TSTP Solution File: SET764+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n019.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 04:17:22 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.00/0.10 % Command : goeland -dmt -presko -proof %s
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 07:52:05 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 [DMT] DMT loaded with preskolemization
% 0.10/0.31 [EQ] equality loaded.
% 0.10/0.31 [0.000031s][1][MAIN] Problem : theBenchmark.p
% 0.10/0.31 Conjecture not found
% 0.15/0.32 Conjecture not found
% 0.15/0.32 Start search
% 0.15/0.32 nb_step : 1 - limit : 51
% 0.15/0.32 Launch Gotab with destructive = true
% 0.15/0.39 % SZS output start Proof for theBenchmark.p
% 0.15/0.40 [0] ALPHA_AND : ((! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))) & (! [G61_61, F62_62, A63_63, B64_64, C65_65, X66_66, Z67_67] : (((member(X66_66, A63_63) & member(Z67_67, C65_65)) => (apply(compose_function(G61_61, F62_62, A63_63, B64_64, C65_65), X66_66, Z67_67) <=> ? [Y68_68] : (((member(Y68_68, B64_64) & apply(F62_62, X66_66, Y68_68)) & apply(G61_61, Y68_68, Z67_67)))))) & ! [F99_99, A100_100, B101_101, X102_102, Y103_103] : (((member(X102_102, A100_100) & member(Y103_103, B101_101)) => (apply(F99_99, X102_102, Y103_103) <=> apply(inverse_function(F99_99, A100_100, B101_101), Y103_103, X102_102))))) & ~! [F149_149, A150_150, B151_151] : ((maps(F149_149, A150_150, B151_151) => equal_set(inverse_image2(F149_149, empty_set), empty_set))))
% 0.15/0.40 -> [1] (! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))), (! [G61_61, F62_62, A63_63, B64_64, C65_65, X66_66, Z67_67] : (((member(X66_66, A63_63) & member(Z67_67, C65_65)) => (apply(compose_function(G61_61, F62_62, A63_63, B64_64, C65_65), X66_66, Z67_67) <=> ? [Y68_68] : (((member(Y68_68, B64_64) & apply(F62_62, X66_66, Y68_68)) & apply(G61_61, Y68_68, Z67_67)))))) & ! [F99_99, A100_100, B101_101, X102_102, Y103_103] : (((member(X102_102, A100_100) & member(Y103_103, B101_101)) => (apply(F99_99, X102_102, Y103_103) <=> apply(inverse_function(F99_99, A100_100, B101_101), Y103_103, X102_102))))), ~! [F149_149, A150_150, B151_151] : ((maps(F149_149, A150_150, B151_151) => equal_set(inverse_image2(F149_149, empty_set), empty_set)))
% 0.15/0.40
% 0.15/0.40 [1] ALPHA_AND : (! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24))))
% 0.15/0.40 -> [2] ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))), ! [X19_19] : (~member(X19_19, empty_set)), ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 0.15/0.40
% 0.15/0.40 [2] ALPHA_AND : (! [G61_61, F62_62, A63_63, B64_64, C65_65, X66_66, Z67_67] : (((member(X66_66, A63_63) & member(Z67_67, C65_65)) => (apply(compose_function(G61_61, F62_62, A63_63, B64_64, C65_65), X66_66, Z67_67) <=> ? [Y68_68] : (((member(Y68_68, B64_64) & apply(F62_62, X66_66, Y68_68)) & apply(G61_61, Y68_68, Z67_67)))))) & ! [F99_99, A100_100, B101_101, X102_102, Y103_103] : (((member(X102_102, A100_100) & member(Y103_103, B101_101)) => (apply(F99_99, X102_102, Y103_103) <=> apply(inverse_function(F99_99, A100_100, B101_101), Y103_103, X102_102)))))
% 0.15/0.40 -> [3] ! [G61_61, F62_62, A63_63, B64_64, C65_65, X66_66, Z67_67] : (((member(X66_66, A63_63) & member(Z67_67, C65_65)) => (apply(compose_function(G61_61, F62_62, A63_63, B64_64, C65_65), X66_66, Z67_67) <=> ? [Y68_68] : (((member(Y68_68, B64_64) & apply(F62_62, X66_66, Y68_68)) & apply(G61_61, Y68_68, Z67_67)))))), ! [F99_99, A100_100, B101_101, X102_102, Y103_103] : (((member(X102_102, A100_100) & member(Y103_103, B101_101)) => (apply(F99_99, X102_102, Y103_103) <=> apply(inverse_function(F99_99, A100_100, B101_101), Y103_103, X102_102))))
% 0.15/0.40
% 0.15/0.40 [3] DELTA_NOT_FORALL : ~! [F149_149, A150_150, B151_151] : ((maps(F149_149, A150_150, B151_151) => equal_set(inverse_image2(F149_149, empty_set), empty_set)))
% 0.15/0.40 -> [4] ~(maps(skolem_F149149, skolem_A150150, skolem_B151151) => equal_set(inverse_image2(skolem_F149149, empty_set), empty_set))
% 0.15/0.40
% 0.15/0.40 [4] ALPHA_NOT_IMPLY : ~(maps(skolem_F149149, skolem_A150150, skolem_B151151) => equal_set(inverse_image2(skolem_F149149, empty_set), empty_set))
% 0.15/0.40 -> [5] maps(skolem_F149149, skolem_A150150, skolem_B151151), ~equal_set(inverse_image2(skolem_F149149, empty_set), empty_set)
% 0.15/0.40
% 0.15/0.40 [5] Rewrite : maps(skolem_F149149, skolem_A150150, skolem_B151151)
% 0.15/0.40 -> [6] (! [X47_47] : ((member(X47_47, skolem_A150150) => ? [Y48_48] : ((member(Y48_48, skolem_B151151) & apply(skolem_F149149, X47_47, Y48_48))))) & ! [X49_49, Y150_50, Y251_51] : ((((member(X49_49, skolem_A150150) & member(Y150_50, skolem_B151151)) & member(Y251_51, skolem_B151151)) => ((apply(skolem_F149149, X49_49, Y150_50) & apply(skolem_F149149, X49_49, Y251_51)) => =(Y150_50, Y251_51)))))
% 0.15/0.40
% 0.15/0.40 [6] Rewrite : ~equal_set(inverse_image2(skolem_F149149, empty_set), empty_set)
% 0.15/0.40 -> [7] ~(subset(inverse_image2(skolem_F149149, empty_set), empty_set) & subset(empty_set, inverse_image2(skolem_F149149, empty_set)))
% 0.15/0.40
% 0.15/0.40 [7] ALPHA_AND : (! [X47_47] : ((member(X47_47, skolem_A150150) => ? [Y48_48] : ((member(Y48_48, skolem_B151151) & apply(skolem_F149149, X47_47, Y48_48))))) & ! [X49_49, Y150_50, Y251_51] : ((((member(X49_49, skolem_A150150) & member(Y150_50, skolem_B151151)) & member(Y251_51, skolem_B151151)) => ((apply(skolem_F149149, X49_49, Y150_50) & apply(skolem_F149149, X49_49, Y251_51)) => =(Y150_50, Y251_51)))))
% 0.15/0.40 -> [8] ! [X47_47] : ((member(X47_47, skolem_A150150) => ? [Y48_48] : ((member(Y48_48, skolem_B151151) & apply(skolem_F149149, X47_47, Y48_48))))), ! [X49_49, Y150_50, Y251_51] : ((((member(X49_49, skolem_A150150) & member(Y150_50, skolem_B151151)) & member(Y251_51, skolem_B151151)) => ((apply(skolem_F149149, X49_49, Y150_50) & apply(skolem_F149149, X49_49, Y251_51)) => =(Y150_50, Y251_51))))
% 0.15/0.40
% 0.15/0.40 [8] BETA_NOT_AND : ~(subset(inverse_image2(skolem_F149149, empty_set), empty_set) & subset(empty_set, inverse_image2(skolem_F149149, empty_set)))
% 0.15/0.40 -> [9] ~subset(inverse_image2(skolem_F149149, empty_set), empty_set)
% 0.15/0.40 -> [10] ~subset(empty_set, inverse_image2(skolem_F149149, empty_set))
% 0.15/0.40
% 0.15/0.40 [10] Rewrite : ~subset(empty_set, inverse_image2(skolem_F149149, empty_set))
% 0.15/0.40 -> [12] ~(member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), empty_set) => member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), inverse_image2(skolem_F149149, empty_set)))
% 0.15/0.40
% 0.15/0.40 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), empty_set) => member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), inverse_image2(skolem_F149149, empty_set)))
% 0.15/0.40 -> [14] member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), empty_set), ~member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), inverse_image2(skolem_F149149, empty_set))
% 0.15/0.40
% 0.15/0.40 [14] Rewrite : ~member(skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), inverse_image2(skolem_F149149, empty_set))
% 0.15/0.40 -> [16] ~? [Y116_116] : ((member(Y116_116, empty_set) & apply(skolem_F149149, skolem_X88(empty_set, inverse_image2(skolem_F149149, empty_set)), Y116_116)))
% 0.15/0.40
% 0.15/0.40 [16] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 0.15/0.40 -> [17] (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 0.15/0.40
% 0.15/0.40 [17] BETA_EQUIV : (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 0.15/0.40 -> [18] ~member(X11_0_0, power_set(X11_0_0)), ~subset(X11_0_0, X11_0_0)
% 0.15/0.40 -> [19] member(X11_0_0, power_set(X11_0_0)), subset(X11_0_0, X11_0_0)
% 0.15/0.40
% 0.15/0.40 [19] Rewrite : subset(X11_0_0, X11_0_0)
% 0.15/0.40 -> [21] ! [X8_8] : ((member(X8_8, X11_0_0) => member(X8_8, X11_0_0)))
% 0.15/0.40
% 0.15/0.40 [21] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 0.15/0.40 -> [22] ~member(X19_0_1, empty_set)
% 0.15/0.40
% 0.15/0.40 [22] CLOSURE : ~member(X19_0_1, empty_set)
% 0.15/0.40
% 0.15/0.40 [18] Rewrite : ~subset(X11_0_0, X11_0_0)
% 0.15/0.40 -> [23] ~(member(skolem_X88(X11_0_0, X11_0_0), X11_0_0) => member(skolem_X88(X11_0_0, X11_0_0), X11_0_0))
% 0.15/0.40
% 0.15/0.40 [23] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_0_0, X11_0_0), X11_0_0) => member(skolem_X88(X11_0_0, X11_0_0), X11_0_0))
% 0.15/0.40 -> [24] member(skolem_X88(X11_0_0, X11_0_0), X11_0_0), ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 0.15/0.40
% 0.15/0.40 [24] CLOSURE : ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 0.15/0.40
% 0.15/0.40 [9] Rewrite : ~subset(inverse_image2(skolem_F149149, empty_set), empty_set)
% 0.15/0.40 -> [11] ~(member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), inverse_image2(skolem_F149149, empty_set)) => member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), empty_set))
% 0.15/0.40
% 0.15/0.40 [11] ALPHA_NOT_IMPLY : ~(member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), inverse_image2(skolem_F149149, empty_set)) => member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), empty_set))
% 0.15/0.40 -> [13] member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), inverse_image2(skolem_F149149, empty_set)), ~member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), empty_set)
% 0.15/0.40
% 0.15/0.40 [13] Rewrite : member(skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), inverse_image2(skolem_F149149, empty_set))
% 0.15/0.40 -> [15] (member(skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set)), empty_set) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set))))
% 0.15/0.40
% 0.15/0.40 [15] ALPHA_AND : (member(skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set)), empty_set) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set))))
% 0.15/0.40 -> [20] member(skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set)), empty_set), apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set), skolem_Y116116(empty_set, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, empty_set), empty_set)))
% 0.15/0.40
% 0.15/0.40 [20] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 0.15/0.40 -> [25] (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 0.15/0.40
% 0.15/0.40 [25] BETA_EQUIV : (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 0.15/0.40 -> [26] ~member(X11_1_0, power_set(X11_1_0)), ~subset(X11_1_0, X11_1_0)
% 0.15/0.40 -> [27] member(X11_1_0, power_set(X11_1_0)), subset(X11_1_0, X11_1_0)
% 0.15/0.40
% 0.15/0.40 [27] Rewrite : subset(X11_1_0, X11_1_0)
% 0.15/0.40 -> [29] ! [X8_8] : ((member(X8_8, X11_1_0) => member(X8_8, X11_1_0)))
% 0.15/0.40
% 0.15/0.40 [29] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 0.15/0.40 -> [31] ~member(X19_1_1, empty_set)
% 0.15/0.40
% 0.15/0.40 [31] CLOSURE : ~member(X19_1_1, empty_set)
% 0.15/0.40
% 0.15/0.40 [26] Rewrite : ~subset(X11_1_0, X11_1_0)
% 0.15/0.40 -> [28] ~(member(skolem_X88(X11_1_0, X11_1_0), X11_1_0) => member(skolem_X88(X11_1_0, X11_1_0), X11_1_0))
% 0.15/0.40
% 0.15/0.40 [28] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_1_0, X11_1_0), X11_1_0) => member(skolem_X88(X11_1_0, X11_1_0), X11_1_0))
% 0.15/0.40 -> [30] member(skolem_X88(X11_1_0, X11_1_0), X11_1_0), ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 0.15/0.40
% 0.15/0.40 [30] CLOSURE : ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 0.15/0.40
% 0.15/0.40 % SZS output end Proof for theBenchmark.p
% 0.15/0.40 [0.088281s][1][Res] 394 goroutines created
% 0.15/0.40 ==== Result ====
% 0.15/0.40 [0.088326s][1][Res] VALID
% 0.15/0.40 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------