%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET711+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET711+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 05:38:22 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(apply_type, type, (
% 0.14/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_X_14_type, type, (
% 0.14/0.40 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_G_42_type, type, (
% 0.14/0.40 tptp_fun_G_42: $i)).
% 0.14/0.40 tff(tptp_fun_H_41_type, type, (
% 0.14/0.40 tptp_fun_H_41: $i)).
% 0.14/0.40 tff(tptp_fun_B_39_type, type, (
% 0.14/0.40 tptp_fun_B_39: $i)).
% 0.14/0.40 tff(tptp_fun_A_40_type, type, (
% 0.14/0.40 tptp_fun_A_40: $i)).
% 0.14/0.40 tff(tptp_fun_Y2_12_type, type, (
% 0.14/0.40 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_F_43_type, type, (
% 0.14/0.40 tptp_fun_F_43: $i)).
% 0.14/0.40 tff(member_type, type, (
% 0.14/0.40 member: ( $i * $i ) > $o)).
% 0.14/0.40 tff(inverse_predicate_type, type, (
% 0.14/0.40 inverse_predicate: ( $i * $i * $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_X_22_type, type, (
% 0.14/0.40 tptp_fun_X_22: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_Y_21_type, type, (
% 0.14/0.40 tptp_fun_Y_21: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.40 tff(one_to_one_type, type, (
% 0.14/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(maps_type, type, (
% 0.14/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(equal_maps_type, type, (
% 0.14/0.40 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_Y1_13_type, type, (
% 0.14/0.40 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.14/0.40 tff(injective_type, type, (
% 0.14/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_X2_17_type, type, (
% 0.14/0.40 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_X1_18_type, type, (
% 0.14/0.40 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_Y_16_type, type, (
% 0.14/0.40 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.14/0.40 tff(surjective_type, type, (
% 0.14/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[G: $i, F: $i, A: $i, B: $i] : refl((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (^[G: $i, F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))) <=> (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), rewrite((inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))), rewrite((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.40 tff(11,axiom,(![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_predicate')).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.14/0.40 tff(14,plain,(
% 0.14/0.40 ![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))))))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 ((~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(H!41, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)))))))) <=> (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41)))))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(H!41, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))))))))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(H!41, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(H!41, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41)))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~(inverse_predicate(H!41, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, H!41), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, H!41), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, H!41), tptp_fun_Y_21(B!39, A!40, F!43, H!41)) <=> apply(H!41, tptp_fun_Y_21(B!39, A!40, F!43, H!41), tptp_fun_X_22(B!39, A!40, F!43, H!41)))))))) | ((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 ((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((((maps(F, A, B) & one_to_one(F, A, B)) & inverse_predicate(G, F, A, B)) & inverse_predicate(H, F, A, B)) => equal_maps(G, H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((((maps(F, A, B) & one_to_one(F, A, B)) & inverse_predicate(G, F, A, B)) & inverse_predicate(H, F, A, B)) => equal_maps(G, H, B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII03a')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B) & inverse_predicate(G, F, A, B) & inverse_predicate(H, F, A, B))) | equal_maps(G, H, B, A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.41 tff(33,plain,(
% 0.21/0.41 ~((~(maps(F!43, A!40, B!39) & one_to_one(F!43, A!40, B!39) & inverse_predicate(G!42, F!43, A!40, B!39) & inverse_predicate(H!41, F!43, A!40, B!39))) | equal_maps(G!42, H!41, B!39, A!40))),
% 0.21/0.41 inference(skolemize,[status(sab)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (maps(F!43, A!40, B!39) & one_to_one(F!43, A!40, B!39) & inverse_predicate(G!42, F!43, A!40, B!39) & inverse_predicate(H!41, F!43, A!40, B!39)),
% 0.21/0.41 inference(or_elim,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (inverse_predicate(H!41, F!43, A!40, B!39)),
% 0.21/0.41 inference(and_elim,[status(thm)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | (~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~((~inverse_predicate(H!41, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X))))) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[37, 25])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.42 tff(49,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.42 tff(52,plain,(
% 0.21/0.42 ![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[51])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))))))) <=> (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (~((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[60, 54])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (((~((~equal_maps(G!42, H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(G!42, X, Y1))))) | (~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))))) | (equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (~equal_maps(G!42, H!41, B!39, A!40)),
% 0.21/0.44 inference(or_elim,[status(thm)],[33])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 ((~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))) | equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 ((~(equal_maps(G!42, H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))))) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(H!41, Y, X)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 71, 69, 38])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 67])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ((~(apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((~(apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(G!42, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)))))))) <=> (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(G!42, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(G!42, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((apply(F!43, X, Y) <=> apply(G!42, Y, X)) | (~member(Y, B!39)) | (~member(X, A!40))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42)))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (~((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42))))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[86, 16])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~(inverse_predicate(G!42, F!43, A!40, B!39) | (~((~member(tptp_fun_Y_21(B!39, A!40, F!43, G!42), B!39)) | (~member(tptp_fun_X_22(B!39, A!40, F!43, G!42), A!40)) | (apply(F!43, tptp_fun_X_22(B!39, A!40, F!43, G!42), tptp_fun_Y_21(B!39, A!40, F!43, G!42)) <=> apply(G!42, tptp_fun_Y_21(B!39, A!40, F!43, G!42), tptp_fun_X_22(B!39, A!40, F!43, G!42)))))))) | ((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (inverse_predicate(G!42, F!43, A!40, B!39)),
% 0.21/0.46 inference(and_elim,[status(thm)],[34])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 ((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | (~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 ((~((~inverse_predicate(G!42, F!43, A!40, B!39)) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X))))) | ![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[94, 67])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~member(Y, B!39)) | (~member(X, A!40)) | (apply(F!43, X, Y) <=> apply(G!42, Y, X)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[98, 95, 69, 93])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[100, 67])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42)))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42)))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 99])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (^[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)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (![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))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (^[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)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (![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))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (![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))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (^[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))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (^[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))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.47 tff(115,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/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.47 tff(118,plain,(
% 0.21/0.47 ![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)))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[117])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))) <=> (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), 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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), 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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 ((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 ((~![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(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[126, 120])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))))))) | ((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 ((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (^[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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(135,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.48 tff(137,plain,(
% 0.21/0.48 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[136])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (~(((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (one_to_one(F!43, A!40, B!39)),
% 0.21/0.48 inference(and_elim,[status(thm)],[34])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 ((((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)) | (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))) | (~one_to_one(F!43, A!40, B!39))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 ((((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)) | (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) | injective(F!43, A!40, B!39)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (injective(F!43, A!40, B!39)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[149, 129])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))) | (~(tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (~(tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[151, 67])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, G!42), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, G!42), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, G!42)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, G!42), tptp_fun_X_14(A!40, B!39, H!41, G!42)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[158, 71, 95, 69, 152, 150, 104, 80])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------