TSTP Solution File: SET628+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n020.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 04:16:57 EDT 2022
% Result : Theorem 16.42s 5.17s
% Output : Proof 16.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 07:03:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 10
% 0.13/0.35 Launch Gotab with destructive = true
% 16.42/5.17 % SZS output start Proof for theBenchmark.p
% 16.42/5.17 [0] ALPHA_AND : (! [B6_6] : (~member(B6_6, empty_set)) & ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> ! [D9_9] : ((member(D9_9, B7_7) <=> member(D9_9, C8_8))))) & ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11))) & ! [B12_12, C13_13] : ((intersect(B12_12, C13_13) => intersect(C13_13, B12_12))) & ~! [B16_16] : ((intersect(B16_16, B16_16) <=> not_equal(B16_16, empty_set))))
% 16.42/5.17 -> [1] ! [B6_6] : (~member(B6_6, empty_set)), ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> ! [D9_9] : ((member(D9_9, B7_7) <=> member(D9_9, C8_8))))), ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11))), ! [B12_12, C13_13] : ((intersect(B12_12, C13_13) => intersect(C13_13, B12_12))), ~! [B16_16] : ((intersect(B16_16, B16_16) <=> not_equal(B16_16, empty_set)))
% 16.42/5.17
% 16.42/5.17 [1] DELTA_NOT_FORALL : ~! [B16_16] : ((intersect(B16_16, B16_16) <=> not_equal(B16_16, empty_set)))
% 16.42/5.17 -> [2] ~(intersect(skolem_B1616, skolem_B1616) <=> not_equal(skolem_B1616, empty_set))
% 16.42/5.17
% 16.42/5.17 [2] BETA_NOT_EQUIV : ~(intersect(skolem_B1616, skolem_B1616) <=> not_equal(skolem_B1616, empty_set))
% 16.42/5.17 -> [3] ~intersect(skolem_B1616, skolem_B1616), not_equal(skolem_B1616, empty_set)
% 16.42/5.17 -> [4] intersect(skolem_B1616, skolem_B1616), ~not_equal(skolem_B1616, empty_set)
% 16.42/5.17
% 16.42/5.17 [4] Rewrite : intersect(skolem_B1616, skolem_B1616)
% 16.42/5.17 -> [6] (member(skolem_D55(skolem_B1616, skolem_B1616), skolem_B1616) & member(skolem_D55(skolem_B1616, skolem_B1616), skolem_B1616))
% 16.42/5.17
% 16.42/5.17 [6] ALPHA_AND : (member(skolem_D55(skolem_B1616, skolem_B1616), skolem_B1616) & member(skolem_D55(skolem_B1616, skolem_B1616), skolem_B1616))
% 16.42/5.17 -> [8] member(skolem_D55(skolem_B1616, skolem_B1616), skolem_B1616)
% 16.42/5.17
% 16.42/5.17 [8] GAMMA_FORALL : ! [B6_6] : (~member(B6_6, empty_set))
% 16.42/5.17 -> [10] ~member(skolem_D55(skolem_B1616, skolem_B1616), empty_set)
% 16.42/5.17
% 16.42/5.17 [10] GAMMA_FORALL : ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> ! [D9_9] : ((member(D9_9, B7_7) <=> member(D9_9, C8_8)))))
% 16.42/5.17 -> [14] (=(C8_1_1, C8_1_1) <=> ! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1))))
% 16.42/5.17
% 16.42/5.17 [14] BETA_EQUIV : (=(C8_1_1, C8_1_1) <=> ! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1))))
% 16.42/5.17 -> [15] ~=(C8_1_1, C8_1_1), ~! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1)))
% 16.42/5.17 -> [16] =(C8_1_1, C8_1_1), ! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1)))
% 16.42/5.17
% 16.42/5.17 [15] DELTA_NOT_FORALL : ~! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1)))
% 16.42/5.17 -> [20] ~(member(skolem_D99(C8_1_1, C8_1_1), C8_1_1) <=> member(skolem_D99(C8_1_1, C8_1_1), C8_1_1))
% 16.42/5.17
% 16.42/5.17 [20] CLOSURE : ~! [D9_9] : ((member(D9_9, C8_1_1) <=> member(D9_9, C8_1_1)))
% 16.42/5.17
% 16.42/5.17 [16] GAMMA_FORALL : ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11)))
% 16.42/5.17 -> [22] (not_equal(skolem_B1616, empty_set) <=> ~=(skolem_B1616, empty_set))
% 16.42/5.17
% 16.42/5.17 [22] BETA_EQUIV : (not_equal(skolem_B1616, empty_set) <=> ~=(skolem_B1616, empty_set))
% 16.42/5.17 -> [23] ~not_equal(skolem_B1616, empty_set), ~~=(skolem_B1616, empty_set)
% 16.42/5.17 -> [24] not_equal(skolem_B1616, empty_set), ~=(skolem_B1616, empty_set)
% 16.42/5.17
% 16.42/5.17 [24] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [40] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [3] Rewrite : ~intersect(skolem_B1616, skolem_B1616)
% 16.42/5.17 -> [5] ~? [D5_5] : ((member(D5_5, skolem_B1616) & member(D5_5, skolem_B1616)))
% 16.42/5.17
% 16.42/5.17 [5] GAMMA_FORALL : ! [B6_6] : (~member(B6_6, empty_set))
% 16.42/5.17 -> [7] ~member(skolem_D55(empty_set, empty_set), empty_set)
% 16.42/5.17
% 16.42/5.17 [7] GAMMA_FORALL : ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> ! [D9_9] : ((member(D9_9, B7_7) <=> member(D9_9, C8_8)))))
% 16.42/5.17 -> [9] (=(skolem_B1616, empty_set) <=> ! [D9_9] : ((member(D9_9, skolem_B1616) <=> member(D9_9, empty_set))))
% 16.42/5.17
% 16.42/5.17 [9] BETA_EQUIV : (=(skolem_B1616, empty_set) <=> ! [D9_9] : ((member(D9_9, skolem_B1616) <=> member(D9_9, empty_set))))
% 16.42/5.17 -> [11] ~=(skolem_B1616, empty_set), ~! [D9_9] : ((member(D9_9, skolem_B1616) <=> member(D9_9, empty_set)))
% 16.42/5.17 -> [12] =(skolem_B1616, empty_set), ! [D9_9] : ((member(D9_9, skolem_B1616) <=> member(D9_9, empty_set)))
% 16.42/5.17
% 16.42/5.17 [12] GAMMA_FORALL : ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11)))
% 16.42/5.17 -> [17] (not_equal(skolem_B1616, empty_set) <=> ~=(skolem_B1616, empty_set))
% 16.42/5.17
% 16.42/5.17 [17] BETA_EQUIV : (not_equal(skolem_B1616, empty_set) <=> ~=(skolem_B1616, empty_set))
% 16.42/5.17 -> [18] ~not_equal(skolem_B1616, empty_set), ~~=(skolem_B1616, empty_set)
% 16.42/5.17 -> [19] not_equal(skolem_B1616, empty_set), ~=(skolem_B1616, empty_set)
% 16.42/5.17
% 16.42/5.17 [18] ALPHA_NOT_NOT : ~~=(skolem_B1616, empty_set)
% 16.42/5.17 -> [21] =(skolem_B1616, empty_set)
% 16.42/5.17
% 16.42/5.17 [21] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [19] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [13] BETA_NOT_EQUIV : ~(member(skolem_D99(skolem_B1616, empty_set), skolem_B1616) <=> member(skolem_D99(skolem_B1616, empty_set), empty_set))
% 16.42/5.17 -> [486] ~member(skolem_D99(skolem_B1616, empty_set), skolem_B1616), member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17 -> [487] member(skolem_D99(skolem_B1616, empty_set), skolem_B1616), ~member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17
% 16.42/5.17 [487] GAMMA_FORALL : ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11)))
% 16.42/5.17 -> [488] (not_equal(C11_9_2, C11_9_2) <=> ~=(C11_9_2, C11_9_2))
% 16.42/5.17
% 16.42/5.17 [488] BETA_EQUIV : (not_equal(C11_9_2, C11_9_2) <=> ~=(C11_9_2, C11_9_2))
% 16.42/5.17 -> [489] ~not_equal(C11_9_2, C11_9_2), ~~=(C11_9_2, C11_9_2)
% 16.42/5.17 -> [490] not_equal(C11_9_2, C11_9_2), ~=(C11_9_2, C11_9_2)
% 16.42/5.17
% 16.42/5.17 [490] CLOSURE : ~=(C11_9_2, C11_9_2)
% 16.42/5.17
% 16.42/5.17 [491] GAMMA_FORALL : ! [B12_12, C13_13] : ((intersect(B12_12, C13_13) => intersect(C13_13, B12_12)))
% 16.42/5.17 -> [492] (intersect(B12_4_3, empty_set) => intersect(empty_set, B12_4_3))
% 16.42/5.17
% 16.42/5.17 [492] BETA_IMPLY : (intersect(B12_4_3, empty_set) => intersect(empty_set, B12_4_3))
% 16.42/5.17 -> [493] ~intersect(B12_4_3, empty_set)
% 16.42/5.17 -> [494] intersect(empty_set, B12_4_3)
% 16.42/5.17
% 16.42/5.17 [493] Rewrite : ~intersect(B12_4_3, empty_set)
% 16.42/5.17 -> [496] ~? [D5_5] : ((member(D5_5, B12_4_3) & member(D5_5, empty_set)))
% 16.42/5.17
% 16.42/5.17 [496] GAMMA_NOT_EXISTS : ~? [D5_5] : ((member(D5_5, skolem_B1616) & member(D5_5, skolem_B1616)))
% 16.42/5.17 -> [498] ~(member(skolem_D99(skolem_B1616, empty_set), skolem_B1616) & member(skolem_D99(skolem_B1616, empty_set), skolem_B1616))
% 16.42/5.17
% 16.42/5.17 [498] BETA_NOT_AND : ~(member(skolem_D99(skolem_B1616, empty_set), skolem_B1616) & member(skolem_D99(skolem_B1616, empty_set), skolem_B1616))
% 16.42/5.17 -> [499] ~member(skolem_D99(skolem_B1616, empty_set), skolem_B1616)
% 16.42/5.17 -> [500] ~member(skolem_D99(skolem_B1616, empty_set), skolem_B1616)
% 16.42/5.17
% 16.42/5.17 [499] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [500] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [494] Rewrite : intersect(empty_set, B12_4_3)
% 16.42/5.17 -> [495] (member(skolem_D55(empty_set, B12_4_3), empty_set) & member(skolem_D55(empty_set, B12_4_3), B12_4_3))
% 16.42/5.17
% 16.42/5.17 [495] ALPHA_AND : (member(skolem_D55(empty_set, B12_4_3), empty_set) & member(skolem_D55(empty_set, B12_4_3), B12_4_3))
% 16.42/5.17 -> [497] member(skolem_D55(empty_set, B12_4_3), empty_set), member(skolem_D55(empty_set, B12_4_3), B12_4_3)
% 16.42/5.17
% 16.42/5.17 [497] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [486] GAMMA_FORALL : ! [B10_10, C11_11] : ((not_equal(B10_10, C11_11) <=> ~=(B10_10, C11_11)))
% 16.42/5.17 -> [501] (not_equal(C11_10_2, C11_10_2) <=> ~=(C11_10_2, C11_10_2))
% 16.42/5.17
% 16.42/5.17 [501] BETA_EQUIV : (not_equal(C11_10_2, C11_10_2) <=> ~=(C11_10_2, C11_10_2))
% 16.42/5.17 -> [502] ~not_equal(C11_10_2, C11_10_2), ~~=(C11_10_2, C11_10_2)
% 16.42/5.17 -> [503] not_equal(C11_10_2, C11_10_2), ~=(C11_10_2, C11_10_2)
% 16.42/5.17
% 16.42/5.17 [503] CLOSURE : ~=(C11_10_2, C11_10_2)
% 16.42/5.17
% 16.42/5.17 [504] GAMMA_FORALL : ! [B12_12, C13_13] : ((intersect(B12_12, C13_13) => intersect(C13_13, B12_12)))
% 16.42/5.17 -> [505] (intersect(empty_set, empty_set) => intersect(empty_set, empty_set))
% 16.42/5.17
% 16.42/5.17 [505] BETA_IMPLY : (intersect(empty_set, empty_set) => intersect(empty_set, empty_set))
% 16.42/5.17 -> [506] ~intersect(empty_set, empty_set)
% 16.42/5.17 -> [507] intersect(empty_set, empty_set)
% 16.42/5.17
% 16.42/5.17 [507] Rewrite : intersect(empty_set, empty_set)
% 16.42/5.17 -> [508] (member(skolem_D55(empty_set, empty_set), empty_set) & member(skolem_D55(empty_set, empty_set), empty_set))
% 16.42/5.17
% 16.42/5.17 [508] ALPHA_AND : (member(skolem_D55(empty_set, empty_set), empty_set) & member(skolem_D55(empty_set, empty_set), empty_set))
% 16.42/5.17 -> [510] member(skolem_D55(empty_set, empty_set), empty_set)
% 16.42/5.17
% 16.42/5.17 [510] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [506] GAMMA_NOT_EXISTS : ~? [D5_5] : ((member(D5_5, skolem_B1616) & member(D5_5, skolem_B1616)))
% 16.42/5.17 -> [520] ~(member(D5_19_4, skolem_B1616) & member(D5_19_4, skolem_B1616))
% 16.42/5.17
% 16.42/5.17 [520] BETA_NOT_AND : ~(member(D5_19_4, skolem_B1616) & member(D5_19_4, skolem_B1616))
% 16.42/5.17 -> [521] ~member(D5_19_4, skolem_B1616)
% 16.42/5.17 -> [522] ~member(D5_19_4, skolem_B1616)
% 16.42/5.17
% 16.42/5.17 [522] GAMMA_NOT_EXISTS : ~? [D5_5] : ((member(D5_5, empty_set) & member(D5_5, empty_set)))
% 16.42/5.17 -> [524] ~(member(skolem_D99(skolem_B1616, empty_set), empty_set) & member(skolem_D99(skolem_B1616, empty_set), empty_set))
% 16.42/5.17
% 16.42/5.17 [524] BETA_NOT_AND : ~(member(skolem_D99(skolem_B1616, empty_set), empty_set) & member(skolem_D99(skolem_B1616, empty_set), empty_set))
% 16.42/5.17 -> [527] ~member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17 -> [528] ~member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17
% 16.42/5.17 [527] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [528] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [521] GAMMA_NOT_EXISTS : ~? [D5_5] : ((member(D5_5, empty_set) & member(D5_5, empty_set)))
% 16.42/5.17 -> [523] ~(member(skolem_D99(skolem_B1616, empty_set), empty_set) & member(skolem_D99(skolem_B1616, empty_set), empty_set))
% 16.42/5.17
% 16.42/5.17 [523] BETA_NOT_AND : ~(member(skolem_D99(skolem_B1616, empty_set), empty_set) & member(skolem_D99(skolem_B1616, empty_set), empty_set))
% 16.42/5.17 -> [525] ~member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17 -> [526] ~member(skolem_D99(skolem_B1616, empty_set), empty_set)
% 16.42/5.17
% 16.42/5.17 [525] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 [526] CLOSURE : =
% 16.42/5.17
% 16.42/5.17 % SZS output end Proof for theBenchmark.p
% 16.42/5.17 [4.819460s][1][Res] 18940 goroutines created
% 16.42/5.17 ==== Result ====
% 16.42/5.17 [4.819481s][1][Res] VALID
% 16.42/5.17 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------