%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET713+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:12 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET713+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:40:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(apply_type, type, (
% 0.21/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_X2_17_type, type, (
% 0.21/0.40 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(inverse_function_type, type, (
% 0.21/0.40 inverse_function: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_B_39_type, type, (
% 0.21/0.40 tptp_fun_B_39: $i)).
% 0.21/0.40 tff(tptp_fun_A_40_type, type, (
% 0.21/0.40 tptp_fun_A_40: $i)).
% 0.21/0.40 tff(tptp_fun_F_41_type, type, (
% 0.21/0.40 tptp_fun_F_41: $i)).
% 0.21/0.40 tff(tptp_fun_Y_16_type, type, (
% 0.21/0.40 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(member_type, type, (
% 0.21/0.40 member: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_X1_18_type, type, (
% 0.21/0.40 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(injective_type, type, (
% 0.21/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(surjective_type, type, (
% 0.21/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y_20_type, type, (
% 0.21/0.40 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_E_19_type, type, (
% 0.21/0.40 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(maps_type, type, (
% 0.21/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.21/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.21/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_X_7_type, type, (
% 0.21/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_X_4_type, type, (
% 0.21/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(one_to_one_type, type, (
% 0.21/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.40 tff(11,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.40 tff(14,plain,(
% 0.21/0.40 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X2, B!39)) | (~member(X1, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))))))) <=> (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X2, B!39)) | (~member(X1, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X2, B!39)) | (~member(X1, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X2, B!39)) | (~member(X1, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (~((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!39)) | (~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X1, Y)) | (~member(X1, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), X2, Y))))) | (~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))) | (injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.42 tff(26,assumption,((~((~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![Y: $i] : ((~member(Y, A!40)) | (~((~member(tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), Y))))))) | (~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))), introduced(assumption)).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.43 tff(37,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.43 tff(40,plain,(
% 0.21/0.43 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[39])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![Y: $i] : ((~member(Y, A!40)) | (~((~member(tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), Y))))))) | (~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[43, 42, 26])).
% 0.21/0.43 tff(45,plain,(~((~((~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![Y: $i] : ((~member(Y, A!40)) | (~((~member(tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), Y))))))) | (~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (((~((~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ![Y: $i] : ((~member(Y, A!40)) | (~((~member(tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_E_19(Y, B!39, inverse_function(F!41, A!40, B!39)), Y))))))) | (~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))) | (surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.43 tff(48,assumption,(~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))), introduced(assumption)).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))) | member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[56, 54])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.44 tff(65,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.44 tff(68,plain,(
% 0.21/0.44 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[67])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[71, 52])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))))))) <=> (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41))))))) | ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => one_to_one(inverse_function(F, A, B), B, A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(84,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => one_to_one(inverse_function(F, A, B), B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII04')).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | one_to_one(inverse_function(F, A, B), B, A))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.21/0.47 tff(89,plain,(
% 0.21/0.47 ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.21/0.47 inference(skolemize,[status(sab)],[88])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.21/0.47 inference(or_elim,[status(thm)],[89])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (maps(F!41, A!40, B!39)),
% 0.21/0.47 inference(and_elim,[status(thm)],[90])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[93, 81])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | ((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | ((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (~((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[99, 96, 50])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)))) | member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))) | ![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[103, 48])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 (((~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 ((~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 ((~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[107, 104, 102])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)))) | apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[109, 100])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 ((~(apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | (~apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (~(apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[111, 110, 108])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.48 tff(120,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.48 tff(123,plain,(
% 0.21/0.48 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[122])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (((apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), B!39)) | (apply(F!41, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41)) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y_3(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39, F!41), tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[131, 125, 50, 102, 112])).
% 0.21/0.49 tff(133,plain,((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(134,plain,
% 0.21/0.49 ((~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))) | surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 ((~(surjective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~![E: $i] : ((~member(E, B!39)) | (~apply(inverse_function(F!41, A!40, B!39), E, tptp_fun_Y_20(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))) | surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 (surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[135, 47])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(138,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(142,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.49 tff(144,plain,(
% 0.21/0.49 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[143])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.21/0.49 tff(146,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (~(((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 (~one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.21/0.49 inference(or_elim,[status(thm)],[89])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 ((((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))) | one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 ((((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> one_to_one(inverse_function(F!41, A!40, B!39), B!39, A!40)) | ((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 ((~((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 ((~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~surjective(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 (~injective(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[154, 136])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 ((~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))) | injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(157,plain,
% 0.21/0.50 ((~(injective(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))) | (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.50 tff(158,plain,
% 0.21/0.50 (~((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[157, 25])).
% 0.21/0.50 tff(159,plain,
% 0.21/0.50 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(160,plain,
% 0.21/0.50 (member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.50 tff(161,plain,
% 0.21/0.50 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(162,plain,
% 0.21/0.50 (member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.21/0.50 tff(163,plain,
% 0.21/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(164,plain,
% 0.21/0.50 (((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(165,plain,
% 0.21/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[164])).
% 0.21/0.51 tff(166,plain,
% 0.21/0.51 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[165, 163])).
% 0.21/0.51 tff(167,plain,
% 0.21/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(168,plain,
% 0.21/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[168, 125, 162, 160])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 (apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[170, 158])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 ((~(apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 ((~(apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.51 tff(174,plain,
% 0.21/0.51 (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[173, 169])).
% 0.21/0.51 tff(175,plain,
% 0.21/0.51 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 (member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[175, 158])).
% 0.21/0.51 tff(177,plain,
% 0.21/0.51 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(178,plain,
% 0.21/0.51 (((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(179,plain,
% 0.21/0.51 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.51 tff(180,plain,
% 0.21/0.51 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[179, 177])).
% 0.21/0.52 tff(181,plain,
% 0.21/0.52 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(182,plain,
% 0.21/0.52 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.52 tff(183,plain,
% 0.21/0.52 (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[182, 125, 160, 176])).
% 0.21/0.52 tff(184,plain,
% 0.21/0.52 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(185,plain,
% 0.21/0.52 (apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[184, 158])).
% 0.21/0.52 tff(186,plain,
% 0.21/0.52 ((~(apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(187,plain,
% 0.21/0.52 ((~(apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.52 tff(188,plain,
% 0.21/0.52 (apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[187, 183])).
% 0.21/0.52 tff(189,plain,
% 0.21/0.52 (((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | (~(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(190,plain,
% 0.21/0.52 (~(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[189, 158])).
% 0.21/0.52 tff(191,plain,
% 0.21/0.52 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(192,plain,
% 0.21/0.52 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[191, 94])).
% 0.21/0.52 tff(193,plain,
% 0.21/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(194,plain,
% 0.21/0.52 (((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39))) <=> ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(195,plain,
% 0.21/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[194])).
% 0.21/0.52 tff(196,plain,
% 0.21/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.37/0.53 inference(transitivity,[status(thm)],[195, 193])).
% 0.37/0.53 tff(197,plain,
% 0.37/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(198,plain,
% 0.37/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X1_18(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y_16(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X2_17(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.37/0.53 tff(199,plain,
% 0.37/0.53 ($false),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[198, 192, 162, 160, 176, 190, 188, 174])).
% 0.37/0.53 % SZS output end Proof
% 0.37/0.53 % E exiting
%------------------------------------------------------------------------------