TSTP Solution File: SET755+4 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n007.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 04:17:21 EDT 2022
% Result : Theorem 6.64s 2.52s
% Output : Proof 6.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 07:30:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Conjecture not found
% 0.13/0.36 Conjecture not found
% 0.13/0.36 Start search
% 0.13/0.36 nb_step : 1 - limit : 51
% 0.13/0.36 Launch Gotab with destructive = true
% 6.64/2.51 % SZS output start Proof for theBenchmark.p
% 6.64/2.52 [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, X152_152, Y153_153] : (((((maps(F149_149, A150_150, B151_151) & subset(X152_152, B151_151)) & subset(Y153_153, B151_151)) & subset(X152_152, Y153_153)) => subset(inverse_image2(F149_149, X152_152), inverse_image2(F149_149, Y153_153)))))
% 6.64/2.52 -> [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, X152_152, Y153_153] : (((((maps(F149_149, A150_150, B151_151) & subset(X152_152, B151_151)) & subset(Y153_153, B151_151)) & subset(X152_152, Y153_153)) => subset(inverse_image2(F149_149, X152_152), inverse_image2(F149_149, Y153_153))))
% 6.64/2.52
% 6.64/2.52 [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))))
% 6.64/2.52 -> [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)))
% 6.64/2.52
% 6.64/2.52 [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)))))
% 6.64/2.52 -> [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))))
% 6.64/2.52
% 6.64/2.52 [3] DELTA_NOT_FORALL : ~! [F149_149, A150_150, B151_151, X152_152, Y153_153] : (((((maps(F149_149, A150_150, B151_151) & subset(X152_152, B151_151)) & subset(Y153_153, B151_151)) & subset(X152_152, Y153_153)) => subset(inverse_image2(F149_149, X152_152), inverse_image2(F149_149, Y153_153))))
% 6.64/2.52 -> [4] ~((((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151)) & subset(skolem_X152152, skolem_Y153153)) => subset(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))
% 6.64/2.52
% 6.64/2.52 [4] ALPHA_NOT_IMPLY : ~((((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151)) & subset(skolem_X152152, skolem_Y153153)) => subset(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))
% 6.64/2.52 -> [5] (((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151)) & subset(skolem_X152152, skolem_Y153153)), ~subset(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))
% 6.64/2.52
% 6.64/2.52 [5] Rewrite : ~subset(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))
% 6.64/2.52 -> [6] ~(member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_X152152)) => member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_Y153153)))
% 6.64/2.52
% 6.64/2.52 [6] ALPHA_AND : (((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151)) & subset(skolem_X152152, skolem_Y153153))
% 6.64/2.52 -> [7] ((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151)), subset(skolem_X152152, skolem_Y153153)
% 6.64/2.52
% 6.64/2.52 [7] Rewrite : subset(skolem_X152152, skolem_Y153153)
% 6.64/2.52 -> [8] ! [X8_8] : ((member(X8_8, skolem_X152152) => member(X8_8, skolem_Y153153)))
% 6.64/2.52
% 6.64/2.52 [8] ALPHA_NOT_IMPLY : ~(member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_X152152)) => member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_Y153153)))
% 6.64/2.52 -> [9] member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_X152152)), ~member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_Y153153))
% 6.64/2.52
% 6.64/2.52 [9] Rewrite : member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_X152152))
% 6.64/2.52 -> [10] (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52
% 6.64/2.52 [10] Rewrite : ~member(skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), inverse_image2(skolem_F149149, skolem_Y153153))
% 6.64/2.52 -> [11] ~? [Y116_116] : ((member(Y116_116, skolem_Y153153) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), Y116_116)))
% 6.64/2.52
% 6.64/2.52 [11] ALPHA_AND : ((maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)) & subset(skolem_Y153153, skolem_B151151))
% 6.64/2.52 -> [12] (maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151)), subset(skolem_Y153153, skolem_B151151)
% 6.64/2.52
% 6.64/2.52 [12] Rewrite : subset(skolem_Y153153, skolem_B151151)
% 6.64/2.52 -> [13] ! [X8_8] : ((member(X8_8, skolem_Y153153) => member(X8_8, skolem_B151151)))
% 6.64/2.52
% 6.64/2.52 [13] ALPHA_AND : (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [14] member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152), apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [14] ALPHA_AND : (maps(skolem_F149149, skolem_A150150, skolem_B151151) & subset(skolem_X152152, skolem_B151151))
% 6.64/2.52 -> [15] maps(skolem_F149149, skolem_A150150, skolem_B151151), subset(skolem_X152152, skolem_B151151)
% 6.64/2.52
% 6.64/2.52 [15] Rewrite : maps(skolem_F149149, skolem_A150150, skolem_B151151)
% 6.64/2.52 -> [16] (! [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)))))
% 6.64/2.52
% 6.64/2.52 [16] Rewrite : subset(skolem_X152152, skolem_B151151)
% 6.64/2.52 -> [17] ! [X8_8] : ((member(X8_8, skolem_X152152) => member(X8_8, skolem_B151151)))
% 6.64/2.52
% 6.64/2.52 [17] 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)))))
% 6.64/2.52 -> [18] ! [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))))
% 6.64/2.52
% 6.64/2.52 [18] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 6.64/2.52 -> [19] (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 6.64/2.52
% 6.64/2.52 [19] BETA_EQUIV : (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 6.64/2.52 -> [20] ~member(X11_0_0, power_set(X11_0_0)), ~subset(X11_0_0, X11_0_0)
% 6.64/2.52 -> [21] member(X11_0_0, power_set(X11_0_0)), subset(X11_0_0, X11_0_0)
% 6.64/2.52
% 6.64/2.52 [20] Rewrite : ~subset(X11_0_0, X11_0_0)
% 6.64/2.52 -> [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))
% 6.64/2.52
% 6.64/2.52 [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))
% 6.64/2.52 -> [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)
% 6.64/2.52
% 6.64/2.52 [24] CLOSURE : ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 6.64/2.52
% 6.64/2.52 [21] Rewrite : subset(X11_0_0, X11_0_0)
% 6.64/2.52 -> [22] ! [X8_8] : ((member(X8_8, X11_0_0) => member(X8_8, X11_0_0)))
% 6.64/2.52
% 6.64/2.52 [22] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 6.64/2.52 -> [25] ~member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set)
% 6.64/2.52
% 6.64/2.52 [25] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 6.64/2.52 -> [26] (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))) <=> =(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52
% 6.64/2.52 [26] BETA_EQUIV : (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))) <=> =(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [27] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))), ~=(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52 -> [28] member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))), =(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [27] CLOSURE : ~=(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [28] GAMMA_FORALL : ! [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))))))
% 6.64/2.52 -> [29] ((member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)) => (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))))
% 6.64/2.52
% 6.64/2.52 [29] BETA_IMPLY : ((member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)) => (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))))
% 6.64/2.52 -> [30] ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152))
% 6.64/2.52 -> [31] (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))))
% 6.64/2.52
% 6.64/2.52 [30] BETA_NOT_AND : ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152))
% 6.64/2.52 -> [32] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)
% 6.64/2.52 -> [33] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)
% 6.64/2.52
% 6.64/2.52 [33] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [32] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [31] BETA_EQUIV : (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))))
% 6.64/2.52 -> [60] ~apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), ~? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))
% 6.64/2.52 -> [61] apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))
% 6.64/2.52
% 6.64/2.52 [61] DELTA_EXISTS : ? [Y68_68] : (((member(Y68_68, empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), Y68_68)) & apply(G61_0_3, Y68_68, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))
% 6.64/2.52 -> [62] ((member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y6868(empty_set, F62_0_3, G61_0_3))) & apply(G61_0_3, skolem_Y6868(empty_set, F62_0_3, G61_0_3), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52
% 6.64/2.52 [62] ALPHA_AND : ((member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y6868(empty_set, F62_0_3, G61_0_3))) & apply(G61_0_3, skolem_Y6868(empty_set, F62_0_3, G61_0_3), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [63] (member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y6868(empty_set, F62_0_3, G61_0_3))), apply(G61_0_3, skolem_Y6868(empty_set, F62_0_3, G61_0_3), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [63] ALPHA_AND : (member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set) & apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y6868(empty_set, F62_0_3, G61_0_3)))
% 6.64/2.52 -> [71] member(skolem_Y6868(empty_set, F62_0_3, G61_0_3), empty_set), apply(F62_0_3, skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y6868(empty_set, F62_0_3, G61_0_3))
% 6.64/2.52
% 6.64/2.52 [71] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [64] BETA_IMPLY : ((member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)) => (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> apply(inverse_function(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))))
% 6.64/2.52 -> [86] ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152))
% 6.64/2.52 -> [87] (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> apply(inverse_function(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52
% 6.64/2.52 [86] BETA_NOT_AND : ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))) & member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), power_set(X11_0_0)))
% 6.64/2.52 -> [88] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [89] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), power_set(X11_0_0))
% 6.64/2.52
% 6.64/2.52 [88] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [89] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [87] BETA_EQUIV : (apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))) <=> apply(inverse_function(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [98] ~apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), ~apply(inverse_function(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52 -> [99] apply(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), apply(inverse_function(compose_function(G61_0_3, F62_0_3, skolem_X152152, empty_set, skolem_X152152), singleton(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))), skolem_X152152), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [99] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [98] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_X152152) => member(X8_8, skolem_Y153153)))
% 6.64/2.52 -> [100] (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) => member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153))
% 6.64/2.52
% 6.64/2.52 [100] BETA_IMPLY : (member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152) => member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153))
% 6.64/2.52 -> [101] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_X152152)
% 6.64/2.52 -> [102] member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153)
% 6.64/2.52
% 6.64/2.52 [101] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [102] GAMMA_NOT_EXISTS : ~? [Y116_116] : ((member(Y116_116, skolem_Y153153) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), Y116_116)))
% 6.64/2.52 -> [103] ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52
% 6.64/2.52 [103] BETA_NOT_AND : ~(member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153) & apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)))))
% 6.64/2.52 -> [104] ~member(skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))), skolem_Y153153)
% 6.64/2.52 -> [105] ~apply(skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153)), skolem_Y116116(skolem_X152152, skolem_F149149, skolem_X88(inverse_image2(skolem_F149149, skolem_X152152), inverse_image2(skolem_F149149, skolem_Y153153))))
% 6.64/2.52
% 6.64/2.52 [105] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 [104] CLOSURE : =
% 6.64/2.52
% 6.64/2.52 % SZS output end Proof for theBenchmark.p
% 6.64/2.52 [2.180498s][1][Res] 3019 goroutines created
% 6.64/2.52 ==== Result ====
% 6.64/2.52 [2.180540s][1][Res] VALID
% 6.64/2.52 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------