TSTP Solution File: SEU263+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:56:12 EDT 2022
% Result : Theorem 225.88s 138.21s
% Output : Proof 225.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat Sep 3 11:16:39 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.33 [DMT] DMT loaded with preskolemization
% 0.13/0.33 [EQ] equality loaded.
% 0.13/0.33 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.33 Start search
% 0.13/0.33 nb_step : 1 - limit : 17
% 0.13/0.33 Launch Gotab with destructive = true
% 225.88/138.20 % SZS output start Proof for theBenchmark.p
% 225.88/138.21 [0] ALPHA_AND : (! [A4_4, B5_5, C6_6] : ((element(C6_6, powerset(cartesian_product2(A4_4, B5_5))) => relation(C6_6))) & ! [A7_7, B8_8, C9_9] : ((relation_of2(C9_9, A7_7, B8_8) <=> subset(C9_9, cartesian_product2(A7_7, B8_8)))) & $true & $true & $true & $true & $true & $true & ! [A10_10, B11_11, C12_12] : ((relation_of2_as_subset(C12_12, A10_10, B11_11) => element(C12_12, powerset(cartesian_product2(A10_10, B11_11))))) & ! [A13_13, B14_14] : (? [C15_15] : (relation_of2(C15_15, A13_13, B14_14))) & ! [A16_16] : (? [B17_17] : (element(B17_17, A16_16))) & ! [A18_18, B19_19] : (? [C20_20] : (relation_of2_as_subset(C20_20, A18_18, B19_19))) & ! [A21_21, B22_22, C23_23] : ((relation_of2_as_subset(C23_23, A21_21, B22_22) <=> relation_of2(C23_23, A21_21, B22_22))) & ! [A24_24, B25_25] : (subset(A24_24, A24_24)) & ! [A26_26, B27_27, C28_28, D29_29] : (((subset(A26_26, B27_27) & subset(C28_28, D29_29)) => subset(cartesian_product2(A26_26, C28_28), cartesian_product2(B27_27, D29_29)))) & ! [A30_30, B31_31, C32_32] : ((relation_of2_as_subset(C32_32, A30_30, B31_31) => (subset(relation_dom(C32_32), A30_30) & subset(relation_rng(C32_32), B31_31)))) & ! [A37_37, B38_38, C39_39] : (((subset(A37_37, B38_38) & subset(B38_38, C39_39)) => subset(A37_37, C39_39))) & ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40))))) & ! [A41_41, B42_42] : ((element(A41_41, powerset(B42_42)) <=> subset(A41_41, B42_42))) & ~! [A33_33, B34_34, C35_35, D36_36] : ((relation_of2_as_subset(D36_36, C35_35, A33_33) => (subset(relation_rng(D36_36), B34_34) => relation_of2_as_subset(D36_36, C35_35, B34_34)))))
% 225.88/138.21 -> [1] ! [A4_4, B5_5, C6_6] : ((element(C6_6, powerset(cartesian_product2(A4_4, B5_5))) => relation(C6_6))), ! [A7_7, B8_8, C9_9] : ((relation_of2(C9_9, A7_7, B8_8) <=> subset(C9_9, cartesian_product2(A7_7, B8_8)))), $true, ! [A10_10, B11_11, C12_12] : ((relation_of2_as_subset(C12_12, A10_10, B11_11) => element(C12_12, powerset(cartesian_product2(A10_10, B11_11))))), ! [A13_13, B14_14] : (? [C15_15] : (relation_of2(C15_15, A13_13, B14_14))), ! [A16_16] : (? [B17_17] : (element(B17_17, A16_16))), ! [A18_18, B19_19] : (? [C20_20] : (relation_of2_as_subset(C20_20, A18_18, B19_19))), ! [A21_21, B22_22, C23_23] : ((relation_of2_as_subset(C23_23, A21_21, B22_22) <=> relation_of2(C23_23, A21_21, B22_22))), ! [A24_24, B25_25] : (subset(A24_24, A24_24)), ! [A26_26, B27_27, C28_28, D29_29] : (((subset(A26_26, B27_27) & subset(C28_28, D29_29)) => subset(cartesian_product2(A26_26, C28_28), cartesian_product2(B27_27, D29_29)))), ! [A30_30, B31_31, C32_32] : ((relation_of2_as_subset(C32_32, A30_30, B31_31) => (subset(relation_dom(C32_32), A30_30) & subset(relation_rng(C32_32), B31_31)))), ! [A37_37, B38_38, C39_39] : (((subset(A37_37, B38_38) & subset(B38_38, C39_39)) => subset(A37_37, C39_39))), ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40))))), ! [A41_41, B42_42] : ((element(A41_41, powerset(B42_42)) <=> subset(A41_41, B42_42))), ~! [A33_33, B34_34, C35_35, D36_36] : ((relation_of2_as_subset(D36_36, C35_35, A33_33) => (subset(relation_rng(D36_36), B34_34) => relation_of2_as_subset(D36_36, C35_35, B34_34))))
% 225.88/138.21
% 225.88/138.21 [1] DELTA_NOT_FORALL : ~! [A33_33, B34_34, C35_35, D36_36] : ((relation_of2_as_subset(D36_36, C35_35, A33_33) => (subset(relation_rng(D36_36), B34_34) => relation_of2_as_subset(D36_36, C35_35, B34_34))))
% 225.88/138.21 -> [2] ~(relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_rng(skolem_D3636), skolem_B3434) => relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434)))
% 225.88/138.21
% 225.88/138.21 [2] ALPHA_NOT_IMPLY : ~(relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_rng(skolem_D3636), skolem_B3434) => relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [3] relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333), ~(subset(relation_rng(skolem_D3636), skolem_B3434) => relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [3] ALPHA_NOT_IMPLY : ~(subset(relation_rng(skolem_D3636), skolem_B3434) => relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434))
% 225.88/138.21 -> [4] subset(relation_rng(skolem_D3636), skolem_B3434), ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [4] GAMMA_FORALL : ! [A4_4, B5_5, C6_6] : ((element(C6_6, powerset(cartesian_product2(A4_4, B5_5))) => relation(C6_6)))
% 225.88/138.21 -> [5] (element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))) => relation(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [5] BETA_IMPLY : (element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))) => relation(skolem_D3636))
% 225.88/138.21 -> [6] ~element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21 -> [7] relation(skolem_D3636)
% 225.88/138.21
% 225.88/138.21 [6] GAMMA_FORALL : ! [A7_7, B8_8, C9_9] : ((relation_of2(C9_9, A7_7, B8_8) <=> subset(C9_9, cartesian_product2(A7_7, B8_8))))
% 225.88/138.21 -> [8] (relation_of2(C9_0_1, A7_0_1, B8_0_1) <=> subset(C9_0_1, cartesian_product2(A7_0_1, B8_0_1)))
% 225.88/138.21
% 225.88/138.21 [8] BETA_EQUIV : (relation_of2(C9_0_1, A7_0_1, B8_0_1) <=> subset(C9_0_1, cartesian_product2(A7_0_1, B8_0_1)))
% 225.88/138.21 -> [10] ~relation_of2(C9_0_1, A7_0_1, B8_0_1), ~subset(C9_0_1, cartesian_product2(A7_0_1, B8_0_1))
% 225.88/138.21 -> [11] relation_of2(C9_0_1, A7_0_1, B8_0_1), subset(C9_0_1, cartesian_product2(A7_0_1, B8_0_1))
% 225.88/138.21
% 225.88/138.21 [10] GAMMA_FORALL : ! [A10_10, B11_11, C12_12] : ((relation_of2_as_subset(C12_12, A10_10, B11_11) => element(C12_12, powerset(cartesian_product2(A10_10, B11_11)))))
% 225.88/138.21 -> [14] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21
% 225.88/138.21 [14] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21 -> [15] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [16] element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [15] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [16] CLOSURE : element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [11] GAMMA_FORALL : ! [A10_10, B11_11, C12_12] : ((relation_of2_as_subset(C12_12, A10_10, B11_11) => element(C12_12, powerset(cartesian_product2(A10_10, B11_11)))))
% 225.88/138.21 -> [18] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21
% 225.88/138.21 [18] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21 -> [20] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [21] element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [20] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [21] CLOSURE : element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [9] BETA_EQUIV : (relation_of2(skolem_C1515(A13_2326_3, B14_2326_3), A13_2326_3, B14_2326_3) <=> subset(skolem_C1515(A13_2326_3, B14_2326_3), cartesian_product2(A13_2326_3, B14_2326_3)))
% 225.88/138.21 -> [17838] ~relation_of2(skolem_C1515(A13_2326_3, B14_2326_3), A13_2326_3, B14_2326_3), ~subset(skolem_C1515(A13_2326_3, B14_2326_3), cartesian_product2(A13_2326_3, B14_2326_3))
% 225.88/138.21 -> [17839] relation_of2(skolem_C1515(A13_2326_3, B14_2326_3), A13_2326_3, B14_2326_3), subset(skolem_C1515(A13_2326_3, B14_2326_3), cartesian_product2(A13_2326_3, B14_2326_3))
% 225.88/138.21
% 225.88/138.21 [17838] GAMMA_FORALL : ! [A10_10, B11_11, C12_12] : ((relation_of2_as_subset(C12_12, A10_10, B11_11) => element(C12_12, powerset(cartesian_product2(A10_10, B11_11)))))
% 225.88/138.21 -> [17841] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21
% 225.88/138.21 [17841] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333))))
% 225.88/138.21 -> [17844] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [17845] element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [17844] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [17848] CLOSURE : relation_of2(skolem_C1515(A13_2326_3, B14_2326_3), A13_2326_3, B14_2326_3)
% 225.88/138.21
% 225.88/138.21 [17840] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)) => element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))))
% 225.88/138.21 -> [17931] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636))
% 225.88/138.21 -> [17932] element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [17932] GAMMA_FORALL : ! [A13_13, B14_14] : (? [C15_15] : (relation_of2(C15_15, A13_13, B14_14)))
% 225.88/138.21 -> [17933] ? [C15_15] : (relation_of2(C15_15, A13_2330_3, B14_2330_3))
% 225.88/138.21
% 225.88/138.21 [17933] DELTA_EXISTS : ? [C15_15] : (relation_of2(C15_15, A13_2330_3, B14_2330_3))
% 225.88/138.21 -> [17934] relation_of2(skolem_C1515(A13_2330_3, B14_2330_3), A13_2330_3, B14_2330_3)
% 225.88/138.21
% 225.88/138.21 [17934] GAMMA_FORALL : ! [A16_16] : (? [B17_17] : (element(B17_17, A16_16)))
% 225.88/138.21 -> [17935] ? [B17_17] : (element(B17_17, powerset(cartesian_product2(A4_186_0, B5_186_0))))
% 225.88/138.21
% 225.88/138.21 [17935] DELTA_EXISTS : ? [B17_17] : (element(B17_17, powerset(cartesian_product2(A4_186_0, B5_186_0))))
% 225.88/138.21 -> [17936] element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0)))
% 225.88/138.21
% 225.88/138.21 [17936] GAMMA_FORALL : ! [A18_18, B19_19] : (? [C20_20] : (relation_of2_as_subset(C20_20, A18_18, B19_19)))
% 225.88/138.21 -> [17937] ? [C20_20] : (relation_of2_as_subset(C20_20, A18_3_5, B19_3_5))
% 225.88/138.21
% 225.88/138.21 [17937] DELTA_EXISTS : ? [C20_20] : (relation_of2_as_subset(C20_20, A18_3_5, B19_3_5))
% 225.88/138.21 -> [17938] relation_of2_as_subset(skolem_C2020(A18_3_5, B19_3_5), A18_3_5, B19_3_5)
% 225.88/138.21
% 225.88/138.21 [17938] GAMMA_FORALL : ! [A21_21, B22_22, C23_23] : ((relation_of2_as_subset(C23_23, A21_21, B22_22) <=> relation_of2(C23_23, A21_21, B22_22)))
% 225.88/138.21 -> [17939] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434) <=> relation_of2(skolem_D3636, skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [17939] BETA_EQUIV : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434) <=> relation_of2(skolem_D3636, skolem_C3535, skolem_B3434))
% 225.88/138.21 -> [17940] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434), ~relation_of2(skolem_D3636, skolem_C3535, skolem_B3434)
% 225.88/138.21 -> [17941] relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434), relation_of2(skolem_D3636, skolem_C3535, skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [17941] CLOSURE : relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [17940] GAMMA_FORALL : ! [A24_24, B25_25] : (subset(A24_24, A24_24))
% 225.88/138.21 -> [17942] subset(skolem_C3535, skolem_C3535)
% 225.88/138.21
% 225.88/138.21 [17942] GAMMA_FORALL : ! [A26_26, B27_27, C28_28, D29_29] : (((subset(A26_26, B27_27) & subset(C28_28, D29_29)) => subset(cartesian_product2(A26_26, C28_28), cartesian_product2(B27_27, D29_29))))
% 225.88/138.21 -> [17943] ((subset(skolem_C3535, skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_B3434)) => subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21
% 225.88/138.21 [17943] BETA_IMPLY : ((subset(skolem_C3535, skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_B3434)) => subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [17944] ~(subset(skolem_C3535, skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_B3434))
% 225.88/138.21 -> [17945] subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [17944] BETA_NOT_AND : ~(subset(skolem_C3535, skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_B3434))
% 225.88/138.21 -> [17946] ~subset(skolem_C3535, skolem_C3535)
% 225.88/138.21 -> [17947] ~subset(relation_rng(skolem_D3636), skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [17947] CLOSURE : ~subset(relation_rng(skolem_D3636), skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [17946] CLOSURE : ~subset(skolem_C3535, skolem_C3535)
% 225.88/138.21
% 225.88/138.21 [17948] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333)))
% 225.88/138.21 -> [19108] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [19109] (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333))
% 225.88/138.21
% 225.88/138.21 [19108] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [19111] BETA_IMPLY : ((subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))) & subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434))) => subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [19734] ~(subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))) & subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [19735] subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [19735] GAMMA_FORALL : ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40)))))
% 225.88/138.21 -> [19738] (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [19738] BETA_IMPLY : (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21 -> [19739] ~relation(skolem_D3636)
% 225.88/138.21 -> [19740] subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19739] CLOSURE : ~relation(skolem_D3636)
% 225.88/138.21
% 225.88/138.21 [19741] BETA_EQUIV : (element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0))) <=> subset(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), cartesian_product2(A4_186_0, B5_186_0)))
% 225.88/138.21 -> [19758] ~element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0))), ~subset(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), cartesian_product2(A4_186_0, B5_186_0))
% 225.88/138.21 -> [19759] element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0))), subset(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), cartesian_product2(A4_186_0, B5_186_0))
% 225.88/138.21
% 225.88/138.21 [19758] CLOSURE : ~subset(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), cartesian_product2(A4_186_0, B5_186_0))
% 225.88/138.21
% 225.88/138.21 [19761] BETA_IMPLY : (element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0))) => relation(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0)))))
% 225.88/138.21 -> [19770] ~element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0)))
% 225.88/138.21 -> [19771] relation(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))))
% 225.88/138.21
% 225.88/138.21 [19770] CLOSURE : ~element(skolem_B1717(powerset(cartesian_product2(A4_186_0, B5_186_0))), powerset(cartesian_product2(A4_186_0, B5_186_0)))
% 225.88/138.21
% 225.88/138.21 [19773] BETA_EQUIV : (relation_of2(skolem_D3636, skolem_C3535, skolem_B3434) <=> subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [19776] ~relation_of2(skolem_D3636, skolem_C3535, skolem_B3434), ~subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21 -> [19777] relation_of2(skolem_D3636, skolem_C3535, skolem_B3434), subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [19776] CLOSURE : ~subset(skolem_D3636, cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [19777] CLOSURE : relation_of2(skolem_D3636, skolem_C3535, skolem_B3434)
% 225.88/138.21
% 225.88/138.21 [19734] BETA_NOT_AND : ~(subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))) & subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434)))
% 225.88/138.21 -> [19792] ~subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21 -> [19793] ~subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [19793] CLOSURE : ~subset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, skolem_B3434))
% 225.88/138.21
% 225.88/138.21 [19792] GAMMA_FORALL : ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40)))))
% 225.88/138.21 -> [19794] (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [19794] BETA_IMPLY : (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21 -> [19795] ~relation(skolem_D3636)
% 225.88/138.21 -> [19796] subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19795] CLOSURE : ~relation(skolem_D3636)
% 225.88/138.21
% 225.88/138.21 [19797] BETA_EQUIV : (element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))) <=> subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [19800] ~element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))), ~subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21 -> [19801] element(skolem_D3636, powerset(cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))), subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19800] CLOSURE : ~subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19801] CLOSURE : subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [17931] GAMMA_FORALL : ! [A13_13, B14_14] : (? [C15_15] : (relation_of2(C15_15, A13_13, B14_14)))
% 225.88/138.21 -> [19909] ? [C15_15] : (relation_of2(C15_15, A13_2547_3, B14_2547_3))
% 225.88/138.21
% 225.88/138.21 [19909] DELTA_EXISTS : ? [C15_15] : (relation_of2(C15_15, A13_2547_3, B14_2547_3))
% 225.88/138.21 -> [19910] relation_of2(skolem_C1515(A13_2547_3, B14_2547_3), A13_2547_3, B14_2547_3)
% 225.88/138.21
% 225.88/138.21 [19910] GAMMA_FORALL : ! [A16_16] : (? [B17_17] : (element(B17_17, A16_16)))
% 225.88/138.21 -> [19911] ? [B17_17] : (element(B17_17, A16_4_4))
% 225.88/138.21
% 225.88/138.21 [19911] DELTA_EXISTS : ? [B17_17] : (element(B17_17, A16_4_4))
% 225.88/138.21 -> [19912] element(skolem_B1717(A16_4_4), A16_4_4)
% 225.88/138.21
% 225.88/138.21 [19912] GAMMA_FORALL : ! [A18_18, B19_19] : (? [C20_20] : (relation_of2_as_subset(C20_20, A18_18, B19_19)))
% 225.88/138.21 -> [19913] ? [C20_20] : (relation_of2_as_subset(C20_20, A18_4_5, B19_4_5))
% 225.88/138.21
% 225.88/138.21 [19913] DELTA_EXISTS : ? [C20_20] : (relation_of2_as_subset(C20_20, A18_4_5, B19_4_5))
% 225.88/138.21 -> [19914] relation_of2_as_subset(skolem_C2020(A18_4_5, B19_4_5), A18_4_5, B19_4_5)
% 225.88/138.21
% 225.88/138.21 [19914] GAMMA_FORALL : ! [A21_21, B22_22, C23_23] : ((relation_of2_as_subset(C23_23, A21_21, B22_22) <=> relation_of2(C23_23, A21_21, B22_22)))
% 225.88/138.21 -> [19915] (relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)) <=> relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19915] BETA_EQUIV : (relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)) <=> relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21 -> [19916] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)), ~relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636))
% 225.88/138.21 -> [19917] relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)), relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [19917] CLOSURE : relation_of2_as_subset(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [19916] GAMMA_FORALL : ! [A24_24, B25_25] : (subset(A24_24, A24_24))
% 225.88/138.21 -> [19918] subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [19918] GAMMA_FORALL : ! [A26_26, B27_27, C28_28, D29_29] : (((subset(A26_26, B27_27) & subset(C28_28, D29_29)) => subset(cartesian_product2(A26_26, C28_28), cartesian_product2(B27_27, D29_29))))
% 225.88/138.21 -> [19919] ((subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636))) => subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [19919] BETA_IMPLY : ((subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636))) => subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [19920] ~(subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21 -> [19921] subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19921] GAMMA_FORALL : ! [A30_30, B31_31, C32_32] : ((relation_of2_as_subset(C32_32, A30_30, B31_31) => (subset(relation_dom(C32_32), A30_30) & subset(relation_rng(C32_32), B31_31))))
% 225.88/138.21 -> [19924] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [19924] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333)))
% 225.88/138.21 -> [19925] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [19926] (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333))
% 225.88/138.21
% 225.88/138.21 [19925] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [19928] BETA_IMPLY : ((subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))) & subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))) => subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [21793] ~(subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))) & subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [21794] subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [21794] GAMMA_FORALL : ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40)))))
% 225.88/138.21 -> [21797] (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [21797] BETA_IMPLY : (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21 -> [21798] ~relation(skolem_D3636)
% 225.88/138.21 -> [21799] subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [21798] CLOSURE : ~relation(skolem_D3636)
% 225.88/138.21
% 225.88/138.21 [21800] BETA_EQUIV : (element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0))) <=> subset(skolem_C1515(A4_219_0, B5_219_0), cartesian_product2(A4_219_0, B5_219_0)))
% 225.88/138.21 -> [21817] ~element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0))), ~subset(skolem_C1515(A4_219_0, B5_219_0), cartesian_product2(A4_219_0, B5_219_0))
% 225.88/138.21 -> [21818] element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0))), subset(skolem_C1515(A4_219_0, B5_219_0), cartesian_product2(A4_219_0, B5_219_0))
% 225.88/138.21
% 225.88/138.21 [21817] CLOSURE : ~subset(skolem_C1515(A4_219_0, B5_219_0), cartesian_product2(A4_219_0, B5_219_0))
% 225.88/138.21
% 225.88/138.21 [21820] BETA_IMPLY : (element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0))) => relation(skolem_C1515(A4_219_0, B5_219_0)))
% 225.88/138.21 -> [21827] ~element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0)))
% 225.88/138.21 -> [21828] relation(skolem_C1515(A4_219_0, B5_219_0))
% 225.88/138.21
% 225.88/138.21 [21827] CLOSURE : ~element(skolem_C1515(A4_219_0, B5_219_0), powerset(cartesian_product2(A4_219_0, B5_219_0)))
% 225.88/138.21
% 225.88/138.21 [21830] BETA_EQUIV : (relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)) <=> subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [21833] ~relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)), ~subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21 -> [21834] relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636)), subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [21834] CLOSURE : relation_of2(skolem_D3636, skolem_C3535, relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [21833] CLOSURE : ~subset(skolem_D3636, cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [21793] BETA_NOT_AND : ~(subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))) & subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636))))
% 225.88/138.21 -> [22293] ~subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21 -> [22294] ~subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [22294] CLOSURE : ~subset(cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)), cartesian_product2(skolem_C3535, relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [22293] GAMMA_FORALL : ! [A40_40] : ((relation(A40_40) => subset(A40_40, cartesian_product2(relation_dom(A40_40), relation_rng(A40_40)))))
% 225.88/138.21 -> [22794] (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21
% 225.88/138.21 [22794] BETA_IMPLY : (relation(skolem_D3636) => subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636))))
% 225.88/138.21 -> [22795] ~relation(skolem_D3636)
% 225.88/138.21 -> [22796] subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [22795] CLOSURE : ~relation(skolem_D3636)
% 225.88/138.21
% 225.88/138.21 [22796] CLOSURE : subset(skolem_D3636, cartesian_product2(relation_dom(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21
% 225.88/138.21 [19920] BETA_NOT_AND : ~(subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636)))
% 225.88/138.21 -> [27690] ~subset(relation_dom(skolem_D3636), skolem_C3535)
% 225.88/138.21 -> [27691] ~subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [27691] CLOSURE : ~subset(relation_rng(skolem_D3636), relation_rng(skolem_D3636))
% 225.88/138.21
% 225.88/138.21 [27690] GAMMA_FORALL : ! [A30_30, B31_31, C32_32] : ((relation_of2_as_subset(C32_32, A30_30, B31_31) => (subset(relation_dom(C32_32), A30_30) & subset(relation_rng(C32_32), B31_31))))
% 225.88/138.21 -> [27692] (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333)))
% 225.88/138.21
% 225.88/138.21 [27692] BETA_IMPLY : (relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333) => (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333)))
% 225.88/138.21 -> [27693] ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21 -> [27694] (subset(relation_dom(skolem_D3636), skolem_C3535) & subset(relation_rng(skolem_D3636), skolem_A3333))
% 225.88/138.21
% 225.88/138.21 [27693] CLOSURE : ~relation_of2_as_subset(skolem_D3636, skolem_C3535, skolem_A3333)
% 225.88/138.21
% 225.88/138.21 [27695] CLOSURE : subset(relation_dom(skolem_D3636), skolem_C3535)
% 225.88/138.21
% 225.88/138.21 % SZS output end Proof for theBenchmark.p
% 225.88/138.21 [137.882909s][1][Res] 555947 goroutines created
% 225.88/138.21 ==== Result ====
% 225.88/138.21 [137.882946s][1][Res] VALID
% 225.88/138.21 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------