.30
% 64.02/28.30 [18] ALPHA_AND : ((relation(skolem_A3333) & function(skolem_A3333)) & function_yielding(skolem_A3333))
% 64.02/28.30 -> [19] (relation(skolem_A3333) & function(skolem_A3333)), function_yielding(skolem_A3333)
% 64.02/28.30
% 64.02/28.30 [19] ALPHA_AND : (relation(skolem_A3333) & function(skolem_A3333))
% 64.02/28.30 -> [20] relation(skolem_A3333), function(skolem_A3333)
% 64.02/28.30
% 64.02/28.30 [20] DELTA_EXISTS : ? [A34_34] : ((relation(A34_34) & function(A34_34)))
% 64.02/28.30 -> [21] (relation(skolem_A3434) & function(skolem_A3434))
% 64.02/28.30
% 64.02/28.30 [21] ALPHA_AND : (relation(skolem_A3434) & function(skolem_A3434))
% 64.02/28.30 -> [22] relation(skolem_A3434), function(skolem_A3434)
% 64.02/28.30
% 64.02/28.30 [22] DELTA_EXISTS : ? [A35_35] : (((epsilon_transitive(A35_35) & epsilon_connected(A35_35)) & ordinal(A35_35)))
% 64.02/28.30 -> [23] ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 64.02/28.30
% 64.02/28.30 [23] ALPHA_AND : ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 64.02/28.30 -> [24] (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)), ordinal(skolem_A3535)
% 64.02/28.30
% 64.02/28.30 [24] ALPHA_AND : (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535))
% 64.02/28.30 -> [25] epsilon_transitive(skolem_A3535), epsilon_connected(skolem_A3535)
% 64.02/28.30
% 64.02/28.30 [25] DELTA_EXISTS : ? [A36_36] : ((((epsilon_transitive(A36_36) & epsilon_connected(A36_36)) & ordinal(A36_36)) & being_limit_ordinal(A36_36)))
% 64.02/28.30 -> [26] (((epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636)) & ordinal(skolem_A3636)) & being_limit_ordinal(skolem_A3636))
% 64.02/28.30
% 64.02/28.30 [26] ALPHA_AND : (((epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636)) & ordinal(skolem_A3636)) & being_limit_ordinal(skolem_A3636))
% 64.02/28.30 -> [27] ((epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636)) & ordinal(skolem_A3636)), being_limit_ordinal(skolem_A3636)
% 64.02/28.30
% 64.02/28.30 [27] ALPHA_AND : ((epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636)) & ordinal(skolem_A3636))
% 64.02/28.30 -> [28] (epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636)), ordinal(skolem_A3636)
% 64.02/28.30
% 64.02/28.30 [28] ALPHA_AND : (epsilon_transitive(skolem_A3636) & epsilon_connected(skolem_A3636))
% 64.02/28.30 -> [29] epsilon_transitive(skolem_A3636), epsilon_connected(skolem_A3636)
% 64.02/28.30
% 64.02/28.30 [29] DELTA_EXISTS : ? [A37_37] : ((empty(A37_37) & relation(A37_37)))
% 64.02/28.30 -> [30] (empty(skolem_A3737) & relation(skolem_A3737))
% 64.02/28.30
% 64.02/28.30 [30] ALPHA_AND : (empty(skolem_A3737) & relation(skolem_A3737))
% 64.02/28.30 -> [31] empty(skolem_A3737), relation(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [31] DELTA_EXISTS : ? [A40_40] : (empty(A40_40))
% 64.02/28.30 -> [32] empty(skolem_A4040)
% 64.02/28.30
% 64.02/28.30 [32] DELTA_EXISTS : ? [A41_41] : (((((element(A41_41, positive_rationals) & ~empty(A41_41)) & epsilon_transitive(A41_41)) & epsilon_connected(A41_41)) & ordinal(A41_41)))
% 64.02/28.30 -> [33] ((((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141)) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141))
% 64.02/28.30
% 64.02/28.30 [33] ALPHA_AND : ((((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141)) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141))
% 64.02/28.30 -> [34] (((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141)) & epsilon_connected(skolem_A4141)), ordinal(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [34] ALPHA_AND : (((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141)) & epsilon_connected(skolem_A4141))
% 64.02/28.30 -> [35] ((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141)), epsilon_connected(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [35] ALPHA_AND : ((element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)) & epsilon_transitive(skolem_A4141))
% 64.02/28.30 -> [36] (element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141)), epsilon_transitive(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [36] ALPHA_AND : (element(skolem_A4141, positive_rationals) & ~empty(skolem_A4141))
% 64.02/28.30 -> [37] element(skolem_A4141, positive_rationals), ~empty(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [37] DELTA_EXISTS : ? [A44_44] : (((relation(A44_44) & empty(A44_44)) & function(A44_44)))
% 64.02/28.30 -> [38] ((relation(skolem_A4444) & empty(skolem_A4444)) & function(skolem_A4444))
% 64.02/28.30
% 64.02/28.30 [38] ALPHA_AND : ((relation(skolem_A4444) & empty(skolem_A4444)) & function(skolem_A4444))
% 64.02/28.30 -> [39] (relation(skolem_A4444) & empty(skolem_A4444)), function(skolem_A4444)
% 64.02/28.30
% 64.02/28.30 [39] ALPHA_AND : (relation(skolem_A4444) & empty(skolem_A4444))
% 64.02/28.30 -> [40] relation(skolem_A4444), empty(skolem_A4444)
% 64.02/28.30
% 64.02/28.30 [40] DELTA_EXISTS : ? [A45_45] : (((((((relation(A45_45) & function(A45_45)) & one_to_one(A45_45)) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45)))
% 64.02/28.30 -> [41] ((((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545))
% 64.02/28.30
% 64.02/28.30 [41] ALPHA_AND : ((((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545))
% 64.02/28.30 -> [42] (((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)), ordinal(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [42] ALPHA_AND : (((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545))
% 64.02/28.30 -> [43] ((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)), epsilon_connected(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [43] ALPHA_AND : ((((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545))
% 64.02/28.30 -> [44] (((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545)), epsilon_transitive(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [44] ALPHA_AND : (((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)) & empty(skolem_A4545))
% 64.02/28.30 -> [45] ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)), empty(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [45] ALPHA_AND : ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545))
% 64.02/28.30 -> [46] (relation(skolem_A4545) & function(skolem_A4545)), one_to_one(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [46] ALPHA_AND : (relation(skolem_A4545) & function(skolem_A4545))
% 64.02/28.30 -> [47] relation(skolem_A4545), function(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [47] DELTA_EXISTS : ? [A46_46] : ((((relation(A46_46) & function(A46_46)) & transfinite_sequence(A46_46)) & ordinal_yielding(A46_46)))
% 64.02/28.30 -> [48] (((relation(skolem_A4646) & function(skolem_A4646)) & transfinite_sequence(skolem_A4646)) & ordinal_yielding(skolem_A4646))
% 64.02/28.30
% 64.02/28.30 [48] ALPHA_AND : (((relation(skolem_A4646) & function(skolem_A4646)) & transfinite_sequence(skolem_A4646)) & ordinal_yielding(skolem_A4646))
% 64.02/28.30 -> [49] ((relation(skolem_A4646) & function(skolem_A4646)) & transfinite_sequence(skolem_A4646)), ordinal_yielding(skolem_A4646)
% 64.02/28.30
% 64.02/28.30 [49] ALPHA_AND : ((relation(skolem_A4646) & function(skolem_A4646)) & transfinite_sequence(skolem_A4646))
% 64.02/28.30 -> [50] (relation(skolem_A4646) & function(skolem_A4646)), transfinite_sequence(skolem_A4646)
% 64.02/28.30
% 64.02/28.30 [50] ALPHA_AND : (relation(skolem_A4646) & function(skolem_A4646))
% 64.02/28.30 -> [51] relation(skolem_A4646), function(skolem_A4646)
% 64.02/28.30
% 64.02/28.30 [51] DELTA_EXISTS : ? [A47_47] : ((~empty(A47_47) & relation(A47_47)))
% 64.02/28.30 -> [52] (~empty(skolem_A4747) & relation(skolem_A4747))
% 64.02/28.30
% 64.02/28.30 [52] ALPHA_AND : (~empty(skolem_A4747) & relation(skolem_A4747))
% 64.02/28.30 -> [53] ~empty(skolem_A4747), relation(skolem_A4747)
% 64.02/28.30
% 64.02/28.30 [53] DELTA_EXISTS : ? [A50_50] : (~empty(A50_50))
% 64.02/28.30 -> [54] ~empty(skolem_A5050)
% 64.02/28.30
% 64.02/28.30 [54] DELTA_EXISTS : ? [A51_51] : ((((((element(A51_51, positive_rationals) & empty(A51_51)) & epsilon_transitive(A51_51)) & epsilon_connected(A51_51)) & ordinal(A51_51)) & natural(A51_51)))
% 64.02/28.30 -> [55] (((((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151))
% 64.02/28.30
% 64.02/28.30 [55] ALPHA_AND : (((((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151))
% 64.02/28.30 -> [56] ((((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)), natural(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [56] ALPHA_AND : ((((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151))
% 64.02/28.30 -> [57] (((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151)), ordinal(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [57] ALPHA_AND : (((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)) & epsilon_connected(skolem_A5151))
% 64.02/28.30 -> [58] ((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151)), epsilon_connected(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [58] ALPHA_AND : ((element(skolem_A5151, positive_rationals) & empty(skolem_A5151)) & epsilon_transitive(skolem_A5151))
% 64.02/28.30 -> [59] (element(skolem_A5151, positive_rationals) & empty(skolem_A5151)), epsilon_transitive(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [59] ALPHA_AND : (element(skolem_A5151, positive_rationals) & empty(skolem_A5151))
% 64.02/28.30 -> [60] element(skolem_A5151, positive_rationals), empty(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [60] DELTA_EXISTS : ? [A54_54] : (((relation(A54_54) & function(A54_54)) & one_to_one(A54_54)))
% 64.02/28.30 -> [61] ((relation(skolem_A5454) & function(skolem_A5454)) & one_to_one(skolem_A5454))
% 64.02/28.30
% 64.02/28.30 [61] ALPHA_AND : ((relation(skolem_A5454) & function(skolem_A5454)) & one_to_one(skolem_A5454))
% 64.02/28.30 -> [62] (relation(skolem_A5454) & function(skolem_A5454)), one_to_one(skolem_A5454)
% 64.02/28.30
% 64.02/28.30 [62] ALPHA_AND : (relation(skolem_A5454) & function(skolem_A5454))
% 64.02/28.30 -> [63] relation(skolem_A5454), function(skolem_A5454)
% 64.02/28.30
% 64.02/28.30 [63] DELTA_EXISTS : ? [A55_55] : ((((~empty(A55_55) & epsilon_transitive(A55_55)) & epsilon_connected(A55_55)) & ordinal(A55_55)))
% 64.02/28.30 -> [64] (((~empty(skolem_A5555) & epsilon_transitive(skolem_A5555)) & epsilon_connected(skolem_A5555)) & ordinal(skolem_A5555))
% 64.02/28.30
% 64.02/28.30 [64] ALPHA_AND : (((~empty(skolem_A5555) & epsilon_transitive(skolem_A5555)) & epsilon_connected(skolem_A5555)) & ordinal(skolem_A5555))
% 64.02/28.30 -> [65] ((~empty(skolem_A5555) & epsilon_transitive(skolem_A5555)) & epsilon_connected(skolem_A5555)), ordinal(skolem_A5555)
% 64.02/28.30
% 64.02/28.30 [65] ALPHA_AND : ((~empty(skolem_A5555) & epsilon_transitive(skolem_A5555)) & epsilon_connected(skolem_A5555))
% 64.02/28.30 -> [66] (~empty(skolem_A5555) & epsilon_transitive(skolem_A5555)), epsilon_connected(skolem_A5555)
% 64.02/28.30
% 64.02/28.30 [66] ALPHA_AND : (~empty(skolem_A5555) & epsilon_transitive(skolem_A5555))
% 64.02/28.30 -> [67] ~empty(skolem_A5555), epsilon_transitive(skolem_A5555)
% 64.02/28.30
% 64.02/28.30 [67] DELTA_EXISTS : ? [A56_56] : ((relation(A56_56) & relation_empty_yielding(A56_56)))
% 64.02/28.30 -> [68] (relation(skolem_A5656) & relation_empty_yielding(skolem_A5656))
% 64.02/28.30
% 64.02/28.30 [68] ALPHA_AND : (relation(skolem_A5656) & relation_empty_yielding(skolem_A5656))
% 64.02/28.30 -> [69] relation(skolem_A5656), relation_empty_yielding(skolem_A5656)
% 64.02/28.30
% 64.02/28.30 [69] DELTA_EXISTS : ? [A57_57] : (((relation(A57_57) & relation_empty_yielding(A57_57)) & function(A57_57)))
% 64.02/28.30 -> [70] ((relation(skolem_A5757) & relation_empty_yielding(skolem_A5757)) & function(skolem_A5757))
% 64.02/28.30
% 64.02/28.30 [70] ALPHA_AND : ((relation(skolem_A5757) & relation_empty_yielding(skolem_A5757)) & function(skolem_A5757))
% 64.02/28.30 -> [71] (relation(skolem_A5757) & relation_empty_yielding(skolem_A5757)), function(skolem_A5757)
% 64.02/28.30
% 64.02/28.30 [71] ALPHA_AND : (relation(skolem_A5757) & relation_empty_yielding(skolem_A5757))
% 64.02/28.30 -> [72] relation(skolem_A5757), relation_empty_yielding(skolem_A5757)
% 64.02/28.30
% 64.02/28.30 [72] DELTA_EXISTS : ? [A58_58] : (((relation(A58_58) & function(A58_58)) & transfinite_sequence(A58_58)))
% 64.02/28.30 -> [73] ((relation(skolem_A5858) & function(skolem_A5858)) & transfinite_sequence(skolem_A5858))
% 64.02/28.30
% 64.02/28.30 [73] ALPHA_AND : ((relation(skolem_A5858) & function(skolem_A5858)) & transfinite_sequence(skolem_A5858))
% 64.02/28.30 -> [74] (relation(skolem_A5858) & function(skolem_A5858)), transfinite_sequence(skolem_A5858)
% 64.02/28.30
% 64.02/28.30 [74] ALPHA_AND : (relation(skolem_A5858) & function(skolem_A5858))
% 64.02/28.30 -> [75] relation(skolem_A5858), function(skolem_A5858)
% 64.02/28.30
% 64.02/28.30 [75] DELTA_EXISTS : ? [A59_59] : (((relation(A59_59) & relation_non_empty(A59_59)) & function(A59_59)))
% 64.02/28.30 -> [76] ((relation(skolem_A5959) & relation_non_empty(skolem_A5959)) & function(skolem_A5959))
% 64.02/28.30
% 64.02/28.30 [76] ALPHA_AND : ((relation(skolem_A5959) & relation_non_empty(skolem_A5959)) & function(skolem_A5959))
% 64.02/28.30 -> [77] (relation(skolem_A5959) & relation_non_empty(skolem_A5959)), function(skolem_A5959)
% 64.02/28.30
% 64.02/28.30 [77] ALPHA_AND : (relation(skolem_A5959) & relation_non_empty(skolem_A5959))
% 64.02/28.30 -> [78] relation(skolem_A5959), relation_non_empty(skolem_A5959)
% 64.02/28.30
% 64.02/28.30 [78] DELTA_NOT_FORALL : ~! [A64_64, B65_65] : ((finite(A64_64) => finite(set_intersection2(A64_64, B65_65))))
% 64.02/28.30 -> [79] ~(finite(skolem_A6464) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [79] ALPHA_NOT_IMPLY : ~(finite(skolem_A6464) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [80] finite(skolem_A6464), ~finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [80] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 64.02/28.30 -> [81] (in(A3_0_0, B4_0_0) => ~in(B4_0_0, A3_0_0))
% 64.02/28.30
% 64.02/28.30 [81] BETA_IMPLY : (in(A3_0_0, B4_0_0) => ~in(B4_0_0, A3_0_0))
% 64.02/28.30 -> [82] ~in(A3_0_0, B4_0_0)
% 64.02/28.30 -> [83] ~in(B4_0_0, A3_0_0)
% 64.02/28.30
% 64.02/28.30 [83] GAMMA_FORALL : ! [A5_5] : ((ordinal(A5_5) => ! [B6_6] : ((element(B6_6, A5_5) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))))
% 64.02/28.30 -> [85] (ordinal(empty_set) => ! [B6_6] : ((element(B6_6, empty_set) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 64.02/28.30
% 64.02/28.30 [85] BETA_IMPLY : (ordinal(empty_set) => ! [B6_6] : ((element(B6_6, empty_set) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 64.02/28.30 -> [88] ~ordinal(empty_set)
% 64.02/28.30 -> [89] ! [B6_6] : ((element(B6_6, empty_set) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))
% 64.02/28.30
% 64.02/28.30 [88] CLOSURE : ~ordinal(empty_set)
% 64.02/28.30
% 64.02/28.30 [89] GAMMA_FORALL : ! [A7_7] : ((empty(A7_7) => finite(A7_7)))
% 64.02/28.30 -> [93] (empty(set_intersection2(skolem_A6464, skolem_B6565)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [93] BETA_IMPLY : (empty(set_intersection2(skolem_A6464, skolem_B6565)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [94] ~empty(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30 -> [95] finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [95] CLOSURE : finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [94] GAMMA_FORALL : ! [A8_8] : ((empty(A8_8) => function(A8_8)))
% 64.02/28.30 -> [97] (empty(empty_set) => function(empty_set))
% 64.02/28.30
% 64.02/28.30 [97] BETA_IMPLY : (empty(empty_set) => function(empty_set))
% 64.02/28.30 -> [100] ~empty(empty_set)
% 64.02/28.30 -> [101] function(empty_set)
% 64.02/28.30
% 64.02/28.30 [100] CLOSURE : ~empty(empty_set)
% 64.02/28.30
% 64.02/28.30 [101] GAMMA_FORALL : ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9))))
% 64.02/28.30 -> [103] (ordinal(skolem_A4545) => (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)))
% 64.02/28.30
% 64.02/28.30 [103] BETA_IMPLY : (ordinal(skolem_A4545) => (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)))
% 64.02/28.30 -> [106] ~ordinal(skolem_A4545)
% 64.02/28.30 -> [107] (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545))
% 64.02/28.30
% 64.02/28.30 [106] CLOSURE : ~ordinal(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [107] ALPHA_AND : (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545))
% 64.02/28.30 -> [109] epsilon_transitive(skolem_A4545), epsilon_connected(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [109] GAMMA_FORALL : ! [A10_10] : ((empty(A10_10) => relation(A10_10)))
% 64.02/28.30 -> [111] (empty(skolem_A4040) => relation(skolem_A4040))
% 64.02/28.30
% 64.02/28.30 [111] BETA_IMPLY : (empty(skolem_A4040) => relation(skolem_A4040))
% 64.02/28.30 -> [114] ~empty(skolem_A4040)
% 64.02/28.30 -> [115] relation(skolem_A4040)
% 64.02/28.30
% 64.02/28.30 [114] CLOSURE : ~empty(skolem_A4040)
% 64.02/28.30
% 64.02/28.30 [115] GAMMA_FORALL : ! [A11_11] : (((empty(A11_11) & ordinal(A11_11)) => (((epsilon_transitive(A11_11) & epsilon_connected(A11_11)) & ordinal(A11_11)) & natural(A11_11))))
% 64.02/28.30 -> [117] ((empty(skolem_A5151) & ordinal(skolem_A5151)) => (((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151)))
% 64.02/28.30
% 64.02/28.30 [117] BETA_IMPLY : ((empty(skolem_A5151) & ordinal(skolem_A5151)) => (((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151)))
% 64.02/28.30 -> [120] ~(empty(skolem_A5151) & ordinal(skolem_A5151))
% 64.02/28.30 -> [121] (((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151))
% 64.02/28.30
% 64.02/28.30 [120] BETA_NOT_AND : ~(empty(skolem_A5151) & ordinal(skolem_A5151))
% 64.02/28.30 -> [122] ~empty(skolem_A5151)
% 64.02/28.30 -> [123] ~ordinal(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [122] CLOSURE : ~empty(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [123] CLOSURE : ~ordinal(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [121] ALPHA_AND : (((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)) & natural(skolem_A5151))
% 64.02/28.30 -> [126] ((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151)), natural(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [126] ALPHA_AND : ((epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)) & ordinal(skolem_A5151))
% 64.02/28.30 -> [128] (epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151)), ordinal(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [128] ALPHA_AND : (epsilon_transitive(skolem_A5151) & epsilon_connected(skolem_A5151))
% 64.02/28.30 -> [130] epsilon_transitive(skolem_A5151), epsilon_connected(skolem_A5151)
% 64.02/28.30
% 64.02/28.30 [130] GAMMA_FORALL : ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13)))))
% 64.02/28.30 -> [132] (finite(skolem_A3232) => ! [B13_13] : ((element(B13_13, powerset(skolem_A3232)) => finite(B13_13))))
% 64.02/28.30
% 64.02/28.30 [132] BETA_IMPLY : (finite(skolem_A3232) => ! [B13_13] : ((element(B13_13, powerset(skolem_A3232)) => finite(B13_13))))
% 64.02/28.30 -> [133] ~finite(skolem_A3232)
% 64.02/28.30 -> [134] ! [B13_13] : ((element(B13_13, powerset(skolem_A3232)) => finite(B13_13)))
% 64.02/28.30
% 64.02/28.30 [133] CLOSURE : ~finite(skolem_A3232)
% 64.02/28.30
% 64.02/28.30 [134] GAMMA_FORALL : ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14))))
% 64.02/28.30 -> [136] (((relation(skolem_A4545) & empty(skolem_A4545)) & function(skolem_A4545)) => ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)))
% 64.02/28.30
% 64.02/28.30 [136] BETA_IMPLY : (((relation(skolem_A4545) & empty(skolem_A4545)) & function(skolem_A4545)) => ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545)))
% 64.02/28.30 -> [139] ~((relation(skolem_A4545) & empty(skolem_A4545)) & function(skolem_A4545))
% 64.02/28.30 -> [140] ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545))
% 64.02/28.30
% 64.02/28.30 [139] BETA_NOT_AND : ~((relation(skolem_A4545) & empty(skolem_A4545)) & function(skolem_A4545))
% 64.02/28.30 -> [141] ~(relation(skolem_A4545) & empty(skolem_A4545))
% 64.02/28.30 -> [142] ~function(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [142] CLOSURE : ~function(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [141] BETA_NOT_AND : ~(relation(skolem_A4545) & empty(skolem_A4545))
% 64.02/28.30 -> [145] ~relation(skolem_A4545)
% 64.02/28.30 -> [146] ~empty(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [146] CLOSURE : ~empty(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [145] CLOSURE : ~relation(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [140] ALPHA_AND : ((relation(skolem_A4545) & function(skolem_A4545)) & one_to_one(skolem_A4545))
% 64.02/28.30 -> [144] (relation(skolem_A4545) & function(skolem_A4545)), one_to_one(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [144] ALPHA_AND : (relation(skolem_A4545) & function(skolem_A4545))
% 64.02/28.30 -> [154] relation(skolem_A4545), function(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [154] GAMMA_FORALL : ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15)))
% 64.02/28.30 -> [156] ((epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9)) => ordinal(A15_0_9))
% 64.02/28.30
% 64.02/28.30 [156] BETA_IMPLY : ((epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9)) => ordinal(A15_0_9))
% 64.02/28.30 -> [157] ~(epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9))
% 64.02/28.30 -> [158] ordinal(A15_0_9)
% 64.02/28.30
% 64.02/28.30 [157] BETA_NOT_AND : ~(epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9))
% 64.02/28.30 -> [159] ~epsilon_transitive(A15_0_9)
% 64.02/28.30 -> [160] ~epsilon_connected(A15_0_9)
% 64.02/28.30
% 64.02/28.30 [160] CLOSURE : ~epsilon_connected(A15_0_9)
% 64.02/28.30
% 64.02/28.30 [159] CLOSURE : ~epsilon_transitive(A15_0_9)
% 64.02/28.30
% 64.02/28.30 [158] GAMMA_FORALL : ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16))))
% 64.02/28.30 -> [164] (empty(skolem_A3737) => ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737)))
% 64.02/28.30
% 64.02/28.30 [164] BETA_IMPLY : (empty(skolem_A3737) => ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737)))
% 64.02/28.30 -> [165] ~empty(skolem_A3737)
% 64.02/28.30 -> [166] ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737))
% 64.02/28.30
% 64.02/28.30 [165] CLOSURE : ~empty(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [166] ALPHA_AND : ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737))
% 64.02/28.30 -> [169] (epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)), ordinal(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [169] ALPHA_AND : (epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737))
% 64.02/28.30 -> [173] epsilon_transitive(skolem_A3737), epsilon_connected(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [173] GAMMA_FORALL : ! [A17_17] : ((element(A17_17, positive_rationals) => (ordinal(A17_17) => (((epsilon_transitive(A17_17) & epsilon_connected(A17_17)) & ordinal(A17_17)) & natural(A17_17)))))
% 64.02/28.30 -> [175] (element(skolem_A4141, positive_rationals) => (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))))
% 64.02/28.30
% 64.02/28.30 [175] BETA_IMPLY : (element(skolem_A4141, positive_rationals) => (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))))
% 64.02/28.30 -> [177] ~element(skolem_A4141, positive_rationals)
% 64.02/28.30 -> [178] (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141)))
% 64.02/28.30
% 64.02/28.30 [177] CLOSURE : ~element(skolem_A4141, positive_rationals)
% 64.02/28.30
% 64.02/28.30 [178] BETA_IMPLY : (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141)))
% 64.02/28.30 -> [179] ~ordinal(skolem_A4141)
% 64.02/28.30 -> [180] (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))
% 64.02/28.30
% 64.02/28.30 [179] CLOSURE : ~ordinal(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [180] ALPHA_AND : (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))
% 64.02/28.30 -> [181] ((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)), natural(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [181] ALPHA_AND : ((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141))
% 64.02/28.30 -> [185] (epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)), ordinal(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [185] ALPHA_AND : (epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141))
% 64.02/28.30 -> [189] epsilon_transitive(skolem_A4141), epsilon_connected(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [189] GAMMA_FORALL : ! [A18_18, B19_19] : (=(set_intersection2(A18_18, B19_19), set_intersection2(B19_19, A18_18)))
% 64.02/28.30 -> [192] =(set_intersection2(A18_0_12, B19_0_12), set_intersection2(B19_0_12, A18_0_12))
% 64.02/28.30
% 64.02/28.30 [192] GAMMA_FORALL : ! [A20_20] : (? [B21_21] : (element(B21_21, A20_20)))
% 64.02/28.30 -> [196] ? [B21_21] : (element(B21_21, A20_1_13))
% 64.02/28.30
% 64.02/28.30 [196] DELTA_EXISTS : ? [B21_21] : (element(B21_21, A20_1_13))
% 64.02/28.30 -> [197] element(skolem_B2121(A20_1_13), A20_1_13)
% 64.02/28.30
% 64.02/28.30 [197] GAMMA_FORALL : ! [A22_22, B23_23] : ((finite(B23_23) => finite(set_intersection2(A22_22, B23_23))))
% 64.02/28.30 -> [201] (finite(skolem_B6565) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [201] BETA_IMPLY : (finite(skolem_B6565) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [202] ~finite(skolem_B6565)
% 64.02/28.30 -> [203] finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [203] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [202] GAMMA_FORALL : ! [A24_24, B25_25] : ((finite(A24_24) => finite(set_intersection2(A24_24, B25_25))))
% 64.02/28.30 -> [207] (finite(skolem_A6464) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [207] BETA_IMPLY : (finite(skolem_A6464) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [208] ~finite(skolem_A6464)
% 64.02/28.30 -> [209] finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [208] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [209] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [82] GAMMA_FORALL : ! [A5_5] : ((ordinal(A5_5) => ! [B6_6] : ((element(B6_6, A5_5) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))))
% 64.02/28.30 -> [84] (ordinal(skolem_A4545) => ! [B6_6] : ((element(B6_6, skolem_A4545) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 64.02/28.30
% 64.02/28.30 [84] BETA_IMPLY : (ordinal(skolem_A4545) => ! [B6_6] : ((element(B6_6, skolem_A4545) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 64.02/28.30 -> [86] ~ordinal(skolem_A4545)
% 64.02/28.30 -> [87] ! [B6_6] : ((element(B6_6, skolem_A4545) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))
% 64.02/28.30
% 64.02/28.30 [86] CLOSURE : ~ordinal(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [87] GAMMA_FORALL : ! [A7_7] : ((empty(A7_7) => finite(A7_7)))
% 64.02/28.30 -> [90] (empty(set_intersection2(skolem_A6464, skolem_B6565)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [90] BETA_IMPLY : (empty(set_intersection2(skolem_A6464, skolem_B6565)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [91] ~empty(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30 -> [92] finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [92] CLOSURE : finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [91] GAMMA_FORALL : ! [A8_8] : ((empty(A8_8) => function(A8_8)))
% 64.02/28.30 -> [96] (empty(skolem_A3737) => function(skolem_A3737))
% 64.02/28.30
% 64.02/28.30 [96] BETA_IMPLY : (empty(skolem_A3737) => function(skolem_A3737))
% 64.02/28.30 -> [98] ~empty(skolem_A3737)
% 64.02/28.30 -> [99] function(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [98] CLOSURE : ~empty(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [99] GAMMA_FORALL : ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9))))
% 64.02/28.30 -> [102] (ordinal(skolem_A3535) => (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)))
% 64.02/28.30
% 64.02/28.30 [102] BETA_IMPLY : (ordinal(skolem_A3535) => (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)))
% 64.02/28.30 -> [104] ~ordinal(skolem_A3535)
% 64.02/28.30 -> [105] (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535))
% 64.02/28.30
% 64.02/28.30 [104] CLOSURE : ~ordinal(skolem_A3535)
% 64.02/28.30
% 64.02/28.30 [105] ALPHA_AND : (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535))
% 64.02/28.30 -> [108] epsilon_transitive(skolem_A3535), epsilon_connected(skolem_A3535)
% 64.02/28.30
% 64.02/28.30 [108] GAMMA_FORALL : ! [A10_10] : ((empty(A10_10) => relation(A10_10)))
% 64.02/28.30 -> [110] (empty(skolem_A4545) => relation(skolem_A4545))
% 64.02/28.30
% 64.02/28.30 [110] BETA_IMPLY : (empty(skolem_A4545) => relation(skolem_A4545))
% 64.02/28.30 -> [112] ~empty(skolem_A4545)
% 64.02/28.30 -> [113] relation(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [112] CLOSURE : ~empty(skolem_A4545)
% 64.02/28.30
% 64.02/28.30 [113] GAMMA_FORALL : ! [A11_11] : (((empty(A11_11) & ordinal(A11_11)) => (((epsilon_transitive(A11_11) & epsilon_connected(A11_11)) & ordinal(A11_11)) & natural(A11_11))))
% 64.02/28.30 -> [116] ((empty(empty_set) & ordinal(empty_set)) => (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set)))
% 64.02/28.30
% 64.02/28.30 [116] BETA_IMPLY : ((empty(empty_set) & ordinal(empty_set)) => (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set)))
% 64.02/28.30 -> [118] ~(empty(empty_set) & ordinal(empty_set))
% 64.02/28.30 -> [119] (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set))
% 64.02/28.30
% 64.02/28.30 [118] BETA_NOT_AND : ~(empty(empty_set) & ordinal(empty_set))
% 64.02/28.30 -> [124] ~empty(empty_set)
% 64.02/28.30 -> [125] ~ordinal(empty_set)
% 64.02/28.30
% 64.02/28.30 [125] CLOSURE : ~ordinal(empty_set)
% 64.02/28.30
% 64.02/28.30 [124] CLOSURE : ~empty(empty_set)
% 64.02/28.30
% 64.02/28.30 [119] ALPHA_AND : (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set))
% 64.02/28.30 -> [127] ((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)), natural(empty_set)
% 64.02/28.30
% 64.02/28.30 [127] ALPHA_AND : ((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set))
% 64.02/28.30 -> [129] (epsilon_transitive(empty_set) & epsilon_connected(empty_set)), ordinal(empty_set)
% 64.02/28.30
% 64.02/28.30 [129] ALPHA_AND : (epsilon_transitive(empty_set) & epsilon_connected(empty_set))
% 64.02/28.30 -> [131] epsilon_transitive(empty_set), epsilon_connected(empty_set)
% 64.02/28.30
% 64.02/28.30 [131] GAMMA_FORALL : ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13)))))
% 64.02/28.30 -> [135] (finite(skolem_A6464) => ! [B13_13] : ((element(B13_13, powerset(skolem_A6464)) => finite(B13_13))))
% 64.02/28.30
% 64.02/28.30 [135] BETA_IMPLY : (finite(skolem_A6464) => ! [B13_13] : ((element(B13_13, powerset(skolem_A6464)) => finite(B13_13))))
% 64.02/28.30 -> [137] ~finite(skolem_A6464)
% 64.02/28.30 -> [138] ! [B13_13] : ((element(B13_13, powerset(skolem_A6464)) => finite(B13_13)))
% 64.02/28.30
% 64.02/28.30 [137] CLOSURE : ~finite(skolem_A6464)
% 64.02/28.30
% 64.02/28.30 [138] GAMMA_FORALL : ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14))))
% 64.02/28.30 -> [143] (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 64.02/28.30
% 64.02/28.30 [143] BETA_IMPLY : (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 64.02/28.30 -> [147] ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 64.02/28.30 -> [148] ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 64.02/28.30
% 64.02/28.30 [147] BETA_NOT_AND : ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 64.02/28.30 -> [149] ~(relation(empty_set) & empty(empty_set))
% 64.02/28.30 -> [150] ~function(empty_set)
% 64.02/28.30
% 64.02/28.30 [150] CLOSURE : ~function(empty_set)
% 64.02/28.30
% 64.02/28.30 [149] BETA_NOT_AND : ~(relation(empty_set) & empty(empty_set))
% 64.02/28.30 -> [152] ~relation(empty_set)
% 64.02/28.30 -> [153] ~empty(empty_set)
% 64.02/28.30
% 64.02/28.30 [152] CLOSURE : ~relation(empty_set)
% 64.02/28.30
% 64.02/28.30 [153] CLOSURE : ~empty(empty_set)
% 64.02/28.30
% 64.02/28.30 [148] ALPHA_AND : ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 64.02/28.30 -> [151] (relation(empty_set) & function(empty_set)), one_to_one(empty_set)
% 64.02/28.30
% 64.02/28.30 [151] ALPHA_AND : (relation(empty_set) & function(empty_set))
% 64.02/28.30 -> [155] relation(empty_set), function(empty_set)
% 64.02/28.30
% 64.02/28.30 [155] GAMMA_FORALL : ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15)))
% 64.02/28.30 -> [161] ((epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9)) => ordinal(A15_1_9))
% 64.02/28.30
% 64.02/28.30 [161] BETA_IMPLY : ((epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9)) => ordinal(A15_1_9))
% 64.02/28.30 -> [162] ~(epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9))
% 64.02/28.30 -> [163] ordinal(A15_1_9)
% 64.02/28.30
% 64.02/28.30 [162] BETA_NOT_AND : ~(epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9))
% 64.02/28.30 -> [167] ~epsilon_transitive(A15_1_9)
% 64.02/28.30 -> [168] ~epsilon_connected(A15_1_9)
% 64.02/28.30
% 64.02/28.30 [168] CLOSURE : ~epsilon_connected(A15_1_9)
% 64.02/28.30
% 64.02/28.30 [167] CLOSURE : ~epsilon_transitive(A15_1_9)
% 64.02/28.30
% 64.02/28.30 [163] GAMMA_FORALL : ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16))))
% 64.02/28.30 -> [170] (empty(skolem_A3737) => ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737)))
% 64.02/28.30
% 64.02/28.30 [170] BETA_IMPLY : (empty(skolem_A3737) => ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737)))
% 64.02/28.30 -> [171] ~empty(skolem_A3737)
% 64.02/28.30 -> [172] ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737))
% 64.02/28.30
% 64.02/28.30 [171] CLOSURE : ~empty(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [172] ALPHA_AND : ((epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)) & ordinal(skolem_A3737))
% 64.02/28.30 -> [174] (epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737)), ordinal(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [174] ALPHA_AND : (epsilon_transitive(skolem_A3737) & epsilon_connected(skolem_A3737))
% 64.02/28.30 -> [176] epsilon_transitive(skolem_A3737), epsilon_connected(skolem_A3737)
% 64.02/28.30
% 64.02/28.30 [176] GAMMA_FORALL : ! [A17_17] : ((element(A17_17, positive_rationals) => (ordinal(A17_17) => (((epsilon_transitive(A17_17) & epsilon_connected(A17_17)) & ordinal(A17_17)) & natural(A17_17)))))
% 64.02/28.30 -> [182] (element(skolem_A4141, positive_rationals) => (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))))
% 64.02/28.30
% 64.02/28.30 [182] BETA_IMPLY : (element(skolem_A4141, positive_rationals) => (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))))
% 64.02/28.30 -> [183] ~element(skolem_A4141, positive_rationals)
% 64.02/28.30 -> [184] (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141)))
% 64.02/28.30
% 64.02/28.30 [183] CLOSURE : ~element(skolem_A4141, positive_rationals)
% 64.02/28.30
% 64.02/28.30 [184] BETA_IMPLY : (ordinal(skolem_A4141) => (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141)))
% 64.02/28.30 -> [186] ~ordinal(skolem_A4141)
% 64.02/28.30 -> [187] (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))
% 64.02/28.30
% 64.02/28.30 [186] CLOSURE : ~ordinal(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [187] ALPHA_AND : (((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)) & natural(skolem_A4141))
% 64.02/28.30 -> [188] ((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141)), natural(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [188] ALPHA_AND : ((epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)) & ordinal(skolem_A4141))
% 64.02/28.30 -> [190] (epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141)), ordinal(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [190] ALPHA_AND : (epsilon_transitive(skolem_A4141) & epsilon_connected(skolem_A4141))
% 64.02/28.30 -> [191] epsilon_transitive(skolem_A4141), epsilon_connected(skolem_A4141)
% 64.02/28.30
% 64.02/28.30 [191] GAMMA_FORALL : ! [A18_18, B19_19] : (=(set_intersection2(A18_18, B19_19), set_intersection2(B19_19, A18_18)))
% 64.02/28.30 -> [193] =(set_intersection2(A18_1_12, B19_1_12), set_intersection2(B19_1_12, A18_1_12))
% 64.02/28.30
% 64.02/28.30 [193] GAMMA_FORALL : ! [A20_20] : (? [B21_21] : (element(B21_21, A20_20)))
% 64.02/28.30 -> [194] ? [B21_21] : (element(B21_21, A20_0_13))
% 64.02/28.30
% 64.02/28.30 [194] DELTA_EXISTS : ? [B21_21] : (element(B21_21, A20_0_13))
% 64.02/28.30 -> [195] element(skolem_B2121(A20_0_13), A20_0_13)
% 64.02/28.30
% 64.02/28.30 [195] GAMMA_FORALL : ! [A22_22, B23_23] : ((finite(B23_23) => finite(set_intersection2(A22_22, B23_23))))
% 64.02/28.30 -> [198] (finite(skolem_A3232) => finite(set_intersection2(A22_0_14, skolem_A3232)))
% 64.02/28.30
% 64.02/28.30 [198] BETA_IMPLY : (finite(skolem_A3232) => finite(set_intersection2(A22_0_14, skolem_A3232)))
% 64.02/28.30 -> [199] ~finite(skolem_A3232)
% 64.02/28.30 -> [200] finite(set_intersection2(A22_0_14, skolem_A3232))
% 64.02/28.30
% 64.02/28.30 [199] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [200] GAMMA_FORALL : ! [A24_24, B25_25] : ((finite(A24_24) => finite(set_intersection2(A24_24, B25_25))))
% 64.02/28.30 -> [204] (finite(skolem_A3232) => finite(set_intersection2(skolem_A3232, B25_0_15)))
% 64.02/28.30
% 64.02/28.30 [204] BETA_IMPLY : (finite(skolem_A3232) => finite(set_intersection2(skolem_A3232, B25_0_15)))
% 64.02/28.30 -> [205] ~finite(skolem_A3232)
% 64.02/28.30 -> [206] finite(set_intersection2(skolem_A3232, B25_0_15))
% 64.02/28.30
% 64.02/28.30 [205] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [206] GAMMA_FORALL : ! [A26_26, B27_27] : (((relation(A26_26) & relation(B27_27)) => relation(set_intersection2(A26_26, B27_27))))
% 64.02/28.30 -> [210] ((relation(A26_0_16) & relation(skolem_A3333)) => relation(set_intersection2(A26_0_16, skolem_A3333)))
% 64.02/28.30
% 64.02/28.30 [210] BETA_IMPLY : ((relation(A26_0_16) & relation(skolem_A3333)) => relation(set_intersection2(A26_0_16, skolem_A3333)))
% 64.02/28.30 -> [211] ~(relation(A26_0_16) & relation(skolem_A3333))
% 64.02/28.30 -> [212] relation(set_intersection2(A26_0_16, skolem_A3333))
% 64.02/28.30
% 64.02/28.30 [211] BETA_NOT_AND : ~(relation(A26_0_16) & relation(skolem_A3333))
% 64.02/28.30 -> [213] ~relation(A26_0_16)
% 64.02/28.30 -> [214] ~relation(skolem_A3333)
% 64.02/28.30
% 64.02/28.30 [214] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [213] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [212] GAMMA_FORALL : ! [A28_28] : (~empty(powerset(A28_28)))
% 64.02/28.30 -> [215] ~empty(powerset(A28_0_17))
% 64.02/28.30
% 64.02/28.30 [215] GAMMA_FORALL : ! [A29_29, B30_30] : (=(set_intersection2(A29_29, A29_29), A29_29))
% 64.02/28.30 -> [216] =(set_intersection2(A29_0_18, A29_0_18), A29_0_18)
% 64.02/28.30
% 64.02/28.30 [216] GAMMA_FORALL : ! [A38_38] : ((~empty(A38_38) => ? [B39_39] : ((element(B39_39, powerset(A38_38)) & ~empty(B39_39)))))
% 64.02/28.30 -> [217] (~empty(skolem_A3131) => ? [B39_39] : ((element(B39_39, powerset(skolem_A3131)) & ~empty(B39_39))))
% 64.02/28.30
% 64.02/28.30 [217] BETA_IMPLY : (~empty(skolem_A3131) => ? [B39_39] : ((element(B39_39, powerset(skolem_A3131)) & ~empty(B39_39))))
% 64.02/28.30 -> [218] ~~empty(skolem_A3131)
% 64.02/28.30 -> [219] ? [B39_39] : ((element(B39_39, powerset(skolem_A3131)) & ~empty(B39_39)))
% 64.02/28.30
% 64.02/28.30 [218] ALPHA_NOT_NOT : ~~empty(skolem_A3131)
% 64.02/28.30 -> [220] empty(skolem_A3131)
% 64.02/28.30
% 64.02/28.30 [220] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [219] DELTA_EXISTS : ? [B39_39] : ((element(B39_39, powerset(skolem_A3131)) & ~empty(B39_39)))
% 64.02/28.30 -> [221] (element(skolem_B3939(skolem_A3131), powerset(skolem_A3131)) & ~empty(skolem_B3939(skolem_A3131)))
% 64.02/28.30
% 64.02/28.30 [221] ALPHA_AND : (element(skolem_B3939(skolem_A3131), powerset(skolem_A3131)) & ~empty(skolem_B3939(skolem_A3131)))
% 64.02/28.30 -> [222] element(skolem_B3939(skolem_A3131), powerset(skolem_A3131)), ~empty(skolem_B3939(skolem_A3131))
% 64.02/28.30
% 64.02/28.30 [222] GAMMA_FORALL : ! [A42_42] : (? [B43_43] : ((((((((((element(B43_43, powerset(A42_42)) & empty(B43_43)) & relation(B43_43)) & function(B43_43)) & one_to_one(B43_43)) & epsilon_transitive(B43_43)) & epsilon_connected(B43_43)) & ordinal(B43_43)) & natural(B43_43)) & finite(B43_43))))
% 64.02/28.30 -> [223] ? [B43_43] : ((((((((((element(B43_43, powerset(A42_0_20)) & empty(B43_43)) & relation(B43_43)) & function(B43_43)) & one_to_one(B43_43)) & epsilon_transitive(B43_43)) & epsilon_connected(B43_43)) & ordinal(B43_43)) & natural(B43_43)) & finite(B43_43)))
% 64.02/28.30
% 64.02/28.30 [223] DELTA_EXISTS : ? [B43_43] : ((((((((((element(B43_43, powerset(A42_0_20)) & empty(B43_43)) & relation(B43_43)) & function(B43_43)) & one_to_one(B43_43)) & epsilon_transitive(B43_43)) & epsilon_connected(B43_43)) & ordinal(B43_43)) & natural(B43_43)) & finite(B43_43)))
% 64.02/28.30 -> [224] (((((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20))) & natural(skolem_B4343(A42_0_20))) & finite(skolem_B4343(A42_0_20)))
% 64.02/28.30
% 64.02/28.30 [224] ALPHA_AND : (((((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20))) & natural(skolem_B4343(A42_0_20))) & finite(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [225] ((((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20))) & natural(skolem_B4343(A42_0_20))), finite(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [225] ALPHA_AND : ((((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20))) & natural(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [226] (((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20))), natural(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [226] ALPHA_AND : (((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))) & ordinal(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [227] ((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20))), ordinal(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [227] ALPHA_AND : ((((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))) & epsilon_connected(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [228] (((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20))), epsilon_connected(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [228] ALPHA_AND : (((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))) & epsilon_transitive(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [229] ((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20))), epsilon_transitive(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [229] ALPHA_AND : ((((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))) & one_to_one(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [230] (((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20))), one_to_one(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [230] ALPHA_AND : (((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))) & function(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [231] ((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20))), function(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [231] ALPHA_AND : ((element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))) & relation(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [232] (element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20))), relation(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [232] ALPHA_AND : (element(skolem_B4343(A42_0_20), powerset(A42_0_20)) & empty(skolem_B4343(A42_0_20)))
% 64.02/28.30 -> [233] element(skolem_B4343(A42_0_20), powerset(A42_0_20)), empty(skolem_B4343(A42_0_20))
% 64.02/28.30
% 64.02/28.30 [233] GAMMA_FORALL : ! [A48_48] : (? [B49_49] : ((element(B49_49, powerset(A48_48)) & empty(B49_49))))
% 64.02/28.30 -> [234] ? [B49_49] : ((element(B49_49, powerset(A48_0_21)) & empty(B49_49)))
% 64.02/28.30
% 64.02/28.30 [234] DELTA_EXISTS : ? [B49_49] : ((element(B49_49, powerset(A48_0_21)) & empty(B49_49)))
% 64.02/28.30 -> [235] (element(skolem_B4949(A48_0_21), powerset(A48_0_21)) & empty(skolem_B4949(A48_0_21)))
% 64.02/28.30
% 64.02/28.30 [235] ALPHA_AND : (element(skolem_B4949(A48_0_21), powerset(A48_0_21)) & empty(skolem_B4949(A48_0_21)))
% 64.02/28.30 -> [236] element(skolem_B4949(A48_0_21), powerset(A48_0_21)), empty(skolem_B4949(A48_0_21))
% 64.02/28.30
% 64.02/28.30 [236] GAMMA_FORALL : ! [A52_52] : ((~empty(A52_52) => ? [B53_53] : (((element(B53_53, powerset(A52_52)) & ~empty(B53_53)) & finite(B53_53)))))
% 64.02/28.30 -> [237] (~empty(positive_rationals) => ? [B53_53] : (((element(B53_53, powerset(positive_rationals)) & ~empty(B53_53)) & finite(B53_53))))
% 64.02/28.30
% 64.02/28.30 [237] BETA_IMPLY : (~empty(positive_rationals) => ? [B53_53] : (((element(B53_53, powerset(positive_rationals)) & ~empty(B53_53)) & finite(B53_53))))
% 64.02/28.30 -> [238] ~~empty(positive_rationals)
% 64.02/28.30 -> [239] ? [B53_53] : (((element(B53_53, powerset(positive_rationals)) & ~empty(B53_53)) & finite(B53_53)))
% 64.02/28.30
% 64.02/28.30 [238] ALPHA_NOT_NOT : ~~empty(positive_rationals)
% 64.02/28.30 -> [240] empty(positive_rationals)
% 64.02/28.30
% 64.02/28.30 [240] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [239] DELTA_EXISTS : ? [B53_53] : (((element(B53_53, powerset(positive_rationals)) & ~empty(B53_53)) & finite(B53_53)))
% 64.02/28.30 -> [241] ((element(skolem_B5353(positive_rationals), powerset(positive_rationals)) & ~empty(skolem_B5353(positive_rationals))) & finite(skolem_B5353(positive_rationals)))
% 64.02/28.30
% 64.02/28.30 [241] ALPHA_AND : ((element(skolem_B5353(positive_rationals), powerset(positive_rationals)) & ~empty(skolem_B5353(positive_rationals))) & finite(skolem_B5353(positive_rationals)))
% 64.02/28.30 -> [242] (element(skolem_B5353(positive_rationals), powerset(positive_rationals)) & ~empty(skolem_B5353(positive_rationals))), finite(skolem_B5353(positive_rationals))
% 64.02/28.30
% 64.02/28.30 [242] ALPHA_AND : (element(skolem_B5353(positive_rationals), powerset(positive_rationals)) & ~empty(skolem_B5353(positive_rationals)))
% 64.02/28.30 -> [243] element(skolem_B5353(positive_rationals), powerset(positive_rationals)), ~empty(skolem_B5353(positive_rationals))
% 64.02/28.30
% 64.02/28.30 [243] GAMMA_FORALL : ! [A60_60, B61_61] : (subset(A60_60, A60_60))
% 64.02/28.30 -> [244] subset(A60_0_23, A60_0_23)
% 64.02/28.30
% 64.02/28.30 [244] GAMMA_FORALL : ! [A62_62, B63_63] : (((subset(A62_62, B63_63) & finite(B63_63)) => finite(A62_62)))
% 64.02/28.30 -> [245] ((subset(set_intersection2(skolem_A6464, skolem_B6565), skolem_A6464) & finite(skolem_A6464)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30
% 64.02/28.30 [245] BETA_IMPLY : ((subset(set_intersection2(skolem_A6464, skolem_B6565), skolem_A6464) & finite(skolem_A6464)) => finite(set_intersection2(skolem_A6464, skolem_B6565)))
% 64.02/28.30 -> [246] ~(subset(set_intersection2(skolem_A6464, skolem_B6565), skolem_A6464) & finite(skolem_A6464))
% 64.02/28.30 -> [247] finite(set_intersection2(skolem_A6464, skolem_B6565))
% 64.02/28.30
% 64.02/28.30 [247] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [246] BETA_NOT_AND : ~(subset(set_intersection2(skolem_A6464, skolem_B6565), skolem_A6464) & finite(skolem_A6464))
% 64.02/28.30 -> [250] ~subset(set_intersection2(skolem_A6464, skolem_B6565), skolem_A6464)
% 64.02/28.30 -> [251] ~finite(skolem_A6464)
% 64.02/28.30
% 64.02/28.30 [251] CLOSURE : =
% 64.02/28.30
% 64.02/28.30 [250] GAMMA_FORALL : ! [A66_66, B67_67] : (subset(set_intersection2(A66_66, B67_67), A66_66))
% 64.02/28.30 -> [252] subset(set_intersection2(A66_0_25, B67_0_25), A66_0_25)
% 64.02/28.30
% 64.02/28.30 [252] CLOSURE : subset(set_intersection2(A66_0_25, B67_0_25), A66_0_25)
% 64.02/28.30
% 64.02/28.30 % SZS output end Proof for theBenchmark.p
% 64.02/28.30 [27.958154s][1][Res] 112714 goroutines created
% 64.02/28.30 ==== Result ====
% 64.02/28.30 [27.958207s][1][Res] VALID
% 64.02/28.30 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------