TSTP Solution File: SEU085+1 by Goeland---1.0.0

View Problem - 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
%------------------------------------------------------------------------------