%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET750+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:16 AM UTC 2025
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET750+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 05:39:54 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(apply_type, type, (
% 0.23/0.43 apply: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_Y2_27_type, type, (
% 0.23/0.43 tptp_fun_Y2_27: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_F_43_type, type, (
% 0.23/0.43 tptp_fun_F_43: $i)).
% 0.23/0.43 tff(tptp_fun_A_42_type, type, (
% 0.23/0.43 tptp_fun_A_42: $i)).
% 0.23/0.43 tff(tptp_fun_R_40_type, type, (
% 0.23/0.43 tptp_fun_R_40: $i)).
% 0.23/0.43 tff(tptp_fun_B_41_type, type, (
% 0.23/0.43 tptp_fun_B_41: $i)).
% 0.23/0.43 tff(tptp_fun_S_39_type, type, (
% 0.23/0.43 tptp_fun_S_39: $i)).
% 0.23/0.43 tff(tptp_fun_Y1_29_type, type, (
% 0.23/0.43 tptp_fun_Y1_29: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(member_type, type, (
% 0.23/0.43 member: ( $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_X1_30_type, type, (
% 0.23/0.43 tptp_fun_X1_30: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_28_type, type, (
% 0.23/0.43 tptp_fun_X2_28: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(increasing_type, type, (
% 0.23/0.43 increasing: ( $i * $i * $i * $i * $i ) > $o)).
% 0.23/0.43 tff(one_to_one_type, type, (
% 0.23/0.43 one_to_one: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(maps_type, type, (
% 0.23/0.43 maps: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(isomorphism_type, type, (
% 0.23/0.43 isomorphism: ( $i * $i * $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_E_19_type, type, (
% 0.23/0.43 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y1_37_type, type, (
% 0.23/0.43 tptp_fun_Y1_37: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(inverse_function_type, type, (
% 0.23/0.43 inverse_function: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X1_38_type, type, (
% 0.23/0.43 tptp_fun_X1_38: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(surjective_type, type, (
% 0.23/0.43 surjective: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_Y_20_type, type, (
% 0.23/0.43 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(injective_type, type, (
% 0.23/0.43 injective: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_Y2_35_type, type, (
% 0.23/0.43 tptp_fun_Y2_35: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_36_type, type, (
% 0.23/0.43 tptp_fun_X2_36: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_17_type, type, (
% 0.23/0.43 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X1_18_type, type, (
% 0.23/0.43 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y_16_type, type, (
% 0.23/0.43 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(1,assumption,(~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))), introduced(assumption)).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (~apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.23/0.43 tff(6,plain,
% 0.23/0.43 ((~(apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (~(apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[6, 5, 3])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 (member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(13,plain,
% 0.23/0.44 (member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.23/0.44 tff(14,plain,
% 0.23/0.44 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 (member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[14, 1])).
% 0.23/0.44 tff(16,plain,
% 0.23/0.44 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(17,plain,
% 0.23/0.44 (apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[16, 1])).
% 0.23/0.44 tff(18,plain,
% 0.23/0.44 (((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.23/0.44 tff(20,plain,
% 0.23/0.44 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(23,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.23/0.44 tff(24,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[23, 21])).
% 0.23/0.44 tff(25,plain,
% 0.23/0.44 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(26,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[25])).
% 0.23/0.44 tff(27,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(29,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.45 tff(30,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.23/0.45 tff(31,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.23/0.45 tff(32,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.45 tff(33,plain,(
% 0.23/0.45 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[32])).
% 0.23/0.45 tff(34,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.23/0.45 tff(35,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.23/0.45 tff(36,plain,
% 0.23/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43)))))))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(37,plain,
% 0.23/0.45 (~((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43))))))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.23/0.45 tff(38,plain,
% 0.23/0.45 (((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43)))))))))) | ((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(39,plain,
% 0.23/0.45 ((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.23/0.45 tff(40,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(41,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.23/0.45 tff(42,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.45 tff(44,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(45,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.23/0.45 tff(46,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.23/0.45 tff(47,plain,(
% 0.23/0.45 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[46])).
% 0.23/0.45 tff(48,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.23/0.45 tff(49,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.23/0.45 tff(50,plain,
% 0.23/0.45 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) <=> one_to_one(F!43, A!42, B!41)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(51,plain,
% 0.23/0.45 (~(((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) <=> one_to_one(F!43, A!42, B!41))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.23/0.45 tff(52,plain,
% 0.23/0.45 ((~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))) <=> (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R)))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(53,plain,
% 0.23/0.45 ((~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))) <=> (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R)))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(54,axiom,(~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII41')).
% 0.23/0.45 tff(55,plain,
% 0.23/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.23/0.45 tff(56,plain,
% 0.23/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.23/0.45 tff(57,plain,
% 0.23/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.23/0.45 tff(58,plain,
% 0.23/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[57, 52])).
% 0.23/0.45 tff(59,plain,(
% 0.23/0.45 ~((~(maps(F!43, A!42, B!41) & one_to_one(F!43, A!42, B!41))) | (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[58])).
% 0.23/0.45 tff(60,plain,
% 0.23/0.45 (maps(F!43, A!42, B!41) & one_to_one(F!43, A!42, B!41)),
% 0.23/0.45 inference(or_elim,[status(thm)],[59])).
% 0.23/0.45 tff(61,plain,
% 0.23/0.45 (one_to_one(F!43, A!42, B!41)),
% 0.23/0.45 inference(and_elim,[status(thm)],[60])).
% 0.23/0.45 tff(62,plain,
% 0.23/0.45 ((((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) <=> one_to_one(F!43, A!42, B!41)) | (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))) | (~one_to_one(F!43, A!42, B!41))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(63,plain,
% 0.23/0.45 ((((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) <=> one_to_one(F!43, A!42, B!41)) | (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.23/0.45 tff(64,plain,
% 0.23/0.45 (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[63, 51])).
% 0.23/0.45 tff(65,plain,
% 0.23/0.45 (((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) | surjective(F!43, A!42, B!41)),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(66,plain,
% 0.23/0.45 (surjective(F!43, A!42, B!41)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.23/0.45 tff(67,plain,
% 0.23/0.45 ((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(68,plain,
% 0.23/0.45 ((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.23/0.45 tff(69,plain,
% 0.23/0.45 (![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[68, 39])).
% 0.23/0.45 tff(70,assumption,(~isomorphism(F!43, A!42, R!40, B!41, S!39)), introduced(assumption)).
% 0.23/0.45 tff(71,plain,
% 0.23/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(72,plain,
% 0.23/0.45 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.23/0.45 tff(73,plain,
% 0.23/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(74,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[73])).
% 0.23/0.46 tff(75,plain,
% 0.23/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(76,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.46 tff(77,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[76, 74])).
% 0.23/0.46 tff(78,plain,
% 0.23/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))) <=> (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))), ((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))), rewrite((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))), ((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))), ((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))), rewrite((((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))), ((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(79,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.23/0.46 tff(80,plain,
% 0.23/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))) <=> (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(81,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.46 tff(82,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(83,plain,
% 0.23/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(84,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.23/0.46 tff(85,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','isomorphism')).
% 0.23/0.46 tff(86,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.46 tff(87,plain,
% 0.23/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.23/0.46 tff(88,plain,(
% 0.23/0.46 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[87])).
% 0.23/0.47 tff(89,plain,
% 0.23/0.47 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.23/0.47 tff(90,plain,
% 0.23/0.47 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.23/0.47 tff(91,plain,
% 0.23/0.47 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.23/0.47 tff(92,plain,
% 0.23/0.47 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[91, 72])).
% 0.23/0.47 tff(93,plain,
% 0.23/0.47 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(94,plain,
% 0.23/0.47 ((~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))) <=> (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(95,plain,
% 0.23/0.48 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[94])).
% 0.23/0.48 tff(96,plain,
% 0.23/0.48 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[95, 93])).
% 0.23/0.48 tff(97,plain,
% 0.23/0.48 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(98,plain,
% 0.23/0.49 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.23/0.49 tff(99,plain,
% 0.23/0.49 (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[98, 92])).
% 0.23/0.49 tff(100,plain,
% 0.23/0.49 (((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))) | (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(101,plain,
% 0.23/0.49 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.23/0.49 tff(102,plain,
% 0.23/0.49 (maps(F!43, A!42, B!41)),
% 0.23/0.49 inference(and_elim,[status(thm)],[60])).
% 0.23/0.49 tff(103,plain,
% 0.23/0.49 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(104,plain,
% 0.23/0.50 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[103, 102, 61])).
% 0.23/0.50 tff(105,plain,
% 0.23/0.50 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.23/0.50 tff(106,plain,
% 0.23/0.50 (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[105, 70])).
% 0.23/0.50 tff(107,plain,
% 0.23/0.50 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(108,plain,
% 0.23/0.50 (member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.23/0.50 tff(109,plain,
% 0.23/0.50 (((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))) <=> ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(110,plain,
% 0.23/0.50 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(111,plain,
% 0.23/0.50 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.23/0.50 tff(112,plain,
% 0.23/0.50 (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[111, 108, 69])).
% 0.23/0.50 tff(113,plain,
% 0.23/0.50 (((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(114,plain,
% 0.23/0.50 (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.23/0.50 tff(115,plain,
% 0.23/0.50 (((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(116,plain,
% 0.23/0.50 (member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.23/0.50 tff(117,plain,
% 0.23/0.50 (^[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)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(118,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[117])).
% 0.23/0.50 tff(119,plain,
% 0.23/0.50 (^[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)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(120,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[119])).
% 0.23/0.50 tff(121,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[120, 118])).
% 0.23/0.50 tff(122,plain,
% 0.23/0.50 (^[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))))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(123,plain,
% 0.23/0.50 (![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))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[122])).
% 0.23/0.51 tff(124,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(125,plain,
% 0.23/0.51 (^[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))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(126,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[125])).
% 0.23/0.51 tff(127,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.23/0.51 tff(128,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.23/0.51 tff(129,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.23/0.51 tff(130,plain,(
% 0.23/0.51 ![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)))))))),
% 0.23/0.51 inference(skolemize,[status(sab)],[129])).
% 0.23/0.51 tff(131,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.23/0.51 tff(132,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.23/0.51 tff(133,plain,
% 0.23/0.51 (((~![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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, 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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(134,plain,
% 0.23/0.51 ((~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))) <=> (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(135,plain,
% 0.23/0.51 (((~![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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[134])).
% 0.23/0.51 tff(136,plain,
% 0.23/0.51 (((~![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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[135, 133])).
% 0.23/0.51 tff(137,plain,
% 0.23/0.51 ((~![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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(138,plain,
% 0.23/0.51 ((~![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!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.23/0.51 tff(139,plain,
% 0.23/0.51 (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.23/0.51 tff(140,plain,
% 0.23/0.51 (((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))) | ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(141,plain,
% 0.23/0.51 ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.23/0.51 tff(142,plain,
% 0.23/0.51 (((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) | injective(F!43, A!42, B!41)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(143,plain,
% 0.23/0.51 (injective(F!43, A!42, B!41)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[142, 64])).
% 0.23/0.51 tff(144,plain,
% 0.23/0.51 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(145,plain,
% 0.23/0.51 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.23/0.51 tff(146,plain,
% 0.23/0.51 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[145, 141])).
% 0.23/0.51 tff(147,plain,
% 0.23/0.51 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(148,plain,
% 0.23/0.51 (member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[147, 106])).
% 0.23/0.51 tff(149,plain,
% 0.23/0.51 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(150,plain,
% 0.23/0.51 (apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[149, 106])).
% 0.23/0.51 tff(151,plain,
% 0.23/0.51 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(152,plain,
% 0.23/0.52 (((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) <=> ((~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(153,plain,
% 0.23/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[152])).
% 0.23/0.52 tff(154,plain,
% 0.23/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.52 inference(transitivity,[status(thm)],[153, 151])).
% 0.23/0.52 tff(155,plain,
% 0.23/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(156,plain,
% 0.23/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.23/0.52 tff(157,plain,
% 0.23/0.52 (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[156, 150, 108, 148, 146, 116, 114])).
% 0.23/0.52 tff(158,plain,
% 0.23/0.52 (tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43) = tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43)),
% 0.23/0.52 inference(symmetry,[status(thm)],[157])).
% 0.23/0.52 tff(159,plain,
% 0.23/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[158])).
% 0.23/0.52 tff(160,plain,
% 0.23/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.23/0.52 inference(symmetry,[status(thm)],[159])).
% 0.23/0.52 tff(161,plain,
% 0.23/0.52 ((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) <=> (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.23/0.52 tff(162,plain,
% 0.23/0.52 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(163,plain,
% 0.23/0.52 (member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[162, 106])).
% 0.23/0.52 tff(164,plain,
% 0.23/0.52 (((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) <=> ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(165,plain,
% 0.23/0.52 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(166,plain,
% 0.23/0.52 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.23/0.52 tff(167,plain,
% 0.23/0.52 (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[166, 163, 69])).
% 0.23/0.52 tff(168,plain,
% 0.23/0.52 (((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(169,plain,
% 0.23/0.53 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.23/0.53 tff(170,plain,
% 0.23/0.53 (((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(171,plain,
% 0.23/0.53 (member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[170, 167])).
% 0.23/0.53 tff(172,plain,
% 0.23/0.53 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(173,plain,
% 0.23/0.53 (member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[172, 106])).
% 0.23/0.53 tff(174,plain,
% 0.23/0.53 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(175,plain,
% 0.23/0.53 (apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[174, 106])).
% 0.23/0.53 tff(176,plain,
% 0.23/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(177,plain,
% 0.23/0.53 (((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) <=> ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(178,plain,
% 0.23/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[177])).
% 0.23/0.53 tff(179,plain,
% 0.23/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.53 inference(transitivity,[status(thm)],[178, 176])).
% 0.23/0.53 tff(180,plain,
% 0.23/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(181,plain,
% 0.23/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.23/0.53 tff(182,plain,
% 0.23/0.53 (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[181, 175, 163, 173, 146, 171, 169])).
% 0.23/0.53 tff(183,assumption,(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)), introduced(assumption)).
% 0.23/0.53 tff(184,plain,
% 0.23/0.53 (tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43) = tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)),
% 0.23/0.53 inference(symmetry,[status(thm)],[183])).
% 0.23/0.53 tff(185,plain,
% 0.23/0.53 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[184])).
% 0.23/0.53 tff(186,plain,
% 0.23/0.53 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.23/0.53 inference(symmetry,[status(thm)],[185])).
% 0.23/0.53 tff(187,plain,
% 0.23/0.53 ((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))) <=> (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[186])).
% 0.23/0.53 tff(188,assumption,(~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.23/0.53 tff(189,plain,
% 0.23/0.53 (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.23/0.53 tff(190,assumption,(member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)), introduced(assumption)).
% 0.23/0.53 tff(191,plain,
% 0.23/0.53 (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[166, 190, 69])).
% 0.23/0.53 tff(192,plain,
% 0.23/0.53 (member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[170, 191])).
% 0.23/0.53 tff(193,plain,
% 0.23/0.53 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(194,plain,
% 0.23/0.53 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[193])).
% 0.23/0.53 tff(195,plain,
% 0.23/0.53 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(196,plain,
% 0.23/0.53 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[195])).
% 0.23/0.53 tff(197,plain,
% 0.23/0.53 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(198,plain,
% 0.23/0.53 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(199,plain,
% 0.23/0.53 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[198])).
% 0.23/0.53 tff(200,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.38/0.54 tff(201,plain,
% 0.38/0.54 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.38/0.54 tff(202,plain,
% 0.38/0.54 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.38/0.54 tff(203,plain,(
% 0.38/0.54 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.38/0.54 inference(skolemize,[status(sab)],[202])).
% 0.38/0.54 tff(204,plain,
% 0.38/0.54 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.38/0.54 tff(205,plain,
% 0.38/0.54 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.38/0.54 tff(206,plain,
% 0.38/0.54 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(207,plain,
% 0.38/0.54 (((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42))) <=> ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(208,plain,
% 0.38/0.54 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[207])).
% 0.38/0.54 tff(209,plain,
% 0.38/0.54 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[208, 206])).
% 0.38/0.54 tff(210,plain,
% 0.38/0.54 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(211,plain,
% 0.38/0.54 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.38/0.54 tff(212,plain,
% 0.38/0.54 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[211, 205, 190, 192])).
% 0.38/0.54 tff(213,plain,
% 0.38/0.54 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[168, 191])).
% 0.38/0.54 tff(214,plain,
% 0.38/0.54 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(215,plain,
% 0.38/0.54 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.38/0.54 tff(216,plain,
% 0.38/0.54 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.38/0.54 tff(217,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[216, 189])).
% 0.38/0.54 tff(218,plain,(apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(219,plain,
% 0.38/0.54 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[218, 182, 163])).
% 0.38/0.54 tff(220,plain,
% 0.38/0.54 (((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | (~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(221,plain,
% 0.38/0.54 (~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[220, 106])).
% 0.38/0.54 tff(222,plain,
% 0.38/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(223,plain,
% 0.38/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[222])).
% 0.38/0.54 tff(224,plain,
% 0.38/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(225,plain,
% 0.38/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[224])).
% 0.38/0.54 tff(226,plain,
% 0.38/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[225, 223])).
% 0.38/0.54 tff(227,plain,
% 0.38/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) <=> (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), rewrite((increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))), rewrite((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(228,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[227])).
% 0.38/0.55 tff(229,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(230,plain,
% 0.38/0.55 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(231,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[230])).
% 0.38/0.55 tff(232,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','increasing_function')).
% 0.38/0.55 tff(233,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.38/0.55 tff(234,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.38/0.55 tff(235,plain,(
% 0.38/0.55 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))),
% 0.38/0.55 inference(skolemize,[status(sab)],[234])).
% 0.38/0.55 tff(236,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.38/0.55 tff(237,plain,
% 0.38/0.55 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[236, 226])).
% 0.38/0.55 tff(238,plain,
% 0.38/0.55 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(239,plain,
% 0.38/0.55 ((~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))) <=> (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(240,plain,
% 0.38/0.55 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[239])).
% 0.40/0.56 tff(241,plain,
% 0.40/0.56 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[240, 238])).
% 0.40/0.56 tff(242,plain,
% 0.40/0.56 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(243,plain,
% 0.40/0.56 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.40/0.56 tff(244,plain,
% 0.40/0.56 (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[243, 237])).
% 0.40/0.56 tff(245,plain,
% 0.40/0.56 (((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))) | ((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(246,plain,
% 0.40/0.56 ((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.40/0.56 tff(247,plain,
% 0.40/0.56 ((~(~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))) <=> (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(248,plain,
% 0.40/0.56 ((~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39))) <=> (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(249,plain,
% 0.40/0.56 ((isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))) <=> (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(250,plain,
% 0.40/0.56 ((increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(251,plain,
% 0.40/0.56 ((isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[250])).
% 0.40/0.56 tff(252,plain,
% 0.40/0.56 ((isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[251, 249])).
% 0.40/0.56 tff(253,plain,
% 0.40/0.56 ((isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[252, 248])).
% 0.40/0.56 tff(254,plain,
% 0.40/0.56 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) <=> (~(~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[253])).
% 0.40/0.56 tff(255,plain,
% 0.40/0.56 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) <=> (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39))),
% 0.40/0.56 inference(transitivity,[status(thm)],[254, 247])).
% 0.40/0.56 tff(256,plain,
% 0.40/0.56 (~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))),
% 0.40/0.56 inference(or_elim,[status(thm)],[59])).
% 0.40/0.56 tff(257,plain,
% 0.40/0.56 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.40/0.56 tff(258,plain,
% 0.40/0.56 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) | isomorphism(F!43, A!42, R!40, B!41, S!39) | (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(259,plain,
% 0.40/0.56 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) | isomorphism(F!43, A!42, R!40, B!41, S!39)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.40/0.56 tff(260,plain,
% 0.40/0.56 (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[259, 70])).
% 0.40/0.56 tff(261,plain,
% 0.40/0.56 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(262,plain,
% 0.40/0.56 (increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.40/0.56 tff(263,plain,
% 0.40/0.56 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(264,plain,
% 0.40/0.57 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.40/0.57 tff(265,plain,
% 0.40/0.57 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[264, 246])).
% 0.40/0.57 tff(266,assumption,(~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.40/0.57 tff(267,assumption,(~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))), introduced(assumption)).
% 0.40/0.57 tff(268,plain,
% 0.40/0.57 ((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(269,plain,
% 0.40/0.57 (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[268, 266, 267])).
% 0.40/0.57 tff(270,assumption,(![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))), introduced(assumption)).
% 0.40/0.57 tff(271,assumption,(member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)), introduced(assumption)).
% 0.40/0.57 tff(272,assumption,(member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)), introduced(assumption)).
% 0.40/0.57 tff(273,assumption,(member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)), introduced(assumption)).
% 0.40/0.57 tff(274,assumption,(apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.40/0.57 tff(275,assumption,(apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.40/0.57 tff(276,plain,
% 0.40/0.57 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(277,plain,
% 0.40/0.57 (((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))) <=> ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(278,plain,
% 0.40/0.57 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[277])).
% 0.40/0.57 tff(279,plain,
% 0.40/0.57 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[278, 276])).
% 0.40/0.57 tff(280,plain,
% 0.40/0.57 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(281,plain,
% 0.40/0.57 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.40/0.57 tff(282,plain,
% 0.40/0.57 (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[281, 275, 274, 190, 273, 272, 271, 270])).
% 0.40/0.58 tff(283,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[282, 269, 266])).
% 0.40/0.58 tff(284,plain,(apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(285,plain,
% 0.40/0.58 (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[284, 175, 150, 163, 173, 108, 148, 265, 221])).
% 0.40/0.58 tff(286,plain,
% 0.40/0.58 ((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.58 inference(tautology,[status(thm)],[])).
% 0.40/0.58 tff(287,plain,
% 0.40/0.58 (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[286, 285, 221])).
% 0.40/0.58 tff(288,plain,
% 0.40/0.58 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(289,plain,
% 0.40/0.58 ((~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))) <=> (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(290,plain,
% 0.40/0.58 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[289])).
% 0.40/0.58 tff(291,plain,
% 0.40/0.58 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.40/0.59 inference(transitivity,[status(thm)],[290, 288])).
% 0.40/0.59 tff(292,plain,
% 0.40/0.59 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(293,plain,
% 0.40/0.59 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.40/0.59 tff(294,plain,
% 0.40/0.59 (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[293, 237])).
% 0.40/0.59 tff(295,plain,
% 0.40/0.59 (((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))) | ((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))),
% 0.40/0.59 inference(tautology,[status(thm)],[])).
% 0.40/0.59 tff(296,plain,
% 0.40/0.59 ((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[295, 294])).
% 0.40/0.59 tff(297,plain,
% 0.40/0.59 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.40/0.59 inference(tautology,[status(thm)],[])).
% 0.40/0.59 tff(298,plain,
% 0.40/0.59 (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[297, 260])).
% 0.40/0.59 tff(299,plain,
% 0.40/0.59 ((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.40/0.59 inference(tautology,[status(thm)],[])).
% 0.40/0.59 tff(300,plain,
% 0.40/0.59 ((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.40/0.59 tff(301,plain,
% 0.40/0.59 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[300, 296])).
% 0.40/0.59 tff(302,plain,
% 0.40/0.59 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(303,plain,
% 0.40/0.60 (((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))) <=> ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(304,plain,
% 0.40/0.60 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[303])).
% 0.40/0.60 tff(305,plain,
% 0.40/0.60 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.60 inference(transitivity,[status(thm)],[304, 302])).
% 0.40/0.60 tff(306,plain,
% 0.40/0.60 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(307,plain,
% 0.40/0.60 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.40/0.60 tff(308,plain,
% 0.40/0.60 (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[307, 163, 173, 108, 148, 301])).
% 0.40/0.60 tff(309,plain,
% 0.40/0.60 (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[308, 287, 285, 219])).
% 0.40/0.60 tff(310,plain,
% 0.40/0.60 (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[309, 161])).
% 0.40/0.60 tff(311,plain,
% 0.40/0.60 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(312,plain,
% 0.40/0.60 (((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42))) <=> ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(313,plain,
% 0.40/0.60 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[312])).
% 0.40/0.61 tff(314,plain,
% 0.40/0.61 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.40/0.61 inference(transitivity,[status(thm)],[313, 311])).
% 0.40/0.61 tff(315,plain,
% 0.40/0.61 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(316,plain,
% 0.40/0.61 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.40/0.61 tff(317,plain,
% 0.40/0.61 (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[316, 205, 108, 116])).
% 0.40/0.61 tff(318,plain,
% 0.40/0.61 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.40/0.61 inference(tautology,[status(thm)],[])).
% 0.40/0.61 tff(319,plain,
% 0.40/0.61 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[318, 114])).
% 0.40/0.61 tff(320,plain,
% 0.40/0.61 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[319, 317])).
% 0.40/0.61 tff(321,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[320, 310])).
% 0.40/0.61 tff(322,plain,(isomorphism(F!43, A!42, R!40, B!41, S!39)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(323,plain,
% 0.40/0.61 (((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))) | ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))),
% 0.40/0.61 inference(tautology,[status(thm)],[])).
% 0.40/0.61 tff(324,plain,
% 0.40/0.61 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[323, 99])).
% 0.40/0.61 tff(325,plain,
% 0.40/0.61 ((~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))) | (~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.40/0.61 inference(tautology,[status(thm)],[])).
% 0.40/0.61 tff(326,plain,
% 0.40/0.61 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.40/0.61 tff(327,plain,
% 0.40/0.61 (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[326, 322])).
% 0.40/0.61 tff(328,plain,
% 0.40/0.61 (((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))),
% 0.40/0.61 inference(tautology,[status(thm)],[])).
% 0.40/0.61 tff(329,plain,
% 0.40/0.61 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.40/0.61 tff(330,plain,
% 0.40/0.61 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(331,plain,
% 0.40/0.61 (((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) <=> ((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(332,plain,
% 0.40/0.62 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[331])).
% 0.40/0.62 tff(333,plain,
% 0.40/0.62 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[332, 330])).
% 0.40/0.62 tff(334,plain,
% 0.40/0.62 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(335,plain,
% 0.40/0.62 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.40/0.62 tff(336,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[335, 329, 19, 17, 15, 13, 11, 9, 7])).
% 0.40/0.62 tff(337,plain,((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(338,assumption,((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))), introduced(assumption)).
% 0.40/0.62 tff(339,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[293, 237, 338])).
% 0.40/0.62 tff(340,plain,(~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(341,plain,
% 0.40/0.62 (((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))) | (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.40/0.62 inference(tautology,[status(thm)],[])).
% 0.40/0.62 tff(342,plain,
% 0.40/0.62 (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[341, 340])).
% 0.40/0.62 tff(343,assumption,(~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))), introduced(assumption)).
% 0.40/0.62 tff(344,plain,
% 0.40/0.62 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.40/0.63 inference(tautology,[status(thm)],[])).
% 0.40/0.63 tff(345,plain,
% 0.40/0.63 (member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[344, 343])).
% 0.40/0.63 tff(346,plain,
% 0.40/0.63 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.40/0.63 inference(tautology,[status(thm)],[])).
% 0.40/0.63 tff(347,plain,
% 0.40/0.63 (member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[346, 343])).
% 0.40/0.63 tff(348,plain,
% 0.40/0.63 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(349,plain,
% 0.40/0.63 (((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42))) <=> ((~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(350,plain,
% 0.40/0.63 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.40/0.63 inference(monotonicity,[status(thm)],[349])).
% 0.40/0.63 tff(351,plain,
% 0.40/0.63 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.40/0.63 inference(transitivity,[status(thm)],[350, 348])).
% 0.48/0.63 tff(352,plain,
% 0.48/0.63 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(353,plain,
% 0.48/0.63 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.48/0.63 tff(354,plain,
% 0.48/0.63 (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[353, 205, 347, 345])).
% 0.48/0.63 tff(355,plain,
% 0.48/0.63 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(356,plain,
% 0.48/0.63 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[355, 343])).
% 0.48/0.63 tff(357,plain,
% 0.48/0.63 ((~(apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(358,plain,
% 0.48/0.64 ((~(apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.48/0.64 tff(359,plain,
% 0.48/0.64 (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[358, 354])).
% 0.48/0.64 tff(360,plain,
% 0.48/0.64 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(361,plain,
% 0.48/0.64 (member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[360, 343])).
% 0.48/0.64 tff(362,plain,
% 0.48/0.64 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(363,plain,
% 0.48/0.64 (member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[362, 343])).
% 0.48/0.64 tff(364,plain,
% 0.48/0.64 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(365,plain,
% 0.48/0.64 (((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42))) <=> ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(366,plain,
% 0.48/0.64 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[365])).
% 0.48/0.64 tff(367,plain,
% 0.48/0.64 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[366, 364])).
% 0.48/0.64 tff(368,plain,
% 0.48/0.64 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(369,plain,
% 0.48/0.64 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.48/0.64 tff(370,plain,
% 0.48/0.64 (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[369, 205, 363, 361])).
% 0.48/0.64 tff(371,plain,
% 0.48/0.64 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(372,plain,
% 0.48/0.64 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[371, 343])).
% 0.48/0.64 tff(373,plain,
% 0.48/0.64 ((~(apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(374,plain,
% 0.48/0.64 ((~(apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[373, 372])).
% 0.48/0.64 tff(375,plain,
% 0.48/0.64 (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[374, 370])).
% 0.48/0.64 tff(376,plain,
% 0.48/0.64 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(377,plain,
% 0.48/0.64 (~apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[376, 343])).
% 0.48/0.65 tff(378,plain,
% 0.48/0.65 (((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(379,plain,
% 0.48/0.65 (apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[378, 343])).
% 0.48/0.65 tff(380,plain,
% 0.48/0.65 ((~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(381,plain,
% 0.48/0.65 (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[380, 379, 377])).
% 0.48/0.65 tff(382,plain,
% 0.48/0.65 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(383,plain,
% 0.48/0.65 (((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) <=> ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(384,plain,
% 0.48/0.65 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[383])).
% 0.48/0.65 tff(385,plain,
% 0.48/0.65 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[384, 382])).
% 0.48/0.66 tff(386,plain,
% 0.48/0.66 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(387,plain,
% 0.48/0.66 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.48/0.66 tff(388,plain,
% 0.48/0.66 ((~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[387, 329, 363, 361, 347, 345, 381])).
% 0.48/0.66 tff(389,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[388, 375, 359])).
% 0.48/0.66 tff(390,plain,((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(391,plain,
% 0.48/0.66 ((~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))) | increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(392,plain,
% 0.48/0.66 ((~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))) | increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.48/0.66 tff(393,plain,
% 0.48/0.66 (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[392, 342])).
% 0.48/0.66 tff(394,plain,
% 0.48/0.66 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | (~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~(((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> isomorphism(F!43, A!42, R!40, B!41, S!39)))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(395,plain,
% 0.48/0.66 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | (~isomorphism(F!43, A!42, R!40, B!41, S!39))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[394, 257])).
% 0.48/0.66 tff(396,plain,
% 0.48/0.66 ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[395, 322])).
% 0.48/0.66 tff(397,plain,
% 0.48/0.66 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) | (~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(398,plain,
% 0.48/0.66 ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[397, 396])).
% 0.48/0.66 tff(399,plain,
% 0.48/0.66 (~increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[398, 393])).
% 0.48/0.66 tff(400,plain,
% 0.48/0.66 ((~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))) | increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(401,plain,
% 0.48/0.66 (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[400, 399, 337])).
% 0.48/0.67 tff(402,plain,
% 0.48/0.67 (((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))) | (increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(403,plain,
% 0.48/0.67 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~((~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[402, 401])).
% 0.48/0.67 tff(404,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[243, 237, 403])).
% 0.48/0.67 % SZS output end Proof
% 0.48/0.67 % E exiting
%------------------------------------------------------------------------------