TSTP Solution File: SEU123+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n002.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 05:55:25 EDT 2022
% Result : Theorem 9.19s 2.29s
% Output : Proof 9.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n002.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 09:45:17 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 [0.000040s][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
% 9.19/2.28 % SZS output start Proof for theBenchmark.p
% 9.19/2.29 [0] ALPHA_AND : (! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2))) & ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4)))) & $true & empty(empty_set) & ? [A6_6] : (empty(A6_6)) & ? [A7_7] : (~empty(A7_7)) & ! [A8_8, B9_9] : (subset(A8_8, A8_8)) & ! [A10_10] : (subset(empty_set, A10_10)) & ! [A12_12] : ((empty(A12_12) => =(A12_12, empty_set))) & ! [A13_13, B14_14] : (~(in(A13_13, B14_14) & empty(B14_14))) & ! [A15_15, B16_16] : (~((empty(A15_15) & ~=(A15_15, B16_16)) & empty(B16_16))) & ~! [A11_11] : ((subset(A11_11, empty_set) => =(A11_11, empty_set))))
% 9.19/2.29 -> [1] ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2))), ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4)))), $true, empty(empty_set), ? [A6_6] : (empty(A6_6)), ? [A7_7] : (~empty(A7_7)), ! [A8_8, B9_9] : (subset(A8_8, A8_8)), ! [A10_10] : (subset(empty_set, A10_10)), ! [A12_12] : ((empty(A12_12) => =(A12_12, empty_set))), ! [A13_13, B14_14] : (~(in(A13_13, B14_14) & empty(B14_14))), ! [A15_15, B16_16] : (~((empty(A15_15) & ~=(A15_15, B16_16)) & empty(B16_16))), ~! [A11_11] : ((subset(A11_11, empty_set) => =(A11_11, empty_set)))
% 9.19/2.29
% 9.19/2.29 [1] DELTA_EXISTS : ? [A6_6] : (empty(A6_6))
% 9.19/2.29 -> [2] empty(skolem_A66)
% 9.19/2.29
% 9.19/2.29 [2] DELTA_EXISTS : ? [A7_7] : (~empty(A7_7))
% 9.19/2.29 -> [3] ~empty(skolem_A77)
% 9.19/2.29
% 9.19/2.29 [3] DELTA_NOT_FORALL : ~! [A11_11] : ((subset(A11_11, empty_set) => =(A11_11, empty_set)))
% 9.19/2.29 -> [4] ~(subset(skolem_A1111, empty_set) => =(skolem_A1111, empty_set))
% 9.19/2.29
% 9.19/2.29 [4] ALPHA_NOT_IMPLY : ~(subset(skolem_A1111, empty_set) => =(skolem_A1111, empty_set))
% 9.19/2.29 -> [5] subset(skolem_A1111, empty_set), ~=(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [5] GAMMA_FORALL : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29 -> [6] (in(A2_0_0, B3_0_0) => ~in(B3_0_0, A2_0_0))
% 9.19/2.29
% 9.19/2.29 [6] BETA_IMPLY : (in(A2_0_0, B3_0_0) => ~in(B3_0_0, A2_0_0))
% 9.19/2.29 -> [7] ~in(A2_0_0, B3_0_0)
% 9.19/2.29 -> [8] ~in(B3_0_0, A2_0_0)
% 9.19/2.29
% 9.19/2.29 [7] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [9] (=(B5_0_1, B5_0_1) <=> (subset(B5_0_1, B5_0_1) & subset(B5_0_1, B5_0_1)))
% 9.19/2.29
% 9.19/2.29 [9] BETA_EQUIV : (=(B5_0_1, B5_0_1) <=> (subset(B5_0_1, B5_0_1) & subset(B5_0_1, B5_0_1)))
% 9.19/2.29 -> [11] ~=(B5_0_1, B5_0_1), ~(subset(B5_0_1, B5_0_1) & subset(B5_0_1, B5_0_1))
% 9.19/2.29 -> [12] =(B5_0_1, B5_0_1), (subset(B5_0_1, B5_0_1) & subset(B5_0_1, B5_0_1))
% 9.19/2.29
% 9.19/2.29 [11] CLOSURE : ~=(B5_0_1, B5_0_1)
% 9.19/2.29
% 9.19/2.29 [15] GAMMA_FORALL : ! [A8_8, B9_9] : (subset(A8_8, A8_8))
% 9.19/2.29 -> [17] subset(A8_0_2, A8_0_2)
% 9.19/2.29
% 9.19/2.29 [17] GAMMA_FORALL : ! [A10_10] : (subset(empty_set, A10_10))
% 9.19/2.29 -> [19] subset(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [19] GAMMA_FORALL : ! [A12_12] : ((empty(A12_12) => =(A12_12, empty_set)))
% 9.19/2.29 -> [21] (empty(empty_set) => =(empty_set, empty_set))
% 9.19/2.29
% 9.19/2.29 [21] BETA_IMPLY : (empty(empty_set) => =(empty_set, empty_set))
% 9.19/2.29 -> [22] ~empty(empty_set)
% 9.19/2.29 -> [23] =(empty_set, empty_set)
% 9.19/2.29
% 9.19/2.29 [22] CLOSURE : ~empty(empty_set)
% 9.19/2.29
% 9.19/2.29 [23] GAMMA_FORALL : ! [A13_13, B14_14] : (~(in(A13_13, B14_14) & empty(B14_14)))
% 9.19/2.29 -> [27] ~(in(A13_0_5, skolem_A66) & empty(skolem_A66))
% 9.19/2.29
% 9.19/2.29 [27] BETA_NOT_AND : ~(in(A13_0_5, skolem_A66) & empty(skolem_A66))
% 9.19/2.29 -> [28] ~in(A13_0_5, skolem_A66)
% 9.19/2.29 -> [29] ~empty(skolem_A66)
% 9.19/2.29
% 9.19/2.29 [29] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [33] BETA_NOT_AND : ~((empty(empty_set) & ~=(empty_set, skolem_A1111)) & empty(skolem_A1111))
% 9.19/2.29 -> [121] ~(empty(empty_set) & ~=(empty_set, skolem_A1111))
% 9.19/2.29 -> [122] ~empty(skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [121] BETA_NOT_AND : ~(empty(empty_set) & ~=(empty_set, skolem_A1111))
% 9.19/2.29 -> [123] ~empty(empty_set)
% 9.19/2.29 -> [124] ~~=(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [123] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [125] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [122] : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29 -> [133] ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29
% 9.19/2.29 [133] GAMMA_FORALL : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29 -> [134] (in(A2_3_0, B3_3_0) => ~in(B3_3_0, A2_3_0))
% 9.19/2.29
% 9.19/2.29 [134] BETA_IMPLY : (in(A2_3_0, B3_3_0) => ~in(B3_3_0, A2_3_0))
% 9.19/2.29 -> [135] ~in(A2_3_0, B3_3_0)
% 9.19/2.29 -> [136] ~in(B3_3_0, A2_3_0)
% 9.19/2.29
% 9.19/2.29 [135] : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [137] ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29
% 9.19/2.29 [137] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [139] (=(empty_set, skolem_A1111) <=> (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set)))
% 9.19/2.29
% 9.19/2.29 [139] BETA_EQUIV : (=(empty_set, skolem_A1111) <=> (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set)))
% 9.19/2.29 -> [141] ~=(empty_set, skolem_A1111), ~(subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [142] =(empty_set, skolem_A1111), (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29
% 9.19/2.29 [142] ALPHA_AND : (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [149] subset(empty_set, skolem_A1111), subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [149] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [141] BETA_NOT_AND : ~(subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [181] ~subset(empty_set, skolem_A1111)
% 9.19/2.29 -> [182] ~subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [182] CLOSURE : ~subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [181] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [136] : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [138] ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29
% 9.19/2.29 [138] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [140] (=(skolem_A1111, empty_set) <=> (subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111)))
% 9.19/2.29
% 9.19/2.29 [140] BETA_EQUIV : (=(skolem_A1111, empty_set) <=> (subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111)))
% 9.19/2.29 -> [143] ~=(skolem_A1111, empty_set), ~(subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111))
% 9.19/2.29 -> [144] =(skolem_A1111, empty_set), (subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111))
% 9.19/2.29
% 9.19/2.29 [144] ALPHA_AND : (subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111))
% 9.19/2.29 -> [150] subset(skolem_A1111, empty_set), subset(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [150] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [143] BETA_NOT_AND : ~(subset(skolem_A1111, empty_set) & subset(empty_set, skolem_A1111))
% 9.19/2.29 -> [207] ~subset(skolem_A1111, empty_set)
% 9.19/2.29 -> [208] ~subset(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [207] CLOSURE : ~subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [208] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [8] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [10] (=(B5_1_1, B5_1_1) <=> (subset(B5_1_1, B5_1_1) & subset(B5_1_1, B5_1_1)))
% 9.19/2.29
% 9.19/2.29 [10] BETA_EQUIV : (=(B5_1_1, B5_1_1) <=> (subset(B5_1_1, B5_1_1) & subset(B5_1_1, B5_1_1)))
% 9.19/2.29 -> [13] ~=(B5_1_1, B5_1_1), ~(subset(B5_1_1, B5_1_1) & subset(B5_1_1, B5_1_1))
% 9.19/2.29 -> [14] =(B5_1_1, B5_1_1), (subset(B5_1_1, B5_1_1) & subset(B5_1_1, B5_1_1))
% 9.19/2.29
% 9.19/2.29 [13] CLOSURE : ~=(B5_1_1, B5_1_1)
% 9.19/2.29
% 9.19/2.29 [16] GAMMA_FORALL : ! [A8_8, B9_9] : (subset(A8_8, A8_8))
% 9.19/2.29 -> [18] subset(A8_1_2, A8_1_2)
% 9.19/2.29
% 9.19/2.29 [18] GAMMA_FORALL : ! [A10_10] : (subset(empty_set, A10_10))
% 9.19/2.29 -> [20] subset(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [20] GAMMA_FORALL : ! [A12_12] : ((empty(A12_12) => =(A12_12, empty_set)))
% 9.19/2.29 -> [24] (empty(skolem_A66) => =(skolem_A66, empty_set))
% 9.19/2.29
% 9.19/2.29 [24] BETA_IMPLY : (empty(skolem_A66) => =(skolem_A66, empty_set))
% 9.19/2.29 -> [25] ~empty(skolem_A66)
% 9.19/2.29 -> [26] =(skolem_A66, empty_set)
% 9.19/2.29
% 9.19/2.29 [25] CLOSURE : ~empty(skolem_A66)
% 9.19/2.29
% 9.19/2.29 [26] GAMMA_FORALL : ! [A13_13, B14_14] : (~(in(A13_13, B14_14) & empty(B14_14)))
% 9.19/2.29 -> [30] ~(in(A13_1_5, empty_set) & empty(empty_set))
% 9.19/2.29
% 9.19/2.29 [30] BETA_NOT_AND : ~(in(A13_1_5, empty_set) & empty(empty_set))
% 9.19/2.29 -> [31] ~in(A13_1_5, empty_set)
% 9.19/2.29 -> [32] ~empty(empty_set)
% 9.19/2.29
% 9.19/2.29 [32] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [39] BETA_NOT_AND : ~((empty(empty_set) & ~=(empty_set, skolem_A1111)) & empty(skolem_A1111))
% 9.19/2.29 -> [128] ~(empty(empty_set) & ~=(empty_set, skolem_A1111))
% 9.19/2.29 -> [129] ~empty(skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [128] BETA_NOT_AND : ~(empty(empty_set) & ~=(empty_set, skolem_A1111))
% 9.19/2.29 -> [130] ~empty(empty_set)
% 9.19/2.29 -> [131] ~~=(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [131] ALPHA_NOT_NOT : ~~=(empty_set, skolem_A1111)
% 9.19/2.29 -> [132] =(empty_set, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [132] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [130] CLOSURE : ~empty(empty_set)
% 9.19/2.29
% 9.19/2.29 [129] : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29 -> [145] ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29
% 9.19/2.29 [145] GAMMA_FORALL : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 9.19/2.29 -> [146] (in(A2_4_0, B3_4_0) => ~in(B3_4_0, A2_4_0))
% 9.19/2.29
% 9.19/2.29 [146] BETA_IMPLY : (in(A2_4_0, B3_4_0) => ~in(B3_4_0, A2_4_0))
% 9.19/2.29 -> [147] ~in(A2_4_0, B3_4_0)
% 9.19/2.29 -> [148] ~in(B3_4_0, A2_4_0)
% 9.19/2.29
% 9.19/2.29 [147] : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [151] ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29
% 9.19/2.29 [151] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [152] (=(empty_set, skolem_A1111) <=> (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set)))
% 9.19/2.29
% 9.19/2.29 [152] BETA_EQUIV : (=(empty_set, skolem_A1111) <=> (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set)))
% 9.19/2.29 -> [153] ~=(empty_set, skolem_A1111), ~(subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [154] =(empty_set, skolem_A1111), (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29
% 9.19/2.29 [154] ALPHA_AND : (subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [164] subset(empty_set, skolem_A1111), subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [164] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [153] BETA_NOT_AND : ~(subset(empty_set, skolem_A1111) & subset(skolem_A1111, empty_set))
% 9.19/2.29 -> [185] ~subset(empty_set, skolem_A1111)
% 9.19/2.29 -> [186] ~subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [186] CLOSURE : ~subset(skolem_A1111, empty_set)
% 9.19/2.29
% 9.19/2.29 [185] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [148] : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [155] ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29
% 9.19/2.29 [155] GAMMA_FORALL : ! [A4_4, B5_5] : ((=(A4_4, B5_5) <=> (subset(A4_4, B5_5) & subset(B5_5, A4_4))))
% 9.19/2.29 -> [156] (=(skolem_A1111, skolem_A66) <=> (subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111)))
% 9.19/2.29
% 9.19/2.29 [156] BETA_EQUIV : (=(skolem_A1111, skolem_A66) <=> (subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111)))
% 9.19/2.29 -> [157] ~=(skolem_A1111, skolem_A66), ~(subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111))
% 9.19/2.29 -> [158] =(skolem_A1111, skolem_A66), (subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111))
% 9.19/2.29
% 9.19/2.29 [158] ALPHA_AND : (subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111))
% 9.19/2.29 -> [163] subset(skolem_A1111, skolem_A66), subset(skolem_A66, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [163] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [157] BETA_NOT_AND : ~(subset(skolem_A1111, skolem_A66) & subset(skolem_A66, skolem_A1111))
% 9.19/2.29 -> [213] ~subset(skolem_A1111, skolem_A66)
% 9.19/2.29 -> [214] ~subset(skolem_A66, skolem_A1111)
% 9.19/2.29
% 9.19/2.29 [213] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 [214] CLOSURE : =
% 9.19/2.29
% 9.19/2.29 % SZS output end Proof for theBenchmark.p
% 9.19/2.29 [1.936288s][1][Res] 17755 goroutines created
% 9.19/2.29 ==== Result ====
% 9.19/2.29 [1.936325s][1][Res] VALID
% 9.19/2.29 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------