TSTP Solution File: SET624+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n010.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 04:16:55 EDT 2022
% Result : Theorem 26.61s 3.89s
% Output : Proof 26.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.10 % Command : goeland -dmt -presko -proof %s
% 0.10/0.30 % Computer : n010.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 06:53:12 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 [DMT] DMT loaded with preskolemization
% 0.10/0.31 [EQ] equality loaded.
% 0.10/0.31 [0.000032s][1][MAIN] Problem : theBenchmark.p
% 0.10/0.31 Start search
% 0.10/0.31 nb_step : 1 - limit : 8
% 0.10/0.31 Launch Gotab with destructive = true
% 26.61/3.88 % SZS output start Proof for theBenchmark.p
% 26.61/3.89 [0] ALPHA_AND : (! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9))) & ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11))) & ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14))))) & ~! [B16_16, C17_17, D18_18] : ((intersect(B16_16, union(C17_17, D18_18)) <=> (intersect(B16_16, C17_17) | intersect(B16_16, D18_18)))))
% 26.61/3.89 -> [1] ! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9))), ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11))), ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14))))), ~! [B16_16, C17_17, D18_18] : ((intersect(B16_16, union(C17_17, D18_18)) <=> (intersect(B16_16, C17_17) | intersect(B16_16, D18_18))))
% 26.61/3.89
% 26.61/3.89 [1] DELTA_NOT_FORALL : ~! [B16_16, C17_17, D18_18] : ((intersect(B16_16, union(C17_17, D18_18)) <=> (intersect(B16_16, C17_17) | intersect(B16_16, D18_18))))
% 26.61/3.89 -> [2] ~(intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)) <=> (intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818)))
% 26.61/3.89
% 26.61/3.89 [2] BETA_NOT_EQUIV : ~(intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)) <=> (intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818)))
% 26.61/3.89 -> [3] ~intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)), (intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818))
% 26.61/3.89 -> [4] intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)), ~(intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [4] Rewrite : intersect(skolem_B1616, union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [6] (member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89
% 26.61/3.89 [6] ALPHA_NOT_OR : ~(intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818))
% 26.61/3.89 -> [9] ~intersect(skolem_B1616, skolem_C1717), ~intersect(skolem_B1616, skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [9] Rewrite : ~intersect(skolem_B1616, skolem_C1717)
% 26.61/3.89 -> [11] ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, skolem_C1717)))
% 26.61/3.89
% 26.61/3.89 [11] Rewrite : ~intersect(skolem_B1616, skolem_D1818)
% 26.61/3.89 -> [13] ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, skolem_D1818)))
% 26.61/3.89
% 26.61/3.89 [13] ALPHA_AND : (member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89 -> [14] member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616), member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), union(skolem_C1717, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [14] Rewrite : member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [17] (member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717) | member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [17] BETA_OR : (member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717) | member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818))
% 26.61/3.89 -> [18] member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717)
% 26.61/3.89 -> [19] member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [18] GAMMA_FORALL : ! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9)))
% 26.61/3.89 -> [26] =(union(B9_3_0, C10_3_0), union(C10_3_0, B9_3_0))
% 26.61/3.89
% 26.61/3.89 [26] GAMMA_FORALL : ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11)))
% 26.61/3.89 -> [52] (intersect(B11_3_1, C12_3_1) => intersect(C12_3_1, B11_3_1))
% 26.61/3.89
% 26.61/3.89 [52] BETA_IMPLY : (intersect(B11_3_1, C12_3_1) => intersect(C12_3_1, B11_3_1))
% 26.61/3.89 -> [54] ~intersect(B11_3_1, C12_3_1)
% 26.61/3.89 -> [55] intersect(C12_3_1, B11_3_1)
% 26.61/3.89
% 26.61/3.89 [54] Rewrite : ~intersect(B11_3_1, C12_3_1)
% 26.61/3.89 -> [61] ~? [D8_8] : ((member(D8_8, B11_3_1) & member(D8_8, C12_3_1)))
% 26.61/3.89
% 26.61/3.89 [61] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [63] (=(C14_4_2, C14_4_2) <=> ! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2))))
% 26.61/3.89
% 26.61/3.89 [63] BETA_EQUIV : (=(C14_4_2, C14_4_2) <=> ! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2))))
% 26.61/3.89 -> [69] ~=(C14_4_2, C14_4_2), ~! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2)))
% 26.61/3.89 -> [70] =(C14_4_2, C14_4_2), ! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2)))
% 26.61/3.89
% 26.61/3.89 [69] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2)))
% 26.61/3.89 -> [86] ~(member(skolem_D1515(C14_4_2, C14_4_2), C14_4_2) <=> member(skolem_D1515(C14_4_2, C14_4_2), C14_4_2))
% 26.61/3.89
% 26.61/3.89 [86] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_4_2) <=> member(D15_15, C14_4_2)))
% 26.61/3.89
% 26.61/3.89 [70] GAMMA_NOT_EXISTS : ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, skolem_C1717)))
% 26.61/3.89 -> [94] ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717))
% 26.61/3.89
% 26.61/3.89 [94] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717))
% 26.61/3.89 -> [95] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616)
% 26.61/3.89 -> [96] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [95] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [96] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [55] Rewrite : intersect(C12_3_1, B11_3_1)
% 26.61/3.89 -> [60] (member(skolem_D88(C12_3_1, B11_3_1), C12_3_1) & member(skolem_D88(C12_3_1, B11_3_1), B11_3_1))
% 26.61/3.89
% 26.61/3.89 [60] ALPHA_AND : (member(skolem_D88(C12_3_1, B11_3_1), C12_3_1) & member(skolem_D88(C12_3_1, B11_3_1), B11_3_1))
% 26.61/3.89 -> [64] member(skolem_D88(C12_3_1, B11_3_1), C12_3_1), member(skolem_D88(C12_3_1, B11_3_1), B11_3_1)
% 26.61/3.89
% 26.61/3.89 [64] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [73] (=(C14_6_2, C14_6_2) <=> ! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2))))
% 26.61/3.89
% 26.61/3.89 [73] BETA_EQUIV : (=(C14_6_2, C14_6_2) <=> ! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2))))
% 26.61/3.89 -> [76] ~=(C14_6_2, C14_6_2), ~! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2)))
% 26.61/3.89 -> [77] =(C14_6_2, C14_6_2), ! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2)))
% 26.61/3.89
% 26.61/3.89 [76] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2)))
% 26.61/3.89 -> [81] ~(member(skolem_D1515(C14_6_2, C14_6_2), C14_6_2) <=> member(skolem_D1515(C14_6_2, C14_6_2), C14_6_2))
% 26.61/3.89
% 26.61/3.89 [81] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_6_2) <=> member(D15_15, C14_6_2)))
% 26.61/3.89
% 26.61/3.89 [101] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717))
% 26.61/3.89 -> [106] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616)
% 26.61/3.89 -> [107] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [107] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [106] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [19] GAMMA_FORALL : ! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9)))
% 26.61/3.89 -> [24] =(union(B9_1_0, C10_1_0), union(C10_1_0, B9_1_0))
% 26.61/3.89
% 26.61/3.89 [24] GAMMA_FORALL : ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11)))
% 26.61/3.89 -> [33] (intersect(skolem_C1717, skolem_B1616) => intersect(skolem_B1616, skolem_C1717))
% 26.61/3.89
% 26.61/3.89 [33] BETA_IMPLY : (intersect(skolem_C1717, skolem_B1616) => intersect(skolem_B1616, skolem_C1717))
% 26.61/3.89 -> [35] ~intersect(skolem_C1717, skolem_B1616)
% 26.61/3.89 -> [36] intersect(skolem_B1616, skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [35] Rewrite : ~intersect(skolem_C1717, skolem_B1616)
% 26.61/3.89 -> [39] ~? [D8_8] : ((member(D8_8, skolem_C1717) & member(D8_8, skolem_B1616)))
% 26.61/3.89
% 26.61/3.89 [39] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [41] (=(C14_1_2, C14_1_2) <=> ! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2))))
% 26.61/3.89
% 26.61/3.89 [41] BETA_EQUIV : (=(C14_1_2, C14_1_2) <=> ! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2))))
% 26.61/3.89 -> [45] ~=(C14_1_2, C14_1_2), ~! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2)))
% 26.61/3.89 -> [46] =(C14_1_2, C14_1_2), ! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2)))
% 26.61/3.89
% 26.61/3.89 [45] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2)))
% 26.61/3.89 -> [71] ~(member(skolem_D1515(C14_1_2, C14_1_2), C14_1_2) <=> member(skolem_D1515(C14_1_2, C14_1_2), C14_1_2))
% 26.61/3.89
% 26.61/3.89 [71] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_1_2) <=> member(D15_15, C14_1_2)))
% 26.61/3.89
% 26.61/3.89 [91] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717))
% 26.61/3.89 -> [104] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616)
% 26.61/3.89 -> [105] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [104] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [105] GAMMA_NOT_EXISTS : ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, skolem_D1818)))
% 26.61/3.89 -> [110] ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [110] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616) & member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818))
% 26.61/3.89 -> [111] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_B1616)
% 26.61/3.89 -> [112] ~member(skolem_D88(skolem_B1616, union(skolem_C1717, skolem_D1818)), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [112] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [111] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [36] Rewrite : intersect(skolem_B1616, skolem_C1717)
% 26.61/3.89 -> [59] (member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717))
% 26.61/3.89
% 26.61/3.89 [59] ALPHA_AND : (member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717))
% 26.61/3.89 -> [62] member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616), member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [62] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [87] (=(C14_7_2, C14_7_2) <=> ! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2))))
% 26.61/3.89
% 26.61/3.89 [87] BETA_EQUIV : (=(C14_7_2, C14_7_2) <=> ! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2))))
% 26.61/3.89 -> [88] ~=(C14_7_2, C14_7_2), ~! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2)))
% 26.61/3.89 -> [89] =(C14_7_2, C14_7_2), ! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2)))
% 26.61/3.89
% 26.61/3.89 [88] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2)))
% 26.61/3.89 -> [97] ~(member(skolem_D1515(C14_7_2, C14_7_2), C14_7_2) <=> member(skolem_D1515(C14_7_2, C14_7_2), C14_7_2))
% 26.61/3.89
% 26.61/3.89 [97] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_7_2) <=> member(D15_15, C14_7_2)))
% 26.61/3.89
% 26.61/3.89 [98] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717))
% 26.61/3.89 -> [117] ~member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616)
% 26.61/3.89 -> [118] ~member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [117] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [118] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [3] Rewrite : ~intersect(skolem_B1616, union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [5] ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, union(skolem_C1717, skolem_D1818))))
% 26.61/3.89
% 26.61/3.89 [5] BETA_OR : (intersect(skolem_B1616, skolem_C1717) | intersect(skolem_B1616, skolem_D1818))
% 26.61/3.89 -> [7] intersect(skolem_B1616, skolem_C1717)
% 26.61/3.89 -> [8] intersect(skolem_B1616, skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [7] Rewrite : intersect(skolem_B1616, skolem_C1717)
% 26.61/3.89 -> [10] (member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717))
% 26.61/3.89
% 26.61/3.89 [10] ALPHA_AND : (member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717))
% 26.61/3.89 -> [12] member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616), member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717)
% 26.61/3.89
% 26.61/3.89 [12] GAMMA_FORALL : ! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9)))
% 26.61/3.89 -> [15] =(union(B9_0_0, C10_0_0), union(C10_0_0, B9_0_0))
% 26.61/3.89
% 26.61/3.89 [15] GAMMA_FORALL : ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11)))
% 26.61/3.89 -> [21] (intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)) => intersect(union(skolem_C1717, skolem_D1818), skolem_B1616))
% 26.61/3.89
% 26.61/3.89 [21] BETA_IMPLY : (intersect(skolem_B1616, union(skolem_C1717, skolem_D1818)) => intersect(union(skolem_C1717, skolem_D1818), skolem_B1616))
% 26.61/3.89 -> [22] ~intersect(skolem_B1616, union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [23] intersect(union(skolem_C1717, skolem_D1818), skolem_B1616)
% 26.61/3.89
% 26.61/3.89 [22] Rewrite : ~intersect(skolem_B1616, union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [27] ~? [D8_8] : ((member(D8_8, skolem_B1616) & member(D8_8, union(skolem_C1717, skolem_D1818))))
% 26.61/3.89
% 26.61/3.89 [27] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [29] (=(C14_0_2, C14_0_2) <=> ! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2))))
% 26.61/3.89
% 26.61/3.89 [29] BETA_EQUIV : (=(C14_0_2, C14_0_2) <=> ! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2))))
% 26.61/3.89 -> [31] ~=(C14_0_2, C14_0_2), ~! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2)))
% 26.61/3.89 -> [32] =(C14_0_2, C14_0_2), ! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2)))
% 26.61/3.89
% 26.61/3.89 [31] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2)))
% 26.61/3.89 -> [56] ~(member(skolem_D1515(C14_0_2, C14_0_2), C14_0_2) <=> member(skolem_D1515(C14_0_2, C14_0_2), C14_0_2))
% 26.61/3.89
% 26.61/3.89 [56] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_0_2) <=> member(D15_15, C14_0_2)))
% 26.61/3.89
% 26.61/3.89 [40] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_C1717), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89 -> [108] ~member(skolem_D88(skolem_B1616, skolem_C1717), skolem_B1616)
% 26.61/3.89 -> [109] ~member(skolem_D88(skolem_B1616, skolem_C1717), union(skolem_C1717, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [108] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [109] Rewrite : ~member(skolem_D88(skolem_B1616, skolem_C1717), union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [113] ~(member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_C1717), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [113] ALPHA_NOT_OR : ~(member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_C1717), skolem_D1818))
% 26.61/3.89 -> [114] ~member(skolem_D88(skolem_B1616, skolem_C1717), skolem_C1717), ~member(skolem_D88(skolem_B1616, skolem_C1717), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [114] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [23] Rewrite : intersect(union(skolem_C1717, skolem_D1818), skolem_B1616)
% 26.61/3.89 -> [28] (member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), union(skolem_C1717, skolem_D1818)) & member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), skolem_B1616))
% 26.61/3.89
% 26.61/3.89 [28] ALPHA_AND : (member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), union(skolem_C1717, skolem_D1818)) & member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), skolem_B1616))
% 26.61/3.89 -> [30] member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), union(skolem_C1717, skolem_D1818)), member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), skolem_B1616)
% 26.61/3.89
% 26.61/3.89 [30] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [48] (=(C14_2_2, C14_2_2) <=> ! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2))))
% 26.61/3.89
% 26.61/3.89 [48] BETA_EQUIV : (=(C14_2_2, C14_2_2) <=> ! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2))))
% 26.61/3.89 -> [49] ~=(C14_2_2, C14_2_2), ~! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2)))
% 26.61/3.89 -> [50] =(C14_2_2, C14_2_2), ! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2)))
% 26.61/3.89
% 26.61/3.89 [49] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2)))
% 26.61/3.89 -> [68] ~(member(skolem_D1515(C14_2_2, C14_2_2), C14_2_2) <=> member(skolem_D1515(C14_2_2, C14_2_2), C14_2_2))
% 26.61/3.89
% 26.61/3.89 [68] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_2_2) <=> member(D15_15, C14_2_2)))
% 26.61/3.89
% 26.61/3.89 [65] BETA_NOT_AND : ~(member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), skolem_B1616) & member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89 -> [121] ~member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), skolem_B1616)
% 26.61/3.89 -> [122] ~member(skolem_D88(union(skolem_C1717, skolem_D1818), skolem_B1616), union(skolem_C1717, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [121] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [122] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [8] Rewrite : intersect(skolem_B1616, skolem_D1818)
% 26.61/3.89 -> [16] (member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [16] ALPHA_AND : (member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89 -> [20] member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616), member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [20] GAMMA_FORALL : ! [B9_9, C10_10] : (=(union(B9_9, C10_10), union(C10_10, B9_9)))
% 26.61/3.89 -> [25] =(union(B9_2_0, C10_2_0), union(C10_2_0, B9_2_0))
% 26.61/3.89
% 26.61/3.89 [25] GAMMA_FORALL : ! [B11_11, C12_12] : ((intersect(B11_11, C12_12) => intersect(C12_12, B11_11)))
% 26.61/3.89 -> [34] (intersect(B11_2_1, C12_2_1) => intersect(C12_2_1, B11_2_1))
% 26.61/3.89
% 26.61/3.89 [34] BETA_IMPLY : (intersect(B11_2_1, C12_2_1) => intersect(C12_2_1, B11_2_1))
% 26.61/3.89 -> [37] ~intersect(B11_2_1, C12_2_1)
% 26.61/3.89 -> [38] intersect(C12_2_1, B11_2_1)
% 26.61/3.89
% 26.61/3.89 [37] Rewrite : ~intersect(B11_2_1, C12_2_1)
% 26.61/3.89 -> [44] ~? [D8_8] : ((member(D8_8, B11_2_1) & member(D8_8, C12_2_1)))
% 26.61/3.89
% 26.61/3.89 [44] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [51] (=(C14_3_2, C14_3_2) <=> ! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2))))
% 26.61/3.89
% 26.61/3.89 [51] BETA_EQUIV : (=(C14_3_2, C14_3_2) <=> ! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2))))
% 26.61/3.89 -> [57] ~=(C14_3_2, C14_3_2), ~! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2)))
% 26.61/3.89 -> [58] =(C14_3_2, C14_3_2), ! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2)))
% 26.61/3.89
% 26.61/3.89 [57] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2)))
% 26.61/3.89 -> [90] ~(member(skolem_D1515(C14_3_2, C14_3_2), C14_3_2) <=> member(skolem_D1515(C14_3_2, C14_3_2), C14_3_2))
% 26.61/3.89
% 26.61/3.89 [90] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_3_2) <=> member(D15_15, C14_3_2)))
% 26.61/3.89
% 26.61/3.89 [78] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89 -> [115] ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616)
% 26.61/3.89 -> [116] ~member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [115] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [116] Rewrite : ~member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [119] ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [119] ALPHA_NOT_OR : ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89 -> [120] ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717), ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [120] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [38] Rewrite : intersect(C12_2_1, B11_2_1)
% 26.61/3.89 -> [47] (member(skolem_D88(C12_2_1, B11_2_1), C12_2_1) & member(skolem_D88(C12_2_1, B11_2_1), B11_2_1))
% 26.61/3.89
% 26.61/3.89 [47] ALPHA_AND : (member(skolem_D88(C12_2_1, B11_2_1), C12_2_1) & member(skolem_D88(C12_2_1, B11_2_1), B11_2_1))
% 26.61/3.89 -> [53] member(skolem_D88(C12_2_1, B11_2_1), C12_2_1), member(skolem_D88(C12_2_1, B11_2_1), B11_2_1)
% 26.61/3.89
% 26.61/3.89 [53] GAMMA_FORALL : ! [B13_13, C14_14] : ((=(B13_13, C14_14) <=> ! [D15_15] : ((member(D15_15, B13_13) <=> member(D15_15, C14_14)))))
% 26.61/3.89 -> [72] (=(C14_5_2, C14_5_2) <=> ! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2))))
% 26.61/3.89
% 26.61/3.89 [72] BETA_EQUIV : (=(C14_5_2, C14_5_2) <=> ! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2))))
% 26.61/3.89 -> [74] ~=(C14_5_2, C14_5_2), ~! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2)))
% 26.61/3.89 -> [75] =(C14_5_2, C14_5_2), ! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2)))
% 26.61/3.89
% 26.61/3.89 [74] DELTA_NOT_FORALL : ~! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2)))
% 26.61/3.89 -> [83] ~(member(skolem_D1515(C14_5_2, C14_5_2), C14_5_2) <=> member(skolem_D1515(C14_5_2, C14_5_2), C14_5_2))
% 26.61/3.89
% 26.61/3.89 [83] CLOSURE : ~! [D15_15] : ((member(D15_15, C14_5_2) <=> member(D15_15, C14_5_2)))
% 26.61/3.89
% 26.61/3.89 [82] BETA_NOT_AND : ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616) & member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818)))
% 26.61/3.89 -> [123] ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_B1616)
% 26.61/3.89 -> [124] ~member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [123] CLOSURE : =
% 26.61/3.89
% 26.61/3.89 [124] Rewrite : ~member(skolem_D88(skolem_B1616, skolem_D1818), union(skolem_C1717, skolem_D1818))
% 26.61/3.89 -> [125] ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89
% 26.61/3.89 [125] ALPHA_NOT_OR : ~(member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717) | member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818))
% 26.61/3.89 -> [126] ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_C1717), ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 [126] CLOSURE : ~member(skolem_D88(skolem_B1616, skolem_D1818), skolem_D1818)
% 26.61/3.89
% 26.61/3.89 % SZS output end Proof for theBenchmark.p
% 26.61/3.89 [3.580706s][1][Res] 19457 goroutines created
% 26.61/3.89 ==== Result ====
% 26.61/3.89 [3.580751s][1][Res] VALID
% 26.61/3.89 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------