TSTP Solution File: ITP019+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : ITP019+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 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 : Sat Sep 17 02:56:14 EDT 2022
% Result : Theorem 4.81s 1.68s
% Output : Proof 4.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP019+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n022.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 : Thu Sep 1 03:16:10 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 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 32
% 0.13/0.35 Launch Gotab with destructive = true
% 4.81/1.68 % SZS output start Proof for theBenchmark.p
% 4.81/1.68 [0] ALPHA_AND : ((ne(bool) & ne(ind) & ! [A14_14] : ((ne(A14_14) => ! [B15_15] : ((ne(B15_15) => ne(arr(A14_14, B15_15)))))) & ! [A16_16, B17_17, F18_18] : ((mem(F18_18, arr(A16_16, B17_17)) => ! [X19_19] : ((mem(X19_19, A16_16) => mem(ap(F18_18, X19_19), B17_17))))) & ! [Q20_20] : ((mem(Q20_20, bool) => ! [R21_21] : ((mem(R21_21, bool) => ((p(Q20_20) <=> p(R21_21)) => =(Q20_20, R21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [G25_25] : ((mem(G25_25, arr(A22_22, B23_23)) => (! [X26_26] : ((mem(X26_26, A22_22) => =(ap(F24_24, X26_26), ap(G25_25, X26_26)))) => =(F24_24, G25_25)))))) & ! [A27_27, Y28_28, X29_29] : ((mem(X29_29, A27_27) => =(ap(k(A27_27, Y28_28), X29_29), Y28_28))) & ! [A30_30, X31_31] : ((mem(X31_31, A30_30) => =(ap(i(A30_30), X31_31), X31_31)))) & mem(c_2Ebool_2E_7E, arr(bool, bool)) & ! [Q32_32] : ((mem(Q32_32, bool) => (p(ap(c_2Ebool_2E_7E, Q32_32)) <=> ~p(Q32_32)))) & mem(c_2Ebool_2EF, bool) & ~p(c_2Ebool_2EF) & mem(c_2Ebool_2ET, bool) & p(c_2Ebool_2ET) & mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))) & ! [Q33_33] : ((mem(Q33_33, bool) => ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, Q33_33), R34_34)) <=> (p(Q33_33) => p(R34_34))))))) & mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))) & ! [Q35_35] : ((mem(Q35_35, bool) => ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, Q35_35), R36_36)) <=> (p(Q35_35) & p(R36_36))))))) & ne(ty_2Enum_2Enum) & mem(c_2Enum_2E0, ty_2Enum_2Enum) & ne(ty_2Erealax_2Ereal) & ! [A037_37] : ((ne(A037_37) => ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(A037_37, A138_38)))))) & mem(c_2Ecomplex_2Ecomplex__of__num, arr(ty_2Enum_2Enum, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) & mem(c_2Ecomplex_2Ecomplex__inv, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) & ! [A_27a39_39] : ((ne(A_27a39_39) => mem(c_2Emin_2E_3D(A_27a39_39), arr(A_27a39_39, arr(A_27a39_39, bool))))) & ! [A40_40] : ((ne(A40_40) => ! [X41_41] : ((mem(X41_41, A40_40) => ! [Y42_42] : ((mem(Y42_42, A40_40) => (p(ap(ap(c_2Emin_2E_3D(A40_40), X41_41), Y42_42)) <=> =(X41_41, Y42_42)))))))) & ! [A_27a43_43] : ((ne(A_27a43_43) => mem(c_2Ebool_2E_21(A_27a43_43), arr(arr(A_27a43_43, bool), bool)))) & ! [A44_44] : ((ne(A44_44) => ! [Q45_45] : ((mem(Q45_45, arr(A44_44, bool)) => (p(ap(c_2Ebool_2E_21(A44_44), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, A44_44) => p(ap(Q45_45, X46_46))))))))) & $true & ! [A_27a47_47] : ((ne(A_27a47_47) => ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, A_27a47_47) => p(V0t48_48))) <=> p(V0t48_48)))))) & ! [V0t50_50] : ((mem(V0t50_50, bool) => (((((($true => p(V0t50_50)) <=> p(V0t50_50)) & ((p(V0t50_50) => $true) <=> $true)) & (($false => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => $false) <=> ~p(V0t50_50))))) & ! [V0z51_51] : ((mem(V0z51_51, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, V0z51_51), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(V0z51_51, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) & ~! [V0z52_52] : ((mem(V0z52_52, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (~=(V0z52_52, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, V0z52_52), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))))
% 4.81/1.68 -> [1] (ne(bool) & ne(ind) & ! [A14_14] : ((ne(A14_14) => ! [B15_15] : ((ne(B15_15) => ne(arr(A14_14, B15_15)))))) & ! [A16_16, B17_17, F18_18] : ((mem(F18_18, arr(A16_16, B17_17)) => ! [X19_19] : ((mem(X19_19, A16_16) => mem(ap(F18_18, X19_19), B17_17))))) & ! [Q20_20] : ((mem(Q20_20, bool) => ! [R21_21] : ((mem(R21_21, bool) => ((p(Q20_20) <=> p(R21_21)) => =(Q20_20, R21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [G25_25] : ((mem(G25_25, arr(A22_22, B23_23)) => (! [X26_26] : ((mem(X26_26, A22_22) => =(ap(F24_24, X26_26), ap(G25_25, X26_26)))) => =(F24_24, G25_25)))))) & ! [A27_27, Y28_28, X29_29] : ((mem(X29_29, A27_27) => =(ap(k(A27_27, Y28_28), X29_29), Y28_28))) & ! [A30_30, X31_31] : ((mem(X31_31, A30_30) => =(ap(i(A30_30), X31_31), X31_31)))), mem(c_2Ebool_2E_7E, arr(bool, bool)), ! [Q32_32] : ((mem(Q32_32, bool) => (p(ap(c_2Ebool_2E_7E, Q32_32)) <=> ~p(Q32_32)))), mem(c_2Ebool_2EF, bool), ~p(c_2Ebool_2EF), mem(c_2Ebool_2ET, bool), p(c_2Ebool_2ET), mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))), ! [Q33_33] : ((mem(Q33_33, bool) => ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, Q33_33), R34_34)) <=> (p(Q33_33) => p(R34_34))))))), mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))), ! [Q35_35] : ((mem(Q35_35, bool) => ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, Q35_35), R36_36)) <=> (p(Q35_35) & p(R36_36))))))), ne(ty_2Enum_2Enum), mem(c_2Enum_2E0, ty_2Enum_2Enum), ne(ty_2Erealax_2Ereal), ! [A037_37] : ((ne(A037_37) => ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(A037_37, A138_38)))))), mem(c_2Ecomplex_2Ecomplex__of__num, arr(ty_2Enum_2Enum, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))), mem(c_2Ecomplex_2Ecomplex__inv, arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal), ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))), ! [A_27a39_39] : ((ne(A_27a39_39) => mem(c_2Emin_2E_3D(A_27a39_39), arr(A_27a39_39, arr(A_27a39_39, bool))))), ! [A40_40] : ((ne(A40_40) => ! [X41_41] : ((mem(X41_41, A40_40) => ! [Y42_42] : ((mem(Y42_42, A40_40) => (p(ap(ap(c_2Emin_2E_3D(A40_40), X41_41), Y42_42)) <=> =(X41_41, Y42_42)))))))), ! [A_27a43_43] : ((ne(A_27a43_43) => mem(c_2Ebool_2E_21(A_27a43_43), arr(arr(A_27a43_43, bool), bool)))), ! [A44_44] : ((ne(A44_44) => ! [Q45_45] : ((mem(Q45_45, arr(A44_44, bool)) => (p(ap(c_2Ebool_2E_21(A44_44), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, A44_44) => p(ap(Q45_45, X46_46))))))))), $true, ! [A_27a47_47] : ((ne(A_27a47_47) => ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, A_27a47_47) => p(V0t48_48))) <=> p(V0t48_48)))))), ! [V0t50_50] : ((mem(V0t50_50, bool) => (((((($true => p(V0t50_50)) <=> p(V0t50_50)) & ((p(V0t50_50) => $true) <=> $true)) & (($false => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => $false) <=> ~p(V0t50_50))))), ! [V0z51_51] : ((mem(V0z51_51, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, V0z51_51), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(V0z51_51, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))), ~! [V0z52_52] : ((mem(V0z52_52, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (~=(V0z52_52, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, V0z52_52), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))
% 4.81/1.68
% 4.81/1.68 [1] ALPHA_AND : (ne(bool) & ne(ind) & ! [A14_14] : ((ne(A14_14) => ! [B15_15] : ((ne(B15_15) => ne(arr(A14_14, B15_15)))))) & ! [A16_16, B17_17, F18_18] : ((mem(F18_18, arr(A16_16, B17_17)) => ! [X19_19] : ((mem(X19_19, A16_16) => mem(ap(F18_18, X19_19), B17_17))))) & ! [Q20_20] : ((mem(Q20_20, bool) => ! [R21_21] : ((mem(R21_21, bool) => ((p(Q20_20) <=> p(R21_21)) => =(Q20_20, R21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [G25_25] : ((mem(G25_25, arr(A22_22, B23_23)) => (! [X26_26] : ((mem(X26_26, A22_22) => =(ap(F24_24, X26_26), ap(G25_25, X26_26)))) => =(F24_24, G25_25)))))) & ! [A27_27, Y28_28, X29_29] : ((mem(X29_29, A27_27) => =(ap(k(A27_27, Y28_28), X29_29), Y28_28))) & ! [A30_30, X31_31] : ((mem(X31_31, A30_30) => =(ap(i(A30_30), X31_31), X31_31))))
% 4.81/1.68 -> [2] ne(bool), ne(ind), ! [A14_14] : ((ne(A14_14) => ! [B15_15] : ((ne(B15_15) => ne(arr(A14_14, B15_15)))))), ! [A16_16, B17_17, F18_18] : ((mem(F18_18, arr(A16_16, B17_17)) => ! [X19_19] : ((mem(X19_19, A16_16) => mem(ap(F18_18, X19_19), B17_17))))), ! [Q20_20] : ((mem(Q20_20, bool) => ! [R21_21] : ((mem(R21_21, bool) => ((p(Q20_20) <=> p(R21_21)) => =(Q20_20, R21_21)))))), ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [G25_25] : ((mem(G25_25, arr(A22_22, B23_23)) => (! [X26_26] : ((mem(X26_26, A22_22) => =(ap(F24_24, X26_26), ap(G25_25, X26_26)))) => =(F24_24, G25_25)))))), ! [A27_27, Y28_28, X29_29] : ((mem(X29_29, A27_27) => =(ap(k(A27_27, Y28_28), X29_29), Y28_28))), ! [A30_30, X31_31] : ((mem(X31_31, A30_30) => =(ap(i(A30_30), X31_31), X31_31)))
% 4.81/1.68
% 4.81/1.68 [2] DELTA_NOT_FORALL : ~! [V0z52_52] : ((mem(V0z52_52, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (~=(V0z52_52, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, V0z52_52), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))
% 4.81/1.68 -> [3] ~(mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68
% 4.81/1.68 [3] ALPHA_NOT_IMPLY : ~(mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68 -> [4] mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)), ~(~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68
% 4.81/1.68 [4] ALPHA_NOT_IMPLY : ~(~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) => ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68 -> [5] ~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)), ~~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68
% 4.81/1.68 [5] ALPHA_NOT_NOT : ~~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68 -> [6] =(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68
% 4.81/1.68 [6] GAMMA_FORALL : ! [Q32_32] : ((mem(Q32_32, bool) => (p(ap(c_2Ebool_2E_7E, Q32_32)) <=> ~p(Q32_32))))
% 4.81/1.68 -> [7] (mem(c_2Ebool_2EF, bool) => (p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)) <=> ~p(c_2Ebool_2EF)))
% 4.81/1.68
% 4.81/1.68 [7] BETA_IMPLY : (mem(c_2Ebool_2EF, bool) => (p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)) <=> ~p(c_2Ebool_2EF)))
% 4.81/1.68 -> [8] ~mem(c_2Ebool_2EF, bool)
% 4.81/1.68 -> [9] (p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)) <=> ~p(c_2Ebool_2EF))
% 4.81/1.68
% 4.81/1.68 [8] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [9] BETA_EQUIV : (p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)) <=> ~p(c_2Ebool_2EF))
% 4.81/1.68 -> [10] ~p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)), ~~p(c_2Ebool_2EF)
% 4.81/1.68 -> [11] p(ap(c_2Ebool_2E_7E, c_2Ebool_2EF)), ~p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [10] ALPHA_NOT_NOT : ~~p(c_2Ebool_2EF)
% 4.81/1.68 -> [12] p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [12] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [11] GAMMA_FORALL : ! [Q33_33] : ((mem(Q33_33, bool) => ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, Q33_33), R34_34)) <=> (p(Q33_33) => p(R34_34)))))))
% 4.81/1.68 -> [13] (mem(c_2Ebool_2EF, bool) => ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, c_2Ebool_2EF), R34_34)) <=> (p(c_2Ebool_2EF) => p(R34_34))))))
% 4.81/1.68
% 4.81/1.68 [13] BETA_IMPLY : (mem(c_2Ebool_2EF, bool) => ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, c_2Ebool_2EF), R34_34)) <=> (p(c_2Ebool_2EF) => p(R34_34))))))
% 4.81/1.68 -> [14] ~mem(c_2Ebool_2EF, bool)
% 4.81/1.68 -> [15] ! [R34_34] : ((mem(R34_34, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, c_2Ebool_2EF), R34_34)) <=> (p(c_2Ebool_2EF) => p(R34_34)))))
% 4.81/1.68
% 4.81/1.68 [14] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [15] GAMMA_FORALL : ! [Q35_35] : ((mem(Q35_35, bool) => ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, Q35_35), R36_36)) <=> (p(Q35_35) & p(R36_36)))))))
% 4.81/1.68 -> [16] (mem(c_2Ebool_2ET, bool) => ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, c_2Ebool_2ET), R36_36)) <=> (p(c_2Ebool_2ET) & p(R36_36))))))
% 4.81/1.68
% 4.81/1.68 [16] BETA_IMPLY : (mem(c_2Ebool_2ET, bool) => ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, c_2Ebool_2ET), R36_36)) <=> (p(c_2Ebool_2ET) & p(R36_36))))))
% 4.81/1.68 -> [17] ~mem(c_2Ebool_2ET, bool)
% 4.81/1.68 -> [18] ! [R36_36] : ((mem(R36_36, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, c_2Ebool_2ET), R36_36)) <=> (p(c_2Ebool_2ET) & p(R36_36)))))
% 4.81/1.68
% 4.81/1.68 [17] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [18] GAMMA_FORALL : ! [A037_37] : ((ne(A037_37) => ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(A037_37, A138_38))))))
% 4.81/1.68 -> [19] (ne(ty_2Enum_2Enum) => ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(ty_2Enum_2Enum, A138_38)))))
% 4.81/1.68
% 4.81/1.68 [19] BETA_IMPLY : (ne(ty_2Enum_2Enum) => ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(ty_2Enum_2Enum, A138_38)))))
% 4.81/1.68 -> [20] ~ne(ty_2Enum_2Enum)
% 4.81/1.68 -> [21] ! [A138_38] : ((ne(A138_38) => ne(ty_2Epair_2Eprod(ty_2Enum_2Enum, A138_38))))
% 4.81/1.68
% 4.81/1.68 [20] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [21] GAMMA_FORALL : ! [A_27a39_39] : ((ne(A_27a39_39) => mem(c_2Emin_2E_3D(A_27a39_39), arr(A_27a39_39, arr(A_27a39_39, bool)))))
% 4.81/1.68 -> [22] (ne(ind) => mem(c_2Emin_2E_3D(ind), arr(ind, arr(ind, bool))))
% 4.81/1.68
% 4.81/1.68 [22] BETA_IMPLY : (ne(ind) => mem(c_2Emin_2E_3D(ind), arr(ind, arr(ind, bool))))
% 4.81/1.68 -> [23] ~ne(ind)
% 4.81/1.68 -> [24] mem(c_2Emin_2E_3D(ind), arr(ind, arr(ind, bool)))
% 4.81/1.68
% 4.81/1.68 [23] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [24] GAMMA_FORALL : ! [A40_40] : ((ne(A40_40) => ! [X41_41] : ((mem(X41_41, A40_40) => ! [Y42_42] : ((mem(Y42_42, A40_40) => (p(ap(ap(c_2Emin_2E_3D(A40_40), X41_41), Y42_42)) <=> =(X41_41, Y42_42))))))))
% 4.81/1.68 -> [25] (ne(ty_2Enum_2Enum) => ! [X41_41] : ((mem(X41_41, ty_2Enum_2Enum) => ! [Y42_42] : ((mem(Y42_42, ty_2Enum_2Enum) => (p(ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum), X41_41), Y42_42)) <=> =(X41_41, Y42_42)))))))
% 4.81/1.68
% 4.81/1.68 [25] BETA_IMPLY : (ne(ty_2Enum_2Enum) => ! [X41_41] : ((mem(X41_41, ty_2Enum_2Enum) => ! [Y42_42] : ((mem(Y42_42, ty_2Enum_2Enum) => (p(ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum), X41_41), Y42_42)) <=> =(X41_41, Y42_42)))))))
% 4.81/1.68 -> [26] ~ne(ty_2Enum_2Enum)
% 4.81/1.68 -> [27] ! [X41_41] : ((mem(X41_41, ty_2Enum_2Enum) => ! [Y42_42] : ((mem(Y42_42, ty_2Enum_2Enum) => (p(ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum), X41_41), Y42_42)) <=> =(X41_41, Y42_42))))))
% 4.81/1.68
% 4.81/1.68 [26] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [27] GAMMA_FORALL : ! [A_27a43_43] : ((ne(A_27a43_43) => mem(c_2Ebool_2E_21(A_27a43_43), arr(arr(A_27a43_43, bool), bool))))
% 4.81/1.68 -> [28] (ne(ind) => mem(c_2Ebool_2E_21(ind), arr(arr(ind, bool), bool)))
% 4.81/1.68
% 4.81/1.68 [28] BETA_IMPLY : (ne(ind) => mem(c_2Ebool_2E_21(ind), arr(arr(ind, bool), bool)))
% 4.81/1.68 -> [29] ~ne(ind)
% 4.81/1.68 -> [30] mem(c_2Ebool_2E_21(ind), arr(arr(ind, bool), bool))
% 4.81/1.68
% 4.81/1.68 [29] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [30] GAMMA_FORALL : ! [A44_44] : ((ne(A44_44) => ! [Q45_45] : ((mem(Q45_45, arr(A44_44, bool)) => (p(ap(c_2Ebool_2E_21(A44_44), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, A44_44) => p(ap(Q45_45, X46_46)))))))))
% 4.81/1.68 -> [31] (ne(ty_2Enum_2Enum) => ! [Q45_45] : ((mem(Q45_45, arr(ty_2Enum_2Enum, bool)) => (p(ap(c_2Ebool_2E_21(ty_2Enum_2Enum), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, ty_2Enum_2Enum) => p(ap(Q45_45, X46_46))))))))
% 4.81/1.68
% 4.81/1.68 [31] BETA_IMPLY : (ne(ty_2Enum_2Enum) => ! [Q45_45] : ((mem(Q45_45, arr(ty_2Enum_2Enum, bool)) => (p(ap(c_2Ebool_2E_21(ty_2Enum_2Enum), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, ty_2Enum_2Enum) => p(ap(Q45_45, X46_46))))))))
% 4.81/1.68 -> [32] ~ne(ty_2Enum_2Enum)
% 4.81/1.68 -> [33] ! [Q45_45] : ((mem(Q45_45, arr(ty_2Enum_2Enum, bool)) => (p(ap(c_2Ebool_2E_21(ty_2Enum_2Enum), Q45_45)) <=> ! [X46_46] : ((mem(X46_46, ty_2Enum_2Enum) => p(ap(Q45_45, X46_46)))))))
% 4.81/1.68
% 4.81/1.68 [32] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [33] GAMMA_FORALL : ! [A_27a47_47] : ((ne(A_27a47_47) => ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, A_27a47_47) => p(V0t48_48))) <=> p(V0t48_48))))))
% 4.81/1.68 -> [34] (ne(ty_2Erealax_2Ereal) => ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, ty_2Erealax_2Ereal) => p(V0t48_48))) <=> p(V0t48_48)))))
% 4.81/1.68
% 4.81/1.68 [34] BETA_IMPLY : (ne(ty_2Erealax_2Ereal) => ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, ty_2Erealax_2Ereal) => p(V0t48_48))) <=> p(V0t48_48)))))
% 4.81/1.68 -> [35] ~ne(ty_2Erealax_2Ereal)
% 4.81/1.68 -> [36] ! [V0t48_48] : ((mem(V0t48_48, bool) => (! [V1x49_49] : ((mem(V1x49_49, ty_2Erealax_2Ereal) => p(V0t48_48))) <=> p(V0t48_48))))
% 4.81/1.68
% 4.81/1.68 [35] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [36] GAMMA_FORALL : ! [V0t50_50] : ((mem(V0t50_50, bool) => (((((($true => p(V0t50_50)) <=> p(V0t50_50)) & ((p(V0t50_50) => $true) <=> $true)) & (($false => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => p(V0t50_50)) <=> $true)) & ((p(V0t50_50) => $false) <=> ~p(V0t50_50)))))
% 4.81/1.68 -> [37] (mem(c_2Ebool_2EF, bool) => (((((($true => p(c_2Ebool_2EF)) <=> p(c_2Ebool_2EF)) & ((p(c_2Ebool_2EF) => $true) <=> $true)) & (($false => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => $false) <=> ~p(c_2Ebool_2EF))))
% 4.81/1.68
% 4.81/1.68 [37] BETA_IMPLY : (mem(c_2Ebool_2EF, bool) => (((((($true => p(c_2Ebool_2EF)) <=> p(c_2Ebool_2EF)) & ((p(c_2Ebool_2EF) => $true) <=> $true)) & (($false => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => $false) <=> ~p(c_2Ebool_2EF))))
% 4.81/1.68 -> [38] ~mem(c_2Ebool_2EF, bool)
% 4.81/1.68 -> [39] (((((($true => p(c_2Ebool_2EF)) <=> p(c_2Ebool_2EF)) & ((p(c_2Ebool_2EF) => $true) <=> $true)) & (($false => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => p(c_2Ebool_2EF)) <=> $true)) & ((p(c_2Ebool_2EF) => $false) <=> ~p(c_2Ebool_2EF)))
% 4.81/1.68
% 4.81/1.68 [38] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [43] BETA_EQUIV : ((p(c_2Ebool_2EF) => $false) <=> ~p(c_2Ebool_2EF))
% 4.81/1.68 -> [78] ~(p(c_2Ebool_2EF) => $false), ~~p(c_2Ebool_2EF)
% 4.81/1.68 -> [79] (p(c_2Ebool_2EF) => $false), ~p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [78] ALPHA_NOT_IMPLY : ~(p(c_2Ebool_2EF) => $false)
% 4.81/1.68 -> [80] p(c_2Ebool_2EF), ~$false
% 4.81/1.68
% 4.81/1.68 [80] CLOSURE : p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [79] BETA_EQUIV : ((p(c_2Ebool_2EF) => p(c_2Ebool_2EF)) <=> $true)
% 4.81/1.68 -> [81] ~(p(c_2Ebool_2EF) => p(c_2Ebool_2EF)), ~$true
% 4.81/1.68 -> [82] (p(c_2Ebool_2EF) => p(c_2Ebool_2EF)), $true
% 4.81/1.68
% 4.81/1.68 [81] CLOSURE : ~$true
% 4.81/1.68
% 4.81/1.68 [82] BETA_EQUIV : (($false => p(c_2Ebool_2EF)) <=> $true)
% 4.81/1.68 -> [83] ~($false => p(c_2Ebool_2EF)), ~$true
% 4.81/1.68 -> [84] ($false => p(c_2Ebool_2EF)), $true
% 4.81/1.68
% 4.81/1.68 [83] CLOSURE : ~$true
% 4.81/1.68
% 4.81/1.68 [84] BETA_EQUIV : (($true => p(c_2Ebool_2EF)) <=> p(c_2Ebool_2EF))
% 4.81/1.68 -> [85] ~($true => p(c_2Ebool_2EF)), ~p(c_2Ebool_2EF)
% 4.81/1.68 -> [86] ($true => p(c_2Ebool_2EF)), p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [86] CLOSURE : p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [85] ALPHA_NOT_IMPLY : ~($true => p(c_2Ebool_2EF))
% 4.81/1.68 -> [87] $true, ~p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [87] BETA_EQUIV : ((p(c_2Ebool_2EF) => $true) <=> $true)
% 4.81/1.68 -> [88] ~(p(c_2Ebool_2EF) => $true), ~$true
% 4.81/1.68 -> [89] (p(c_2Ebool_2EF) => $true), $true
% 4.81/1.68
% 4.81/1.68 [88] CLOSURE : ~$true
% 4.81/1.68
% 4.81/1.68 [89] BETA_IMPLY : (p(c_2Ebool_2EF) => $false)
% 4.81/1.68 -> [90] ~p(c_2Ebool_2EF)
% 4.81/1.68 -> [91] $false
% 4.81/1.68
% 4.81/1.68 [91] CLOSURE : $false
% 4.81/1.68
% 4.81/1.68 [90] BETA_IMPLY : (p(c_2Ebool_2EF) => p(c_2Ebool_2EF))
% 4.81/1.68 -> [92] ~p(c_2Ebool_2EF)
% 4.81/1.68 -> [93] p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [93] CLOSURE : p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [92] BETA_IMPLY : ($false => p(c_2Ebool_2EF))
% 4.81/1.68 -> [94] ~$false
% 4.81/1.68 -> [95] p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [95] CLOSURE : p(c_2Ebool_2EF)
% 4.81/1.68
% 4.81/1.68 [94] BETA_IMPLY : (p(c_2Ebool_2EF) => $true)
% 4.81/1.68 -> [96] ~p(c_2Ebool_2EF)
% 4.81/1.68 -> [97] $true
% 4.81/1.68
% 4.81/1.68 [96] GAMMA_FORALL : ! [V0z51_51] : ((mem(V0z51_51, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, V0z51_51), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(V0z51_51, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))
% 4.81/1.68 -> [98] (mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68
% 4.81/1.68 [98] BETA_IMPLY : (mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68 -> [100] ~mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))
% 4.81/1.68 -> [101] (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68
% 4.81/1.68 [100] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [101] BETA_EQUIV : (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68 -> [104] ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)), ~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68 -> [105] =(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)), =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68
% 4.81/1.68 [104] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [105] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [97] GAMMA_FORALL : ! [V0z51_51] : ((mem(V0z51_51, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, V0z51_51), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(V0z51_51, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))
% 4.81/1.68 -> [99] (mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68
% 4.81/1.68 [99] BETA_IMPLY : (mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))
% 4.81/1.68 -> [102] ~mem(skolem_V0z5252, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))
% 4.81/1.68 -> [103] (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68
% 4.81/1.68 [102] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [103] BETA_EQUIV : (=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))
% 4.81/1.68 -> [106] ~=(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)), ~=(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68 -> [107] =(ap(c_2Ecomplex_2Ecomplex__inv, skolem_V0z5252), ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)), =(skolem_V0z5252, ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))
% 4.81/1.68
% 4.81/1.68 [106] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 [107] CLOSURE : =
% 4.81/1.68
% 4.81/1.68 % SZS output end Proof for theBenchmark.p
% 4.81/1.68 [1.336877s][1][Res] 7709 goroutines created
% 4.81/1.68 ==== Result ====
% 4.81/1.68 [1.336897s][1][Res] VALID
% 4.81/1.68 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------