TSTP Solution File: SEU320+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU320+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 05:56:29 EDT 2022
% Result : Theorem 53.84s 10.42s
% Output : Proof 53.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.14 % Command : goeland -dmt -presko -proof %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 12:15:32 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 [DMT] DMT loaded with preskolemization
% 0.14/0.36 [EQ] equality loaded.
% 0.14/0.36 [0.000025s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.36 Start search
% 0.14/0.36 nb_step : 1 - limit : 13
% 0.14/0.36 Launch Gotab with destructive = true
% 53.84/10.42 % SZS output start Proof for theBenchmark.p
% 53.84/10.42 [0] ALPHA_AND : ($true & ! [A2_2, B3_3] : ((element(B3_3, powerset(A2_2)) => element(subset_complement(A2_2, B3_3), powerset(A2_2)))) & ! [A4_4] : ((top_str(A4_4) => one_sorted_str(A4_4))) & $true & $true & $true & ? [A5_5] : (top_str(A5_5)) & ? [A6_6] : (one_sorted_str(A6_6)) & ! [A7_7] : (? [B8_8] : (element(B8_8, A7_7))) & ! [A9_9, B10_10] : ((element(B10_10, powerset(A9_9)) => =(subset_complement(A9_9, subset_complement(A9_9, B10_10)), B10_10))) & ! [A11_11, B12_12] : (subset(A11_11, A11_11)) & ! [A13_13] : ((top_str(A13_13) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(A13_13))) => (closed_subset(B14_14, A13_13) <=> open_subset(subset_complement(the_carrier(A13_13), B14_14), A13_13)))))) & ! [A17_17, B18_18] : ((element(A17_17, powerset(B18_18)) <=> subset(A17_17, B18_18))) & ~! [A15_15] : ((top_str(A15_15) => ! [B16_16] : ((element(B16_16, powerset(the_carrier(A15_15))) => (open_subset(B16_16, A15_15) <=> closed_subset(subset_complement(the_carrier(A15_15), B16_16), A15_15)))))))
% 53.84/10.42 -> [1] $true, ! [A2_2, B3_3] : ((element(B3_3, powerset(A2_2)) => element(subset_complement(A2_2, B3_3), powerset(A2_2)))), ! [A4_4] : ((top_str(A4_4) => one_sorted_str(A4_4))), ? [A5_5] : (top_str(A5_5)), ? [A6_6] : (one_sorted_str(A6_6)), ! [A7_7] : (? [B8_8] : (element(B8_8, A7_7))), ! [A9_9, B10_10] : ((element(B10_10, powerset(A9_9)) => =(subset_complement(A9_9, subset_complement(A9_9, B10_10)), B10_10))), ! [A11_11, B12_12] : (subset(A11_11, A11_11)), ! [A13_13] : ((top_str(A13_13) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(A13_13))) => (closed_subset(B14_14, A13_13) <=> open_subset(subset_complement(the_carrier(A13_13), B14_14), A13_13)))))), ! [A17_17, B18_18] : ((element(A17_17, powerset(B18_18)) <=> subset(A17_17, B18_18))), ~! [A15_15] : ((top_str(A15_15) => ! [B16_16] : ((element(B16_16, powerset(the_carrier(A15_15))) => (open_subset(B16_16, A15_15) <=> closed_subset(subset_complement(the_carrier(A15_15), B16_16), A15_15))))))
% 53.84/10.42
% 53.84/10.42 [1] DELTA_EXISTS : ? [A5_5] : (top_str(A5_5))
% 53.84/10.42 -> [2] top_str(skolem_A55)
% 53.84/10.42
% 53.84/10.42 [2] DELTA_EXISTS : ? [A6_6] : (one_sorted_str(A6_6))
% 53.84/10.42 -> [3] one_sorted_str(skolem_A66)
% 53.84/10.42
% 53.84/10.42 [3] DELTA_NOT_FORALL : ~! [A15_15] : ((top_str(A15_15) => ! [B16_16] : ((element(B16_16, powerset(the_carrier(A15_15))) => (open_subset(B16_16, A15_15) <=> closed_subset(subset_complement(the_carrier(A15_15), B16_16), A15_15))))))
% 53.84/10.42 -> [4] ~(top_str(skolem_A1515) => ! [B16_16] : ((element(B16_16, powerset(the_carrier(skolem_A1515))) => (open_subset(B16_16, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), B16_16), skolem_A1515)))))
% 53.84/10.42
% 53.84/10.42 [4] ALPHA_NOT_IMPLY : ~(top_str(skolem_A1515) => ! [B16_16] : ((element(B16_16, powerset(the_carrier(skolem_A1515))) => (open_subset(B16_16, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), B16_16), skolem_A1515)))))
% 53.84/10.42 -> [5] top_str(skolem_A1515), ~! [B16_16] : ((element(B16_16, powerset(the_carrier(skolem_A1515))) => (open_subset(B16_16, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), B16_16), skolem_A1515))))
% 53.84/10.42
% 53.84/10.42 [5] DELTA_NOT_FORALL : ~! [B16_16] : ((element(B16_16, powerset(the_carrier(skolem_A1515))) => (open_subset(B16_16, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), B16_16), skolem_A1515))))
% 53.84/10.42 -> [6] ~(element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => (open_subset(skolem_B1616, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [6] ALPHA_NOT_IMPLY : ~(element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => (open_subset(skolem_B1616, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515)))
% 53.84/10.42 -> [7] element(skolem_B1616, powerset(the_carrier(skolem_A1515))), ~(open_subset(skolem_B1616, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515))
% 53.84/10.42
% 53.84/10.42 [7] BETA_NOT_EQUIV : ~(open_subset(skolem_B1616, skolem_A1515) <=> closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515))
% 53.84/10.42 -> [8] ~open_subset(skolem_B1616, skolem_A1515), closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515)
% 53.84/10.42 -> [9] open_subset(skolem_B1616, skolem_A1515), ~closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [8] GAMMA_FORALL : ! [A2_2, B3_3] : ((element(B3_3, powerset(A2_2)) => element(subset_complement(A2_2, B3_3), powerset(A2_2))))
% 53.84/10.42 -> [10] (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))))
% 53.84/10.42
% 53.84/10.42 [10] BETA_IMPLY : (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))))
% 53.84/10.42 -> [11] ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [12] element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [11] CLOSURE : ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [12] GAMMA_FORALL : ! [A4_4] : ((top_str(A4_4) => one_sorted_str(A4_4)))
% 53.84/10.42 -> [16] (top_str(skolem_A55) => one_sorted_str(skolem_A55))
% 53.84/10.42
% 53.84/10.42 [16] BETA_IMPLY : (top_str(skolem_A55) => one_sorted_str(skolem_A55))
% 53.84/10.42 -> [17] ~top_str(skolem_A55)
% 53.84/10.42 -> [18] one_sorted_str(skolem_A55)
% 53.84/10.42
% 53.84/10.42 [17] CLOSURE : ~top_str(skolem_A55)
% 53.84/10.42
% 53.84/10.42 [26] BETA_IMPLY : (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => =(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_B1616))
% 53.84/10.42 -> [650] ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [651] =(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_B1616)
% 53.84/10.42
% 53.84/10.42 [651] GAMMA_FORALL : ! [A11_11, B12_12] : (subset(A11_11, A11_11))
% 53.84/10.42 -> [652] subset(A11_25_4, A11_25_4)
% 53.84/10.42
% 53.84/10.42 [652] GAMMA_FORALL : ! [A13_13] : ((top_str(A13_13) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(A13_13))) => (closed_subset(B14_14, A13_13) <=> open_subset(subset_complement(the_carrier(A13_13), B14_14), A13_13))))))
% 53.84/10.42 -> [653] (top_str(skolem_A1515) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(skolem_A1515))) => (closed_subset(B14_14, skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), B14_14), skolem_A1515)))))
% 53.84/10.42
% 53.84/10.42 [653] BETA_IMPLY : (top_str(skolem_A1515) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(skolem_A1515))) => (closed_subset(B14_14, skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), B14_14), skolem_A1515)))))
% 53.84/10.42 -> [654] ~top_str(skolem_A1515)
% 53.84/10.42 -> [655] ! [B14_14] : ((element(B14_14, powerset(the_carrier(skolem_A1515))) => (closed_subset(B14_14, skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), B14_14), skolem_A1515))))
% 53.84/10.42
% 53.84/10.42 [654] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [656] BETA_EQUIV : (element(skolem_B88(powerset(B18_4_6)), powerset(B18_4_6)) <=> subset(skolem_B88(powerset(B18_4_6)), B18_4_6))
% 53.84/10.42 -> [862] ~element(skolem_B88(powerset(B18_4_6)), powerset(B18_4_6)), ~subset(skolem_B88(powerset(B18_4_6)), B18_4_6)
% 53.84/10.42 -> [863] element(skolem_B88(powerset(B18_4_6)), powerset(B18_4_6)), subset(skolem_B88(powerset(B18_4_6)), B18_4_6)
% 53.84/10.42
% 53.84/10.42 [862] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [864] BETA_IMPLY : (element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))) => (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)))
% 53.84/10.42 -> [918] ~element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [919] (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515))
% 53.84/10.42
% 53.84/10.42 [919] BETA_EQUIV : (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515))
% 53.84/10.42 -> [920] ~closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515), ~open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)
% 53.84/10.42 -> [921] closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515), open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [921] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [920] CLOSURE : ~closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [918] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [650] CLOSURE : ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [9] GAMMA_FORALL : ! [A2_2, B3_3] : ((element(B3_3, powerset(A2_2)) => element(subset_complement(A2_2, B3_3), powerset(A2_2))))
% 53.84/10.42 -> [13] (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))))
% 53.84/10.42
% 53.84/10.42 [13] BETA_IMPLY : (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))))
% 53.84/10.42 -> [14] ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [15] element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [14] CLOSURE : ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [19] BETA_IMPLY : (top_str(skolem_A1515) => one_sorted_str(skolem_A1515))
% 53.84/10.42 -> [1078] ~top_str(skolem_A1515)
% 53.84/10.42 -> [1079] one_sorted_str(skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [1078] CLOSURE : ~top_str(skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [1079] GAMMA_FORALL : ! [A7_7] : (? [B8_8] : (element(B8_8, A7_7)))
% 53.84/10.42 -> [1080] ? [B8_8] : (element(B8_8, A7_50_2))
% 53.84/10.42
% 53.84/10.42 [1080] DELTA_EXISTS : ? [B8_8] : (element(B8_8, A7_50_2))
% 53.84/10.42 -> [1081] element(skolem_B88(A7_50_2), A7_50_2)
% 53.84/10.42
% 53.84/10.42 [1081] GAMMA_FORALL : ! [A9_9, B10_10] : ((element(B10_10, powerset(A9_9)) => =(subset_complement(A9_9, subset_complement(A9_9, B10_10)), B10_10)))
% 53.84/10.42 -> [1082] (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => =(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_B1616))
% 53.84/10.42
% 53.84/10.42 [1082] BETA_IMPLY : (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) => =(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_B1616))
% 53.84/10.42 -> [1083] ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [1084] =(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_B1616)
% 53.84/10.42
% 53.84/10.42 [1083] CLOSURE : ~element(skolem_B1616, powerset(the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [1086] BETA_IMPLY : (top_str(skolem_A1515) => ! [B14_14] : ((element(B14_14, powerset(the_carrier(skolem_A1515))) => (closed_subset(B14_14, skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), B14_14), skolem_A1515)))))
% 53.84/10.42 -> [1226] ~top_str(skolem_A1515)
% 53.84/10.42 -> [1227] ! [B14_14] : ((element(B14_14, powerset(the_carrier(skolem_A1515))) => (closed_subset(B14_14, skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), B14_14), skolem_A1515))))
% 53.84/10.42
% 53.84/10.42 [1226] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [1227] GAMMA_FORALL : ! [A17_17, B18_18] : ((element(A17_17, powerset(B18_18)) <=> subset(A17_17, B18_18)))
% 53.84/10.42 -> [1228] (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) <=> subset(skolem_B1616, the_carrier(skolem_A1515)))
% 53.84/10.42
% 53.84/10.42 [1228] BETA_EQUIV : (element(skolem_B1616, powerset(the_carrier(skolem_A1515))) <=> subset(skolem_B1616, the_carrier(skolem_A1515)))
% 53.84/10.42 -> [1229] ~element(skolem_B1616, powerset(the_carrier(skolem_A1515))), ~subset(skolem_B1616, the_carrier(skolem_A1515))
% 53.84/10.42 -> [1230] element(skolem_B1616, powerset(the_carrier(skolem_A1515))), subset(skolem_B1616, the_carrier(skolem_A1515))
% 53.84/10.42
% 53.84/10.42 [1229] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [1231] BETA_IMPLY : (element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515))) => (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)))
% 53.84/10.42 -> [1236] ~element(subset_complement(the_carrier(skolem_A1515), skolem_B1616), powerset(the_carrier(skolem_A1515)))
% 53.84/10.42 -> [1237] (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515))
% 53.84/10.42
% 53.84/10.42 [1237] BETA_EQUIV : (closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515) <=> open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515))
% 53.84/10.42 -> [1238] ~closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515), ~open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)
% 53.84/10.42 -> [1239] closed_subset(subset_complement(the_carrier(skolem_A1515), skolem_B1616), skolem_A1515), open_subset(subset_complement(the_carrier(skolem_A1515), subset_complement(the_carrier(skolem_A1515), skolem_B1616)), skolem_A1515)
% 53.84/10.42
% 53.84/10.42 [1238] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [1239] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 [1236] CLOSURE : =
% 53.84/10.42
% 53.84/10.42 % SZS output end Proof for theBenchmark.p
% 53.84/10.42 [10.060364s][1][Res] 92261 goroutines created
% 53.84/10.42 ==== Result ====
% 53.84/10.42 [10.060400s][1][Res] VALID
% 53.84/10.42 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------