TSTP Solution File: ITP010+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : ITP010+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 02:55:51 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 02:28:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000047s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.35 nb_step : 1 - limit : 57
% 0.12/0.35 Launch Gotab with destructive = true
% 0.19/0.50 % SZS output start Proof for theBenchmark.p
% 0.19/0.50 [0] ALPHA_AND : ((ne(bool) & ne(ind) & ! [A20_20] : ((ne(A20_20) => ! [B21_21] : ((ne(B21_21) => ne(arr(A20_20, B21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [X25_25] : ((mem(X25_25, A22_22) => mem(ap(F24_24, X25_25), B23_23))))) & ! [Q26_26] : ((mem(Q26_26, bool) => ! [R27_27] : ((mem(R27_27, bool) => ((p(Q26_26) <=> p(R27_27)) => =(Q26_26, R27_27)))))) & ! [A28_28, B29_29, F30_30] : ((mem(F30_30, arr(A28_28, B29_29)) => ! [G31_31] : ((mem(G31_31, arr(A28_28, B29_29)) => (! [X32_32] : ((mem(X32_32, A28_28) => =(ap(F30_30, X32_32), ap(G31_31, X32_32)))) => =(F30_30, G31_31)))))) & ! [A33_33, Y34_34, X35_35] : ((mem(X35_35, A33_33) => =(ap(k(A33_33, Y34_34), X35_35), Y34_34))) & ! [A36_36, X37_37] : ((mem(X37_37, A36_36) => =(ap(i(A36_36), X37_37), X37_37)))) & mem(c_2Ebool_2ET, bool) & p(c_2Ebool_2ET) & ! [A_27a38_38] : ((ne(A_27a38_38) => ! [A_27b39_39] : ((ne(A_27b39_39) => mem(c_2Ecardinal_2Ecardleq(A_27a38_38, A_27b39_39), arr(arr(A_27a38_38, bool), arr(arr(A_27b39_39, bool), bool))))))) & mem(c_2Ebool_2EF, bool) & ~p(c_2Ebool_2EF) & mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))) & ! [Q40_40] : ((mem(Q40_40, bool) => ! [R41_41] : ((mem(R41_41, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, Q40_40), R41_41)) <=> (p(Q40_40) => p(R41_41))))))) & mem(c_2Ebool_2E_5C_2F, arr(bool, arr(bool, bool))) & ! [Q42_42] : ((mem(Q42_42, bool) => ! [R43_43] : ((mem(R43_43, bool) => (p(ap(ap(c_2Ebool_2E_5C_2F, Q42_42), R43_43)) <=> (p(Q42_42) | p(R43_43))))))) & mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))) & ! [Q44_44] : ((mem(Q44_44, bool) => ! [R45_45] : ((mem(R45_45, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, Q44_44), R45_45)) <=> (p(Q44_44) & p(R45_45))))))) & mem(c_2Ebool_2E_7E, arr(bool, bool)) & ! [Q46_46] : ((mem(Q46_46, bool) => (p(ap(c_2Ebool_2E_7E, Q46_46)) <=> ~p(Q46_46)))) & ! [A_27a47_47] : ((ne(A_27a47_47) => mem(c_2Emin_2E_3D(A_27a47_47), arr(A_27a47_47, arr(A_27a47_47, bool))))) & ! [A48_48] : ((ne(A48_48) => ! [X49_49] : ((mem(X49_49, A48_48) => ! [Y50_50] : ((mem(Y50_50, A48_48) => (p(ap(ap(c_2Emin_2E_3D(A48_48), X49_49), Y50_50)) <=> =(X49_49, Y50_50)))))))) & ! [A_27a51_51] : ((ne(A_27a51_51) => mem(c_2Ebool_2E_21(A_27a51_51), arr(arr(A_27a51_51, bool), bool)))) & ! [A52_52] : ((ne(A52_52) => ! [Q53_53] : ((mem(Q53_53, arr(A52_52, bool)) => (p(ap(c_2Ebool_2E_21(A52_52), Q53_53)) <=> ! [X54_54] : ((mem(X54_54, A52_52) => p(ap(Q53_53, X54_54))))))))) & $true & ! [V0t55_55] : ((mem(V0t55_55, bool) => ($false => p(V0t55_55)))) & ! [A_27a56_56] : ((ne(A_27a56_56) => ! [V0t57_57] : ((mem(V0t57_57, bool) => (! [V1x58_58] : ((mem(V1x58_58, A_27a56_56) => p(V0t57_57))) <=> p(V0t57_57)))))) & ! [V0t59_59] : ((mem(V0t59_59, bool) => (((((($true => p(V0t59_59)) <=> p(V0t59_59)) & ((p(V0t59_59) => $true) <=> $true)) & (($false => p(V0t59_59)) <=> $true)) & ((p(V0t59_59) => p(V0t59_59)) <=> $true)) & ((p(V0t59_59) => $false) <=> ~p(V0t59_59))))) & ((! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))) & (~$true <=> $false)) & (~$false <=> $true)) & ! [A_27a61_61] : ((ne(A_27a61_61) => ! [V0x62_62] : ((mem(V0x62_62, A_27a61_61) => (=(V0x62_62, V0x62_62) <=> $true))))) & ! [V0t63_63] : ((mem(V0t63_63, bool) => ((((($true <=> p(V0t63_63)) <=> p(V0t63_63)) & ((p(V0t63_63) <=> $true) <=> p(V0t63_63))) & (($false <=> p(V0t63_63)) <=> ~p(V0t63_63))) & ((p(V0t63_63) <=> $false) <=> ~p(V0t63_63))))) & ! [A_27a64_64] : ((ne(A_27a64_64) => ! [A_27b65_65] : ((ne(A_27b65_65) => ! [V0s66_66] : ((mem(V0s66_66, arr(A_27a64_64, bool)) => ! [V1t67_67] : ((mem(V1t67_67, arr(A_27b65_65, bool)) => (p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a64_64, A_27b65_65), V0s66_66), V1t67_67)) | p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b65_65, A_27a64_64), V1t67_67), V0s66_66))))))))))) & ! [V0t68_68] : ((mem(V0t68_68, bool) => (~~p(V0t68_68) <=> p(V0t68_68)))) & ! [V0A69_69] : ((mem(V0A69_69, bool) => (p(V0A69_69) => (~p(V0A69_69) => $false)))) & ! [V0A70_70] : ((mem(V0A70_70, bool) => ! [V1B71_71] : ((mem(V1B71_71, bool) => ((~(p(V0A70_70) | p(V1B71_71)) => $false) <=> ((p(V0A70_70) => $false) => (~p(V1B71_71) => $false))))))) & ! [V0A72_72] : ((mem(V0A72_72, bool) => ! [V1B73_73] : ((mem(V1B73_73, bool) => ((~(~p(V0A72_72) | p(V1B73_73)) => $false) <=> (p(V0A72_72) => (~p(V1B73_73) => $false))))))) & ! [V0A74_74] : ((mem(V0A74_74, bool) => ((~p(V0A74_74) => $false) => ((p(V0A74_74) => $false) => $false)))) & ! [V0p75_75] : ((mem(V0p75_75, bool) => ! [V1q76_76] : ((mem(V1q76_76, bool) => ! [V2r77_77] : ((mem(V2r77_77, bool) => ((p(V0p75_75) <=> (p(V1q76_76) <=> p(V2r77_77))) <=> (((((p(V0p75_75) | p(V1q76_76)) | p(V2r77_77)) & ((p(V0p75_75) | ~p(V2r77_77)) | ~p(V1q76_76))) & ((p(V1q76_76) | ~p(V2r77_77)) | ~p(V0p75_75))) & ((p(V2r77_77) | ~p(V1q76_76)) | ~p(V0p75_75)))))))))) & ! [V0p78_78] : ((mem(V0p78_78, bool) => ! [V1q79_79] : ((mem(V1q79_79, bool) => ((p(V0p78_78) <=> ~p(V1q79_79)) <=> ((p(V0p78_78) | p(V1q79_79)) & (~p(V1q79_79) | ~p(V0p78_78)))))))) & ~! [A_27a80_80] : ((ne(A_27a80_80) => ! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(A_27a80_80, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83))))))))))))
% 0.19/0.50 -> [1] (ne(bool) & ne(ind) & ! [A20_20] : ((ne(A20_20) => ! [B21_21] : ((ne(B21_21) => ne(arr(A20_20, B21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [X25_25] : ((mem(X25_25, A22_22) => mem(ap(F24_24, X25_25), B23_23))))) & ! [Q26_26] : ((mem(Q26_26, bool) => ! [R27_27] : ((mem(R27_27, bool) => ((p(Q26_26) <=> p(R27_27)) => =(Q26_26, R27_27)))))) & ! [A28_28, B29_29, F30_30] : ((mem(F30_30, arr(A28_28, B29_29)) => ! [G31_31] : ((mem(G31_31, arr(A28_28, B29_29)) => (! [X32_32] : ((mem(X32_32, A28_28) => =(ap(F30_30, X32_32), ap(G31_31, X32_32)))) => =(F30_30, G31_31)))))) & ! [A33_33, Y34_34, X35_35] : ((mem(X35_35, A33_33) => =(ap(k(A33_33, Y34_34), X35_35), Y34_34))) & ! [A36_36, X37_37] : ((mem(X37_37, A36_36) => =(ap(i(A36_36), X37_37), X37_37)))), mem(c_2Ebool_2ET, bool), p(c_2Ebool_2ET), ! [A_27a38_38] : ((ne(A_27a38_38) => ! [A_27b39_39] : ((ne(A_27b39_39) => mem(c_2Ecardinal_2Ecardleq(A_27a38_38, A_27b39_39), arr(arr(A_27a38_38, bool), arr(arr(A_27b39_39, bool), bool))))))), mem(c_2Ebool_2EF, bool), ~p(c_2Ebool_2EF), mem(c_2Emin_2E_3D_3D_3E, arr(bool, arr(bool, bool))), ! [Q40_40] : ((mem(Q40_40, bool) => ! [R41_41] : ((mem(R41_41, bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E, Q40_40), R41_41)) <=> (p(Q40_40) => p(R41_41))))))), mem(c_2Ebool_2E_5C_2F, arr(bool, arr(bool, bool))), ! [Q42_42] : ((mem(Q42_42, bool) => ! [R43_43] : ((mem(R43_43, bool) => (p(ap(ap(c_2Ebool_2E_5C_2F, Q42_42), R43_43)) <=> (p(Q42_42) | p(R43_43))))))), mem(c_2Ebool_2E_2F_5C, arr(bool, arr(bool, bool))), ! [Q44_44] : ((mem(Q44_44, bool) => ! [R45_45] : ((mem(R45_45, bool) => (p(ap(ap(c_2Ebool_2E_2F_5C, Q44_44), R45_45)) <=> (p(Q44_44) & p(R45_45))))))), mem(c_2Ebool_2E_7E, arr(bool, bool)), ! [Q46_46] : ((mem(Q46_46, bool) => (p(ap(c_2Ebool_2E_7E, Q46_46)) <=> ~p(Q46_46)))), ! [A_27a47_47] : ((ne(A_27a47_47) => mem(c_2Emin_2E_3D(A_27a47_47), arr(A_27a47_47, arr(A_27a47_47, bool))))), ! [A48_48] : ((ne(A48_48) => ! [X49_49] : ((mem(X49_49, A48_48) => ! [Y50_50] : ((mem(Y50_50, A48_48) => (p(ap(ap(c_2Emin_2E_3D(A48_48), X49_49), Y50_50)) <=> =(X49_49, Y50_50)))))))), ! [A_27a51_51] : ((ne(A_27a51_51) => mem(c_2Ebool_2E_21(A_27a51_51), arr(arr(A_27a51_51, bool), bool)))), ! [A52_52] : ((ne(A52_52) => ! [Q53_53] : ((mem(Q53_53, arr(A52_52, bool)) => (p(ap(c_2Ebool_2E_21(A52_52), Q53_53)) <=> ! [X54_54] : ((mem(X54_54, A52_52) => p(ap(Q53_53, X54_54))))))))), $true, ! [V0t55_55] : ((mem(V0t55_55, bool) => ($false => p(V0t55_55)))), ! [A_27a56_56] : ((ne(A_27a56_56) => ! [V0t57_57] : ((mem(V0t57_57, bool) => (! [V1x58_58] : ((mem(V1x58_58, A_27a56_56) => p(V0t57_57))) <=> p(V0t57_57)))))), ! [V0t59_59] : ((mem(V0t59_59, bool) => (((((($true => p(V0t59_59)) <=> p(V0t59_59)) & ((p(V0t59_59) => $true) <=> $true)) & (($false => p(V0t59_59)) <=> $true)) & ((p(V0t59_59) => p(V0t59_59)) <=> $true)) & ((p(V0t59_59) => $false) <=> ~p(V0t59_59))))), ((! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))) & (~$true <=> $false)) & (~$false <=> $true)), ! [A_27a61_61] : ((ne(A_27a61_61) => ! [V0x62_62] : ((mem(V0x62_62, A_27a61_61) => (=(V0x62_62, V0x62_62) <=> $true))))), ! [V0t63_63] : ((mem(V0t63_63, bool) => ((((($true <=> p(V0t63_63)) <=> p(V0t63_63)) & ((p(V0t63_63) <=> $true) <=> p(V0t63_63))) & (($false <=> p(V0t63_63)) <=> ~p(V0t63_63))) & ((p(V0t63_63) <=> $false) <=> ~p(V0t63_63))))), ! [A_27a64_64] : ((ne(A_27a64_64) => ! [A_27b65_65] : ((ne(A_27b65_65) => ! [V0s66_66] : ((mem(V0s66_66, arr(A_27a64_64, bool)) => ! [V1t67_67] : ((mem(V1t67_67, arr(A_27b65_65, bool)) => (p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a64_64, A_27b65_65), V0s66_66), V1t67_67)) | p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b65_65, A_27a64_64), V1t67_67), V0s66_66))))))))))), ! [V0t68_68] : ((mem(V0t68_68, bool) => (~~p(V0t68_68) <=> p(V0t68_68)))), ! [V0A69_69] : ((mem(V0A69_69, bool) => (p(V0A69_69) => (~p(V0A69_69) => $false)))), ! [V0A70_70] : ((mem(V0A70_70, bool) => ! [V1B71_71] : ((mem(V1B71_71, bool) => ((~(p(V0A70_70) | p(V1B71_71)) => $false) <=> ((p(V0A70_70) => $false) => (~p(V1B71_71) => $false))))))), ! [V0A72_72] : ((mem(V0A72_72, bool) => ! [V1B73_73] : ((mem(V1B73_73, bool) => ((~(~p(V0A72_72) | p(V1B73_73)) => $false) <=> (p(V0A72_72) => (~p(V1B73_73) => $false))))))), ! [V0A74_74] : ((mem(V0A74_74, bool) => ((~p(V0A74_74) => $false) => ((p(V0A74_74) => $false) => $false)))), ! [V0p75_75] : ((mem(V0p75_75, bool) => ! [V1q76_76] : ((mem(V1q76_76, bool) => ! [V2r77_77] : ((mem(V2r77_77, bool) => ((p(V0p75_75) <=> (p(V1q76_76) <=> p(V2r77_77))) <=> (((((p(V0p75_75) | p(V1q76_76)) | p(V2r77_77)) & ((p(V0p75_75) | ~p(V2r77_77)) | ~p(V1q76_76))) & ((p(V1q76_76) | ~p(V2r77_77)) | ~p(V0p75_75))) & ((p(V2r77_77) | ~p(V1q76_76)) | ~p(V0p75_75)))))))))), ! [V0p78_78] : ((mem(V0p78_78, bool) => ! [V1q79_79] : ((mem(V1q79_79, bool) => ((p(V0p78_78) <=> ~p(V1q79_79)) <=> ((p(V0p78_78) | p(V1q79_79)) & (~p(V1q79_79) | ~p(V0p78_78)))))))), ~! [A_27a80_80] : ((ne(A_27a80_80) => ! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(A_27a80_80, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83)))))))))))
% 0.19/0.50
% 0.19/0.50 [1] ALPHA_AND : (ne(bool) & ne(ind) & ! [A20_20] : ((ne(A20_20) => ! [B21_21] : ((ne(B21_21) => ne(arr(A20_20, B21_21)))))) & ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [X25_25] : ((mem(X25_25, A22_22) => mem(ap(F24_24, X25_25), B23_23))))) & ! [Q26_26] : ((mem(Q26_26, bool) => ! [R27_27] : ((mem(R27_27, bool) => ((p(Q26_26) <=> p(R27_27)) => =(Q26_26, R27_27)))))) & ! [A28_28, B29_29, F30_30] : ((mem(F30_30, arr(A28_28, B29_29)) => ! [G31_31] : ((mem(G31_31, arr(A28_28, B29_29)) => (! [X32_32] : ((mem(X32_32, A28_28) => =(ap(F30_30, X32_32), ap(G31_31, X32_32)))) => =(F30_30, G31_31)))))) & ! [A33_33, Y34_34, X35_35] : ((mem(X35_35, A33_33) => =(ap(k(A33_33, Y34_34), X35_35), Y34_34))) & ! [A36_36, X37_37] : ((mem(X37_37, A36_36) => =(ap(i(A36_36), X37_37), X37_37))))
% 0.19/0.50 -> [2] ne(bool), ne(ind), ! [A20_20] : ((ne(A20_20) => ! [B21_21] : ((ne(B21_21) => ne(arr(A20_20, B21_21)))))), ! [A22_22, B23_23, F24_24] : ((mem(F24_24, arr(A22_22, B23_23)) => ! [X25_25] : ((mem(X25_25, A22_22) => mem(ap(F24_24, X25_25), B23_23))))), ! [Q26_26] : ((mem(Q26_26, bool) => ! [R27_27] : ((mem(R27_27, bool) => ((p(Q26_26) <=> p(R27_27)) => =(Q26_26, R27_27)))))), ! [A28_28, B29_29, F30_30] : ((mem(F30_30, arr(A28_28, B29_29)) => ! [G31_31] : ((mem(G31_31, arr(A28_28, B29_29)) => (! [X32_32] : ((mem(X32_32, A28_28) => =(ap(F30_30, X32_32), ap(G31_31, X32_32)))) => =(F30_30, G31_31)))))), ! [A33_33, Y34_34, X35_35] : ((mem(X35_35, A33_33) => =(ap(k(A33_33, Y34_34), X35_35), Y34_34))), ! [A36_36, X37_37] : ((mem(X37_37, A36_36) => =(ap(i(A36_36), X37_37), X37_37)))
% 0.19/0.50
% 0.19/0.50 [2] ALPHA_AND : ((! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))) & (~$true <=> $false)) & (~$false <=> $true))
% 0.19/0.50 -> [3] (! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))) & (~$true <=> $false)), (~$false <=> $true)
% 0.19/0.50
% 0.19/0.50 [3] ALPHA_AND : (! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))) & (~$true <=> $false))
% 0.19/0.50 -> [4] ! [V0t60_60] : ((mem(V0t60_60, bool) => (~~p(V0t60_60) <=> p(V0t60_60)))), (~$true <=> $false)
% 0.19/0.50
% 0.19/0.50 [4] DELTA_NOT_FORALL : ~! [A_27a80_80] : ((ne(A_27a80_80) => ! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(A_27a80_80, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a80_80, A_27b81_81), V0s82_82), V1t83_83)))))))))))
% 0.19/0.50 -> [5] ~(ne(skolem_A_27a8080) => ! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83))))))))))
% 0.19/0.50
% 0.19/0.50 [5] ALPHA_NOT_IMPLY : ~(ne(skolem_A_27a8080) => ! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83))))))))))
% 0.19/0.50 -> [6] ne(skolem_A_27a8080), ~! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)))))))))
% 0.19/0.50
% 0.19/0.50 [6] DELTA_NOT_FORALL : ~! [A_27b81_81] : ((ne(A_27b81_81) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(A_27b81_81, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, A_27b81_81), V0s82_82), V1t83_83)))))))))
% 0.19/0.50 -> [7] ~(ne(skolem_A_27b8181) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83))))))))
% 0.19/0.50
% 0.19/0.50 [7] ALPHA_NOT_IMPLY : ~(ne(skolem_A_27b8181) => ! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83))))))))
% 0.19/0.50 -> [8] ne(skolem_A_27b8181), ~! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)))))))
% 0.19/0.50
% 0.19/0.50 [8] DELTA_NOT_FORALL : ~! [V0s82_82] : ((mem(V0s82_82, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), V0s82_82), V1t83_83)))))))
% 0.19/0.50 -> [9] ~(mem(skolem_V0s8282, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83))))))
% 0.19/0.50
% 0.19/0.50 [9] ALPHA_NOT_IMPLY : ~(mem(skolem_V0s8282, arr(skolem_A_27a8080, bool)) => ! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83))))))
% 0.19/0.50 -> [10] mem(skolem_V0s8282, arr(skolem_A_27a8080, bool)), ~! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)))))
% 0.19/0.50
% 0.19/0.50 [10] DELTA_NOT_FORALL : ~! [V1t83_83] : ((mem(V1t83_83, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), V1t83_83)))))
% 0.19/0.50 -> [11] ~(mem(skolem_V1t8383, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))))
% 0.19/0.50
% 0.19/0.50 [11] ALPHA_NOT_IMPLY : ~(mem(skolem_V1t8383, arr(skolem_A_27b8181, bool)) => (~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))))
% 0.19/0.50 -> [12] mem(skolem_V1t8383, arr(skolem_A_27b8181, bool)), ~(~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)))
% 0.19/0.50
% 0.19/0.50 [12] BETA_EQUIV : (~$false <=> $true)
% 0.19/0.50 -> [13] ~~$false, ~$true
% 0.19/0.50 -> [14] ~$false, $true
% 0.19/0.50
% 0.19/0.50 [13] CLOSURE : ~$true
% 0.19/0.50
% 0.19/0.50 [14] BETA_EQUIV : (~$true <=> $false)
% 0.19/0.50 -> [15] ~~$true, ~$false
% 0.19/0.50 -> [16] ~$true, $false
% 0.19/0.50
% 0.19/0.50 [16] CLOSURE : ~$true
% 0.19/0.50
% 0.19/0.50 [15] ALPHA_NOT_NOT : ~~$true
% 0.19/0.50 -> [17] $true
% 0.19/0.50
% 0.19/0.50 [17] BETA_NOT_EQUIV : ~(~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)) <=> ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)))
% 0.19/0.50 -> [18] ~~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)), ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50 -> [19] ~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383)), ~~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50
% 0.19/0.50 [18] ALPHA_NOT_NOT : ~~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50 -> [20] p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50
% 0.19/0.50 [20] CLOSURE : p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50
% 0.19/0.50 [19] ALPHA_NOT_NOT : ~~p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50 -> [21] p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50
% 0.19/0.50 [21] CLOSURE : p(ap(ap(c_2Ecardinal_2Ecardleq(skolem_A_27a8080, skolem_A_27b8181), skolem_V0s8282), skolem_V1t8383))
% 0.19/0.50
% 0.19/0.50 % SZS output end Proof for theBenchmark.p
% 0.19/0.50 [0.168046s][1][Res] 83 goroutines created
% 0.19/0.50 ==== Result ====
% 0.19/0.50 [0.168092s][1][Res] VALID
% 0.19/0.50 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------