TSTP Solution File: SEU085+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU085+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:55:19 EDT 2022
% Result : Theorem 3.53s 2.20s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU085+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:18:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000049s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.36 Start search
% 0.12/0.36 nb_step : 1 - limit : 62
% 0.12/0.36 Launch Gotab with destructive = true
% 3.53/2.19 % SZS output start Proof for theBenchmark.p
% 3.53/2.20 [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] : (element(B19_19, A18_18))) & ! [A20_20, B21_21] : ((finite(A20_20) => finite(set_difference(A20_20, B21_21)))) & ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)) & ! [A22_22] : (~empty(powerset(A22_22))) & 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)) & ! [A23_23, B24_24] : (((relation(A23_23) & relation(B24_24)) => relation(set_difference(A23_23, B24_24)))) & (empty(empty_set) & relation(empty_set)) & ~empty(positive_rationals) & ? [A25_25] : (((((~empty(A25_25) & epsilon_transitive(A25_25)) & epsilon_connected(A25_25)) & ordinal(A25_25)) & natural(A25_25))) & ? [A26_26] : ((~empty(A26_26) & finite(A26_26))) & ? [A27_27] : (((relation(A27_27) & function(A27_27)) & function_yielding(A27_27))) & ? [A28_28] : ((relation(A28_28) & function(A28_28))) & ? [A29_29] : (((epsilon_transitive(A29_29) & epsilon_connected(A29_29)) & ordinal(A29_29))) & ? [A30_30] : ((((epsilon_transitive(A30_30) & epsilon_connected(A30_30)) & ordinal(A30_30)) & being_limit_ordinal(A30_30))) & ? [A31_31] : ((empty(A31_31) & relation(A31_31))) & ! [A32_32] : ((~empty(A32_32) => ? [B33_33] : ((element(B33_33, powerset(A32_32)) & ~empty(B33_33))))) & ? [A34_34] : (empty(A34_34)) & ? [A35_35] : (((((element(A35_35, positive_rationals) & ~empty(A35_35)) & epsilon_transitive(A35_35)) & epsilon_connected(A35_35)) & ordinal(A35_35))) & ! [A36_36] : (? [B37_37] : ((((((((((element(B37_37, powerset(A36_36)) & empty(B37_37)) & relation(B37_37)) & function(B37_37)) & one_to_one(B37_37)) & epsilon_transitive(B37_37)) & epsilon_connected(B37_37)) & ordinal(B37_37)) & natural(B37_37)) & finite(B37_37)))) & ? [A38_38] : (((relation(A38_38) & empty(A38_38)) & function(A38_38))) & ? [A39_39] : (((((((relation(A39_39) & function(A39_39)) & one_to_one(A39_39)) & empty(A39_39)) & epsilon_transitive(A39_39)) & epsilon_connected(A39_39)) & ordinal(A39_39))) & ? [A40_40] : ((((relation(A40_40) & function(A40_40)) & transfinite_sequence(A40_40)) & ordinal_yielding(A40_40))) & ? [A41_41] : ((~empty(A41_41) & relation(A41_41))) & ! [A42_42] : (? [B43_43] : ((element(B43_43, powerset(A42_42)) & empty(B43_43)))) & ? [A44_44] : (~empty(A44_44)) & ? [A45_45] : ((((((element(A45_45, positive_rationals) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45)) & natural(A45_45))) & ! [A46_46] : ((~empty(A46_46) => ? [B47_47] : (((element(B47_47, powerset(A46_46)) & ~empty(B47_47)) & finite(B47_47))))) & ? [A48_48] : (((relation(A48_48) & function(A48_48)) & one_to_one(A48_48))) & ? [A49_49] : ((((~empty(A49_49) & epsilon_transitive(A49_49)) & epsilon_connected(A49_49)) & ordinal(A49_49))) & ? [A50_50] : ((relation(A50_50) & relation_empty_yielding(A50_50))) & ? [A51_51] : (((relation(A51_51) & relation_empty_yielding(A51_51)) & function(A51_51))) & ? [A52_52] : (((relation(A52_52) & function(A52_52)) & transfinite_sequence(A52_52))) & ? [A53_53] : (((relation(A53_53) & relation_non_empty(A53_53)) & function(A53_53))) & ! [A54_54, B55_55] : (subset(A54_54, A54_54)) & ! [A56_56, B57_57] : (((subset(A56_56, B57_57) & finite(B57_57)) => finite(A56_56))) & ! [A60_60, B61_61] : ((in(A60_60, B61_61) => element(A60_60, B61_61))) & ! [A62_62, B63_63] : ((element(A62_62, B63_63) => (empty(B63_63) | in(A62_62, B63_63)))) & ! [A64_64, B65_65] : (subset(set_difference(A64_64, B65_65), A64_64)) & ! [A66_66] : (=(set_difference(A66_66, empty_set), A66_66)) & ! [A67_67, B68_68] : ((element(A67_67, powerset(B68_68)) <=> subset(A67_67, B68_68))) & ! [A69_69] : (=(set_difference(empty_set, A69_69), empty_set)) & ! [A70_70, B71_71, C72_72] : (((in(A70_70, B71_71) & element(B71_71, powerset(C72_72))) => element(A70_70, C72_72))) & ! [A73_73, B74_74, C75_75] : (~((in(A73_73, B74_74) & element(B74_74, powerset(C75_75))) & empty(C75_75))) & ! [A76_76] : ((empty(A76_76) => =(A76_76, empty_set))) & ! [A77_77, B78_78] : (~(in(A77_77, B78_78) & empty(B78_78))) & ! [A79_79, B80_80] : (~((empty(A79_79) & ~=(A79_79, B80_80)) & empty(B80_80))) & ~! [A58_58, B59_59] : ((finite(A58_58) => finite(set_difference(A58_58, B59_59)))))
% 3.53/2.20 -> [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] : (element(B19_19, A18_18))), ! [A20_20, B21_21] : ((finite(A20_20) => finite(set_difference(A20_20, B21_21)))), ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), ! [A22_22] : (~empty(powerset(A22_22))), 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)), ! [A23_23, B24_24] : (((relation(A23_23) & relation(B24_24)) => relation(set_difference(A23_23, B24_24)))), (empty(empty_set) & relation(empty_set)), ~empty(positive_rationals), ? [A25_25] : (((((~empty(A25_25) & epsilon_transitive(A25_25)) & epsilon_connected(A25_25)) & ordinal(A25_25)) & natural(A25_25))), ? [A26_26] : ((~empty(A26_26) & finite(A26_26))), ? [A27_27] : (((relation(A27_27) & function(A27_27)) & function_yielding(A27_27))), ? [A28_28] : ((relation(A28_28) & function(A28_28))), ? [A29_29] : (((epsilon_transitive(A29_29) & epsilon_connected(A29_29)) & ordinal(A29_29))), ? [A30_30] : ((((epsilon_transitive(A30_30) & epsilon_connected(A30_30)) & ordinal(A30_30)) & being_limit_ordinal(A30_30))), ? [A31_31] : ((empty(A31_31) & relation(A31_31))), ! [A32_32] : ((~empty(A32_32) => ? [B33_33] : ((element(B33_33, powerset(A32_32)) & ~empty(B33_33))))), ? [A34_34] : (empty(A34_34)), ? [A35_35] : (((((element(A35_35, positive_rationals) & ~empty(A35_35)) & epsilon_transitive(A35_35)) & epsilon_connected(A35_35)) & ordinal(A35_35))), ! [A36_36] : (? [B37_37] : ((((((((((element(B37_37, powerset(A36_36)) & empty(B37_37)) & relation(B37_37)) & function(B37_37)) & one_to_one(B37_37)) & epsilon_transitive(B37_37)) & epsilon_connected(B37_37)) & ordinal(B37_37)) & natural(B37_37)) & finite(B37_37)))), ? [A38_38] : (((relation(A38_38) & empty(A38_38)) & function(A38_38))), ? [A39_39] : (((((((relation(A39_39) & function(A39_39)) & one_to_one(A39_39)) & empty(A39_39)) & epsilon_transitive(A39_39)) & epsilon_connected(A39_39)) & ordinal(A39_39))), ? [A40_40] : ((((relation(A40_40) & function(A40_40)) & transfinite_sequence(A40_40)) & ordinal_yielding(A40_40))), ? [A41_41] : ((~empty(A41_41) & relation(A41_41))), ! [A42_42] : (? [B43_43] : ((element(B43_43, powerset(A42_42)) & empty(B43_43)))), ? [A44_44] : (~empty(A44_44)), ? [A45_45] : ((((((element(A45_45, positive_rationals) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45)) & natural(A45_45))), ! [A46_46] : ((~empty(A46_46) => ? [B47_47] : (((element(B47_47, powerset(A46_46)) & ~empty(B47_47)) & finite(B47_47))))), ? [A48_48] : (((relation(A48_48) & function(A48_48)) & one_to_one(A48_48))), ? [A49_49] : ((((~empty(A49_49) & epsilon_transitive(A49_49)) & epsilon_connected(A49_49)) & ordinal(A49_49))), ? [A50_50] : ((relation(A50_50) & relation_empty_yielding(A50_50))), ? [A51_51] : (((relation(A51_51) & relation_empty_yielding(A51_51)) & function(A51_51))), ? [A52_52] : (((relation(A52_52) & function(A52_52)) & transfinite_sequence(A52_52))), ? [A53_53] : (((relation(A53_53) & relation_non_empty(A53_53)) & function(A53_53))), ! [A54_54, B55_55] : (subset(A54_54, A54_54)), ! [A56_56, B57_57] : (((subset(A56_56, B57_57) & finite(B57_57)) => finite(A56_56))), ! [A60_60, B61_61] : ((in(A60_60, B61_61) => element(A60_60, B61_61))), ! [A62_62, B63_63] : ((element(A62_62, B63_63) => (empty(B63_63) | in(A62_62, B63_63)))), ! [A64_64, B65_65] : (subset(set_difference(A64_64, B65_65), A64_64)), ! [A66_66] : (=(set_difference(A66_66, empty_set), A66_66)), ! [A67_67, B68_68] : ((element(A67_67, powerset(B68_68)) <=> subset(A67_67, B68_68))), ! [A69_69] : (=(set_difference(empty_set, A69_69), empty_set)), ! [A70_70, B71_71, C72_72] : (((in(A70_70, B71_71) & element(B71_71, powerset(C72_72))) => element(A70_70, C72_72))), ! [A73_73, B74_74, C75_75] : (~((in(A73_73, B74_74) & element(B74_74, powerset(C75_75))) & empty(C75_75))), ! [A76_76] : ((empty(A76_76) => =(A76_76, empty_set))), ! [A77_77, B78_78] : (~(in(A77_77, B78_78) & empty(B78_78))), ! [A79_79, B80_80] : (~((empty(A79_79) & ~=(A79_79, B80_80)) & empty(B80_80))), ~! [A58_58, B59_59] : ((finite(A58_58) => finite(set_difference(A58_58, B59_59))))
% 3.53/2.20
% 3.53/2.20 [1] ALPHA_AND : ((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set))
% 3.53/2.20 -> [2] (empty(empty_set) & relation(empty_set)), relation_empty_yielding(empty_set)
% 3.53/2.20
% 3.53/2.20 [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))
% 3.53/2.20 -> [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)
% 3.53/2.20
% 3.53/2.20 [3] ALPHA_AND : (empty(empty_set) & relation(empty_set))
% 3.53/2.20 -> [4] empty(empty_set), relation(empty_set)
% 3.53/2.20
% 3.53/2.20 [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))
% 3.53/2.20 -> [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)
% 3.53/2.20
% 3.53/2.20 [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))
% 3.53/2.20 -> [6] ((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)), epsilon_transitive(empty_set)
% 3.53/2.20
% 3.53/2.20 [6] ALPHA_AND : ((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set))
% 3.53/2.20 -> [7] (((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)), empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [7] ALPHA_AND : (((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set))
% 3.53/2.20 -> [8] ((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)), one_to_one(empty_set)
% 3.53/2.20
% 3.53/2.20 [8] ALPHA_AND : ((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set))
% 3.53/2.20 -> [9] (relation(empty_set) & relation_empty_yielding(empty_set)), function(empty_set)
% 3.53/2.20
% 3.53/2.20 [9] ALPHA_AND : (relation(empty_set) & relation_empty_yielding(empty_set))
% 3.53/2.20 -> [10] relation(empty_set), relation_empty_yielding(empty_set)
% 3.53/2.20
% 3.53/2.20 [10] DELTA_EXISTS : ? [A25_25] : (((((~empty(A25_25) & epsilon_transitive(A25_25)) & epsilon_connected(A25_25)) & ordinal(A25_25)) & natural(A25_25)))
% 3.53/2.20 -> [11] ((((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525)) & ordinal(skolem_A2525)) & natural(skolem_A2525))
% 3.53/2.20
% 3.53/2.20 [11] ALPHA_AND : ((((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525)) & ordinal(skolem_A2525)) & natural(skolem_A2525))
% 3.53/2.20 -> [12] (((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525)) & ordinal(skolem_A2525)), natural(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [12] ALPHA_AND : (((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525)) & ordinal(skolem_A2525))
% 3.53/2.20 -> [13] ((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525)), ordinal(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [13] ALPHA_AND : ((~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)) & epsilon_connected(skolem_A2525))
% 3.53/2.20 -> [14] (~empty(skolem_A2525) & epsilon_transitive(skolem_A2525)), epsilon_connected(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [14] ALPHA_AND : (~empty(skolem_A2525) & epsilon_transitive(skolem_A2525))
% 3.53/2.20 -> [15] ~empty(skolem_A2525), epsilon_transitive(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [15] DELTA_EXISTS : ? [A26_26] : ((~empty(A26_26) & finite(A26_26)))
% 3.53/2.20 -> [16] (~empty(skolem_A2626) & finite(skolem_A2626))
% 3.53/2.20
% 3.53/2.20 [16] ALPHA_AND : (~empty(skolem_A2626) & finite(skolem_A2626))
% 3.53/2.20 -> [17] ~empty(skolem_A2626), finite(skolem_A2626)
% 3.53/2.20
% 3.53/2.20 [17] DELTA_EXISTS : ? [A27_27] : (((relation(A27_27) & function(A27_27)) & function_yielding(A27_27)))
% 3.53/2.20 -> [18] ((relation(skolem_A2727) & function(skolem_A2727)) & function_yielding(skolem_A2727))
% 3.53/2.20
% 3.53/2.20 [18] ALPHA_AND : ((relation(skolem_A2727) & function(skolem_A2727)) & function_yielding(skolem_A2727))
% 3.53/2.20 -> [19] (relation(skolem_A2727) & function(skolem_A2727)), function_yielding(skolem_A2727)
% 3.53/2.20
% 3.53/2.20 [19] ALPHA_AND : (relation(skolem_A2727) & function(skolem_A2727))
% 3.53/2.20 -> [20] relation(skolem_A2727), function(skolem_A2727)
% 3.53/2.20
% 3.53/2.20 [20] DELTA_EXISTS : ? [A28_28] : ((relation(A28_28) & function(A28_28)))
% 3.53/2.20 -> [21] (relation(skolem_A2828) & function(skolem_A2828))
% 3.53/2.20
% 3.53/2.20 [21] ALPHA_AND : (relation(skolem_A2828) & function(skolem_A2828))
% 3.53/2.20 -> [22] relation(skolem_A2828), function(skolem_A2828)
% 3.53/2.20
% 3.53/2.20 [22] DELTA_EXISTS : ? [A29_29] : (((epsilon_transitive(A29_29) & epsilon_connected(A29_29)) & ordinal(A29_29)))
% 3.53/2.20 -> [23] ((epsilon_transitive(skolem_A2929) & epsilon_connected(skolem_A2929)) & ordinal(skolem_A2929))
% 3.53/2.20
% 3.53/2.20 [23] ALPHA_AND : ((epsilon_transitive(skolem_A2929) & epsilon_connected(skolem_A2929)) & ordinal(skolem_A2929))
% 3.53/2.20 -> [24] (epsilon_transitive(skolem_A2929) & epsilon_connected(skolem_A2929)), ordinal(skolem_A2929)
% 3.53/2.20
% 3.53/2.20 [24] ALPHA_AND : (epsilon_transitive(skolem_A2929) & epsilon_connected(skolem_A2929))
% 3.53/2.20 -> [25] epsilon_transitive(skolem_A2929), epsilon_connected(skolem_A2929)
% 3.53/2.20
% 3.53/2.20 [25] DELTA_EXISTS : ? [A30_30] : ((((epsilon_transitive(A30_30) & epsilon_connected(A30_30)) & ordinal(A30_30)) & being_limit_ordinal(A30_30)))
% 3.53/2.20 -> [26] (((epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030)) & ordinal(skolem_A3030)) & being_limit_ordinal(skolem_A3030))
% 3.53/2.20
% 3.53/2.20 [26] ALPHA_AND : (((epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030)) & ordinal(skolem_A3030)) & being_limit_ordinal(skolem_A3030))
% 3.53/2.20 -> [27] ((epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030)) & ordinal(skolem_A3030)), being_limit_ordinal(skolem_A3030)
% 3.53/2.20
% 3.53/2.20 [27] ALPHA_AND : ((epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030)) & ordinal(skolem_A3030))
% 3.53/2.20 -> [28] (epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030)), ordinal(skolem_A3030)
% 3.53/2.20
% 3.53/2.20 [28] ALPHA_AND : (epsilon_transitive(skolem_A3030) & epsilon_connected(skolem_A3030))
% 3.53/2.20 -> [29] epsilon_transitive(skolem_A3030), epsilon_connected(skolem_A3030)
% 3.53/2.20
% 3.53/2.20 [29] DELTA_EXISTS : ? [A31_31] : ((empty(A31_31) & relation(A31_31)))
% 3.53/2.20 -> [30] (empty(skolem_A3131) & relation(skolem_A3131))
% 3.53/2.20
% 3.53/2.20 [30] ALPHA_AND : (empty(skolem_A3131) & relation(skolem_A3131))
% 3.53/2.20 -> [31] empty(skolem_A3131), relation(skolem_A3131)
% 3.53/2.20
% 3.53/2.20 [31] DELTA_EXISTS : ? [A34_34] : (empty(A34_34))
% 3.53/2.20 -> [32] empty(skolem_A3434)
% 3.53/2.20
% 3.53/2.20 [32] DELTA_EXISTS : ? [A35_35] : (((((element(A35_35, positive_rationals) & ~empty(A35_35)) & epsilon_transitive(A35_35)) & epsilon_connected(A35_35)) & ordinal(A35_35)))
% 3.53/2.20 -> [33] ((((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535)) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 3.53/2.20
% 3.53/2.20 [33] ALPHA_AND : ((((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535)) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 3.53/2.20 -> [34] (((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535)) & epsilon_connected(skolem_A3535)), ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [34] ALPHA_AND : (((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535)) & epsilon_connected(skolem_A3535))
% 3.53/2.20 -> [35] ((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535)), epsilon_connected(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [35] ALPHA_AND : ((element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)) & epsilon_transitive(skolem_A3535))
% 3.53/2.20 -> [36] (element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535)), epsilon_transitive(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [36] ALPHA_AND : (element(skolem_A3535, positive_rationals) & ~empty(skolem_A3535))
% 3.53/2.20 -> [37] element(skolem_A3535, positive_rationals), ~empty(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [37] DELTA_EXISTS : ? [A38_38] : (((relation(A38_38) & empty(A38_38)) & function(A38_38)))
% 3.53/2.20 -> [38] ((relation(skolem_A3838) & empty(skolem_A3838)) & function(skolem_A3838))
% 3.53/2.20
% 3.53/2.20 [38] ALPHA_AND : ((relation(skolem_A3838) & empty(skolem_A3838)) & function(skolem_A3838))
% 3.53/2.20 -> [39] (relation(skolem_A3838) & empty(skolem_A3838)), function(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [39] ALPHA_AND : (relation(skolem_A3838) & empty(skolem_A3838))
% 3.53/2.20 -> [40] relation(skolem_A3838), empty(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [40] DELTA_EXISTS : ? [A39_39] : (((((((relation(A39_39) & function(A39_39)) & one_to_one(A39_39)) & empty(A39_39)) & epsilon_transitive(A39_39)) & epsilon_connected(A39_39)) & ordinal(A39_39)))
% 3.53/2.20 -> [41] ((((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939)) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939))
% 3.53/2.20
% 3.53/2.20 [41] ALPHA_AND : ((((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939)) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939))
% 3.53/2.20 -> [42] (((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939)) & epsilon_connected(skolem_A3939)), ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [42] ALPHA_AND : (((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939)) & epsilon_connected(skolem_A3939))
% 3.53/2.20 -> [43] ((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939)), epsilon_connected(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [43] ALPHA_AND : ((((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)) & epsilon_transitive(skolem_A3939))
% 3.53/2.20 -> [44] (((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939)), epsilon_transitive(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [44] ALPHA_AND : (((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)) & empty(skolem_A3939))
% 3.53/2.20 -> [45] ((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939)), empty(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [45] ALPHA_AND : ((relation(skolem_A3939) & function(skolem_A3939)) & one_to_one(skolem_A3939))
% 3.53/2.20 -> [46] (relation(skolem_A3939) & function(skolem_A3939)), one_to_one(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [46] ALPHA_AND : (relation(skolem_A3939) & function(skolem_A3939))
% 3.53/2.20 -> [47] relation(skolem_A3939), function(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [47] DELTA_EXISTS : ? [A40_40] : ((((relation(A40_40) & function(A40_40)) & transfinite_sequence(A40_40)) & ordinal_yielding(A40_40)))
% 3.53/2.20 -> [48] (((relation(skolem_A4040) & function(skolem_A4040)) & transfinite_sequence(skolem_A4040)) & ordinal_yielding(skolem_A4040))
% 3.53/2.20
% 3.53/2.20 [48] ALPHA_AND : (((relation(skolem_A4040) & function(skolem_A4040)) & transfinite_sequence(skolem_A4040)) & ordinal_yielding(skolem_A4040))
% 3.53/2.20 -> [49] ((relation(skolem_A4040) & function(skolem_A4040)) & transfinite_sequence(skolem_A4040)), ordinal_yielding(skolem_A4040)
% 3.53/2.20
% 3.53/2.20 [49] ALPHA_AND : ((relation(skolem_A4040) & function(skolem_A4040)) & transfinite_sequence(skolem_A4040))
% 3.53/2.20 -> [50] (relation(skolem_A4040) & function(skolem_A4040)), transfinite_sequence(skolem_A4040)
% 3.53/2.20
% 3.53/2.20 [50] ALPHA_AND : (relation(skolem_A4040) & function(skolem_A4040))
% 3.53/2.20 -> [51] relation(skolem_A4040), function(skolem_A4040)
% 3.53/2.20
% 3.53/2.20 [51] DELTA_EXISTS : ? [A41_41] : ((~empty(A41_41) & relation(A41_41)))
% 3.53/2.20 -> [52] (~empty(skolem_A4141) & relation(skolem_A4141))
% 3.53/2.20
% 3.53/2.20 [52] ALPHA_AND : (~empty(skolem_A4141) & relation(skolem_A4141))
% 3.53/2.20 -> [53] ~empty(skolem_A4141), relation(skolem_A4141)
% 3.53/2.20
% 3.53/2.20 [53] DELTA_EXISTS : ? [A44_44] : (~empty(A44_44))
% 3.53/2.20 -> [54] ~empty(skolem_A4444)
% 3.53/2.20
% 3.53/2.20 [54] DELTA_EXISTS : ? [A45_45] : ((((((element(A45_45, positive_rationals) & empty(A45_45)) & epsilon_transitive(A45_45)) & epsilon_connected(A45_45)) & ordinal(A45_45)) & natural(A45_45)))
% 3.53/2.20 -> [55] (((((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545)) & natural(skolem_A4545))
% 3.53/2.20
% 3.53/2.20 [55] ALPHA_AND : (((((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545)) & natural(skolem_A4545))
% 3.53/2.20 -> [56] ((((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545)), natural(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [56] ALPHA_AND : ((((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545))
% 3.53/2.20 -> [57] (((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545)), ordinal(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [57] ALPHA_AND : (((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)) & epsilon_connected(skolem_A4545))
% 3.53/2.20 -> [58] ((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545)), epsilon_connected(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [58] ALPHA_AND : ((element(skolem_A4545, positive_rationals) & empty(skolem_A4545)) & epsilon_transitive(skolem_A4545))
% 3.53/2.20 -> [59] (element(skolem_A4545, positive_rationals) & empty(skolem_A4545)), epsilon_transitive(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [59] ALPHA_AND : (element(skolem_A4545, positive_rationals) & empty(skolem_A4545))
% 3.53/2.20 -> [60] element(skolem_A4545, positive_rationals), empty(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [60] DELTA_EXISTS : ? [A48_48] : (((relation(A48_48) & function(A48_48)) & one_to_one(A48_48)))
% 3.53/2.20 -> [61] ((relation(skolem_A4848) & function(skolem_A4848)) & one_to_one(skolem_A4848))
% 3.53/2.20
% 3.53/2.20 [61] ALPHA_AND : ((relation(skolem_A4848) & function(skolem_A4848)) & one_to_one(skolem_A4848))
% 3.53/2.20 -> [62] (relation(skolem_A4848) & function(skolem_A4848)), one_to_one(skolem_A4848)
% 3.53/2.20
% 3.53/2.20 [62] ALPHA_AND : (relation(skolem_A4848) & function(skolem_A4848))
% 3.53/2.20 -> [63] relation(skolem_A4848), function(skolem_A4848)
% 3.53/2.20
% 3.53/2.20 [63] DELTA_EXISTS : ? [A49_49] : ((((~empty(A49_49) & epsilon_transitive(A49_49)) & epsilon_connected(A49_49)) & ordinal(A49_49)))
% 3.53/2.20 -> [64] (((~empty(skolem_A4949) & epsilon_transitive(skolem_A4949)) & epsilon_connected(skolem_A4949)) & ordinal(skolem_A4949))
% 3.53/2.20
% 3.53/2.20 [64] ALPHA_AND : (((~empty(skolem_A4949) & epsilon_transitive(skolem_A4949)) & epsilon_connected(skolem_A4949)) & ordinal(skolem_A4949))
% 3.53/2.20 -> [65] ((~empty(skolem_A4949) & epsilon_transitive(skolem_A4949)) & epsilon_connected(skolem_A4949)), ordinal(skolem_A4949)
% 3.53/2.20
% 3.53/2.20 [65] ALPHA_AND : ((~empty(skolem_A4949) & epsilon_transitive(skolem_A4949)) & epsilon_connected(skolem_A4949))
% 3.53/2.20 -> [66] (~empty(skolem_A4949) & epsilon_transitive(skolem_A4949)), epsilon_connected(skolem_A4949)
% 3.53/2.20
% 3.53/2.20 [66] ALPHA_AND : (~empty(skolem_A4949) & epsilon_transitive(skolem_A4949))
% 3.53/2.20 -> [67] ~empty(skolem_A4949), epsilon_transitive(skolem_A4949)
% 3.53/2.20
% 3.53/2.20 [67] DELTA_EXISTS : ? [A50_50] : ((relation(A50_50) & relation_empty_yielding(A50_50)))
% 3.53/2.20 -> [68] (relation(skolem_A5050) & relation_empty_yielding(skolem_A5050))
% 3.53/2.20
% 3.53/2.20 [68] ALPHA_AND : (relation(skolem_A5050) & relation_empty_yielding(skolem_A5050))
% 3.53/2.20 -> [69] relation(skolem_A5050), relation_empty_yielding(skolem_A5050)
% 3.53/2.20
% 3.53/2.20 [69] DELTA_EXISTS : ? [A51_51] : (((relation(A51_51) & relation_empty_yielding(A51_51)) & function(A51_51)))
% 3.53/2.20 -> [70] ((relation(skolem_A5151) & relation_empty_yielding(skolem_A5151)) & function(skolem_A5151))
% 3.53/2.20
% 3.53/2.20 [70] ALPHA_AND : ((relation(skolem_A5151) & relation_empty_yielding(skolem_A5151)) & function(skolem_A5151))
% 3.53/2.20 -> [71] (relation(skolem_A5151) & relation_empty_yielding(skolem_A5151)), function(skolem_A5151)
% 3.53/2.20
% 3.53/2.20 [71] ALPHA_AND : (relation(skolem_A5151) & relation_empty_yielding(skolem_A5151))
% 3.53/2.20 -> [72] relation(skolem_A5151), relation_empty_yielding(skolem_A5151)
% 3.53/2.20
% 3.53/2.20 [72] DELTA_EXISTS : ? [A52_52] : (((relation(A52_52) & function(A52_52)) & transfinite_sequence(A52_52)))
% 3.53/2.20 -> [73] ((relation(skolem_A5252) & function(skolem_A5252)) & transfinite_sequence(skolem_A5252))
% 3.53/2.20
% 3.53/2.20 [73] ALPHA_AND : ((relation(skolem_A5252) & function(skolem_A5252)) & transfinite_sequence(skolem_A5252))
% 3.53/2.20 -> [74] (relation(skolem_A5252) & function(skolem_A5252)), transfinite_sequence(skolem_A5252)
% 3.53/2.20
% 3.53/2.20 [74] ALPHA_AND : (relation(skolem_A5252) & function(skolem_A5252))
% 3.53/2.20 -> [75] relation(skolem_A5252), function(skolem_A5252)
% 3.53/2.20
% 3.53/2.20 [75] DELTA_EXISTS : ? [A53_53] : (((relation(A53_53) & relation_non_empty(A53_53)) & function(A53_53)))
% 3.53/2.20 -> [76] ((relation(skolem_A5353) & relation_non_empty(skolem_A5353)) & function(skolem_A5353))
% 3.53/2.20
% 3.53/2.20 [76] ALPHA_AND : ((relation(skolem_A5353) & relation_non_empty(skolem_A5353)) & function(skolem_A5353))
% 3.53/2.20 -> [77] (relation(skolem_A5353) & relation_non_empty(skolem_A5353)), function(skolem_A5353)
% 3.53/2.20
% 3.53/2.20 [77] ALPHA_AND : (relation(skolem_A5353) & relation_non_empty(skolem_A5353))
% 3.53/2.20 -> [78] relation(skolem_A5353), relation_non_empty(skolem_A5353)
% 3.53/2.20
% 3.53/2.20 [78] DELTA_NOT_FORALL : ~! [A58_58, B59_59] : ((finite(A58_58) => finite(set_difference(A58_58, B59_59))))
% 3.53/2.20 -> [79] ~(finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20
% 3.53/2.20 [79] ALPHA_NOT_IMPLY : ~(finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20 -> [80] finite(skolem_A5858), ~finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [80] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 3.53/2.20 -> [81] (in(A3_0_0, B4_0_0) => ~in(B4_0_0, A3_0_0))
% 3.53/2.20
% 3.53/2.20 [81] BETA_IMPLY : (in(A3_0_0, B4_0_0) => ~in(B4_0_0, A3_0_0))
% 3.53/2.20 -> [82] ~in(A3_0_0, B4_0_0)
% 3.53/2.20 -> [83] ~in(B4_0_0, A3_0_0)
% 3.53/2.20
% 3.53/2.20 [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))))))
% 3.53/2.20 -> [84] (ordinal(skolem_A3535) => ! [B6_6] : ((element(B6_6, skolem_A3535) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 3.53/2.20
% 3.53/2.20 [84] BETA_IMPLY : (ordinal(skolem_A3535) => ! [B6_6] : ((element(B6_6, skolem_A3535) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 3.53/2.20 -> [85] ~ordinal(skolem_A3535)
% 3.53/2.20 -> [86] ! [B6_6] : ((element(B6_6, skolem_A3535) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))
% 3.53/2.20
% 3.53/2.20 [85] CLOSURE : ~ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [86] GAMMA_FORALL : ! [A7_7] : ((empty(A7_7) => finite(A7_7)))
% 3.53/2.20 -> [90] (empty(set_difference(skolem_A5858, skolem_B5959)) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20
% 3.53/2.20 [90] BETA_IMPLY : (empty(set_difference(skolem_A5858, skolem_B5959)) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20 -> [91] ~empty(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20 -> [92] finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [92] CLOSURE : finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [91] GAMMA_FORALL : ! [A8_8] : ((empty(A8_8) => function(A8_8)))
% 3.53/2.20 -> [97] (empty(skolem_A3838) => function(skolem_A3838))
% 3.53/2.20
% 3.53/2.20 [97] BETA_IMPLY : (empty(skolem_A3838) => function(skolem_A3838))
% 3.53/2.20 -> [100] ~empty(skolem_A3838)
% 3.53/2.20 -> [101] function(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [100] CLOSURE : ~empty(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [101] GAMMA_FORALL : ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9))))
% 3.53/2.20 -> [103] (ordinal(skolem_A2525) => (epsilon_transitive(skolem_A2525) & epsilon_connected(skolem_A2525)))
% 3.53/2.20
% 3.53/2.20 [103] BETA_IMPLY : (ordinal(skolem_A2525) => (epsilon_transitive(skolem_A2525) & epsilon_connected(skolem_A2525)))
% 3.53/2.20 -> [106] ~ordinal(skolem_A2525)
% 3.53/2.20 -> [107] (epsilon_transitive(skolem_A2525) & epsilon_connected(skolem_A2525))
% 3.53/2.20
% 3.53/2.20 [106] CLOSURE : ~ordinal(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [107] ALPHA_AND : (epsilon_transitive(skolem_A2525) & epsilon_connected(skolem_A2525))
% 3.53/2.20 -> [109] epsilon_transitive(skolem_A2525), epsilon_connected(skolem_A2525)
% 3.53/2.20
% 3.53/2.20 [109] GAMMA_FORALL : ! [A10_10] : ((empty(A10_10) => relation(A10_10)))
% 3.53/2.20 -> [110] (empty(skolem_A3838) => relation(skolem_A3838))
% 3.53/2.20
% 3.53/2.20 [110] BETA_IMPLY : (empty(skolem_A3838) => relation(skolem_A3838))
% 3.53/2.20 -> [112] ~empty(skolem_A3838)
% 3.53/2.20 -> [113] relation(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [112] CLOSURE : ~empty(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [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))))
% 3.53/2.20 -> [116] ((empty(empty_set) & ordinal(empty_set)) => (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set)))
% 3.53/2.20
% 3.53/2.20 [116] BETA_IMPLY : ((empty(empty_set) & ordinal(empty_set)) => (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set)))
% 3.53/2.20 -> [117] ~(empty(empty_set) & ordinal(empty_set))
% 3.53/2.20 -> [118] (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set))
% 3.53/2.20
% 3.53/2.20 [117] BETA_NOT_AND : ~(empty(empty_set) & ordinal(empty_set))
% 3.53/2.20 -> [122] ~empty(empty_set)
% 3.53/2.20 -> [123] ~ordinal(empty_set)
% 3.53/2.20
% 3.53/2.20 [122] CLOSURE : ~empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [123] CLOSURE : ~ordinal(empty_set)
% 3.53/2.20
% 3.53/2.20 [118] ALPHA_AND : (((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)) & natural(empty_set))
% 3.53/2.20 -> [124] ((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set)), natural(empty_set)
% 3.53/2.20
% 3.53/2.20 [124] ALPHA_AND : ((epsilon_transitive(empty_set) & epsilon_connected(empty_set)) & ordinal(empty_set))
% 3.53/2.20 -> [128] (epsilon_transitive(empty_set) & epsilon_connected(empty_set)), ordinal(empty_set)
% 3.53/2.20
% 3.53/2.20 [128] ALPHA_AND : (epsilon_transitive(empty_set) & epsilon_connected(empty_set))
% 3.53/2.20 -> [130] epsilon_transitive(empty_set), epsilon_connected(empty_set)
% 3.53/2.20
% 3.53/2.20 [130] GAMMA_FORALL : ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13)))))
% 3.53/2.20 -> [132] (finite(skolem_A2626) => ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13))))
% 3.53/2.20
% 3.53/2.20 [132] BETA_IMPLY : (finite(skolem_A2626) => ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13))))
% 3.53/2.20 -> [134] ~finite(skolem_A2626)
% 3.53/2.20 -> [135] ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13)))
% 3.53/2.20
% 3.53/2.20 [134] CLOSURE : ~finite(skolem_A2626)
% 3.53/2.20
% 3.53/2.20 [135] GAMMA_FORALL : ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14))))
% 3.53/2.20 -> [138] (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 3.53/2.20
% 3.53/2.20 [138] BETA_IMPLY : (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 3.53/2.20 -> [140] ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 3.53/2.20 -> [141] ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 3.53/2.20
% 3.53/2.20 [140] BETA_NOT_AND : ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 3.53/2.20 -> [144] ~(relation(empty_set) & empty(empty_set))
% 3.53/2.20 -> [145] ~function(empty_set)
% 3.53/2.20
% 3.53/2.20 [145] CLOSURE : ~function(empty_set)
% 3.53/2.20
% 3.53/2.20 [144] BETA_NOT_AND : ~(relation(empty_set) & empty(empty_set))
% 3.53/2.20 -> [150] ~relation(empty_set)
% 3.53/2.20 -> [151] ~empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [151] CLOSURE : ~empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [150] CLOSURE : ~relation(empty_set)
% 3.53/2.20
% 3.53/2.20 [141] ALPHA_AND : ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 3.53/2.20 -> [146] (relation(empty_set) & function(empty_set)), one_to_one(empty_set)
% 3.53/2.20
% 3.53/2.20 [146] ALPHA_AND : (relation(empty_set) & function(empty_set))
% 3.53/2.20 -> [154] relation(empty_set), function(empty_set)
% 3.53/2.20
% 3.53/2.20 [154] GAMMA_FORALL : ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15)))
% 3.53/2.20 -> [156] ((epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9)) => ordinal(A15_0_9))
% 3.53/2.20
% 3.53/2.20 [156] BETA_IMPLY : ((epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9)) => ordinal(A15_0_9))
% 3.53/2.20 -> [157] ~(epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9))
% 3.53/2.20 -> [158] ordinal(A15_0_9)
% 3.53/2.20
% 3.53/2.20 [157] BETA_NOT_AND : ~(epsilon_transitive(A15_0_9) & epsilon_connected(A15_0_9))
% 3.53/2.20 -> [160] ~epsilon_transitive(A15_0_9)
% 3.53/2.20 -> [161] ~epsilon_connected(A15_0_9)
% 3.53/2.20
% 3.53/2.20 [160] CLOSURE : ~epsilon_transitive(A15_0_9)
% 3.53/2.20
% 3.53/2.20 [161] CLOSURE : ~epsilon_connected(A15_0_9)
% 3.53/2.20
% 3.53/2.20 [158] GAMMA_FORALL : ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16))))
% 3.53/2.20 -> [166] (empty(skolem_A4545) => ((epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545)))
% 3.53/2.20
% 3.53/2.20 [166] BETA_IMPLY : (empty(skolem_A4545) => ((epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545)))
% 3.53/2.20 -> [167] ~empty(skolem_A4545)
% 3.53/2.20 -> [168] ((epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545))
% 3.53/2.20
% 3.53/2.20 [167] CLOSURE : ~empty(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [168] ALPHA_AND : ((epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)) & ordinal(skolem_A4545))
% 3.53/2.20 -> [169] (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545)), ordinal(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [169] ALPHA_AND : (epsilon_transitive(skolem_A4545) & epsilon_connected(skolem_A4545))
% 3.53/2.20 -> [171] epsilon_transitive(skolem_A4545), epsilon_connected(skolem_A4545)
% 3.53/2.20
% 3.53/2.20 [171] 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)))))
% 3.53/2.20 -> [175] (element(skolem_A3535, positive_rationals) => (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))))
% 3.53/2.20
% 3.53/2.20 [175] BETA_IMPLY : (element(skolem_A3535, positive_rationals) => (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))))
% 3.53/2.20 -> [176] ~element(skolem_A3535, positive_rationals)
% 3.53/2.20 -> [177] (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535)))
% 3.53/2.20
% 3.53/2.20 [176] CLOSURE : ~element(skolem_A3535, positive_rationals)
% 3.53/2.20
% 3.53/2.20 [177] BETA_IMPLY : (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535)))
% 3.53/2.20 -> [179] ~ordinal(skolem_A3535)
% 3.53/2.20 -> [180] (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))
% 3.53/2.20
% 3.53/2.20 [179] CLOSURE : ~ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [180] ALPHA_AND : (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))
% 3.53/2.20 -> [181] ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)), natural(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [181] ALPHA_AND : ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 3.53/2.20 -> [183] (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)), ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [183] ALPHA_AND : (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535))
% 3.53/2.20 -> [189] epsilon_transitive(skolem_A3535), epsilon_connected(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [189] GAMMA_FORALL : ! [A18_18] : (? [B19_19] : (element(B19_19, A18_18)))
% 3.53/2.20 -> [191] ? [B19_19] : (element(B19_19, A18_0_12))
% 3.53/2.20
% 3.53/2.20 [191] DELTA_EXISTS : ? [B19_19] : (element(B19_19, A18_0_12))
% 3.53/2.20 -> [193] element(skolem_B1919(A18_0_12), A18_0_12)
% 3.53/2.20
% 3.53/2.20 [193] GAMMA_FORALL : ! [A20_20, B21_21] : ((finite(A20_20) => finite(set_difference(A20_20, B21_21))))
% 3.53/2.20 -> [195] (finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20
% 3.53/2.20 [195] BETA_IMPLY : (finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20 -> [196] ~finite(skolem_A5858)
% 3.53/2.20 -> [197] finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [197] CLOSURE : finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [196] CLOSURE : ~finite(skolem_A5858)
% 3.53/2.20
% 3.53/2.20 [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))))))
% 3.53/2.20 -> [87] (ordinal(skolem_A3939) => ! [B6_6] : ((element(B6_6, skolem_A3939) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 3.53/2.20
% 3.53/2.20 [87] BETA_IMPLY : (ordinal(skolem_A3939) => ! [B6_6] : ((element(B6_6, skolem_A3939) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6)))))
% 3.53/2.20 -> [88] ~ordinal(skolem_A3939)
% 3.53/2.20 -> [89] ! [B6_6] : ((element(B6_6, skolem_A3939) => ((epsilon_transitive(B6_6) & epsilon_connected(B6_6)) & ordinal(B6_6))))
% 3.53/2.20
% 3.53/2.20 [88] CLOSURE : ~ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [89] GAMMA_FORALL : ! [A7_7] : ((empty(A7_7) => finite(A7_7)))
% 3.53/2.20 -> [93] (empty(set_difference(skolem_A5858, skolem_B5959)) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20
% 3.53/2.20 [93] BETA_IMPLY : (empty(set_difference(skolem_A5858, skolem_B5959)) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20 -> [94] ~empty(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20 -> [95] finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [95] CLOSURE : finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [94] GAMMA_FORALL : ! [A8_8] : ((empty(A8_8) => function(A8_8)))
% 3.53/2.20 -> [96] (empty(skolem_A3939) => function(skolem_A3939))
% 3.53/2.20
% 3.53/2.20 [96] BETA_IMPLY : (empty(skolem_A3939) => function(skolem_A3939))
% 3.53/2.20 -> [98] ~empty(skolem_A3939)
% 3.53/2.20 -> [99] function(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [98] CLOSURE : ~empty(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [99] GAMMA_FORALL : ! [A9_9] : ((ordinal(A9_9) => (epsilon_transitive(A9_9) & epsilon_connected(A9_9))))
% 3.53/2.20 -> [102] (ordinal(skolem_A3939) => (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)))
% 3.53/2.20
% 3.53/2.20 [102] BETA_IMPLY : (ordinal(skolem_A3939) => (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)))
% 3.53/2.20 -> [104] ~ordinal(skolem_A3939)
% 3.53/2.20 -> [105] (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939))
% 3.53/2.20
% 3.53/2.20 [104] CLOSURE : ~ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [105] ALPHA_AND : (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939))
% 3.53/2.20 -> [108] epsilon_transitive(skolem_A3939), epsilon_connected(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [108] GAMMA_FORALL : ! [A10_10] : ((empty(A10_10) => relation(A10_10)))
% 3.53/2.20 -> [111] (empty(skolem_A3838) => relation(skolem_A3838))
% 3.53/2.20
% 3.53/2.20 [111] BETA_IMPLY : (empty(skolem_A3838) => relation(skolem_A3838))
% 3.53/2.20 -> [114] ~empty(skolem_A3838)
% 3.53/2.20 -> [115] relation(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [114] CLOSURE : ~empty(skolem_A3838)
% 3.53/2.20
% 3.53/2.20 [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))))
% 3.53/2.20 -> [119] ((empty(skolem_A3939) & ordinal(skolem_A3939)) => (((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939)) & natural(skolem_A3939)))
% 3.53/2.20
% 3.53/2.20 [119] BETA_IMPLY : ((empty(skolem_A3939) & ordinal(skolem_A3939)) => (((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939)) & natural(skolem_A3939)))
% 3.53/2.20 -> [120] ~(empty(skolem_A3939) & ordinal(skolem_A3939))
% 3.53/2.20 -> [121] (((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939)) & natural(skolem_A3939))
% 3.53/2.20
% 3.53/2.20 [120] BETA_NOT_AND : ~(empty(skolem_A3939) & ordinal(skolem_A3939))
% 3.53/2.20 -> [125] ~empty(skolem_A3939)
% 3.53/2.20 -> [126] ~ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [125] CLOSURE : ~empty(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [126] CLOSURE : ~ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [121] ALPHA_AND : (((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939)) & natural(skolem_A3939))
% 3.53/2.20 -> [127] ((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939)), natural(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [127] ALPHA_AND : ((epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)) & ordinal(skolem_A3939))
% 3.53/2.20 -> [129] (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939)), ordinal(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [129] ALPHA_AND : (epsilon_transitive(skolem_A3939) & epsilon_connected(skolem_A3939))
% 3.53/2.20 -> [131] epsilon_transitive(skolem_A3939), epsilon_connected(skolem_A3939)
% 3.53/2.20
% 3.53/2.20 [131] GAMMA_FORALL : ! [A12_12] : ((finite(A12_12) => ! [B13_13] : ((element(B13_13, powerset(A12_12)) => finite(B13_13)))))
% 3.53/2.20 -> [133] (finite(skolem_A2626) => ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13))))
% 3.53/2.20
% 3.53/2.20 [133] BETA_IMPLY : (finite(skolem_A2626) => ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13))))
% 3.53/2.20 -> [136] ~finite(skolem_A2626)
% 3.53/2.20 -> [137] ! [B13_13] : ((element(B13_13, powerset(skolem_A2626)) => finite(B13_13)))
% 3.53/2.20
% 3.53/2.20 [136] CLOSURE : ~finite(skolem_A2626)
% 3.53/2.20
% 3.53/2.20 [137] GAMMA_FORALL : ! [A14_14] : ((((relation(A14_14) & empty(A14_14)) & function(A14_14)) => ((relation(A14_14) & function(A14_14)) & one_to_one(A14_14))))
% 3.53/2.20 -> [139] (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 3.53/2.20
% 3.53/2.20 [139] BETA_IMPLY : (((relation(empty_set) & empty(empty_set)) & function(empty_set)) => ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set)))
% 3.53/2.20 -> [142] ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 3.53/2.20 -> [143] ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 3.53/2.20
% 3.53/2.20 [142] BETA_NOT_AND : ~((relation(empty_set) & empty(empty_set)) & function(empty_set))
% 3.53/2.20 -> [147] ~(relation(empty_set) & empty(empty_set))
% 3.53/2.20 -> [148] ~function(empty_set)
% 3.53/2.20
% 3.53/2.20 [148] CLOSURE : ~function(empty_set)
% 3.53/2.20
% 3.53/2.20 [147] BETA_NOT_AND : ~(relation(empty_set) & empty(empty_set))
% 3.53/2.20 -> [152] ~relation(empty_set)
% 3.53/2.20 -> [153] ~empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [153] CLOSURE : ~empty(empty_set)
% 3.53/2.20
% 3.53/2.20 [152] CLOSURE : ~relation(empty_set)
% 3.53/2.20
% 3.53/2.20 [143] ALPHA_AND : ((relation(empty_set) & function(empty_set)) & one_to_one(empty_set))
% 3.53/2.20 -> [149] (relation(empty_set) & function(empty_set)), one_to_one(empty_set)
% 3.53/2.20
% 3.53/2.20 [149] ALPHA_AND : (relation(empty_set) & function(empty_set))
% 3.53/2.20 -> [155] relation(empty_set), function(empty_set)
% 3.53/2.20
% 3.53/2.20 [155] GAMMA_FORALL : ! [A15_15] : (((epsilon_transitive(A15_15) & epsilon_connected(A15_15)) => ordinal(A15_15)))
% 3.53/2.20 -> [159] ((epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9)) => ordinal(A15_1_9))
% 3.53/2.20
% 3.53/2.20 [159] BETA_IMPLY : ((epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9)) => ordinal(A15_1_9))
% 3.53/2.20 -> [162] ~(epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9))
% 3.53/2.20 -> [163] ordinal(A15_1_9)
% 3.53/2.20
% 3.53/2.20 [162] BETA_NOT_AND : ~(epsilon_transitive(A15_1_9) & epsilon_connected(A15_1_9))
% 3.53/2.20 -> [164] ~epsilon_transitive(A15_1_9)
% 3.53/2.20 -> [165] ~epsilon_connected(A15_1_9)
% 3.53/2.20
% 3.53/2.20 [164] CLOSURE : ~epsilon_transitive(A15_1_9)
% 3.53/2.20
% 3.53/2.20 [165] CLOSURE : ~epsilon_connected(A15_1_9)
% 3.53/2.20
% 3.53/2.20 [163] GAMMA_FORALL : ! [A16_16] : ((empty(A16_16) => ((epsilon_transitive(A16_16) & epsilon_connected(A16_16)) & ordinal(A16_16))))
% 3.53/2.20 -> [170] (empty(skolem_A3434) => ((epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434)) & ordinal(skolem_A3434)))
% 3.53/2.20
% 3.53/2.20 [170] BETA_IMPLY : (empty(skolem_A3434) => ((epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434)) & ordinal(skolem_A3434)))
% 3.53/2.20 -> [172] ~empty(skolem_A3434)
% 3.53/2.20 -> [173] ((epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434)) & ordinal(skolem_A3434))
% 3.53/2.20
% 3.53/2.20 [172] CLOSURE : ~empty(skolem_A3434)
% 3.53/2.20
% 3.53/2.20 [173] ALPHA_AND : ((epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434)) & ordinal(skolem_A3434))
% 3.53/2.20 -> [174] (epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434)), ordinal(skolem_A3434)
% 3.53/2.20
% 3.53/2.20 [174] ALPHA_AND : (epsilon_transitive(skolem_A3434) & epsilon_connected(skolem_A3434))
% 3.53/2.20 -> [178] epsilon_transitive(skolem_A3434), epsilon_connected(skolem_A3434)
% 3.53/2.20
% 3.53/2.20 [178] 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)))))
% 3.53/2.20 -> [182] (element(skolem_A3535, positive_rationals) => (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))))
% 3.53/2.20
% 3.53/2.20 [182] BETA_IMPLY : (element(skolem_A3535, positive_rationals) => (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))))
% 3.53/2.20 -> [184] ~element(skolem_A3535, positive_rationals)
% 3.53/2.20 -> [185] (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535)))
% 3.53/2.20
% 3.53/2.20 [184] CLOSURE : ~element(skolem_A3535, positive_rationals)
% 3.53/2.20
% 3.53/2.20 [185] BETA_IMPLY : (ordinal(skolem_A3535) => (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535)))
% 3.53/2.20 -> [186] ~ordinal(skolem_A3535)
% 3.53/2.20 -> [187] (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))
% 3.53/2.20
% 3.53/2.20 [186] CLOSURE : ~ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [187] ALPHA_AND : (((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)) & natural(skolem_A3535))
% 3.53/2.20 -> [188] ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535)), natural(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [188] ALPHA_AND : ((epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)) & ordinal(skolem_A3535))
% 3.53/2.20 -> [190] (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535)), ordinal(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [190] ALPHA_AND : (epsilon_transitive(skolem_A3535) & epsilon_connected(skolem_A3535))
% 3.53/2.20 -> [192] epsilon_transitive(skolem_A3535), epsilon_connected(skolem_A3535)
% 3.53/2.20
% 3.53/2.20 [192] GAMMA_FORALL : ! [A18_18] : (? [B19_19] : (element(B19_19, A18_18)))
% 3.53/2.20 -> [194] ? [B19_19] : (element(B19_19, A18_1_12))
% 3.53/2.20
% 3.53/2.20 [194] DELTA_EXISTS : ? [B19_19] : (element(B19_19, A18_1_12))
% 3.53/2.20 -> [198] element(skolem_B1919(A18_1_12), A18_1_12)
% 3.53/2.20
% 3.53/2.20 [198] GAMMA_FORALL : ! [A20_20, B21_21] : ((finite(A20_20) => finite(set_difference(A20_20, B21_21))))
% 3.53/2.20 -> [199] (finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20
% 3.53/2.20 [199] BETA_IMPLY : (finite(skolem_A5858) => finite(set_difference(skolem_A5858, skolem_B5959)))
% 3.53/2.20 -> [200] ~finite(skolem_A5858)
% 3.53/2.20 -> [201] finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [201] CLOSURE : finite(set_difference(skolem_A5858, skolem_B5959))
% 3.53/2.20
% 3.53/2.20 [200] CLOSURE : ~finite(skolem_A5858)
% 3.53/2.20
% 3.53/2.20 % SZS output end Proof for theBenchmark.p
% 3.53/2.20 [1.852100s][1][Res] 6307 goroutines created
% 3.53/2.20 ==== Result ====
% 3.53/2.20 [1.852144s][1][Res] VALID
% 3.53/2.20 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------